.checkignore

@@ -0,0 +1,2 @@
+# Ignore folder content
+tests/*

.codeclimate.yml

@@ -0,0 +1,20 @@
+
+engines:
+  duplication:
+    enabled: true
+      - mass = 50
+    config:
+      languages:
+         python:
+           mass_threshold: 40
+  fixme:
+    enabled: true
+  radon:
+    enabled: true
+ratings:
+  paths:
+  - "**.py"
+exclude_paths: 
+- wafo/tests/
+- wafo/MSPPT.py
+- wafo/MSO.py

.coveragerc

@@ -0,0 +1,25 @@
+# .coveragerc to control coverage.py
+[run]
+branch = True
+source = wafo
+omit = 
+   tests/*
+   source/*
+
+[report]
+# Regexes for lines to exclude from consideration
+exclude_lines =
+    # Have to re-enable the standard pragma
+    pragma: no cover
+
+    # Don't complain about missing debug-only code:
+    def __repr__
+    if self\.debug
+
+    # Don't complain if tests don't hit defensive assertion code:
+    raise AssertionError
+    raise NotImplementedError
+
+    # Don't complain if non-runnable code isn't run:
+    if 0:
+    if __name__ == .__main__.:

.gitignore

@@ -0,0 +1,42 @@
+# Temporary and binary files
+*~
+*.py[cod]
+*.so
+*.cfg
+!setup.cfg
+*.orig
+*.log
+*.pot
+__pycache__/*
+.cache/*
+.*.swp
+*.mod
+
+# Project files
+.ropeproject
+.project
+.pydevproject
+.settings
+.idea
+
+# Package files
+*.egg
+*.eggs/
+.installed.cfg
+*.egg-info
+
+# Unittest and coverage
+htmlcov/*
+.coverage
+.tox
+junit.xml
+coverage.xml
+
+# Build and docs folder/files
+build/*
+dist/*
+sdist/*
+docs/_rst/*
+docs/_build/*
+cover/*
+MANIFEST

.landscape.yml

@@ -0,0 +1,23 @@
+doc-warnings: yes
+test-warnings: no
+strictness: high
+
+pylint:
+  disable:
+    - too-few-public-methods
+    - no-self-use
+    - too-many-instance-attributes
+    - invalid-name
+    - missing-docstring
+    - star-args
+    - logging-format-interpolation
+    - bad-builtin
+ignore-paths:
+  - docs
+pep8:
+  disable:
+    - E731
+    - E126
+    - E128
+    - E115
+    - N802

.pylintrc

@@ -0,0 +1,400 @@
+[MASTER]
+
+# Specify a configuration file.
+#rcfile=
+
+# Python code to execute, usually for sys.path manipulation such as
+# pygtk.require().
+#init-hook=
+
+# Add files or directories to the blacklist. They should be base names, not
+# paths.
+ignore=CVS
+
+# Add files or directories matching the regex patterns to the blacklist. The
+# regex matches against base names, not paths.
+ignore-patterns=
+
+# Pickle collected data for later comparisons.
+persistent=yes
+
+# List of plugins (as comma separated values of python modules names) to load,
+# usually to register additional checkers. (PAB)
+load-plugins=pylint.extensions.mccabe
+
+# Maximum threshold for cyclomatic complexity (PAB)
+max-complexity=10
+
+# (PAB)
+consider-iterating-dictionary=yes
+
+# Use multiple processes to speed up Pylint.
+jobs=1
+
+# Allow loading of arbitrary C extensions. Extensions are imported into the
+# active Python interpreter and may run arbitrary code.
+unsafe-load-any-extension=no
+
+# A comma-separated list of package or module names from where C extensions may
+# be loaded. Extensions are loading into the active Python interpreter and may
+# run arbitrary code  (PAB)
+extension-pkg-whitelist=numpy
+
+# Allow optimization of some AST trees. This will activate a peephole AST
+# optimizer, which will apply various small optimizations. For instance, it can
+# be used to obtain the result of joining multiple strings with the addition
+# operator. Joining a lot of strings can lead to a maximum recursion error in
+# Pylint and this flag can prevent that. It has one side effect, the resulting
+# AST will be different than the one from reality. This option is deprecated
+# and it will be removed in Pylint 2.0.
+optimize-ast=no
+
+
+[MESSAGES CONTROL]
+
+# Only show warnings with the listed confidence levels. Leave empty to show
+# all. Valid levels: HIGH, INFERENCE, INFERENCE_FAILURE, UNDEFINED
+confidence=
+
+# Enable the message, report, category or checker with the given id(s). You can
+# either give multiple identifier separated by comma (,) or put this option
+# multiple time (only on the command line, not in the configuration file where
+# it should appear only once). See also the "--disable" option for examples.
+#enable=
+
+# Disable the message, report, category or checker with the given id(s). You
+# can either give multiple identifiers separated by comma (,) or put this
+# option multiple times (only on the command line, not in the configuration
+# file where it should appear only once).You can also use "--disable=all" to
+# disable everything first and then reenable specific checks. For example, if
+# you want to run only the similarities checker, you can use "--disable=all
+# --enable=similarities". If you want to run only the classes checker, but have
+# no Warning level messages displayed, use"--disable=all --enable=classes
+# --disable=W"
+# disable=locally-disabled
+disable=import-star-module-level,old-octal-literal,oct-method,print-statement,unpacking-in-except,parameter-unpacking,backtick,old-raise-syntax,old-ne-operator,long-suffix,dict-view-method,dict-iter-method,metaclass-assignment,next-method-called,raising-string,indexing-exception,raw_input-builtin,long-builtin,file-builtin,execfile-builtin,coerce-builtin,cmp-builtin,buffer-builtin,basestring-builtin,apply-builtin,filter-builtin-not-iterating,using-cmp-argument,useless-suppression,range-builtin-not-iterating,suppressed-message,no-absolute-import,old-division,cmp-method,reload-builtin,zip-builtin-not-iterating,intern-builtin,unichr-builtin,reduce-builtin,standarderror-builtin,unicode-builtin,xrange-builtin,coerce-method,delslice-method,getslice-method,setslice-method,input-builtin,round-builtin,hex-method,nonzero-method,map-builtin-not-iterating,W0201
+
+
+[REPORTS]
+
+# Set the output format. Available formats are text, parseable, colorized, msvs
+# (visual studio) and html. You can also give a reporter class, eg
+# mypackage.mymodule.MyReporterClass.
+output-format=parseable
+# output-format=text
+
+# Put messages in a separate file for each module / package specified on the
+# command line instead of printing them on stdout. Reports (if any) will be
+# written in a file name "pylint_global.[txt|html]". This option is deprecated
+# and it will be removed in Pylint 2.0.
+files-output=no
+
+# Tells whether to display a full report or only the messages
+reports=yes
+
+# Python expression which should return a note less than 10 (10 is the highest
+# note). You have access to the variables errors warning, statement which
+# respectively contain the number of errors / warnings messages and the total
+# number of statements analyzed. This is used by the global evaluation report
+# (RP0004).
+evaluation=10.0 - ((float(5 * error + warning + refactor + convention) / statement) * 10)
+
+# Template used to display messages. This is a python new-style format string
+# used to format the message information. See doc for all details
+#msg-template=
+
+
+[BASIC]
+
+# List of builtins function names that should not be used, separated by a comma
+bad-functions=map,filter,input
+
+# Good variable names which should always be accepted, separated by a comma
+good-names=i,j,k,m,n,ex, Run, _, x, y, z, u, v, w, a, b, c, f, g, h, p, q, r, s, t
+
+# Bad variable names which should always be refused, separated by a comma
+bad-names=foo,bar,baz,toto,tutu,tata
+
+# Colon-delimited sets of names that determine each other's naming style when
+# the name regexes allow several styles.
+name-group=
+
+# Include a hint for the correct naming format with invalid-name
+#include-naming-hint=no
+include-naming-hint=yes
+
+# List of decorators that produce properties, such as abc.abstractproperty. Add
+# to this list to register other decorators that produce valid properties.
+property-classes=abc.abstractproperty
+
+# Regular expression matching correct function names
+function-rgx=[a-z_][a-z0-9_]{2,30}$
+
+# Naming hint for function names
+function-name-hint=[a-z_][a-z0-9_]{2,30}$
+
+# Regular expression matching correct variable names
+variable-rgx=[a-z_][a-z0-9_]{2,30}$
+
+# Naming hint for variable names
+variable-name-hint=[a-z_][a-z0-9_]{2,30}$
+
+# Regular expression matching correct dummy-variable names (PAB)
+dummy-variables-rgx=^_
+
+# Regular expression matching correct constant names
+const-rgx=(([A-Z_][A-Z0-9_]*)|(__.*__))$
+
+# Naming hint for constant names
+const-name-hint=(([A-Z_][A-Z0-9_]*)|(__.*__))$
+
+# Regular expression matching correct attribute names
+attr-rgx=[a-z_][a-z0-9_]{2,30}$
+
+# Naming hint for attribute names
+attr-name-hint=[a-z_][a-z0-9_]{2,30}$
+
+# Regular expression matching correct argument names
+argument-rgx=[a-z_][a-z0-9_]{2,30}$
+
+# Naming hint for argument names
+argument-name-hint=[a-z_][a-z0-9_]{2,30}$
+
+# Regular expression matching correct class attribute names
+class-attribute-rgx=([A-Za-z_][A-Za-z0-9_]{2,30}|(__.*__))$
+
+# Naming hint for class attribute names
+class-attribute-name-hint=([A-Za-z_][A-Za-z0-9_]{2,30}|(__.*__))$
+
+# Regular expression matching correct inline iteration names
+inlinevar-rgx=[A-Za-z_][A-Za-z0-9_]*$
+
+# Naming hint for inline iteration names
+inlinevar-name-hint=[A-Za-z_][A-Za-z0-9_]*$
+
+# Regular expression matching correct class names
+class-rgx=[A-Z_][a-zA-Z0-9]+$
+
+# Naming hint for class names
+class-name-hint=[A-Z_][a-zA-Z0-9]+$
+
+# Regular expression matching correct module names
+module-rgx=(([a-z_][a-z0-9_]*)|([A-Z][a-zA-Z0-9]+))$
+
+# Naming hint for module names
+module-name-hint=(([a-z_][a-z0-9_]*)|([A-Z][a-zA-Z0-9]+))$
+
+# Regular expression matching correct method names
+method-rgx=[a-z_][a-z0-9_]{2,30}$
+
+# Naming hint for method names
+method-name-hint=[a-z_][a-z0-9_]{2,30}$
+
+# Regular expression which should only match function or class names that do
+# not require a docstring.
+no-docstring-rgx=^_
+
+# Minimum line length for functions/classes that require docstrings, shorter
+# ones are exempt.
+docstring-min-length=-1
+
+
+[ELIF]
+
+# Maximum number of nested blocks for function / method body
+max-nested-blocks=5
+
+
+[FORMAT]
+
+# Maximum number of characters on a single line.
+max-line-length=100
+
+# Regexp for a line that is allowed to be longer than the limit.
+ignore-long-lines=^\s*(# )?<?https?://\S+>?$
+
+# Allow the body of an if to be on the same line as the test if there is no
+# else.
+single-line-if-stmt=no
+
+# List of optional constructs for which whitespace checking is disabled. `dict-
+# separator` is used to allow tabulation in dicts, etc.: {1  : 1,\n222: 2}.
+# `trailing-comma` allows a space between comma and closing bracket: (a, ).
+# `empty-line` allows space-only lines.
+no-space-check=trailing-comma,dict-separator
+
+# Maximum number of lines in a module
+max-module-lines=1000
+
+# String used as indentation unit. This is usually "    " (4 spaces) or "\t" (1
+# tab).
+indent-string='    '
+
+# Number of spaces of indent required inside a hanging  or continued line.
+indent-after-paren=4
+
+# Expected format of line ending, e.g. empty (any line ending), LF or CRLF.
+expected-line-ending-format=
+
+
+[LOGGING]
+
+# Logging modules to check that the string format arguments are in logging
+# function parameter format
+logging-modules=logging
+
+
+[MISCELLANEOUS]
+
+# List of note tags to take in consideration, separated by a comma.
+notes=FIXME,XXX,TODO
+
+
+[SIMILARITIES]
+
+# Minimum lines number of a similarity.
+min-similarity-lines=4
+
+# Ignore comments when computing similarities.
+ignore-comments=yes
+
+# Ignore docstrings when computing similarities.
+ignore-docstrings=yes
+
+# Ignore imports when computing similarities.
+ignore-imports=no
+
+
+[SPELLING]
+
+# Spelling dictionary name. Available dictionaries: none. To make it working
+# install python-enchant package.
+spelling-dict=
+
+# List of comma separated words that should not be checked.
+spelling-ignore-words=
+
+# A path to a file that contains private dictionary; one word per line.
+spelling-private-dict-file=
+
+# Tells whether to store unknown words to indicated private dictionary in
+# --spelling-private-dict-file option instead of raising a message.
+spelling-store-unknown-words=no
+
+
+[TYPECHECK]
+
+# Tells whether missing members accessed in mixin class should be ignored. A
+# mixin class is detected if its name ends with "mixin" (case insensitive).
+ignore-mixin-members=yes
+
+# List of module names for which member attributes should not be checked
+# (useful for modules/projects where namespaces are manipulated during runtime
+# and thus existing member attributes cannot be deduced by static analysis. It
+# supports qualified module names, as well as Unix pattern matching.
+ignored-modules=
+
+# List of class names for which member attributes should not be checked (useful
+# for classes with dynamically set attributes). This supports the use of
+# qualified names.
+ignored-classes=optparse.Values,thread._local,_thread._local
+
+# List of members which are set dynamically and missed by pylint inference
+# system, and so shouldn't trigger E1101 when accessed. Python regular
+# expressions are accepted.
+generated-members=
+
+# List of decorators that produce context managers, such as
+# contextlib.contextmanager. Add to this list to register other decorators that
+# produce valid context managers.
+contextmanager-decorators=contextlib.contextmanager
+
+
+[CLASSES]
+
+# List of method names used to declare (i.e. assign) instance attributes.
+defining-attr-methods=__init__,__new__,setUp
+
+# List of valid names for the first argument in a class method.
+valid-classmethod-first-arg=cls
+
+# List of valid names for the first argument in a metaclass class method.
+valid-metaclass-classmethod-first-arg=mcs
+
+# List of member names, which should be excluded from the protected access
+# warning.
+exclude-protected=_asdict,_fields,_replace,_source,_make
+
+
+[DESIGN]
+
+# Maximum number of arguments for function / method
+max-args=5
+
+# Argument names that match this expression will be ignored. Default to name
+# with leading underscore
+ignored-argument-names=_.*
+
+# Maximum number of locals for function / method body
+max-locals=15
+
+# Maximum number of return / yield for function / method body
+max-returns=6
+
+# Maximum number of branch for function / method body
+max-branches=12
+
+# Maximum number of statements in function / method body
+max-statements=50
+
+# Maximum number of parents for a class (see R0901).
+max-parents=7
+
+# Maximum number of attributes for a class (see R0902).
+max-attributes=7
+
+# Minimum number of public methods for a class (see R0903).
+min-public-methods=2
+
+# Maximum number of public methods for a class (see R0904).
+max-public-methods=20
+
+# Maximum number of boolean expressions in a if statement
+max-bool-expr=5
+
+
+[IMPORTS]
+
+# Deprecated modules which should not be used, separated by a comma
+deprecated-modules=regsub,TERMIOS,Bastion,rexec
+
+# Create a graph of every (i.e. internal and external) dependencies in the
+# given file (report RP0402 must not be disabled)
+import-graph=
+
+# Create a graph of external dependencies in the given file (report RP0402 must
+# not be disabled)
+ext-import-graph=
+
+# Create a graph of internal dependencies in the given file (report RP0402 must
+# not be disabled)
+int-import-graph=
+
+# Force import order to recognize a module as part of the standard
+# compatibility libraries.
+known-standard-library=
+
+# Force import order to recognize a module as part of a third party library.
+known-third-party=enchant
+
+# Analyse import fallback blocks. This can be used to support both Python 2 and
+# 3 compatible code, which means that the block might have code that exists
+# only in one or another interpreter, leading to false positives when analysed.
+analyse-fallback-blocks=no
+
+
+[EXCEPTIONS]
+
+# Exceptions that will emit a warning when being caught. Defaults to
+# "Exception"
+overgeneral-exceptions=Exception

.travis.yml

@@ -0,0 +1,61 @@
+# Travis configuration file using the build matrix feature
+# Read more under http://docs.travis-ci.com/user/build-configuration/
+# THIS SCRIPT IS SUPPOSED TO BE AN EXAMPLE. MODIFY IT ACCORDING TO YOUR NEEDS!
+sudo: true
+language: python
+python:
+  - 2.7
+#  - 3.4  # Drop support for python 3.4
+  - 3.5
+  - 3.6
+notifications:
+  email: false
+ 
+# Setup anaconda
+before_install:
+  - if [[ "$TRAVIS_PYTHON_VERSION" == "2.7" ]]; then
+      wget https://repo.continuum.io/miniconda/Miniconda-latest-Linux-x86_64.sh -O miniconda.sh;
+    else
+      wget https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O miniconda.sh;
+    fi
+  - chmod +x miniconda.sh
+  - ./miniconda.sh -b
+  - if [[ "$TRAVIS_PYTHON_VERSION" == "2.7" ]]; then
+      export PATH=/home/travis/miniconda2/bin:$PATH;
+    else
+      export PATH=/home/travis/miniconda3/bin:$PATH;
+    fi
+  - conda update --yes conda
+  - conda install --yes conda-build
+  - conda create --yes -n condaenv python=$TRAVIS_PYTHON_VERSION
+  - conda install --yes -n condaenv pip
+  - conda config --add channels https://conda.anaconda.org/omnia
+  - conda config --add channels https://conda.anaconda.org/pbrod
+  - source activate condaenv
+  - sudo apt-get update
+  - sudo apt-get install gfortran
+# Install packages
+install:
+  - conda install --yes python=$TRAVIS_PYTHON_VERSION numpy scipy nose pytest matplotlib pytest-pep8 pytest-cov mpmath pillow numba statsmodels
+  - pip install funcsigs
+  - pip install numdifftools
+  - pip install coveralls
+  - pip install codecov
+  - python setup.py build
+  - python setup.py install
+#  - conda build conda_recipe
+#  - conda install wafo --use-local
+before_script:
+  - "export DISPLAY=:99.0"
+  - "sh -e /etc/init.d/xvfb start"
+  - sleep 3 # give xvfb some time to start
+  - git config --global user.email "per.andreas.brodtkorb@gmail.com"
+  - git config --global user.name "pbrod"
+script:
+   - coverage run --source=wafo setup.py test
+#   - py.test wafo --cov --pep8 --doctest-modules
+after_success:
+  - coveralls
+  - codecov
+cache:
+  - apt

AUTHORS.rst

@@ -0,0 +1,8 @@
+==========
+Developers
+==========
+
+* Per A. Brodtkorb
+* Georg Lindgren
+* David Verelst
+

CHANGES.rst

@@ -0,0 +1,11 @@
+=========
+Changelog
+=========
+
+Version 0.1
+===========
+
+- Feature A added
+- FIX: nasty bug #1729 fixed
+- add your changes here!
+

appveyor.yml

@@ -0,0 +1,131 @@
+environment:
+  global:
+    # SDK v7.0 MSVC Express 2008's SetEnv.cmd script will fail if the
+    # /E:ON and /V:ON options are not enabled in the batch script intepreter
+    # See: http://stackoverflow.com/a/13751649/163740
+    CMD_IN_ENV: "cmd /E:ON /V:ON /C .\\appveyor\\run_with_env.cmd"
+
+  matrix:
+
+    # Python 2.7.10 is the latest version and is not pre-installed.
+
+    - PYTHON: "C:\\Python27.10"
+      PYTHON_VERSION: "2.7.10"
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python27.10-x64"
+      PYTHON_VERSION: "2.7.10"
+      PYTHON_ARCH: "64"
+
+    # Pre-installed Python versions, which Appveyor may upgrade to
+    # a later point release.
+    # See: http://www.appveyor.com/docs/installed-software#python
+
+    - PYTHON: "C:\\Python27"
+      PYTHON_VERSION: "2.7.x" # currently 2.7.9
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python27-x64"
+      PYTHON_VERSION: "2.7.x" # currently 2.7.9
+      PYTHON_ARCH: "64"
+
+    - PYTHON: "C:\\Python33"
+      PYTHON_VERSION: "3.3.x" # currently 3.3.5
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python33-x64"
+      PYTHON_VERSION: "3.3.x" # currently 3.3.5
+      PYTHON_ARCH: "64"
+
+    - PYTHON: "C:\\Python34"
+      PYTHON_VERSION: "3.4.x" # currently 3.4.3
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python34-x64"
+      PYTHON_VERSION: "3.4.x" # currently 3.4.3
+      PYTHON_ARCH: "64"
+
+    # Python versions not pre-installed
+
+    # Python 2.6.6 is the latest Python 2.6 with a Windows installer
+    # See: https://github.com/ogrisel/python-appveyor-demo/issues/10
+
+    - PYTHON: "C:\\Python266"
+      PYTHON_VERSION: "2.6.6"
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python266-x64"
+      PYTHON_VERSION: "2.6.6"
+      PYTHON_ARCH: "64"
+
+    - PYTHON: "C:\\Python35"
+      PYTHON_VERSION: "3.5.0"
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python35-x64"
+      PYTHON_VERSION: "3.5.0"
+      PYTHON_ARCH: "64"
+
+    # Major and minor releases (i.e x.0.0 and x.y.0) prior to 3.3.0 use
+    # a different naming scheme.
+
+    - PYTHON: "C:\\Python270"
+      PYTHON_VERSION: "2.7.0"
+      PYTHON_ARCH: "32"
+
+    - PYTHON: "C:\\Python270-x64"
+      PYTHON_VERSION: "2.7.0"
+      PYTHON_ARCH: "64"
+
+install:
+  - ECHO "Filesystem root:"
+  - ps: "ls \"C:/\""
+
+  - ECHO "Installed SDKs:"
+  - ps: "ls \"C:/Program Files/Microsoft SDKs/Windows\""
+
+  # Install Python (from the official .msi of http://python.org) and pip when
+  # not already installed.
+  - ps: if (-not(Test-Path($env:PYTHON))) { & appveyor\install.ps1 }
+
+  # Prepend newly installed Python to the PATH of this build (this cannot be
+  # done from inside the powershell script as it would require to restart
+  # the parent CMD process).
+  - "SET PATH=%PYTHON%;%PYTHON%\\Scripts;%PATH%"
+
+  # Check that we have the expected version and architecture for Python
+  - "python --version"
+  - "python -c \"import struct; print(struct.calcsize('P') * 8)\""
+
+  # Upgrade to the latest version of pip to avoid it displaying warnings
+  # about it being out of date.
+  - "pip install --disable-pip-version-check --user --upgrade pip"
+
+  # Install the build dependencies of the project. If some dependencies contain
+  # compiled extensions and are not provided as pre-built wheel packages,
+  # pip will build them from source using the MSVC compiler matching the
+  # target Python version and architecture
+  - "%CMD_IN_ENV% pip install -r requirements.txt"
+
+build_script:
+  # Build the compiled extension
+  - "%CMD_IN_ENV% python setup.py build"
+
+test_script:
+  # Run the project tests
+  - "%CMD_IN_ENV% python setup.py test"
+
+after_test:
+  # If tests are successful, create binary packages for the project.
+  - "%CMD_IN_ENV% python setup.py bdist_wheel"
+  - "%CMD_IN_ENV% python setup.py bdist_wininst"
+  - "%CMD_IN_ENV% python setup.py bdist_msi"
+  - ps: "ls dist"
+
+artifacts:
+  # Archive the generated packages in the ci.appveyor.com build report.
+  - path: dist\*
+
+#on_success:
+#  - TODO: upload the content of dist/*.whl to a public wheelhouse
+#

conftest.py

@@ -0,0 +1 @@
+collect_ignore = ["setup.py", "build_all.py"]

docs/Makefile

@@ -0,0 +1,177 @@
+# Makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line.
+SPHINXOPTS    =
+SPHINXBUILD   = sphinx-build
+PAPER         =
+BUILDDIR      = _build
+
+# User-friendly check for sphinx-build
+ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $?), 1)
+$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/)
+endif
+
+# Internal variables.
+PAPEROPT_a4     = -D latex_paper_size=a4
+PAPEROPT_letter = -D latex_paper_size=letter
+ALLSPHINXOPTS   = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
+# the i18n builder cannot share the environment and doctrees with the others
+I18NSPHINXOPTS  = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
+
+.PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext
+
+help:
+	@echo "Please use \`make <target>' where <target> is one of"
+	@echo "  html       to make standalone HTML files"
+	@echo "  dirhtml    to make HTML files named index.html in directories"
+	@echo "  singlehtml to make a single large HTML file"
+	@echo "  pickle     to make pickle files"
+	@echo "  json       to make JSON files"
+	@echo "  htmlhelp   to make HTML files and a HTML help project"
+	@echo "  qthelp     to make HTML files and a qthelp project"
+	@echo "  devhelp    to make HTML files and a Devhelp project"
+	@echo "  epub       to make an epub"
+	@echo "  latex      to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
+	@echo "  latexpdf   to make LaTeX files and run them through pdflatex"
+	@echo "  latexpdfja to make LaTeX files and run them through platex/dvipdfmx"
+	@echo "  text       to make text files"
+	@echo "  man        to make manual pages"
+	@echo "  texinfo    to make Texinfo files"
+	@echo "  info       to make Texinfo files and run them through makeinfo"
+	@echo "  gettext    to make PO message catalogs"
+	@echo "  changes    to make an overview of all changed/added/deprecated items"
+	@echo "  xml        to make Docutils-native XML files"
+	@echo "  pseudoxml  to make pseudoxml-XML files for display purposes"
+	@echo "  linkcheck  to check all external links for integrity"
+	@echo "  doctest    to run all doctests embedded in the documentation (if enabled)"
+
+clean:
+	rm -rf $(BUILDDIR)/*
+
+html:
+	$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
+	@echo
+	@echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
+
+dirhtml:
+	$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
+	@echo
+	@echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
+
+singlehtml:
+	$(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
+	@echo
+	@echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
+
+pickle:
+	$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
+	@echo
+	@echo "Build finished; now you can process the pickle files."
+
+json:
+	$(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
+	@echo
+	@echo "Build finished; now you can process the JSON files."
+
+htmlhelp:
+	$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
+	@echo
+	@echo "Build finished; now you can run HTML Help Workshop with the" \
+	      ".hhp project file in $(BUILDDIR)/htmlhelp."
+
+qthelp:
+	$(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
+	@echo
+	@echo "Build finished; now you can run "qcollectiongenerator" with the" \
+	      ".qhcp project file in $(BUILDDIR)/qthelp, like this:"
+	@echo "# qcollectiongenerator $(BUILDDIR)/qthelp/pywafo.qhcp"
+	@echo "To view the help file:"
+	@echo "# assistant -collectionFile $(BUILDDIR)/qthelp/pywafo.qhc"
+
+devhelp:
+	$(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
+	@echo
+	@echo "Build finished."
+	@echo "To view the help file:"
+	@echo "# mkdir -p $HOME/.local/share/devhelp/pywafo"
+	@echo "# ln -s $(BUILDDIR)/devhelp $HOME/.local/share/devhelp/pywafo"
+	@echo "# devhelp"
+
+epub:
+	$(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
+	@echo
+	@echo "Build finished. The epub file is in $(BUILDDIR)/epub."
+
+latex:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo
+	@echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
+	@echo "Run \`make' in that directory to run these through (pdf)latex" \
+	      "(use \`make latexpdf' here to do that automatically)."
+
+latexpdf:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo "Running LaTeX files through pdflatex..."
+	$(MAKE) -C $(BUILDDIR)/latex all-pdf
+	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+
+latexpdfja:
+	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
+	@echo "Running LaTeX files through platex and dvipdfmx..."
+	$(MAKE) -C $(BUILDDIR)/latex all-pdf-ja
+	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
+
+text:
+	$(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text
+	@echo
+	@echo "Build finished. The text files are in $(BUILDDIR)/text."
+
+man:
+	$(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man
+	@echo
+	@echo "Build finished. The manual pages are in $(BUILDDIR)/man."
+
+texinfo:
+	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+	@echo
+	@echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
+	@echo "Run \`make' in that directory to run these through makeinfo" \
+	      "(use \`make info' here to do that automatically)."
+
+info:
+	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
+	@echo "Running Texinfo files through makeinfo..."
+	make -C $(BUILDDIR)/texinfo info
+	@echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
+
+gettext:
+	$(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale
+	@echo
+	@echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
+
+changes:
+	$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
+	@echo
+	@echo "The overview file is in $(BUILDDIR)/changes."
+
+linkcheck:
+	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
+	@echo
+	@echo "Link check complete; look for any errors in the above output " \
+	      "or in $(BUILDDIR)/linkcheck/output.txt."
+
+doctest:
+	$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
+	@echo "Testing of doctests in the sources finished, look at the " \
+	      "results in $(BUILDDIR)/doctest/output.txt."
+
+xml:
+	$(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml
+	@echo
+	@echo "Build finished. The XML files are in $(BUILDDIR)/xml."
+
+pseudoxml:
+	$(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml
+	@echo
+	@echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml."

docs/authors.rst

@@ -0,0 +1,2 @@
+.. _authors:
+.. include:: ../AUTHORS.rst

docs/changes.rst

@@ -0,0 +1,2 @@
+.. _changes:
+.. include:: ../CHANGES.rst

docs/conf.py

@@ -0,0 +1,238 @@
+# -*- coding: utf-8 -*-
+#
+# This file is execfile()d with the current directory set to its containing dir.
+#
+# Note that not all possible configuration values are present in this
+# autogenerated file.
+#
+# All configuration values have a default; values that are commented out
+# serve to show the default.
+
+import sys
+import os
+import inspect
+from sphinx import apidoc
+
+
+__location__ = os.path.join(os.getcwd(), os.path.dirname(
+    inspect.getfile(inspect.currentframe())))
+
+package = "wafo"
+namespace = []
+namespace_pkg = ".".join([namespace[-1], package]) if namespace else package
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+# sys.path.insert(0, os.path.abspath('.'))
+
+# -- General configuration -----------------------------------------------------
+
+# If your documentation needs a minimal Sphinx version, state it here.
+# needs_sphinx = '1.0'
+
+# Add any Sphinx extension module names here, as strings. They can be extensions
+# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
+extensions = ['sphinx.ext.autodoc', 'sphinx.ext.intersphinx', 'sphinx.ext.todo',
+              'sphinx.ext.autosummary', 'sphinx.ext.viewcode', 'sphinx.ext.coverage',
+              'sphinx.ext.doctest', 'sphinx.ext.ifconfig', 'sphinx.ext.pngmath']
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# The suffix of source filenames.
+source_suffix = '.rst'
+
+# The encoding of source files.
+# source_encoding = 'utf-8-sig'
+
+# The master toctree document.
+master_doc = 'index'
+
+# General information about the project.
+project = u'pywafo'
+copyright = u'2015, davidovitch'
+
+# The version info for the project you're documenting, acts as replacement for
+# |version| and |release|, also used in various other places throughout the
+# built documents.
+#
+# The short X.Y version.
+version = ''  # Is set by calling `setup.py docs`
+# The full version, including alpha/beta/rc tags.
+release = ''  # Is set by calling `setup.py docs`
+
+# The language for content autogenerated by Sphinx. Refer to documentation
+# for a list of supported languages.
+# language = None
+
+# There are two options for replacing |today|: either, you set today to some
+# non-false value, then it is used:
+# today = ''
+# Else, today_fmt is used as the format for a strftime call.
+# today_fmt = '%B %d, %Y'
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+exclude_patterns = ['_build']
+
+# The reST default role (used for this markup: `text`) to use for all documents.
+# default_role = None
+
+# If true, '()' will be appended to :func: etc. cross-reference text.
+# add_function_parentheses = True
+
+# If true, the current module name will be prepended to all description
+# unit titles (such as .. function::).
+# add_module_names = True
+
+# If true, sectionauthor and moduleauthor directives will be shown in the
+# output. They are ignored by default.
+# show_authors = False
+
+# The name of the Pygments (syntax highlighting) style to use.
+pygments_style = 'sphinx'
+
+# A list of ignored prefixes for module index sorting.
+# modindex_common_prefix = []
+
+# If true, keep warnings as "system message" paragraphs in the built documents.
+# keep_warnings = False
+
+
+# -- Options for HTML output ---------------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+html_theme = 'alabaster'
+
+# Theme options are theme-specific and customize the look and feel of a theme
+# further.  For a list of options available for each theme, see the
+# documentation.
+# html_theme_options = {}
+
+# Add any paths that contain custom themes here, relative to this directory.
+# html_theme_path = []
+
+# The name for this set of Sphinx documents.  If None, it defaults to
+# "<project> v<release> documentation".
+try:
+    from namespace_pkg import __version__ as version
+except ImportError:
+    pass
+else:
+    release = version
+
+# A shorter title for the navigation bar.  Default is the same as html_title.
+# html_short_title = None
+
+# The name of an image file (relative to this directory) to place at the top
+# of the sidebar.
+# html_logo = ""
+
+# The name of an image file (within the static path) to use as favicon of the
+# docs.  This file should be a Windows icon file (.ico) being 16x16 or 32x32
+# pixels large.
+# html_favicon = None
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
+# using the given strftime format.
+# html_last_updated_fmt = '%b %d, %Y'
+
+# If true, SmartyPants will be used to convert quotes and dashes to
+# typographically correct entities.
+# html_use_smartypants = True
+
+# Custom sidebar templates, maps document names to template names.
+# html_sidebars = {}
+
+# Additional templates that should be rendered to pages, maps page names to
+# template names.
+# html_additional_pages = {}
+
+# If false, no module index is generated.
+# html_domain_indices = True
+
+# If false, no index is generated.
+# html_use_index = True
+
+# If true, the index is split into individual pages for each letter.
+# html_split_index = False
+
+# If true, links to the reST sources are added to the pages.
+# html_show_sourcelink = True
+
+# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
+# html_show_sphinx = True
+
+# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
+# html_show_copyright = True
+
+# If true, an OpenSearch description file will be output, and all pages will
+# contain a <link> tag referring to it.  The value of this option must be the
+# base URL from which the finished HTML is served.
+# html_use_opensearch = ''
+
+# This is the file name suffix for HTML files (e.g. ".xhtml").
+# html_file_suffix = None
+
+# Output file base name for HTML help builder.
+htmlhelp_basename = 'wafo-doc'
+
+
+# -- Options for LaTeX output --------------------------------------------------
+
+latex_elements = {
+# The paper size ('letterpaper' or 'a4paper').
+# 'papersize': 'letterpaper',
+
+# The font size ('10pt', '11pt' or '12pt').
+# 'pointsize': '10pt',
+
+# Additional stuff for the LaTeX preamble.
+# 'preamble': '',
+}
+
+# Grouping the document tree into LaTeX files. List of tuples
+# (source start file, target name, title, author, documentclass [howto/manual]).
+latex_documents = [
+  ('index', 'user_guide.tex', u'pywafo Documentation',
+   u'davidovitch', 'manual'),
+]
+
+# The name of an image file (relative to this directory) to place at the top of
+# the title page.
+# latex_logo = ""
+
+# For "manual" documents, if this is true, then toplevel headings are parts,
+# not chapters.
+# latex_use_parts = False
+
+# If true, show page references after internal links.
+# latex_show_pagerefs = False
+
+# If true, show URL addresses after external links.
+# latex_show_urls = False
+
+# Documents to append as an appendix to all manuals.
+# latex_appendices = []
+
+# If false, no module index is generated.
+# latex_domain_indices = True
+
+# -- External mapping ------------------------------------------------------------
+python_version = '.'.join(map(str, sys.version_info[0:2]))
+intersphinx_mapping = {
+    'sphinx': ('http://sphinx.pocoo.org', None),
+    'python': ('http://docs.python.org/' + python_version, None),
+    'matplotlib': ('http://matplotlib.sourceforge.net', None),
+    'numpy': ('http://docs.scipy.org/doc/numpy', None),
+    'sklearn': ('http://scikit-learn.org/stable', None),
+    'pandas': ('http://pandas.pydata.org/pandas-docs/stable', None),
+    'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
+}

docs/index.rst

@@ -0,0 +1,45 @@
+======
+pywafo
+======
+
+This is the documentation of **pywafo**.
+
+.. note::
+
+    This is the main page of your project's `Sphinx <http://sphinx-doc.org/>`_
+    documentation. It is formatted in `reStructuredText
+    <http://sphinx-doc.org/rest.html>`__. Add additional pages by creating
+    rst-files in ``docs`` and adding them to the `toctree
+    <http://sphinx-doc.org/markup/toctree.html>`_ below. Use then
+    `references <http://sphinx-doc.org/markup/inline.html>`__ in order to link
+    them from this page, e.g. :ref:`authors <authors>` and :ref:`changes`.
+    It is also possible to refer to the documentation of other Python packages
+    with the `Python domain syntax
+    <http://sphinx-doc.org/domains.html#the-python-domain>`__. By default you
+    can reference the documentation of `Sphinx <http://sphinx.pocoo.org>`__,
+    `Python <http://docs.python.org/>`__, `matplotlib
+    <http://matplotlib.sourceforge.net>`__, `NumPy
+    <http://docs.scipy.org/doc/numpy>`__, `Scikit-Learn
+    <http://scikit-learn.org/stable>`__, `Pandas
+    <http://pandas.pydata.org/pandas-docs/stable>`__, `SciPy
+    <http://docs.scipy.org/doc/scipy/reference/>`__. You can add more by
+    extending the ``intersphinx_mapping`` in your Sphinx's ``conf.py``.
+
+Contents
+========
+
+.. toctree::
+   :maxdepth: 2
+
+   License <license>
+   Authors <authors>
+   Changelog <changes>
+   Module Reference <api/modules>
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`

docs/license.rst

@@ -0,0 +1,7 @@
+.. _license:
+
+=======
+License
+=======
+
+.. literalinclude:: ../LICENSE.txt

setup.py

@@ -1,10 +1,110 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""
+    Setup file for wafo.
+
+    This file was generated with PyScaffold 2.4.2, a tool that easily
+    puts up a scaffold for your new Python project. Learn more under:
+    http://pyscaffold.readthedocs.org/
+
+Usage:
+Run all tests:
+  python setup.py test
+
+  python setup.py doctests
+
+Build documentation
+
+  python setup.py docs
+
+Install
+  python setup.py install [, --prefix=$PREFIX]
+
+Build
+
+  python setup.py bdist_wininst
+
+  python setup.py bdist_wheel --universal
+
+  python setup.py sdist
+
+PyPi upload:
+  twine upload dist/*
+
+"""
+
+from __future__ import division, absolute_import, print_function
+
+# numpy.distutils will figure out if setuptools is available when imported
+# this allows us to combine setuptools use_pyscaffold=True and f2py extensions
 import setuptools
+from numpy.distutils.core import setup
+from numpy.distutils.misc_util import Configuration
+
+import sys
+
+
+def setup_package_pyscaffold():
+
+    config = Configuration('wafo')
+
+    # -------------------------------------------------------------------------
+    # c_library
+    config.add_extension('c_library',
+                         sources=['wafo/source/c_library/c_library.pyf',
+                                  'wafo/source/c_library/c_functions.c'])
+    # -------------------------------------------------------------------------
+    # mvn
+    config.add_extension('mvn',
+                         sources=['wafo/source/mvn/mvn.pyf',
+                                 'wafo/source/mvn/mvndst.f'])
+
+    # -------------------------------------------------------------------------
+    # mvnprdmod
+    lib_mvnprdmod_src = ['wafo/source/mvnprd/mvnprd.f',
+                         'wafo/source/mvnprd/mvnprodcorrprb.f']
+    config.add_library('_mvnprdmod', sources=lib_mvnprdmod_src)
+    config.add_extension('mvnprdmod',
+                         sources=['wafo/source/mvnprd/mvnprd_interface.f'],
+                         libraries=['_mvnprdmod'],
+                         depends=(lib_mvnprdmod_src))
+
+    # -------------------------------------------------------------------------
+    # cov2mod
+    lib_cov2mod_src = ['wafo/source/mreg/dsvdc.f',
+                       'wafo/source/mreg/mregmodule.f',
+                       'wafo/source/mreg/intfcmod.f']
+    config.add_library('_cov2mod', sources=lib_cov2mod_src)
+    config.add_extension('cov2mod',
+                         sources=['wafo/source/mreg/cov2mmpdfreg_intfc.f'],
+                         libraries=['_cov2mod'],
+                         include_dirs=['wafo/source/mreg/'],
+                         depends=(lib_cov2mod_src))
+
+    # -------------------------------------------------------------------------
+    # rindmod
+    lib_rindmod_src = ['wafo/source/rind2007/intmodule.f',
+                       'wafo/source/rind2007/jacobmod.f',
+                       'wafo/source/rind2007/swapmod.f',
+                       'wafo/source/rind2007/fimod.f',
+                       'wafo/source/rind2007/rindmod.f',
+                       'wafo/source/rind2007/rind71mod.f']
+    config.add_library('_rindmod', sources=lib_rindmod_src)
+    config.add_extension('rindmod',
+                         sources=['wafo/source/rind2007/rind_interface.f'],
+                         libraries=['_rindmod'],
+                         include_dirs=['wafo/source/mreg/'],
+                         depends=(lib_rindmod_src))
+
+    config.add_data_dir(('data', 'wafo/data'))
+
+    needs_sphinx = {'build_sphinx', 'upload_docs'}.intersection(sys.argv)
+    sphinx = ['sphinx'] if needs_sphinx else []
+    setup(setup_requires=['six', 'pyscaffold>=2.4rc1,<2.5a0'] + sphinx,
+          tests_require=['pytest_cov', 'pytest'],
+          use_pyscaffold=True,
+          **config.todict())
+
 
-setuptools.setup(
+if __name__ == "__main__":
-    name='wafo',
+    setup_package_pyscaffold()
-    version='0.11',
-    author='WAFO-group',
-    author_email=None,
-    description='Wave Analysis for Fatigue and Oceanography',
-    packages=setuptools.find_packages(),
-)

wafo/SpecData1D.mm

@@ -0,0 +1,69 @@
+<map version="0.8.1">
+<!-- To view this file, download free mind mapping software FreeMind from http://freemind.sourceforge.net -->
+<node CREATED="1268907205249" ID="Freemind_Link_1834025809" MODIFIED="1268920224244" STYLE="fork" TEXT="WAFO Objects">
+<font NAME="SansSerif" SIZE="11"/>
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+<node CREATED="1268908695254" ID="Freemind_Link_834391422" MODIFIED="1268908707582" TEXT="bandwidth"/>
+<node CREATED="1268908733082" ID="Freemind_Link_1433599166" MODIFIED="1268908736348" TEXT="characteristic"/>
+<node CREATED="1268908690441" ID="Freemind_Link_1284342306" MODIFIED="1268908694941" TEXT="normalize"/>
+<node CREATED="1268908669144" ID="Freemind_Link_1815459961" MODIFIED="1268908677316" TEXT="nyquist_freq"/>
+<node CREATED="1268908664160" ID="Freemind_Link_703739784" MODIFIED="1268919800253" TEXT="moment" VSHIFT="4"/>
+<node CREATED="1268908678394" ID="Freemind_Link_1387269779" MODIFIED="1268919203464" TEXT="sampling_period" VSHIFT="3"/>
+<node CREATED="1268908643159" ID="Freemind_Link_895051601" MODIFIED="1268908655410" TEXT="stats_nl"/>
+<node CREATED="1268907362986" ID="Freemind_Link_1959199999" MODIFIED="1268920763548" TEXT="sim">
+<arrowlink DESTINATION="Freemind_Link_1110096845" ENDARROW="Default" ENDINCLINATION="-26;-470;" ID="Freemind_Arrow_Link_658989110" STARTARROW="None" STARTINCLINATION="134;20;"/>
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+</node>
+<node CREATED="1268908656097" ID="Freemind_Link_932055041" MODIFIED="1268920049331" TEXT="testgaussian" VSHIFT="-11"/>
+<node CREATED="1268908524408" ID="Freemind_Link_451836141" MODIFIED="1268920637967" TEXT="tocovdata" VSHIFT="122">
+<arrowlink DESTINATION="Freemind_Link_1298097150" ENDARROW="Default" ENDINCLINATION="22;-61;" ID="Freemind_Arrow_Link_459039584" STARTARROW="None" STARTINCLINATION="155;-17;"/>
+</node>
+<node CREATED="1268907881846" ID="Freemind_Link_961675105" MODIFIED="1268908523861" TEXT="tocov_matrix"/>
+<node CREATED="1268908531877" ID="Freemind_Link_1361566099" MODIFIED="1268920224244" TEXT="to_linspec"/>
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+</node>
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+<node CREATED="1268918767833" ID="Freemind_Link_1037382917" MODIFIED="1268920384363" STYLE="fork" TEXT="tocovdata"/>
+<node CREATED="1268918809021" ID="Freemind_Link_767625747" MODIFIED="1268918816990" STYLE="fork" TEXT="wave_periods"/>
+<node CREATED="1268918817396" ID="Freemind_Link_294440483" MODIFIED="1268918823943" STYLE="fork" TEXT="reconstruct"/>
+<node CREATED="1268918824365" ID="Freemind_Link_1893872699" MODIFIED="1268920714281" STYLE="fork" TEXT="plot_wave" VSHIFT="29"/>
+<node CREATED="1268918835318" ID="Freemind_Link_1625232632" MODIFIED="1268918848897" STYLE="fork" TEXT="plot_sp_wave"/>
+<node CREATED="1268918669644" ID="Freemind_Link_525365373" MODIFIED="1268918757817" STYLE="fork" TEXT="sampling_period"/>
+<node CREATED="1268918800427" ID="Freemind_Link_540262488" MODIFIED="1268920657436" STYLE="fork" TEXT="through_crest" VSHIFT="11">
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+</node>
+<node CREATED="1268918781115" ID="Freemind_Link_191369931" MODIFIED="1268920652670" STYLE="fork" TEXT="turning_points">
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+</node>
+</node>
+<node CREATED="1268917687085" ID="Freemind_Link_1298097150" MODIFIED="1268920673171" POSITION="right" STYLE="bubble" TEXT="CovData1D" VSHIFT="-212">
+<node CREATED="1268917901666" ID="Freemind_Link_1791940512" MODIFIED="1268919887910" STYLE="fork" TEXT="tospecdata">
+<arrowlink DESTINATION="Freemind_Link_823244205" ENDARROW="Default" ENDINCLINATION="14;87;" ID="Freemind_Arrow_Link_728651707" STARTARROW="None" STARTINCLINATION="-21;-38;"/>
+</node>
+<node CREATED="1268918164841" ID="Freemind_Link_1718380955" MODIFIED="1268918173622" STYLE="fork" TEXT="sampling_period"/>
+<node CREATED="1268918174044" ID="Freemind_Link_1888500587" MODIFIED="1268920740704" STYLE="fork" TEXT="sim">
+<arrowlink DESTINATION="Freemind_Link_1110096845" ENDARROW="Default" ENDINCLINATION="-2;21;" ID="Freemind_Arrow_Link_174025984" STARTARROW="None" STARTINCLINATION="271;12;"/>
+</node>
+<node CREATED="1268918178013" ID="Freemind_Link_757742844" MODIFIED="1268920750954" STYLE="fork" TEXT="simcond">
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+</node>
+</node>
+<node CREATED="1268918904132" ID="Freemind_Link_1866699423" MODIFIED="1268920673171" POSITION="right" STYLE="bubble" TEXT="TurningPoints">
+<node CREATED="1268918978226" ID="Freemind_Link_1033172969" MODIFIED="1268918989023" STYLE="fork" TEXT="cycle_pairs"/>
+</node>
+<node CREATED="1268918988977" ID="Freemind_Link_280025207" MODIFIED="1268920787861" POSITION="right" STYLE="bubble" TEXT="CyclePairs" VSHIFT="91">
+<node CREATED="1268919011477" ID="Freemind_Link_867889153" MODIFIED="1268919019180" STYLE="fork" TEXT="amplitudes"/>
+<node CREATED="1268919019586" ID="Freemind_Link_40128767" MODIFIED="1268919024414" STYLE="fork" TEXT="damage"/>
+<node CREATED="1268919025024" ID="Freemind_Link_1194799087" MODIFIED="1268919033727" STYLE="fork" TEXT="level_crossings"/>
+</node>
+<node CREATED="1268919295668" ID="Freemind_Link_106637151" MODIFIED="1268919305606" POSITION="right" STYLE="bubble" TEXT="LevelCrossings">
+<node CREATED="1268919349809" ID="Freemind_Link_1941466065" MODIFIED="1268920453960" STYLE="fork" TEXT="sim"/>
+<node CREATED="1268919305574" ID="Freemind_Link_1378561112" MODIFIED="1268919349122" STYLE="fork" TEXT="trdata"/>
+</node>
+<node CREATED="1268920796033" ID="_" MODIFIED="1268920800424" POSITION="right" STYLE="bubble" TEXT="TrData"/>
+</node>
+</map>

wafo/__init__.py

@@ -2,28 +2,28 @@ from __future__ import division, print_function, absolute_import
 
 from .info import __doc__
 
-# from . import misc
+from . import misc
-# from . import data
+from . import data
-# from . import demos
+from . import demos
-# from . import kdetools
+from . import kdetools
-# from . import objects
+from . import objects
-# from . import spectrum
+from . import spectrum
-# from . import transform
+from . import transform
-# from . import definitions
+from . import definitions
-# from . import polynomial
+from . import polynomial
-# from . import stats
+from . import stats
-# from . import interpolate
+from . import interpolate
-# from . import dctpack
+from . import dctpack
-# from . import wave_theory
+from . import wave_theory
-# try:
+try:
-#     from . import fig
+    from . import fig
-# except ImportError:
+except ImportError:
-#     print('fig import only supported on Windows')
+    print('fig import only supported on Windows')
 
-# try:
+try:
-#     from wafo.version import version as __version__
+    from wafo.version import version as __version__
-# except ImportError:
+except ImportError:
-#     __version__ = 'nobuilt'
+    __version__ = 'nobuilt'
 
-# from numpy.testing import Tester
+from numpy.testing import Tester
-# test = Tester().test
+test = Tester().test

wafo/bitwise.py

@@ -0,0 +1,97 @@
+"""
+Module extending the bitoperator capabilites of numpy
+"""
+
+from numpy import (bitwise_and, bitwise_or,
+                   bitwise_not, binary_repr,  # @UnusedImport
+                   bitwise_xor, where, arange)  # @UnusedImport
+__all__ = ['bitwise_and', 'bitwise_or', 'bitwise_not', 'binary_repr',
+           'bitwise_xor', 'getbit', 'setbit', 'getbits', 'setbits']
+
+
+def getbit(i, bit):
+    """
+    Get bit at specified position
+
+    Parameters
+    ----------
+    i : array-like of uints, longs
+        value to
+    bit : array-like of ints or longs
+        bit position between 0 and the number of bits in the uint class.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> binary_repr(13)
+    '1101'
+    >>> getbit(13,np.arange(3,-1,-1))
+    array([1, 1, 0, 1])
+    >>> getbit(5, np.r_[0:4])
+    array([1, 0, 1, 0])
+    """
+    return bitwise_and(i, 1 << bit) >> bit
+
+
+def getbits(i, numbits=8):
+    """
+    Returns bits of i in a list
+    """
+    return getbit(i, arange(0, numbits))
+
+
+def setbit(i, bit, value=1):
+    """
+    Set bit at specified position
+
+    Parameters
+    ----------
+    i : array-like of uints, longs
+        value to
+    bit : array-like of ints or longs
+        bit position between 0 and the number of bits in the uint class.
+    value : array-like of 0 or 1
+        value to set the bit to.
+
+    Examples
+    --------
+    Set bit fifth bit in the five bit binary binary representation of 9 (01001)
+    yields 25 (11001)
+    >>> setbit(9,4)
+    array(25)
+    """
+    val1 = 1 << bit
+    val0 = bitwise_not(val1)
+    return where((value == 0) & (i == i) & (bit == bit), bitwise_and(i, val0),
+                 bitwise_or(i, val1))
+
+
+def setbits(bitlist):
+    """
+    Set bits of val to values in bitlist
+
+    Example
+    -------
+    >>> setbits([1,1])
+    3
+    >>> setbits([1,0])
+    1
+    """
+    val = 0
+    for i, j in enumerate(bitlist):
+        val |= j << i
+    return val
+
+if __name__ == '__main__':
+    from wafo.testing import test_docstrings
+    test_docstrings(__file__)
+
+#    t = set(np.arange(8),1,1)
+#    t=get(0x84,np.arange(0,8))
+#    t=getbyte(0x84)
+#    t=get(0x84,[0, 1, 2, 3, 4, 5, 6, 7])
+#    t=get(0x20, 6)
+#    bit = [0 for i in range(8)]
+#    bit[7]=1
+#    t = setbits(bit)
+#    print(hex(t))

wafo/conftest.py

@@ -0,0 +1,3 @@
+# TODO Fix doctests in fig.py
+collect_ignore = ["fig.py", "MSO.py", "MSPPT.py", "powerpoint.py",
+                  "win32_utils.py"]

wafo/covariance/core.py

@@ -25,7 +25,7 @@ from numpy.random import randn
 import scipy.interpolate as interpolate
 from scipy.linalg import toeplitz, lstsq
 from scipy import sparse
-# from pylab import stineman_interp
+from pylab import stineman_interp
 
 from ..containers import PlotData
 from ..misc import sub_dict_select, nextpow2  # , JITImport

wafo/data/__init__.py

@@ -0,0 +1,3 @@
+from __future__ import absolute_import
+from .info import __doc__
+from .info import *

wafo/data/atlantic.dat

@@ -0,0 +1,582 @@
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wafo/data/info.py

@@ -0,0 +1,485 @@
+"""
+Data package in WAFO Toolbox.
+
+Contents
+--------
+atlantic - Significant wave-height data recorded in the Atlantic Ocean
+gfaks89  - Surface elevation measured at Gullfaks C 24.12.1989
+gfaksr89 - Reconstructed surface elevation measured at Gullfaks C 24.12.1989.
+japansea - coastline map of The Japan Sea
+northsea - coastline map of The Nortsea
+sea      - Surface elevation dataset used in WAT version 1.1.
+sfa89    - Wind measurements at Statfjord A 24.12.1989
+sn       - Fatigue experiment, constant-amplitude loading.
+yura87   - Surface elevation measured off the coast of Yura
+
+
+
+This module gives gives detailed information and easy access to all datasets
+included in WAFO
+
+"""
+import numpy as np
+
+import os
+__path2data = os.path.dirname(os.path.realpath(__file__))
+
+__all__ = ['atlantic', 'gfaks89', 'gfaksr89', 'japansea', 'northsea', 'sea',
+           'sfa89', 'sn', 'yura87']
+
+_NANS = set(['nan', 'NaN', '-1.#IND00+00', '1.#IND00+00', '-1.#INF00+00'])
+
+
+def _tofloat(x):
+    return np.nan if x in _NANS else float(x or 0)
+
+
+_MYCONVERTER = {}
+for i in range(2):
+    _MYCONVERTER[i] = _tofloat
+
+
+def _load(file):  # @ReservedAssignment
+    """ local load function
+    """
+    return np.loadtxt(os.path.join(__path2data, file))
+
+
+def _loadnan(file):  # @ReservedAssignment
+    """ local load function accepting nan's
+    """
+    return np.loadtxt(os.path.join(__path2data, file), converters=_MYCONVERTER)
+
+
+def atlantic():
+    """
+    Return Significant wave-height data recorded in the Atlantic Ocean
+
+    Data summary
+    ------------
+    Size             :     582 X 1
+    Sampling Rate    :     ~ 14 times a month
+    Device           :
+    Source           :
+    Format           :    ascii
+
+    Description
+    ------------
+    atlantic.dat contains average significant wave-height data recorded
+    approximately 14 times a month in December-February during 7 years and
+    at 2 locations in the Atlantic Ocean
+
+    Example
+    --------
+    >>> import pylab
+    >>> import wafo
+    >>> Hs = wafo.data.atlantic()
+    >>> np.allclose(Hs[:3], [ 5.48296296,  4.3615    ,  5.26023256])
+    True
+
+    h = pylab.plot(Hs)
+
+    Acknowledgement:
+    ---------------
+    This dataset were made available by Dr. David Carter
+    and Dr. David Cotton, Satellite Observing Systems, UK.
+    """
+    return _load('atlantic.dat')
+
+
+def gfaks89():
+    """
+    Return Surface elevation measured at Gullfaks C 24.12.1989
+
+    Data summary
+    ------------
+    Size             :    39000 X 2
+    Sampling Rate    :    2.5 Hz
+    Device           :    EMI laser
+    Source           :    STATOIL
+    Format           :    ascii, c1: time c2: surface elevation
+
+    Description
+    ------------
+    The wave data was measured 24th December 1989 at the Gullfaks C platform
+    in the North Sea from 17.00 to 21.20. The period from 20.00 to 20.20
+    is missing and contains NaNs.  The water depth of 218 m is
+    regarded as deep water for the most important wave components.
+    There are two EMI laser sensors named 219 and 220. This data set is
+    obtained from sensor 219, which is located in the Northwest
+    corner approximately two platform leg diameters away from
+    the closest leg.
+    Thus the wave elevation is not expected to be significantly
+    affected by diffraction effects for incoming waves in the western sector.
+    The wind direction for this period is from the south.
+    Some difficulties in calibration of the instruments have been reported
+    resulting in several consecutive measured values being equal or almost
+    equal in the observed data set.
+
+    This dataset is for non-commercial use only.
+
+    Hm0 = 6.8m, Tm02 = 8s, Tp = 10.5
+
+    Example
+    -------
+    >>> import pylab
+    >>> import wafo
+    >>> x = wafo.data.gfaks89()
+    >>> np.allclose(x[:3, 1], [-0.19667949, -0.46667949, -0.38667949])
+    True
+
+    h = pylab.plot(x[:,0],x[:,1])
+
+    Acknowledgement:
+    ---------------
+    This dataset were prepared and made available by Dr. S. Haver,
+    STATOIL, Norway
+
+    See also
+    --------
+    gfaksr89, northsea
+
+    """
+    return _loadnan('gfaks89.dat')
+
+
+def gfaksr89():
+    """
+    Return a reconstruction of surface elevation measured at Gullfaks C
+    24.12.1989.
+
+
+    Data summary
+    ------------
+    Size             :    39000 X 2
+    Sampling Rate    :    2.5 Hz
+    Device           :    EMI laser
+    Source           :    STATOIL
+    Format           :    ascii, c1: time c2: surface elevation
+
+    Description
+    -----------
+    This is a reconstructed version of the data in the GFAKS89.DAT file.
+    The following calls were made to reconstruct the data:
+
+                inds = findoutliers(gfaks89,.02,2,1.23);
+            gfaksr89 = reconstruct(gfaks89,inds,6);
+
+    The wave data was measured 24th December 1989 at the Gullfaks C platform
+    in the North Sea from 17.00 to 21.20. The period from 20.00 to 20.20
+    is missing in the original data.  The  water depth of 218 m is
+    regarded as deep water for the most important wave components.
+    There are two EMI laser sensors named 219 and 220. This data set is
+    obtained from sensor 219, which is located in the Northwest
+    corner approximately two platform leg diameters away from
+    the closest leg.
+    Thus the wave elevation is not expected to be significantly
+    affected by diffraction effects for incoming waves in the western sector.
+    The wind direction for this period is from the south.
+    Some difficulties in calibration of the instruments have been reported
+    resulting in several consecutive measured values being equal or almost
+    equal in the observed data set.
+
+    Hm0 = 6.8m, Tm02 = 8s, Tp = 10.5
+
+
+    Example
+    -------
+    >>> import pylab
+    >>> import wafo
+    >>> x = wafo.data.gfaksr89()
+
+    h = pylab.plot(x[:,0],x[:,1])
+
+    See also
+    --------
+    gfaks89
+    """
+    return _loadnan('gfaksr89.dat')
+
+
+def japansea():
+    """
+    Return coastline map of The Japan Sea
+
+
+    Data summary
+    ------------
+    Size             :     692 X 2
+    Sampling Rate    :
+    Device           :
+    Source           :    http://crusty.er.usgs.gov/coast/getcoast.html
+    Format           :    ascii, c1: longitude c2: latitude
+
+    Description
+    -----------
+    JAPANSEA.DAT contains data for plotting a map of The Japan Sea.
+    The data is obtained from USGS coastline extractor.
+
+    Example:
+    -------
+    #the map is seen by
+
+    >>> import pylab
+    >>> import wafo
+    >>> map1 = wafo.data.japansea()
+    >>> np.allclose(map1[1:4, 0], [ 141.960057,  142.058624,  142.103214])
+    True
+
+    h = pylab.plot(map1[:,0],map1[:,1])
+    lon_loc = [131,132,132,135,139.5,139]
+    lat_loc = [46, 43, 40, 35, 38.3, 35.7]
+    loc = ['China','Vladivostok','Japan Sea', 'Japan', 'Yura','Tokyo']
+    algn = 'right'
+    for lon, lat, name in zip(lon_loc,lat_loc,loc):
+        pylab.text(lon,lat,name,horizontalalignment=algn)
+
+
+    # If you have the m_map toolbox (see http://www.ocgy.ubc.ca/~rich/):
+    m_proj('lambert','long',[130 148],'lat',[30 48]);
+    m_line(map(:,1),map(:,2));
+    m_grid('box','fancy','tickdir','out');
+    m_text(131,46,'China');
+    m_text(132,43,'Vladivostok');
+    m_text(132,40,'Japan Sea');
+    m_text(135,35,'Japan');
+    m_text(139.5,38.3,'Yura');
+    m_text(139,35.7,'Tokyo');
+    """
+    return _loadnan('japansea.dat')
+
+
+def northsea():
+    """
+    NORTHSEA  coastline map of The Nortsea
+
+    Data summary
+    -------------
+    Size             :     60646 X 2
+    Sampling Rate    :
+    Device           :
+    Source           :    http://crusty.er.usgs.gov/coast/getcoast.html
+    Format           :    ascii, c1: longitude c2: latitude
+
+    Description
+    -----------
+    NORTHSEA.DAT contains data for plotting a map of The Northsea.
+    The data is obtained from USGS coastline extractor.
+
+    Example
+    -------
+    # the map is seen by
+
+    >>> import pylab
+    >>> import wafo
+    >>> map1 = wafo.data.northsea()
+    >>> np.allclose(map1[1:4, 0], [ 1.261996,  1.264064,  1.268171])
+    True
+
+    h = pylab.plot(map1[:,0],map1[:,1])
+    lon_pltfrm = [1.8,   2.3,  2.,  1.9, 2.6]
+    lat_pltfrm = [61.2, 61.2, 59.9, 58.4, 57.7]
+    pltfrm = ['Statfjord A', 'Gullfaks C', 'Frigg', 'Sleipner', 'Draupner']
+    h = pylab.scatter(lon_pltfrm,lat_pltfrm);
+    algn = 'right'
+    for lon, lat, name in zip(lon_pltfrm,lat_pltfrm,pltfrm):
+        pylab.text(lon,lat,name,horizontalalignment=algn); algn = 'left'
+
+
+    lon_city = [10.8, 10.8, 5.52, 5.2]
+    lat_city = [59.85, 63.4, 58.9, 60.3]
+    city = ['Oslo','Trondheim','Stavanger', 'Bergen']
+    h = pylab.scatter(lon_city,lat_city);
+    algn = 'right'
+    for lon, lat, name in zip(lon_city,lat_city,city):
+         pylab.text(lon,lat,name,horizontalalignment=algn)
+
+    # If you have the mpl_toolkits.basemap installed
+    from mpl_toolkits.basemap import Basemap
+    import matplotlib.pyplot as plt
+
+    # setup Lambert Conformal basemap.
+    m = Basemap(width=1200000,height=900000,projection='lcc',
+            resolution='f',lat_1=56.,lat_2=64,lat_0=58,lon_0=5.)
+    m.drawcoastlines()
+    h = m.scatter(lon_pltfrm,lat_pltfrm);
+    algn = 'right'
+    for lon, lat, name in zip(lon_pltfrm,lat_pltfrm,pltfrm):
+         m.text(lon,lat,name,horizontalalignment=algn); algn = 'left'
+    m.scatter(lon_city,lat_city)
+    algn = 'right'
+    for lon, lat, name in zip(lon_city,lat_city,city):
+         m.text(lon,lat,name,horizontalalignment=algn)
+    """
+    return _loadnan('northsea.dat')
+
+
+def sea():
+    """
+    Return Surface elevation dataset used in WAT version 1.1.
+
+    Data summary
+    ------------
+    Size             :    9524    X    2
+    Sampling Rate    :    4.0 Hz
+    Device           :    unknown
+    Source           :    unknown
+    Format           :    ascii, c1: time c2: surface elevation
+
+    Description
+    -----------
+    The wave data was used in one of WAFO predecessors, i.e. the Wave
+    Analysis Toolbox version 1.1 (WAT)
+    Hm0 = 1.9m, Tm02 = 4.0s, Tp2 = 11.5s Tp1=5.6s
+
+    Example
+    -------
+    >>> import pylab
+    >>> import wafo
+    >>> x = wafo.data.sea()
+    >>> np.allclose(x[:3,1],[-1.2004945 , -1.0904945 , -0.79049454])
+    True
+
+    h = pylab.plot(x[:,0],x[:,1])
+    """
+    return _load('sea.dat')
+
+
+def sfa89():
+    """
+    Return Wind measurements at Statfjord A 24.12.1989
+
+    Data summary
+    ------------
+    Size             :    144 X 3
+    Sampling Rate    :     1/600 Hz
+    Device           :
+    Source           :    DNMI (The Norwegian Meteorological Institute)
+    Format           :    ascii, c1: time     (hours)
+                              c2: velocity (m/s)
+                              c3: direction (degrees)
+    Description
+    -----------
+    The registration of wind speeds at the Gullfaks field
+    started up on Statfjord A in 1978 and continued until 1990.
+    The dataregistration was transferred to Gullfaks C in Nov 1989.
+    Due to some difficulties of the windregistration on Gullfaks C in
+    the beginning, they continued to use the registered data from
+    Statfjord A.
+    The windspeed is measured in  (meter/second), 110 m above mean water
+    level (MWL) and the wind direction is given in degrees for the data.
+    The data are a mean value of every 10 minutes.
+    Wind directions are defined in the meteorological convention, i.e.,
+    0 degrees = wind approaching from North, 90 degrees = wind from East, etc.
+    This dataset is for non-commercial use only.
+
+     Example
+    -------
+    >>> import pylab
+    >>> import wafo
+    >>> x = wafo.data.sfa89()
+
+    h = pylab.plot(x[:,0],x[:,1])
+
+    Acknowledgement
+    ----------------
+    These data are made available by Knut A. Iden, DNMI.
+
+    See also
+    --------
+    northsea
+    """
+    return _load('sfa89.dat')
+
+
+def sn():
+    """
+    Return SN Fatigue experiment, constant-amplitude loading.
+
+
+    Data summary
+    ------------
+    Size             :    40    X    2
+    Source           :    unknown
+    Format           :    ascii, c1: Amplitude MPa c2: Number of cycles
+
+    Description
+    -----------
+    A fatigue experiment with constant amplitudes at five levels:
+    10,15,20,25 and 30 MPa. For each level is related 8 observations of
+    the number of cycles to failure.
+
+    The origin of the data is unknown.
+
+     Example
+    -------
+    >>> import pylab
+    >>> import wafo
+    >>> x = wafo.data.sn()
+
+    h = pylab.plot(x[:,0],x[:,1])
+
+    See also
+    --------
+    The same data appear in the directory wdemos/itmkurs/
+    as SN.mat.
+
+    """
+    return _load('sn.dat')
+
+
+def yura87():
+    """
+    Return Surface elevation measured off the coast of Yura.
+
+
+    Data summary
+    -----------
+      Size             :    85547 X 4
+      Sampling Rate    :    1 Hz
+      Device           :    ultrasonic wave gauges
+      Source           :    SRI, Ministry of Transport, Japan
+      Format           :    ascii, c1: time (sec) c2-4: surface elevation (m)
+
+    Description
+    -----------
+    The wave data was measured at the Poseidon platform
+    in the Japan Sea from 24th November 1987 08.12 hours to 25th November
+    1987 07.57 hours. Poseidon was located 3 km off the coast of Yura
+    in the Yamagata prefecture, in the Japan Sea during the measurements.
+    The most important wave components are to some extent influenced by the
+    water depth of 42 m. The data are measured with three ultrasonic wave
+    gauges located at the sea floor and the relative coordinates of the
+    gauges are as follows (x-axis points to the East, y-axis points to
+    the North):
+                 X (m)    Y (m)
+          c2:   -4.93,    25.02
+          c3:    5.80,    92.12
+          c4:    0.00,     0.00
+
+        This dataset is for non-commercial use only.
+
+        Hm0 = 5.1m, Tm02 = 7.7s, Tp = 12.8s
+    Example
+    -------
+    >>> import pylab
+    >>> import wafo
+    >>> x = wafo.data.yura87()
+
+    h = pylab.plot(x[:,0],x[:,1])
+
+    Acknowledgement:
+    -----------------
+    This dataset were prepared and made available by Dr. Sc. H. Tomita,
+    Ship Research Institute, Ministry of Transport, Japan.
+
+    See also
+    --------
+    japansea
+    """
+    return _load('yura87.dat')
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()

wafo/data/japansea.dat

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wafo/data/sea.m

@@ -0,0 +1,16 @@
+%SEA Surface elevation dataset used in WAT version 1.1.
+%   
+% CALL:  xn = load('sea.dat');
+%  
+% Size             :    9524    X    2
+% Sampling Rate    :    4.0 Hz
+% Device           :    unknown
+% Source           :    unknown
+% Format           :    ascii, c1: time c2: surface elevation
+% Description      :
+%   The wave data was used in one of WAFO predecessors, i.e. the Wave 
+%   Analysis Toolbox version 1.1 (WAT)
+%  
+%   Hm0 = 1.9m, Tm02 = 4.0s, Tp2 = 11.5s Tp1=5.6s
+%
+% See also  

wafo/data/sfa89.dat

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wafo/data/sn.dat

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wafo/definitions.py

@@ -0,0 +1,310 @@
+"""
+WAFO defintions and numenclature
+
+    crossings :
+    cycle_pairs :
+    turning_points :
+    wave_amplitudes :
+    wave_periods :
+    waves :
+
+Examples
+--------
+In order to view the documentation do the following in an ipython window:
+
+import wafo.definitions as wd
+wd.crossings()
+
+or
+
+wd.crossings?
+
+
+"""
+
+
+def wave_amplitudes():
+    r"""
+    Wave amplitudes and heights definitions and nomenclature
+
+    Definition of wave amplitudes and wave heights
+    ---------------------------------------------
+
+                <----- Direction of wave propagation
+
+
+               |..............c_..........|
+               |             /| \         |
+           Hd  |           _/ |  \        |  Hu
+       M       |          /   |   \       |
+      / \      |     M   / Ac |    \_     |     c_
+     F   \     |    / \m/     |      \    |    /  \
+    ------d----|---u------------------d---|---u----d------ level v
+           \   |  /|                   \  |  /      \L
+            \_ | / | At                 \_|_/
+              \|/..|                      t
+               t
+
+    Parameters
+    ----------
+    Ac : crest amplitude
+    At : trough amplitude
+    Hd : wave height as defined for down crossing waves
+    Hu : wave height as defined for up crossing waves
+
+    See also
+    --------
+    waves, crossings, turning_points
+    """
+    print(wave_amplitudes.__doc__)
+
+
+def crossings():
+    r"""
+    Level v crossing definitions and nomenclature
+
+    Definition of level v crossings
+    -------------------------------
+          M
+        .   .                  M                   M
+      .      . .             .                   .   .
+    F            d               .             .       L
+    -----------------------u-------d-------o----------------- level v
+                   .     .           .   .   u
+                     .                 m
+                           m
+
+    Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the
+    figure above denote local minimum, maximum, first value, last
+    value, down- and up-crossing, respectively. The remaining
+    sampled values are indicated with a '.'. Values that are identical
+    with v, but do not cross the level is indicated with the letter 'o'.
+    We have a level up-crossing at index, k, if
+
+       x(k) <  v and v < x(k+1)
+    or if
+       x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1
+
+    where di is  the index to the previous downcrossing.
+    Similarly there is a level down-crossing at index, k, if
+
+       x(k) >  v and v > x(k+1)
+    or if
+       x(k) == v and v > x(k+1) and x(r) > v  for some ui < r <= k-1
+
+    where ui is  the index to the previous upcrossing.
+
+    The first (F) value is a up crossing if  x(1) = v and x(2) > v.
+    Similarly, it is a down crossing if      x(1) = v and x(2) < v.
+
+    See also
+    --------
+    wave_periods, waves, turning_points, findcross, findtp
+    """
+    print(crossings.__doc__)
+
+
+def cycle_pairs():
+    r"""
+    Cycle pairs definitions and numenclature
+
+    Definition of Max2min and min2Max cycle pair
+    --------------------------------------------
+    A min2Max cycle pair (mM) is defined as the pair of a minimum
+    and the following Maximum. Similarly a Max2min cycle pair (Mm)
+    is defined as the pair of a Maximum and the following minimum.
+    (all turning points possibly rainflowfiltered before pairing into cycles.)
+
+    See also
+    --------
+    turning_points
+    """
+    print(cycle_pairs.__doc__)
+
+
+def wave_periods():
+    r"""
+    Wave periods (lengths) definitions and nomenclature
+
+    Definition of wave periods (lengths)
+    ------------------------------------
+
+
+               <----- Direction of wave propagation
+
+                   <-------Tu--------->
+                   :                  :
+                   <---Tc----->       :
+                   :          :       : <------Tcc---->
+       M           :      c   :       : :             :
+      / \          : M   / \_ :       : c_            c
+     F   \         :/ \m/    \:       :/  \          / \
+    ------d--------u----------d-------u----d--------u---d-------- level v
+           \      /            \     /     :\_    _/:   :\_   L
+            \_   /              \_t_/      :  \t_/  :   :  \m/
+              \t/                 :        :        :   :
+               :                  :        <---Tt--->   :
+               <--------Ttt------->        :            :
+                                           <-----Td----->
+    Tu   = Up crossing period
+    Td   = Down crossing period
+    Tc   = Crest period, i.e., period between up crossing and
+           the next down crossing
+    Tt   = Trough period, i.e., period between down crossing and
+           the next up crossing
+    Ttt  = Trough2trough period
+    Tcc  = Crest2crest period
+
+
+               <----- Direction of wave propagation
+
+                    <--Tcf->                              Tuc
+                   :      :               <-Tcb->        <->
+       M            :      c               :     :        : :
+      / \           : M   / \_             c_    :        : c
+     F   \          :/ \m/    \           /  \___:        :/ \
+    ------d---------u----------d---------u-------d--------u---d------ level v
+          :\_      /            \     __/:        \_    _/     \_   L
+          :  \_   /              \_t_/   :          \t_/         \m/
+          :    \t/                 :     :
+          :     :                  :     :
+         <-Ttf->                  <-Ttb->
+
+
+    Tcf  = Crest front period, i.e., period between up crossing and crest
+    Tcb  = Crest back period, i.e., period between crest and down crossing
+    Ttf  = Trough front period, i.e., period between down crossing and trough
+    Ttb  = Trough back period, i.e., period between trough and up crossing
+        Also note that Tcf and Ttf can also be abbreviated by their crossing
+        marker, e.g. Tuc (u2c)  and Tdt (d2t), respectively. Similar applies
+        to all the other wave periods and wave lengths.
+
+    (The nomenclature for wave length is similar, just substitute T and
+     period with L and length, respectively)
+
+                 <----- Direction of wave propagation
+
+                          <--TMm-->
+               <-TmM->    :       :
+       M       :     :    M       :
+      / \      :     M   /:\_     :     M_            M
+     F   \     :    / \m/ :  \    :    /: \          / \
+          \    :   /      :   \   :   / :  \        /   \
+           \   :  /       :    \  :  /  :   \_    _/     \_   L
+            \_ : /        :     \_m_/   :     \m_/         \m/
+              \m/         :             :      :            :
+                          <-----TMM----->      <----Tmm----->
+
+
+    TmM = Period between minimum and the following Maximum
+    TMm = Period between Maximum and the following minimum
+    TMM = Period between Maximum and the following Maximum
+    Tmm = Period between minimum and the following minimum
+
+    See also
+    --------
+    waves,
+    wave_amplitudes,
+    crossings,
+    turning_points
+    """
+    print(wave_periods.__doc__)
+
+
+def turning_points():
+    r"""
+    Turning points definitions and numenclature
+
+    Definition of turningpoints
+    ---------------------------
+                      <----- Direction of wave propagation
+
+       M                  M
+      / \       .... M   /:\_           M_            M
+     F   \     |    / \m/ :  \         /: \          / \
+          \  h |   /      :   \       / :  \        /   \
+           \   |  /       :    \     /  :   \_    _/     \_   L
+            \_ | /        :     \_m_/   :     \m_/         \m/
+              \m/         :             :      :            :
+                          <------Mw----->      <-----mw----->
+
+    Local minimum or maximum are indicated with the
+    letters 'm' or 'M'. Turning points in this connection are all
+    local max (M) and min (m) and the last (L) value and the
+    first (F) value if the first local extremum is a max.
+
+    (This choice is made in order to get the exact up-crossing intensity
+    from rfc by mm2lc(tp2mm(rfc)) )
+
+
+    See also
+    --------
+    waves,
+    crossings,
+    cycle_pairs
+    findtp
+
+    """
+    print(turning_points.__doc__)
+
+
+def waves():
+    r"""
+    Wave definitions and nomenclature
+
+    Definition of trough and crest
+    ------------------------------
+    A trough (t) is defined as the global minimum between a
+    level v down-crossing (d) and the next up-crossing (u)
+    and a crest (c) is defined as the global maximum between a
+    level v up-crossing and the following down-crossing.
+
+    Definition of down- and up -crossing waves
+    ------------------------------------------
+    A level v-down-crossing wave (dw) is a wave from a
+    down-crossing to the following down-crossing.
+    Similarly, a level v-up-crossing wave (uw) is a wave from an up-crossing
+    to the next up-crossing.
+
+    Definition of trough and crest waves
+    ------------------------------------
+    A trough-to-trough wave (tw) is a wave from a trough (t) to the
+    following trough. The crest-to-crest wave (cw) is defined similarly.
+
+
+    Definition of min2min and Max2Max wave
+    --------------------------------------
+    A min2min wave (mw) is defined starting from a minimum (m) and
+    ending in the following minimum.
+    Similarly a Max2Max wave (Mw) is thus a wave from a maximum (M)
+    to the next maximum (all waves optionally rainflow filtered).
+
+               <----- Direction of wave propagation
+
+
+       <------Mw-----> <----mw---->
+       M             : :  c       :
+      / \            M : / \_     :     c_            c
+     F   \          / \m/    \    :    /: \          /:\
+    ------d--------u----------d-------u----d--------u---d------ level v
+           \      /:           \  :  /: :  :\_    _/  : :\_   L
+            \_   / :            \_t_/ : :  :  \t_/    : :  \m/
+              \t/  <-------uw---------> :  <-----dw----->
+               :                  :     :             :
+               <--------tw-------->     <------cw----->
+
+     (F=first value and L=last value).
+
+    See also
+    --------
+    turning_points,
+    crossings,
+    wave_periods
+    findtc,
+    findcross
+    """
+    print(waves.__doc__)
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)

wafo/demos.py

@@ -0,0 +1,146 @@
+"""
+Created on 20. jan. 2011
+
+@author: pab
+"""
+import numpy as np
+from numpy import exp, meshgrid
+__all__ = ['peaks', 'humps', 'magic']
+
+
+def _magic_odd_order(n):
+    ix = np.arange(n) + 1
+    J, I = np.meshgrid(ix, ix)
+    A = np.mod(I + J - (n + 3) / 2, n)
+    B = np.mod(I + 2 * J - 2, n)
+    M = n * A + B + 1
+    return M
+
+
+def _magic_doubly_even_order(n):
+    M = np.arange(1, n * n + 1).reshape(n, n)
+    ix = np.mod(np.arange(n) + 1, 4) // 2
+    J, I = np.meshgrid(ix, ix)
+    iz = np.flatnonzero(I == J)
+    M.put(iz, n * n + 1 - M.flat[iz])
+    return M
+
+
+def _magic_even_order(n):
+    p = n // 2
+    M0 = magic(p)
+    M = np.hstack((np.vstack((M0, M0 + 3 * p * p)),
+                   np.vstack((M0 + 2 * p * p, M0 + p * p))))
+    if n > 2:
+        k = (n - 2) // 4
+        jvec = np.hstack((np.arange(k), np.arange(n - k + 1, n)))
+        for i in range(p):
+            for j in jvec:
+                temp = M[i][j]
+                M[i][j] = M[i + p][j]
+                M[i + p][j] = temp
+
+        i = k
+        j = 0
+        temp = M[i][j]
+        M[i][j] = M[i + p][j]
+        M[i + p][j] = temp
+        j = i
+        temp = M[i + p][j]
+        M[i + p][j] = M[i][j]
+        M[i][j] = temp
+    return M
+
+
+def magic(n):
+    """
+    Return magic square  for n of any orders > 2.
+
+    A magic square has the property that the sum of every row and column,
+    as well as both diagonals, is the same number.
+
+    Examples
+    --------
+    >>> np.allclose(magic(3),
+    ...    [[8, 1, 6],
+    ...    [3, 5, 7],
+    ...    [4, 9, 2]])
+    True
+
+    >>> np.allclose(magic(4),
+    ...    [[16,  2,  3, 13],
+    ...    [ 5, 11, 10,  8],
+    ...    [ 9,  7,  6, 12],
+    ...    [ 4, 14, 15,  1]])
+    True
+
+    >>> np.allclose(magic(6),
+    ...    [[35,  1,  6, 26, 19, 24],
+    ...    [ 3, 32,  7, 21, 23, 25],
+    ...    [31,  9,  2, 22, 27, 20],
+    ...    [ 8, 28, 33, 17, 10, 15],
+    ...    [30,  5, 34, 12, 14, 16],
+    ...    [ 4, 36, 29, 13, 18, 11]])
+    True
+    """
+    if (n < 3):
+        raise ValueError('n must be greater than 2.')
+
+    if np.mod(n, 2) == 1:
+        return _magic_odd_order(n)
+    elif np.mod(n, 4) == 0:
+        return _magic_doubly_even_order(n)
+    return _magic_even_order(n)
+
+
+def peaks(x=None, y=None, n=51):
+    """
+    Return the "well" known MatLab (R) peaks function
+    evaluated in the [-3,3] x,y range
+
+    Example
+    -------
+    >>> import matplotlib.pyplot as plt
+    >>> x,y,z = peaks()
+
+    h = plt.contourf(x,y,z)
+
+    """
+    if x is None:
+        x = np.linspace(-3, 3, n)
+    if y is None:
+        y = np.linspace(-3, 3, n)
+
+    [x1, y1] = meshgrid(x, y)
+
+    z = (3 * (1 - x1) ** 2 * exp(-(x1 ** 2) - (y1 + 1) ** 2) -
+         10 * (x1 / 5 - x1 ** 3 - y1 ** 5) * exp(-x1 ** 2 - y1 ** 2) -
+         1. / 3 * exp(-(x1 + 1) ** 2 - y1 ** 2))
+
+    return x1, y1, z
+
+
+def humps(x=None):
+    """
+    Computes a function that has three roots, and some humps.
+
+     Example
+    -------
+    >>> import matplotlib.pyplot as plt
+    >>> x = np.linspace(0,1)
+    >>> y = humps(x)
+
+    h = plt.plot(x,y)
+    """
+    if x is None:
+        y = np.linspace(0, 1)
+    else:
+        y = np.asarray(x)
+
+    return 1.0 / ((y - 0.3) ** 2 + 0.01) + 1.0 / ((y - 0.9) ** 2 + 0.04) + \
+        2 * y - 5.2
+
+
+if __name__ == '__main__':
+    from wafo.testing import test_docstrings
+    test_docstrings(__file__)

wafo/doc/tutorial_scripts/WAFO Chapter 3.ipynb

@@ -0,0 +1,73 @@
+{
+ "metadata": {
+  "name": "WAFO Chapter 3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "CHAPTER3  Demonstrates distributions of wave characteristics\n",
+      "=============================================================\n",
+      "\n",
+      "Chapter3 contains the commands used in Chapter3 in the tutorial.\n",
+      " \n",
+      "Some of the commands are edited for fast computation. \n",
+      "\n",
+      "Section 3.2 Estimation of wave characteristics from data\n",
+      "----------------------------------------------------------\n",
+      "Example 1\n",
+      "~~~~~~~~~~ "
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "speed = 'fast'\n",
+      "#speed = 'slow'\n",
+      "\n",
+      "import wafo.data as wd\n",
+      "import wafo.misc as wm\n",
+      "import wafo.objects as wo\n",
+      "xx = wd.sea() \n",
+      "xx[:,1] = wm.detrendma(xx[:,1],len(xx))\n",
+      "ts = wo.mat2timeseries(xx)\n",
+      "Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8)\n",
+      "Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "ename": "AssertionError",
+       "evalue": "",
+       "output_type": "pyerr",
+       "traceback": [
+        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
+        "\u001b[1;32m<ipython-input-12-5b70e90102e6>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mxx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdetrendma\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[0mts\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwo\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmat2timeseries\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mxx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[0mTcrcr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mix\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mts\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwave_periods\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvh\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpdef\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'c2c'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwdef\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'tw'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrate\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m8\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     11\u001b[0m \u001b[0mTc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mixc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mts\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mwave_periods\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvh\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpdef\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'u2d'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwdef\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'tw'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrate\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m8\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+        "\u001b[1;32mc:\\pab\\workspace\\pywafo_svn\\pywafo\\src\\wafo\\objects.pyc\u001b[0m in \u001b[0;36mwave_periods\u001b[1;34m(self, vh, pdef, wdef, index, rate)\u001b[0m\n\u001b[0;32m   1980\u001b[0m             \u001b[0mn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mceil\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msize\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mrate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1981\u001b[0m             \u001b[0mti\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlinspace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1982\u001b[1;33m             \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mstineman_interp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mti\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1983\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1984\u001b[0m             \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+        "\u001b[1;32mC:\\Python27\\lib\\site-packages\\matplotlib\\mlab.pyc\u001b[0m in \u001b[0;36mstineman_interp\u001b[1;34m(xi, x, y, yp)\u001b[0m\n\u001b[0;32m   2932\u001b[0m     \u001b[0mx\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat_\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2933\u001b[0m     \u001b[0my\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat_\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2934\u001b[1;33m     \u001b[1;32massert\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2935\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2936\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0myp\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+        "\u001b[1;31mAssertionError\u001b[0m: "
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}

wafo/doc/tutorial_scripts/chapter1.py

@@ -0,0 +1,192 @@
+import wafo.plotbackend.plotbackend as plt
+import numpy as np
+# pyreport -o chapter1.html chapter1.py
+
+#! CHAPTER1 demonstrates some applications of WAFO
+#!================================================
+#!
+#! CHAPTER1 gives an overview through examples some of the capabilities of
+#! WAFO. WAFO is a toolbox of Matlab routines for statistical analysis and
+#! simulation of random waves and loads.
+#!
+#! The commands are edited for fast computation.
+
+
+#! Section 1.4 Some applications of WAFO
+#!---------------------------------------
+#! Section 1.4.1 Simulation from spectrum, estimation of spectrum
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#! Simulation of the sea surface from spectrum
+#! The following code generates 200 seconds of data sampled with 10Hz from
+#! the Torsethaugen spectrum
+import wafo.spectrum.models as wsm
+S = wsm.Torsethaugen(Hm0=6, Tp=8)
+S1 = S.tospecdata()
+S1.plot()
+plt.show()
+
+
+##
+import wafo.objects as wo
+xs = S1.sim(ns=2000, dt=0.1)
+ts = wo.mat2timeseries(xs)
+ts.plot_wave('-')
+plt.show()
+
+
+#! Estimation of spectrum
+#!~~~~~~~~~~~~~~~~~~~~~~~
+#! A common situation is that one wants to estimate the spectrum for wave
+#! measurements. The following code simulate 20 minutes signal sampled at 4Hz
+#! and compare the spectral estimate with the original Torsethaugen spectum.
+plt.clf()
+Fs = 4
+xs = S1.sim(ns=np.fix(20 * 60 * Fs), dt=1. / Fs)
+ts = wo.mat2timeseries(xs)
+Sest = ts.tospecdata(L=400)
+S1.plot()
+Sest.plot('--')
+plt.axis([0, 3, 0, 5])
+plt.show()
+
+#! Section 1.4.2 Probability distributions of wave characteristics.
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#! Probability distribution of wave trough period:
+#! WAFO gives the possibility of computing the exact probability
+#! distributions for a number of characteristics given a spectral density.
+#! In the following example we study the trough period extracted from the
+#! time series and compared with the theoretical density computed with exact
+#! spectrum, S1, and the estimated spectrum, Sest.
+plt.clf()
+import wafo.misc as wm
+dtyex = S1.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
+dtyest = Sest.to_t_pdf(pdef='Tt', paramt=(0, 10, 51), nit=3)
+
+T, index = ts.wave_periods(vh=0, pdef='d2u')
+bins = wm.good_bins(T, num_bins=25, odd=True)
+wm.plot_histgrm(T, bins=bins, normed=True)
+
+dtyex.plot()
+dtyest.plot('-.')
+plt.axis([0, 10, 0, 0.35])
+plt.show()
+
+#! Section 1.4.3 Directional spectra
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#! Here are a few lines of code, which produce directional spectra
+#! with frequency independent and frequency dependent spreading.
+plt.clf()
+plotflag = 1
+Nt = 101      # number of angles
+th0 = np.pi / 2  # primary direction of waves
+Sp = 15       # spreading parameter
+
+D1 = wsm.Spreading(type='cos', theta0=th0, method=None)
+D12 = wsm.Spreading(type='cos', theta0=0, method='mitsuyasu')
+
+SD1 = D1.tospecdata2d(S1)
+SD12 = D12.tospecdata2d(S1)
+SD1.plot()
+SD12.plot()  # linestyle='dashdot')
+plt.show()
+
+#! 3D Simulation of the sea surface
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#! The simulations show that frequency dependent spreading leads to
+#! much more irregular surface so the orientation of waves is less
+#! transparent compared to the frequency independent case.
+#
+#! Frequency independent spreading
+#plotflag = 1; iseed = 1;
+#
+#Nx = 2 ^ 8;Ny = Nx;Nt = 1;dx = 0.5; dy = dx; dt = 0.25; fftdim = 2;
+#randn('state', iseed)
+#Y1 = seasim(SD1, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag);
+#wafostamp('', '(ER)')
+#axis('fill')
+#disp('Block = 6'), pause(pstate)
+#
+###
+## Frequency dependent spreading
+#randn('state', iseed)
+#Y12 = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, fftdim, plotflag);
+#wafostamp('', '(ER)')
+#axis('fill')
+#disp('Block = 7'), pause(pstate)
+#
+#! Estimation of directional spectrum
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#!  The figure is not shown in the Tutorial
+#
+# Nx = 3; Ny = 2; Nt = 2 ^ 12; dx = 10; dy = 10;dt = 0.5;
+# F = seasim(SD12, Nx, Ny, Nt, dx, dy, dt, 1, 0);
+# Z = permute(F.Z, [3 1 2]);
+# [X, Y] = meshgrid(F.x, F.y);
+# N = Nx * Ny;
+# types = repmat(sensortypeid('n'), N, 1);
+# bfs = ones(N, 1);
+# pos = [X(:), Y(:), zeros(N, 1)];
+# h = inf;
+# nfft = 128;
+# nt = 101;
+# SDe = dat2dspec([F.t Z(:, :)], [pos types, bfs], h, nfft, nt);
+#plotspec(SDe), hold on
+#plotspec(SD12, '--'), hold off
+#disp('Block = 8'), pause(pstate)
+
+#! Section 1.4.4 Fatigue, Load cycles and Markov models.
+#! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#! Switching Markow chain of turningpoints
+#! In fatigue applications the exact sample path is not important, but
+#! only the tops and bottoms of the load, called the sequence of turning
+#! points (TP). From the turning points one can extract load cycles, from
+#! which damage calculations and fatigue life predictions can be
+#! performed.
+#!
+#! The commands below computes the intensity of rainflowcycles for
+#! the Gaussian model with spectrum S1 using the Markov approximation.
+#! The rainflow cycles found in the simulated load signal are shown in the
+#! figure.
+
+#clf()
+#paramu = [-6 6 61];
+#frfc = spec2cmat(S1, [], 'rfc', [], paramu);
+#pdfplot(frfc);
+#hold on
+#tp = dat2tp(xs);
+#rfc = tp2rfc(tp);
+#plot(rfc(:, 2), rfc(:, 1), '.')
+#wafostamp('', '(ER)')
+#hold off
+#disp('Block = 9'), pause(pstate)
+
+#! Section 1.4.5 Extreme value statistics
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# Plot of yura87 data
+plt.clf()
+import wafo.data as wd
+xn = wd.yura87()
+#xn = load('yura87.dat');
+plt.subplot(211)
+plt.plot(xn[::30, 0] / 3600, xn[::30, 1], '.')
+plt.title('Water level')
+plt.ylabel('(m)')
+
+#! Formation of 5 min maxima
+yura = xn[:85500, 1]
+yura = np.reshape(yura, (285, 300)).T
+maxyura = yura.max(axis=0)
+plt.subplot(212)
+plt.plot(xn[299:85500:300, 0] / 3600, maxyura, '.')
+plt.xlabel('Time (h)')
+plt.ylabel('(m)')
+plt.title('Maximum 5 min water level')
+plt.show()
+
+#! Estimation of GEV for yuramax
+plt.clf()
+import wafo.stats as ws
+phat = ws.genextreme.fit2(maxyura, method='ml')
+phat.plotfitsummary()
+plt.show()
+#disp('Block = 11, Last block')

wafo/doc/tutorial_scripts/chapter2.py

@@ -0,0 +1,327 @@
+import wafo.plotbackend.plotbackend as plt
+import numpy as np
+
+# pyreport -o chapter2.html chapter2.py
+
+#! CHAPTER2 Modelling random loads and stochastic waves
+#!=======================================================
+#!
+#! Chapter2 contains the commands used in Chapter 2 of the tutorial and
+#! present some tools for analysis of random functions with
+#! respect to their correlation, spectral and distributional properties.
+#! The presentation is divided into three examples:
+#!
+#! Example1 is devoted to estimation of different parameters in the model.
+#! Example2 deals with spectral densities and
+#! Example3 presents the use of WAFO to simulate samples of a Gaussian
+#! process.
+#!
+#! Some of the commands are edited for fast computation.
+#!
+#! Section 2.1 Introduction and preliminary analysis
+#!====================================================
+#! Example 1: Sea data
+#!----------------------
+#! Observed crossings compared to the expected for Gaussian signals
+
+import wafo
+import wafo.objects as wo
+xx = wafo.data.sea()
+me = xx[:, 1].mean()
+sa = xx[:, 1].std()
+xx[:, 1] -= me
+ts = wo.mat2timeseries(xx)
+tp = ts.turning_points()
+
+cc = tp.cycle_pairs()
+lc = cc.level_crossings()
+lc.plot()
+plt.show()
+
+#! Average number of upcrossings per time unit
+#!----------------------------------------------
+#! Next we compute the mean frequency as the average number of upcrossings
+#! per time unit of the mean level (= 0); this may require interpolation in the
+#! crossing intensity curve, as follows.
+T = xx[:, 0].max() - xx[:, 0].min()
+f0 = np.interp(0, lc.args, lc.data, 0) / T  # zero up-crossing frequency
+print('f0 = %g' % f0)
+
+#! Turningpoints and irregularity factor
+#!----------------------------------------
+
+fm = len(tp.data) / (2 * T)   # frequency of maxima
+alfa = f0 / fm                # approx Tm24/Tm02
+
+print('fm = %g, alpha = %g, ' % (fm, alfa))
+
+#! Visually examine data
+#!------------------------
+#! We finish this section with some remarks about the quality
+#! of the measured data. Especially sea surface measurements can be
+#! of poor quality. We shall now check the  quality of the dataset {\tt xx}.
+#! It is always good practice to visually examine the data
+#! before the analysis to get an impression of the quality,
+#! non-linearities and narrow-bandedness of the data.
+#! First we shall plot the data and zoom in on a specific region.
+#! A part of sea data is visualized with the following commands
+plt.clf()
+ts.plot_wave('k-', tp, '*', nfig=1, nsub=1)
+
+plt.axis([0, 2, -2, 2])
+plt.show()
+
+#! Finding possible spurious points
+#!------------------------------------
+#! However, if the amount of data is too large for visual examinations one
+#! could use the following criteria to find possible spurious points. One
+#! must be careful using the criteria for extremevalue analysis, because
+#! it might remove extreme waves that are OK and not spurious.
+
+import wafo.misc as wm
+dt = ts.sampling_period()
+# dt = np.diff(xx[:2,0])
+dcrit = 5 * dt
+ddcrit = 9.81 / 2 * dt * dt
+zcrit = 0
+inds, indg = wm.findoutliers(ts.data, zcrit, dcrit, ddcrit, verbose=True)
+
+#! Section 2.2 Frequency Modeling of Load Histories
+#!----------------------------------------------------
+#! Periodogram: Raw spectrum
+#!
+plt.clf()
+Lmax = 9500
+S = ts.tospecdata(L=Lmax)
+S.plot()
+plt.axis([0, 5, 0, 0.7])
+plt.show()
+
+#! Calculate moments
+#!-------------------
+mom, text = S.moment(nr=4)
+print('sigma = %g, m0 = %g' % (sa, np.sqrt(mom[0])))
+
+#! Section 2.2.1 Random functions in Spectral Domain - Gaussian processes
+#!--------------------------------------------------------------------------
+#! Smoothing of spectral estimate
+#!----------------------------------
+#! By decreasing Lmax the spectrum estimate becomes smoother.
+
+plt.clf()
+Lmax0 = 200
+Lmax1 = 50
+S1 = ts.tospecdata(L=Lmax0)
+S2 = ts.tospecdata(L=Lmax1)
+S1.plot('-.')
+S2.plot()
+plt.show()
+
+#! Estimated autocovariance
+#!----------------------------
+#! Obviously knowing the spectrum one can compute the covariance
+#! function. The following code will compute the covariance for the
+#! unimodal spectral density S1 and compare it with estimated
+#! covariance of the signal xx.
+plt.clf()
+Lmax = 85
+R1 = S1.tocovdata(nr=1)
+Rest = ts.tocovdata(lag=Lmax)
+R1.plot('.')
+Rest.plot()
+plt.axis([0, 25, -0.1, 0.25])
+plt.show()
+
+#! We can see in Figure below that the covariance function corresponding to
+#! the spectral density S2 significantly differs from the one estimated
+#! directly from data.
+#! It can be seen in Figure above that the covariance corresponding to S1
+#! agrees much better with the estimated covariance function
+
+plt.clf()
+R2 = S2.tocovdata(nr=1)
+R2.plot('.')
+Rest.plot()
+plt.show()
+
+#! Section 2.2.2 Transformed Gaussian models
+#!-------------------------------------------
+#! We begin with computing skewness and kurtosis
+#! for the data set xx and compare it with the second order wave approximation
+#! proposed by Winterstein:
+import wafo.stats as ws
+rho3 = ws.skew(xx[:, 1])
+rho4 = ws.kurtosis(xx[:, 1])
+
+sk, ku = S1.stats_nl(moments='sk')
+
+#! Comparisons of 3 transformations
+plt.clf()
+import wafo.transform.models as wtm
+gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku).trdata()
+g = wtm.TrLinear(mean=me, sigma=sa).trdata()  # Linear transformation
+glc, gemp = lc.trdata(mean=me, sigma=sa)
+
+glc.plot('b-')  # Transf. estimated from level-crossings
+gh.plot('b-.')  # Hermite Transf. estimated from moments
+g.plot('r')
+plt.grid('on')
+plt.show()
+
+#! Test Gaussianity of a stochastic process
+#!------------------------------------------
+#! TESTGAUSSIAN simulates  e(g(u)-u) = int (g(u)-u)^2 du  for Gaussian processes
+#! given the spectral density, S. The result is plotted if test0 is given.
+#! This is useful for testing if the process X(t) is Gaussian.
+#! If 95% of TEST1 is less than TEST0 then X(t) is not Gaussian at a 5% level.
+#!
+#! As we see from the figure below: none of the simulated values of test1 is
+#! above 1.00. Thus the data significantly departs from a Gaussian distribution.
+plt.clf()
+test0 = glc.dist2gauss()
+#! the following test takes time
+N = len(xx)
+test1 = S1.testgaussian(ns=N, cases=50, test0=test0)
+is_gaussian = sum(test1 > test0) > 5
+print(is_gaussian)
+plt.show()
+
+#! Normalplot of data xx
+#!------------------------
+#! indicates that the underlying distribution has a "heavy" upper tail and a
+#! "light" lower tail.
+plt.clf()
+import pylab
+ws.probplot(ts.data.ravel(), dist='norm', plot=pylab)
+plt.show()
+#! Section 2.2.3 Spectral densities of sea data
+#!-----------------------------------------------
+#! Example 2: Different forms of spectra
+#!
+import wafo.spectrum.models as wsm
+plt.clf()
+Hm0 = 7
+Tp = 11
+spec = wsm.Jonswap(Hm0=Hm0, Tp=Tp).tospecdata()
+spec.plot()
+plt.show()
+
+#! Directional spectrum and Encountered directional spectrum
+#! Directional spectrum
+plt.clf()
+D = wsm.Spreading('cos2s')
+Sd = D.tospecdata2d(spec)
+Sd.plot()
+plt.show()
+
+
+##!Encountered directional spectrum
+##!---------------------------------
+#clf()
+#Se = spec2spec(Sd,'encdir',0,10);
+#plotspec(Se), hold on
+#plotspec(Sd,1,'--'), hold off
+##!wafostamp('','(ER)')
+#disp('Block = 17'),pause(pstate)
+#
+##!#! Frequency spectra
+#clf
+#Sd1 =spec2spec(Sd,'freq');
+#Sd2 = spec2spec(Se,'enc');
+#plotspec(spec), hold on
+#plotspec(Sd1,1,'.'),
+#plotspec(Sd2),
+##!wafostamp('','(ER)')
+#hold off
+#disp('Block = 18'),pause(pstate)
+#
+##!#! Wave number spectrum
+#clf
+#Sk = spec2spec(spec,'k1d')
+#Skd = spec2spec(Sd,'k1d')
+#plotspec(Sk), hold on
+#plotspec(Skd,1,'--'), hold off
+##!wafostamp('','(ER)')
+#disp('Block = 19'),pause(pstate)
+#
+##!#! Effect of waterdepth on spectrum
+#clf
+#plotspec(spec,1,'--'), hold on
+#S20 = spec;
+#S20.S = S20.S.*phi1(S20.w,20);
+#S20.h = 20;
+#plotspec(S20),  hold off
+##!wafostamp('','(ER)')
+#disp('Block = 20'),pause(pstate)
+#
+##!#! Section 2.3 Simulation of transformed Gaussian process
+##!#! Example 3: Simulation of random sea
+##! The reconstruct function replaces the spurious points of seasurface by
+##! simulated data on the basis of the remaining data and a transformed Gaussian
+##! process. As noted previously one must be careful using the criteria
+##! for finding spurious points when reconstructing a dataset, because
+##! these criteria might remove the highest and steepest waves as we can see
+##! in this plot where the spurious points is indicated with a '+' sign:
+##!
+#clf
+#[y, grec] = reconstruct(xx,inds);
+#waveplot(y,'-',xx(inds,:),'+',1,1)
+#axis([0 inf -inf inf])
+##!wafostamp('','(ER)')
+#disp('Block = 21'),pause(pstate)
+#
+##! Compare transformation (grec) from reconstructed (y)
+##! with original (glc) from (xx)
+#clf
+#trplot(g), hold on
+#plot(gemp(:,1),gemp(:,2))
+#plot(glc(:,1),glc(:,2),'-.')
+#plot(grec(:,1),grec(:,2)), hold off
+#disp('Block = 22'),pause(pstate)
+#
+##!#!
+#clf
+#L = 200;
+#x = dat2gaus(y,grec);
+#Sx = dat2spec(x,L);
+#disp('Block = 23'),pause(pstate)
+#
+##!#!
+#clf
+#dt = spec2dt(Sx)
+#Ny = fix(2*60/dt) #! = 2 minutes
+#Sx.tr = grec;
+#ysim = spec2sdat(Sx,Ny);
+#waveplot(ysim,'-')
+##!wafostamp('','(CR)')
+#disp('Block = 24'),pause(pstate)
+#
+#! Estimated spectrum compared to Torsethaugen spectrum
+#!-------------------------------------------------------
+
+plt.clf()
+fp = 1.1
+dw = 0.01
+H0 = S1.characteristic('Hm0')[0]
+St = wsm.Torsethaugen(Hm0=H0,Tp=2*np.pi/fp).tospecdata(np.arange(0,5+dw/2,dw))
+S1.plot()
+St.plot('-.')
+plt.axis([0, 6, 0, 0.4])
+plt.show()
+
+
+#! Transformed Gaussian model compared to Gaussian model
+#!--------------------------------------------------------
+dt = St.sampling_period()
+va, sk, ku = St.stats_nl(moments='vsk')
+#sa = sqrt(va)
+gh = wtm.TrHermite(mean=me, sigma=sa, skew=sk, kurt=ku, ysigma=sa)
+
+ysim_t = St.sim(ns=240, dt=0.5)
+xsim_t = ysim_t.copy()
+xsim_t[:, 1] = gh.gauss2dat(ysim_t[:, 1])
+
+ts_y = wo.mat2timeseries(ysim_t)
+ts_x = wo.mat2timeseries(xsim_t)
+ts_y.plot_wave(sym1='r.', ts=ts_x, sym2='b', sigma=sa, nsub=5, nfig=1)
+plt.show()

wafo/doc/tutorial_scripts/chapter3.py

@@ -0,0 +1,615 @@
+from wafo.plotbackend import plotbackend as plt
+import numpy as np
+
+#! CHAPTER3  Demonstrates distributions of wave characteristics
+#!=============================================================
+#!
+#! Chapter3 contains the commands used in Chapter3 in the tutorial.
+#!
+#! Some of the commands are edited for fast computation.
+#!
+#! Section 3.2 Estimation of wave characteristics from data
+#!----------------------------------------------------------
+#! Example 1
+#!~~~~~~~~~~
+
+speed = 'fast'
+#speed = 'slow'
+import scipy.signal as ss
+import wafo.data as wd
+import wafo.misc as wm
+import wafo.objects as wo
+import wafo.stats as ws
+import wafo.spectrum.models as wsm
+xx = wd.sea()
+xx[:, 1] = ss.detrend(xx[:, 1])
+ts = wo.mat2timeseries(xx)
+Tcrcr, ix = ts.wave_periods(vh=0, pdef='c2c', wdef='tw', rate=8)
+Tc, ixc = ts.wave_periods(vh=0, pdef='u2d', wdef='tw', rate=8)
+
+#! Histogram of crestperiod compared to the kernel density estimate
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+import wafo.kdetools as wk
+plt.clf()
+print(Tc.mean())
+print(Tc.max())
+
+t = np.linspace(0.01,8,200);
+ftc = wk.TKDE(Tc, L2=0, inc=128)
+
+plt.plot(t,ftc.eval_grid(t), t, ftc.eval_grid_fast(t),'-.')
+wm.plot_histgrm(Tc, normed=True)
+plt.title('Kernel Density Estimates')
+plt.xlabel('Tc [s]')
+plt.axis([0, 8, 0, 0.5])
+plt.show()
+
+#! Extreme waves - model check: the highest and steepest wave
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+plt.clf()
+S, H = ts.wave_height_steepness(kind=0)
+indS = S.argmax()
+indH = H.argmax()
+ts.plot_sp_wave([indH, indS],'k.')
+plt.show()
+
+#! Does the highest wave contradict a transformed Gaussian model?
+#!----------------------------------------------------------------
+
+# TODO: Fix this
+
+#clf
+#inds1 = (5965:5974)'; #! points to remove
+#Nsim = 10;
+#[y1, grec1, g2, test, tobs, mu1o, mu1oStd] = ...
+#   reconstruct(xx,inds1,Nsim);
+#spwaveplot(y1,indA-10)
+#hold on
+#plot(xx(inds1,1),xx(inds1,2),'+')
+#lamb = 2.;
+#muLstd = tranproc(mu1o-lamb*mu1oStd,fliplr(grec1));
+#muUstd = tranproc(mu1o+lamb*mu1oStd,fliplr(grec1));
+#plot (y1(inds1,1), [muLstd muUstd],'b-')
+#axis([1482 1498 -1 3]),
+#wafostamp([],'(ER)')
+#disp('Block = 6'),
+#pause(pstate)
+#
+##!#! Expected value (solid) compared to data removed
+#clf
+#plot(xx(inds1,1),xx(inds1,2),'+'), hold on
+#mu = tranproc(mu1o,fliplr(grec1));
+#plot(y1(inds1,1), mu), hold off
+#disp('Block = 7'), pause(pstate)
+
+#! Crest height PDF
+#!------------------
+#! Transform data so that kde works better
+plt.clf()
+wave_data = ts.wave_parameters()
+Ac = wave_data['Ac']
+L2 = 0.6
+
+ws.probplot(Ac**L2, dist='norm', plot=plt)
+plt.show()
+
+#!#!
+plt.clf()#
+fac = wk.TKDE(Ac,L2=L2)(np.linspace(0.01,3,200), output='plot')
+fac.plot()
+# wafostamp([],'(ER)')
+print(fac.integrate(a=0.01, b=3))
+print(fac.integrate())
+print('Block = 8'),
+# pause(pstate)
+
+#!#! Empirical crest height CDF
+plt.clf()
+Fac = fac.to_cdf()
+Femp = ws.edf(Ac)
+Fac.plot()
+Femp.plot()
+plt.axis([0, 2, 0, 1])
+
+#wafostamp([],'(ER)')
+#disp('Block = 9'), pause(pstate)
+
+#!#! Empirical crest height CDF compared to a Transformed Rayleigh approximation
+
+# facr = trraylpdf(fac.x{1},'Ac',grec1);
+# Facr = cumtrapz(facr.x{1},facr.f);
+# hold on
+# plot(facr.x{1},Facr,'.')
+# axis([1.25 2.25 0.95 1])
+# wafostamp([],'(ER)')
+# disp('Block = 10'), pause(pstate)
+
+#!#! Joint pdf of crest period and crest amplitude
+plt.clf()
+Tcf = wave_data['Tcf']
+Tcb = wave_data['Tcb']
+Tc = Tcf + Tcb
+fTcAc = wk.TKDE([Tc, Ac],L2=0.5, inc=256).eval_grid_fast(output='plot')
+fTcAc.labels.labx = 'Tc [s]'
+fTcAc.labels.laby = 'Ac [m]'
+fTcAc.plot()
+plt.hold(True)
+plt.plot(Tc, Ac,'k.')
+plt.hold(False)
+plt.show()
+#wafostamp([],'(ER)')
+#disp('Block = 11'), pause(pstate)
+
+#!#! Example 4:  Simple wave characteristics obtained from Jonswap spectrum
+plt.clf()
+S = wsm.Jonswap(Hm0=5, Tp=10).tospecdata()
+m, mt = S.moment(nr=4, even=False)
+print(m)
+print(mt)
+# disp('Block = 12'), pause(pstate)
+
+plt.clf()
+S.bandwidth(['alpha'])
+ch, Sa2, chtxt = S.characteristic(['Hm0', 'Tm02'])
+
+# disp('Block = 13'), pause(pstate)
+
+#!#! Section 3.3.2 Explicit form approximations of wave characteristic densities
+#!#! Longuett-Higgins model for Tc and Ac
+# plt.clf()
+# t = np.linspace(0,15,100)
+# h = np.linspace(0,6,100)
+# flh = lh83pdf(t, h, [m[0],m[1], m[2])
+# #disp('Block = 14'), pause(pstate)
+#
+# #!#! Transformed Longuett-Higgins model for Tc and Ac
+# clf
+# [sk, ku ]=spec2skew(S);
+# sa = sqrt(m(1));
+# gh = hermitetr([],[sa sk ku 0]);
+# flhg = lh83pdf(t,h,[m(1),m(2),m(3)],gh);
+# disp('Block = 15'), pause(pstate)
+
+#!#! Cavanie model for Tc and Ac
+# clf
+# t = np.linspace(0,10,100);
+# h = np.linspace(0,7,100);
+# fcav = cav76pdf(t,h,[m(1) m(2) m(3) m(5)],[]);
+# disp('Block = 16'), pause(pstate)
+#
+# #!#! Example 5 Transformed Rayleigh approximation of crest- vs trough- amplitude
+# clf
+# xx = load('sea.dat');
+# x = xx;
+# x(:,2) = detrend(x(:,2));
+# SS = dat2spec2(x);
+# [sk, ku, me, si ] = spec2skew(SS);
+# gh = hermitetr([],[si sk ku me]);
+# Hs = 4*si;
+# r = (0:0.05:1.1*Hs)';
+# fac_h = trraylpdf(r,'Ac',gh);
+# fat_h = trraylpdf(r,'At',gh);
+# h = (0:0.05:1.7*Hs)';
+# facat_h = trraylpdf(h,'AcAt',gh);
+# pdfplot(fac_h)
+# hold on
+# pdfplot(fat_h,'--')
+# hold off
+# wafostamp([],'(ER)')
+# disp('Block = 17'), pause(pstate)
+#
+# #!#!
+# clf
+# TC = dat2tc(xx, me);
+# tc = tp2mm(TC);
+# Ac = tc(:,2);
+# At = -tc(:,1);
+# AcAt = Ac+At;
+# disp('Block = 18'), pause(pstate)
+#
+# #!#!
+# clf
+# Fac_h = [fac_h.x{1} cumtrapz(fac_h.x{1},fac_h.f)];
+# subplot(3,1,1)
+# Fac = plotedf(Ac,Fac_h);
+# hold on
+# plot(r,1-exp(-8*r.^2/Hs^2),'.')
+# axis([1. 2. 0.9 1])
+# title('Ac CDF')
+#
+# Fat_h = [fat_h.x{1} cumtrapz(fat_h.x{1},fat_h.f)];
+# subplot(3,1,2)
+# Fat = plotedf(At,Fat_h);
+# hold on
+# plot(r,1-exp(-8*r.^2/Hs^2),'.')
+# axis([1. 2. 0.9 1])
+# title('At CDF')
+#
+# Facat_h = [facat_h.x{1} cumtrapz(facat_h.x{1},facat_h.f)];
+# subplot(3,1,3)
+# Facat = plotedf(AcAt,Facat_h);
+# hold on
+# plot(r,1-exp(-2*r.^2/Hs^2),'.')
+# axis([1.5 3.5 0.9 1])
+# title('At+Ac CDF')
+#
+# wafostamp([],'(ER)')
+# disp('Block = 19'), pause(pstate)
+#
+# #!#! Section 3.4 Exact wave distributions in transformed Gaussian Sea
+# #!#! Section 3.4.1 Density of crest period, crest length or encountered crest period
+# clf
+# S1 = torsethaugen([],[6 8],1);
+# D1 = spreading(101,'cos',pi/2,[15],[],0);
+# D12 = spreading(101,'cos',0,[15],S1.w,1);
+# SD1 = mkdspec(S1,D1);
+# SD12 = mkdspec(S1,D12);
+# disp('Block = 20'), pause(pstate)
+#
+# #!#! Crest period
+# clf
+# tic
+# f_tc = spec2tpdf(S1,[],'Tc',[0 11 56],[],4);
+# toc
+# pdfplot(f_tc)
+# wafostamp([],'(ER)')
+# simpson(f_tc.x{1},f_tc.f)
+# disp('Block = 21'), pause(pstate)
+#
+# #!#! Crest length
+#
+# if strncmpi(speed,'slow',1)
+#   opt1 = rindoptset('speed',5,'method',3);
+#   opt2 = rindoptset('speed',5,'nit',2,'method',0);
+# else
+#   #! fast
+#   opt1 = rindoptset('speed',7,'method',3);
+#   opt2 = rindoptset('speed',7,'nit',2,'method',0);
+# end
+#
+#
+# clf
+# if strncmpi(speed,'slow',1)
+#   NITa = 5;
+# else
+#   disp('NIT=5 may take time, running with NIT=3 in the following')
+#   NITa = 3;
+# end
+# #!f_Lc = spec2tpdf2(S1,[],'Lc',[0 200 81],opt1); #! Faster and more accurate
+# f_Lc = spec2tpdf(S1,[],'Lc',[0 200 81],[],NITa);
+# pdfplot(f_Lc,'-.')
+# wafostamp([],'(ER)')
+# disp('Block = 22'), pause(pstate)
+#
+#
+# f_Lc_1 = spec2tpdf(S1,[],'Lc',[0 200 81],1.5,NITa);
+# #!f_Lc_1 = spec2tpdf2(S1,[],'Lc',[0 200 81],1.5,opt1);
+#
+# hold on
+# pdfplot(f_Lc_1)
+# wafostamp([],'(ER)')
+#
+# disp('Block = 23'), pause(pstate)
+# #!#!
+# clf
+# simpson(f_Lc.x{1},f_Lc.f)
+# simpson(f_Lc_1.x{1},f_Lc_1.f)
+#
+# disp('Block = 24'), pause(pstate)
+# #!#!
+# clf
+# tic
+#
+# f_Lc_d1 = spec2tpdf(rotspec(SD1,pi/2),[],'Lc',[0 300 121],[],NITa);
+# f_Lc_d12 = spec2tpdf(SD12,[],'Lc',[0 200 81],[],NITa);
+# #! f_Lc_d1 = spec2tpdf2(rotspec(SD1,pi/2),[],'Lc',[0 300 121],opt1);
+# #! f_Lc_d12 = spec2tpdf2(SD12,[],'Lc',[0 200 81],opt1);
+# toc
+# pdfplot(f_Lc_d1,'-.'), hold on
+# pdfplot(f_Lc_d12),     hold off
+# wafostamp([],'(ER)')
+#
+# disp('Block = 25'), pause(pstate)
+#
+# #!#!
+#
+#
+# clf
+# opt1 = rindoptset('speed',5,'method',3);
+# SD1r = rotspec(SD1,pi/2);
+# if strncmpi(speed,'slow',1)
+#   f_Lc_d1_5 = spec2tpdf(SD1r,[], 'Lc',[0 300 121],[],5);
+#   pdfplot(f_Lc_d1_5),     hold on
+# else
+#   #! fast
+#   disp('Run the following example only if you want a check on computing time')
+#   disp('Edit the command file and remove #!')
+# end
+# f_Lc_d1_3 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],3);
+# f_Lc_d1_2 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],2);
+# f_Lc_d1_0 = spec2tpdf(SD1r,[],'Lc',[0 300 121],[],0);
+# #!f_Lc_d1_n4 = spec2tpdf2(SD1r,[],'Lc',[0 400 161],opt1);
+#
+# pdfplot(f_Lc_d1_3), hold on
+# pdfplot(f_Lc_d1_2)
+# pdfplot(f_Lc_d1_0)
+# #!pdfplot(f_Lc_d1_n4)
+#
+# #!simpson(f_Lc_d1_n4.x{1},f_Lc_d1_n4.f)
+#
+# disp('Block = 26'), pause(pstate)
+#
+# #!#! Section 3.4.2 Density of wave period, wave length or encountered wave period
+# #!#! Example 7: Crest period and high crest waves
+# clf
+# tic
+# xx = load('sea.dat');
+# x = xx;
+# x(:,2) = detrend(x(:,2));
+# SS = dat2spec(x);
+# si = sqrt(spec2mom(SS,1));
+# SS.tr = dat2tr(x);
+# Hs = 4*si
+# method = 0;
+# rate = 2;
+# [S, H, Ac, At, Tcf, Tcb, z_ind, yn] = dat2steep(x,rate,method);
+# Tc = Tcf+Tcb;
+# t = linspace(0.01,8,200);
+# ftc1 = kde(Tc,{'L2',0},t);
+# pdfplot(ftc1)
+# hold on
+# #!      f_t = spec2tpdf(SS,[],'Tc',[0 8 81],0,4);
+# f_t = spec2tpdf(SS,[],'Tc',[0 8 81],0,2);
+# simpson(f_t.x{1},f_t.f)
+# pdfplot(f_t,'-.')
+# hold off
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 27'), pause(pstate)
+#
+# #!#!
+# clf
+# tic
+#
+# if strncmpi(speed,'slow',1)
+#   NIT = 4;
+# else
+#   NIT = 2;
+# end
+# #!      f_t2 = spec2tpdf(SS,[],'Tc',[0 8 81],[Hs/2],4);
+# tic
+# f_t2 = spec2tpdf(SS,[],'Tc',[0 8 81],Hs/2,NIT);
+# toc
+#
+# Pemp = sum(Ac>Hs/2)/sum(Ac>0)
+# simpson(f_t2.x{1},f_t2.f)
+# index = find(Ac>Hs/2);
+# ftc1 = kde(Tc(index),{'L2',0},t);
+# ftc1.f = Pemp*ftc1.f;
+# pdfplot(ftc1)
+# hold on
+# pdfplot(f_t2,'-.')
+# hold off
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 28'), pause(pstate)
+#
+# #!#! Example 8: Wave period for high crest waves
+# #!      clf
+#       tic
+#       f_tcc2 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],-1);
+# toc
+#       simpson(f_tcc2.x{1},f_tcc2.f)
+#       f_tcc3 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],3,5);
+# #!      f_tcc3 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[0],1,5);
+#       simpson(f_tcc3.x{1},f_tcc3.f)
+#       pdfplot(f_tcc2,'-.')
+#       hold on
+#       pdfplot(f_tcc3)
+#       hold off
+#        toc
+# disp('Block = 29'), pause(pstate)
+#
+# #!#!
+# clf
+# [TC tc_ind v_ind] = dat2tc(yn,[],'dw');
+# N = length(tc_ind);
+# t_ind = tc_ind(1:2:N);
+# c_ind = tc_ind(2:2:N);
+# Pemp = sum(yn(t_ind,2)<-Hs/2 & yn(c_ind,2)>Hs/2)/length(t_ind)
+# ind = find(yn(t_ind,2)<-Hs/2 & yn(c_ind,2)>Hs/2);
+# spwaveplot(yn,ind(2:4))
+# wafostamp([],'(ER)')
+# disp('Block = 30'), pause(pstate)
+#
+# #!#!
+# clf
+# Tcc = yn(v_ind(1+2*ind),1)-yn(v_ind(1+2*(ind-1)),1);
+# t = linspace(0.01,14,200);
+# ftcc1 = kde(Tcc,{'kernel' 'epan','L2',0},t);
+# ftcc1.f = Pemp*ftcc1.f;
+# pdfplot(ftcc1,'-.')
+# wafostamp([],'(ER)')
+# disp('Block = 31'), pause(pstate)
+#
+# tic
+# f_tcc22_1 = spec2tccpdf(SS,[],'t>',[0 12 61],[Hs/2],[Hs/2],-1);
+# toc
+# simpson(f_tcc22_1.x{1},f_tcc22_1.f)
+# hold on
+# pdfplot(f_tcc22_1)
+# hold off
+# wafostamp([],'(ER)')
+# disp('Block = 32'), pause(pstate)
+#
+# disp('The rest of this chapter deals with joint densities.')
+# disp('Some calculations may take some time.')
+# disp('You could experiment with other NIT.')
+# #!return
+#
+# #!#! Section 3.4.3 Joint density of crest period and crest height
+# #!#! Example 9. Some preliminary analysis of the data
+# clf
+# tic
+# yy = load('gfaksr89.dat');
+# SS = dat2spec(yy);
+# si = sqrt(spec2mom(SS,1));
+# SS.tr = dat2tr(yy);
+# Hs = 4*si
+# v = gaus2dat([0 0],SS.tr);
+# v = v(2)
+# toc
+# disp('Block = 33'), pause(pstate)
+#
+# #!#!
+# clf
+# tic
+# [TC, tc_ind, v_ind] = dat2tc(yy,v,'dw');
+# N       = length(tc_ind);
+# t_ind   = tc_ind(1:2:N);
+# c_ind   = tc_ind(2:2:N);
+# v_ind_d = v_ind(1:2:N+1);
+# v_ind_u = v_ind(2:2:N+1);
+# T_d     = ecross(yy(:,1),yy(:,2),v_ind_d,v);
+# T_u     = ecross(yy(:,1),yy(:,2),v_ind_u,v);
+#
+# Tc = T_d(2:end)-T_u(1:end);
+# Tt = T_u(1:end)-T_d(1:end-1);
+# Tcf = yy(c_ind,1)-T_u;
+# Ac = yy(c_ind,2)-v;
+# At = v-yy(t_ind,2);
+# toc
+# disp('Block = 34'), pause(pstate)
+#
+# #!#!
+# clf
+# tic
+# t = linspace(0.01,15,200);
+# kopt3 = kdeoptset('hs',0.25,'L2',0);
+# ftc1 = kde(Tc,kopt3,t);
+# ftt1 = kde(Tt,kopt3,t);
+# pdfplot(ftt1,'k')
+# hold on
+# pdfplot(ftc1,'k-.')
+# f_tc4 = spec2tpdf(SS,[],'Tc',[0 12 81],0,4,5);
+# f_tc2 = spec2tpdf(SS,[],'Tc',[0 12 81],0,2,5);
+# f_tc = spec2tpdf(SS,[],'Tc',[0 12 81],0,-1);
+# pdfplot(f_tc,'b')
+# hold off
+# legend('kde(Tt)','kde(Tc)','f_{tc}')
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 35'), pause(pstate)
+#
+# #!#! Example 10: Joint characteristics of a half wave:
+# #!#! position and height of a crest for a wave with given period
+# clf
+# tic
+# ind = find(4.4<Tc & Tc<4.6);
+# f_AcTcf = kde([Tcf(ind) Ac(ind)],{'L2',[1 .5]});
+# pdfplot(f_AcTcf)
+# hold on
+# plot(Tcf(ind), Ac(ind),'.');
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 36'), pause(pstate)
+#
+# #!#!
+# clf
+# tic
+# opt1 = rindoptset('speed',5,'method',3);
+# opt2 = rindoptset('speed',5,'nit',2,'method',0);
+#
+# f_tcfac1 = spec2thpdf(SS,[],'TcfAc',[4.5 4.5 46],[0:0.25:8],opt1);
+# f_tcfac2 = spec2thpdf(SS,[],'TcfAc',[4.5 4.5 46],[0:0.25:8],opt2);
+#
+# pdfplot(f_tcfac1,'-.')
+# hold on
+# pdfplot(f_tcfac2)
+# plot(Tcf(ind), Ac(ind),'.');
+#
+# simpson(f_tcfac1.x{1},simpson(f_tcfac1.x{2},f_tcfac1.f,1))
+# simpson(f_tcfac2.x{1},simpson(f_tcfac2.x{2},f_tcfac2.f,1))
+# f_tcf4=spec2tpdf(SS,[],'Tc',[4.5 4.5 46],[0:0.25:8],6);
+# f_tcf4.f(46)
+# toc
+# wafostamp([],'(ER)')
+# disp('Block = 37'), pause(pstate)
+#
+# #!#!
+# clf
+# f_tcac_s = spec2thpdf(SS,[],'TcAc',[0 12 81],[Hs/2:0.1:2*Hs],opt1);
+# disp('Block = 38'), pause(pstate)
+#
+# clf
+# tic
+# mom = spec2mom(SS,4,[],0);
+# t = f_tcac_s.x{1};
+# h = f_tcac_s.x{2};
+# flh_g = lh83pdf(t',h',[mom(1),mom(2),mom(3)],SS.tr);
+# clf
+# ind=find(Ac>Hs/2);
+# plot(Tc(ind), Ac(ind),'.');
+# hold on
+# pdfplot(flh_g,'k-.')
+# pdfplot(f_tcac_s)
+# toc
+# wafostamp([],'(ER)')
+# disp('Block = 39'), pause(pstate)
+#
+# #!#!
+# clf
+# #!      f_tcac = spec2thpdf(SS,[],'TcAc',[0 12 81],[0:0.2:8],opt1);
+# #!      pdfplot(f_tcac)
+# disp('Block = 40'), pause(pstate)
+#
+# #!#! Section 3.4.4 Joint density of crest and trough height
+# #!#! Section 3.4.5 Min-to-max distributions Markov method
+# #!#! Example 11. (min-max problems with Gullfaks data)
+# #!#! Joint density of maximum and the following minimum
+# clf
+# tic
+# tp = dat2tp(yy);
+# Mm = fliplr(tp2mm(tp));
+# fmm = kde(Mm);
+# f_mM = spec2mmtpdf(SS,[],'mm',[],[-7 7 51],opt2);
+#
+# pdfplot(f_mM,'-.')
+# hold on
+# pdfplot(fmm,'k-')
+# hold off
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 41'), pause(pstate)
+#
+# #!#! The joint density of still water separated  maxima and minima.
+# clf
+# tic
+# ind = find(Mm(:,1)>v & Mm(:,2)<v);
+# Mmv = abs(Mm(ind,:)-v);
+# fmmv = kde(Mmv);
+# f_vmm = spec2mmtpdf(SS,[],'vmm',[],[-7 7 51],opt2);
+# clf
+# pdfplot(fmmv,'k-')
+# hold on
+# pdfplot(f_vmm,'-.')
+# hold off
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 42'), pause(pstate)
+#
+#
+# #!#!
+# clf
+# tic
+# facat = kde([Ac At]);
+# f_acat = spec2mmtpdf(SS,[],'AcAt',[],[-7 7 51],opt2);
+# clf
+# pdfplot(f_acat,'-.')
+# hold on
+# pdfplot(facat,'k-')
+# hold off
+# wafostamp([],'(ER)')
+# toc
+# disp('Block = 43'), pause(pstate)
+

wafo/doc/tutorial_scripts/chapter4.py

@@ -0,0 +1,407 @@
+
+#! CHAPTER4 contains the commands used in Chapter 4 of the tutorial
+#!=================================================================
+#!
+#! CALL:  Chapter4
+#!
+#! Some of the commands are edited for fast computation.
+#! Each set of commands is followed by a 'pause' command.
+#!
+#! This routine also can print the figures;
+#! For printing the figures on directory ../bilder/ edit the file and put
+#!     printing=1;
+
+#! Tested on Matlab 5.3
+#! History
+#! Revised pab sept2005
+#!  Added sections -> easier to evaluate using cellmode evaluation.
+#! revised pab Feb2004
+#! updated call to lc2sdat
+#! Created by GL July 13, 2000
+#! from commands used in Chapter 4
+#!
+
+#! Chapter 4 Fatigue load analysis and rain-flow cycles
+#!------------------------------------------------------
+
+printing = 0
+
+
+#! Section 4.3.1 Crossing intensity
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+import numpy as np
+from wafo.plotbackend import plotbackend as plt
+import wafo.data as wd
+import wafo.objects as wo
+
+xx_sea = wd.sea()
+ts = wo.mat2timeseries(xx_sea)
+tp = ts.turning_points()
+mM = tp.cycle_pairs(kind='min2max')
+lc = mM.level_crossings(intensity=True)
+T_sea = ts.args[-1]-ts.args[0]
+
+plt.subplot(1,2,1)
+lc.plot()
+plt.subplot(1,2,2)
+lc.setplotter(plotmethod='step')
+lc.plot()
+plt.show()
+
+
+m_sea = ts.data.mean()
+f0_sea = np.interp(m_sea, lc.args,lc.data)
+extr_sea = len(tp.data)/(2*T_sea)
+alfa_sea = f0_sea/extr_sea
+print('alfa = %g ' % alfa_sea)
+
+#! Section 4.3.2 Extraction of rainflow cycles
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#! Min-max and rainflow cycle plots
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+mM_rfc = tp.cycle_pairs(h=0.3)
+
+plt.clf()
+plt.subplot(122),
+mM.plot()
+plt.title('min-max cycle pairs')
+plt.subplot(121),
+mM_rfc.plot()
+plt.title('Rainflow filtered cycles')
+plt.show()
+
+#! Min-max and rainflow cycle distributions
+#!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+import wafo.misc as wm
+ampmM_sea = mM.amplitudes()
+ampRFC_sea = mM_rfc.amplitudes()
+plt.clf()
+plt.subplot(121)
+wm.plot_histgrm(ampmM_sea,25)
+ylim = plt.gca().get_ylim()
+plt.title('min-max amplitude distribution')
+plt.subplot(122)
+wm.plot_histgrm(ampRFC_sea,25)
+plt.gca().set_ylim(ylim)
+plt.title('Rainflow amplitude distribution')
+plt.show()
+
+#!#! Section 4.3.3 Simulation of rainflow cycles
+#!#! Simulation of cycles in a Markov model
+# n = 41
+# param_m = [-1, 1, n]
+# param_D = [1, n, n]
+# u_markov=levels(param_m);
+# G_markov=mktestmat(param_m,[-0.2, 0.2],0.15,1);
+# T_markov=5000;
+#xxD_markov=mctpsim({G_markov [,]},T_markov);
+#xx_markov=[(1:T_markov)' u_markov(xxD_markov)'];
+#clf
+#plot(xx_markov(1:50,1),xx_markov(1:50,2))
+#title('Markov chain of turning points')
+#wafostamp([],'(ER)')
+#disp('Block 5'),pause(pstate)
+#
+#
+##!#! Rainflow cycles in a transformed Gaussian model
+##!#! Hermite transformed wave data and rainflow filtered turning points, h = 0.2.
+#me = mean(xx_sea(:,2));
+#sa = std(xx_sea(:,2));
+#Hm0_sea = 4*sa;
+#Tp_sea = 1/max(lc_sea(:,2));
+#spec = jonswap([],[Hm0_sea Tp_sea]);
+#
+#[sk, ku] = spec2skew(spec);
+#spec.tr = hermitetr([],[sa sk ku me]);
+#param_h = [-1.5 2 51];
+#spec_norm = spec;
+#spec_norm.S = spec_norm.S/sa^2;
+#xx_herm = spec2sdat(spec_norm,[2^15 1],0.1);
+##! ????? PJ, JR 11-Apr-2001
+##! NOTE, in the simulation program spec2sdat
+##!the spectrum must be normalized to variance 1
+##! ?????
+#h = 0.2;
+#[dtp,u_herm,xx_herm_1]=dat2dtp(param_h,xx_herm,h);
+#clf
+#plot(xx_herm(:,1),xx_herm(:,2),'k','LineWidth',2); hold on;
+#plot(xx_herm_1(:,1),xx_herm_1(:,2),'k--','Linewidth',2);
+#axis([0 50 -1 1]), hold off;
+#title('Rainflow filtered wave data')
+#wafostamp([],'(ER)')
+#disp('Block 6'),pause(pstate)
+#
+##!#! Rainflow cycles and rainflow filtered rainflow cycles in the transformed Gaussian process.
+#tp_herm=dat2tp(xx_herm);
+#RFC_herm=tp2rfc(tp_herm);
+#mM_herm=tp2mm(tp_herm);
+#h=0.2;
+#[dtp,u,tp_herm_1]=dat2dtp(param_h,xx_herm,h);
+#RFC_herm_1 = tp2rfc(tp_herm_1);
+#clf
+#subplot(121), ccplot(RFC_herm)
+#title('h=0')
+#subplot(122), ccplot(RFC_herm_1)
+#title('h=0.2')
+#if (printing==1), print -deps ../bilder/fatigue_8.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 7'),pause(pstate)
+#
+##!#! Section 4.3.4 Calculating the rainflow matrix
+#
+#
+#Grfc_markov=mctp2rfm({G_markov []});
+#clf
+#subplot(121), cmatplot(u_markov,u_markov,G_markov), axis('square')
+#subplot(122), cmatplot(u_markov,u_markov,Grfc_markov), axis('square')
+#wafostamp([],'(ER)')
+#disp('Block 8'),pause(pstate)
+#
+##!#!
+#clf
+#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},3)
+#wafostamp([],'(ER)')
+#disp('Block 9'),pause(pstate)
+#
+##!#! Min-max-matrix and theoretical rainflow matrix for test Markov sequence.
+#cmatplot(u_markov,u_markov,{G_markov Grfc_markov},4)
+#subplot(121), axis('square'), title('min2max transition matrix')
+#subplot(122), axis('square'), title('Rainflow matrix')
+#if (printing==1), print -deps ../bilder/fatigue_9.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 10'),pause(pstate)
+#
+##!#! Observed and theoretical rainflow matrix for test Markov sequence.
+#n=length(u_markov);
+#Frfc_markov=dtp2rfm(xxD_markov,n);
+#clf
+#cmatplot(u_markov,u_markov,{Frfc_markov Grfc_markov*T_markov/2},3)
+#subplot(121), axis('square'), title('Observed rainflow matrix')
+#subplot(122), axis('square'), title('Theoretical rainflow matrix')
+#if (printing==1), print -deps ../bilder/fatigue_10.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 11'),pause(pstate)
+#
+##!#! Smoothed observed and calculated rainflow matrix for test Markov sequence.
+#tp_markov=dat2tp(xx_markov);
+#RFC_markov=tp2rfc(tp_markov);
+#h=1;
+#Frfc_markov_smooth=cc2cmat(param_m,RFC_markov,[],1,h);
+#clf
+#cmatplot(u_markov,u_markov,{Frfc_markov_smooth Grfc_markov*T_markov/2},4)
+#subplot(121), axis('square'), title('Smoothed observed rainflow matrix')
+#subplot(122), axis('square'), title('Theoretical rainflow matrix')
+#if (printing==1), print -deps ../bilder/fatigue_11.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 12'),pause(pstate)
+#
+##!#! Rainflow matrix from spectrum
+#clf
+##!GmM3_herm=spec2mmtpdf(spec,[],'Mm',[],[],2);
+#GmM3_herm=spec2cmat(spec,[],'Mm',[],param_h,2);
+#pdfplot(GmM3_herm)
+#wafostamp([],'(ER)')
+#disp('Block 13'),pause(pstate)
+#
+#
+##!#! Min-max matrix and theoretical rainflow matrix for Hermite-transformed Gaussian waves.
+#Grfc_herm=mctp2rfm({GmM3_herm.f []});
+#u_herm=levels(param_h);
+#clf
+#cmatplot(u_herm,u_herm,{GmM3_herm.f Grfc_herm},4)
+#subplot(121), axis('square'), title('min-max matrix')
+#subplot(122), axis('square'), title('Theoretical rainflow matrix')
+#if (printing==1), print -deps ../bilder/fatigue_12.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 14'),pause(pstate)
+#
+##!#!
+#clf
+#Grfc_direct_herm=spec2cmat(spec,[],'rfc',[],[],2);
+#subplot(121), pdfplot(GmM3_herm), axis('square'), hold on
+#subplot(122), pdfplot(Grfc_direct_herm), axis('square'), hold off
+#if (printing==1), print -deps ../bilder/fig_mmrfcjfr.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 15'),pause(pstate)
+#
+#
+##!#! Observed smoothed and theoretical min-max matrix,
+##!#! (and observed smoothed and theoretical rainflow matrix for Hermite-transformed Gaussian waves).
+#tp_herm=dat2tp(xx_herm);
+#RFC_herm=tp2rfc(tp_herm);
+#mM_herm=tp2mm(tp_herm);
+#h=0.2;
+#FmM_herm_smooth=cc2cmat(param_h,mM_herm,[],1,h);
+#Frfc_herm_smooth=cc2cmat(param_h,RFC_herm,[],1,h);
+#T_herm=xx_herm(end,1)-xx_herm(1,1);
+#clf
+#cmatplot(u_herm,u_herm,{FmM_herm_smooth GmM3_herm.f*length(mM_herm) ; ...
+#      Frfc_herm_smooth Grfc_herm*length(RFC_herm)},4)
+#subplot(221), axis('square'), title('Observed smoothed min-max matrix')
+#subplot(222), axis('square'), title('Theoretical min-max matrix')
+#subplot(223), axis('square'), title('Observed smoothed rainflow matrix')
+#subplot(224), axis('square'), title('Theoretical rainflow matrix')
+#if (printing==1), print -deps ../bilder/fatigue_13.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 16'),pause(pstate)
+#
+##!#! Section 4.3.5 Simulation from crossings and rainflow structure
+#
+##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)
+##!#! for simulated process with irregularity factor 0.25.
+#clf
+#cross_herm=dat2lc(xx_herm);
+#alpha1=0.25;
+#alpha2=0.75;
+#xx_herm_sim1=lc2sdat(cross_herm,500,alpha1);
+#cross_herm_sim1=dat2lc(xx_herm_sim1);
+#subplot(211)
+#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2)))
+#hold on
+#stairs(cross_herm_sim1(:,1),...
+#    cross_herm_sim1(:,2)/max(cross_herm_sim1(:,2)))
+#hold off
+#title('Crossing intensity, \alpha = 0.25')
+#subplot(212)
+#plot(xx_herm_sim1(:,1),xx_herm_sim1(:,2))
+#title('Simulated load, \alpha = 0.25')
+#if (printing==1), print -deps ../bilder/fatigue_14_25.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 16'),pause(pstate)
+#
+##!#! Crossing spectrum (smooth curve) and obtained spectrum (wiggled curve)
+##!#! for simulated process with irregularity factor 0.75.
+#xx_herm_sim2=lc2sdat(cross_herm,500,alpha2);
+#cross_herm_sim2=dat2lc(xx_herm_sim2);
+#subplot(211)
+#plot(cross_herm(:,1),cross_herm(:,2)/max(cross_herm(:,2)))
+#hold on
+#stairs(cross_herm_sim2(:,1),...
+#    cross_herm_sim2(:,2)/max(cross_herm_sim2(:,2)))
+#hold off
+#title('Crossing intensity, \alpha = 0.75')
+#subplot(212)
+#plot(xx_herm_sim2(:,1),xx_herm_sim2(:,2))
+#title('Simulated load, \alpha = 0.75')
+#if (printing==1), print -deps ../bilder/fatigue_14_75.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 17'),pause(pstate)
+#
+##!#! Section 4.4 Fatigue damage and fatigue life distribution
+##!#! Section 4.4.1 Introduction
+#beta=3.2; gam=5.5E-10; T_sea=xx_sea(end,1)-xx_sea(1,1);
+#d_beta=cc2dam(RFC_sea,beta)/T_sea;
+#time_fail=1/gam/d_beta/3600      #!in hours of the specific storm
+#disp('Block 18'),pause(pstate)
+#
+##!#! Section 4.4.2 Level crossings
+##!#! Crossing intensity as calculated from the Markov matrix (solid curve) and from the observed rainflow matrix (dashed curve).
+#clf
+#mu_markov=cmat2lc(param_m,Grfc_markov);
+#muObs_markov=cmat2lc(param_m,Frfc_markov/(T_markov/2));
+#clf
+#plot(mu_markov(:,1),mu_markov(:,2),muObs_markov(:,1),muObs_markov(:,2),'--')
+#title('Theoretical and observed crossing intensity ')
+#if (printing==1), print -deps ../bilder/fatigue_15.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 19'),pause(pstate)
+#
+##!#! Section 4.4.3 Damage
+##!#! Distribution of damage from different RFC cycles, from calculated theoretical and from observed rainflow matrix.
+#beta = 4;
+#Dam_markov = cmat2dam(param_m,Grfc_markov,beta)
+#DamObs1_markov = cc2dam(RFC_markov,beta)/(T_markov/2)
+#DamObs2_markov = cmat2dam(param_m,Frfc_markov,beta)/(T_markov/2)
+#disp('Block 20'),pause(pstate)
+#
+#Dmat_markov = cmat2dmat(param_m,Grfc_markov,beta);
+#DmatObs_markov = cmat2dmat(param_m,Frfc_markov,beta)/(T_markov/2);
+#clf
+#subplot(121), cmatplot(u_markov,u_markov,Dmat_markov,4)
+#title('Theoretical damage matrix')
+#subplot(122), cmatplot(u_markov,u_markov,DmatObs_markov,4)
+#title('Observed damage matrix')
+#if (printing==1), print -deps ../bilder/fatigue_16.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 21'),pause(pstate)
+#
+#
+##!#!
+##!Damplus_markov = lc2dplus(mu_markov,beta)
+#pause(pstate)
+#
+##!#! Section 4.4.4 Estimation of S-N curve
+#
+##!#! Load SN-data and plot in log-log scale.
+#SN = load('sn.dat');
+#s = SN(:,1);
+#N = SN(:,2);
+#clf
+#loglog(N,s,'o'), axis([0 14e5 10 30])
+##!if (printing==1), print -deps ../bilder/fatigue_?.eps end
+#wafostamp([],'(ER)')
+#disp('Block 22'),pause(pstate)
+#
+#
+##!#! Check of S-N-model on normal probability paper.
+#
+#normplot(reshape(log(N),8,5))
+#if (printing==1), print -deps ../bilder/fatigue_17.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 23'),pause(pstate)
+#
+##!#! Estimation of S-N-model on linear  scale.
+#clf
+#[e0,beta0,s20] = snplot(s,N,12);
+#title('S-N-data with estimated N(s)','FontSize',20)
+#set(gca,'FontSize',20)
+#if (printing==1), print -deps ../bilder/fatigue_18a.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 24'),pause(pstate)
+#
+##!#! Estimation of S-N-model on log-log scale.
+#clf
+#[e0,beta0,s20] = snplot(s,N,14);
+#title('S-N-data with estimated N(s)','FontSize',20)
+#set(gca,'FontSize',20)
+#if (printing==1), print -deps ../bilder/fatigue_18b.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 25'),pause(pstate)
+#
+##!#! Section 4.4.5 From S-N curve to fatigue life distribution
+##!#! Damage intensity as function of $\beta$
+#beta = 3:0.1:8;
+#DRFC = cc2dam(RFC_sea,beta);
+#dRFC = DRFC/T_sea;
+#plot(beta,dRFC), axis([3 8 0 0.25])
+#title('Damage intensity as function of \beta')
+#if (printing==1), print -deps ../bilder/fatigue_19.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 26'),pause(pstate)
+#
+##!#! Fatigue life distribution with sea load.
+#dam0 = cc2dam(RFC_sea,beta0)/T_sea;
+#[t0,F0] = ftf(e0,dam0,s20,0.5,1);
+#[t1,F1] = ftf(e0,dam0,s20,0,1);
+#[t2,F2] = ftf(e0,dam0,s20,5,1);
+#plot(t0,F0,t1,F1,t2,F2)
+#title('Fatigue life distribution function')
+#if (printing==1), print -deps ../bilder/fatigue_20.eps
+#end
+#wafostamp([],'(ER)')
+#disp('Block 27, last block')

wafo/doc/tutorial_scripts/chapter5.py

@@ -0,0 +1,238 @@
+## CHAPTER5 contains the commands used in Chapter 5 of the tutorial
+#
+# CALL:  Chapter5
+#
+# Some of the commands are edited for fast computation.
+# Each set of commands is followed by a 'pause' command.
+#
+
+# Tested on Matlab 5.3
+# History
+# Added Return values by GL August 2008
+# Revised pab sept2005
+# Added sections -> easier to evaluate using cellmode evaluation.
+# Created by GL July 13, 2000
+# from commands used in Chapter 5
+#
+
+## Chapter 5 Extreme value analysis
+
+## Section 5.1 Weibull and Gumbel papers
+from __future__ import division
+import numpy as np
+import scipy.interpolate as si
+from wafo.plotbackend import plotbackend as plt
+import wafo.data as wd
+import wafo.objects as wo
+import wafo.stats as ws
+import wafo.kdetools as wk
+pstate = 'off'
+
+# Significant wave-height data on Weibull paper,
+
+fig = plt.figure()
+ax = fig.add_subplot(111)
+Hs = wd.atlantic()
+wei = ws.weibull_min.fit(Hs)
+tmp = ws.probplot(Hs, wei, ws.weibull_min, plot=ax)
+plt.show()
+#wafostamp([],'(ER)')
+#disp('Block = 1'),pause(pstate)
+
+##
+# Significant wave-height data on Gumbel paper,
+plt.clf()
+ax = fig.add_subplot(111)
+gum = ws.gumbel_r.fit(Hs)
+tmp1 = ws.probplot(Hs, gum, ws.gumbel_r, plot=ax)
+#wafostamp([],'(ER)')
+plt.show()
+#disp('Block = 2'),pause(pstate)
+
+##
+# Significant wave-height data on Normal probability paper,
+plt.clf()
+ax = fig.add_subplot(111)
+phat = ws.norm.fit2(np.log(Hs))
+phat.plotresq()
+#tmp2 = ws.probplot(np.log(Hs), phat, ws.norm, plot=ax)
+
+#wafostamp([],'(ER)')
+plt.show()
+#disp('Block = 3'),pause(pstate)
+
+##
+# Return values in the Gumbel distribution
+plt.clf()
+T = np.r_[1:100000]
+sT = gum[0] - gum[1] * np.log(-np.log1p(-1./T))
+plt.semilogx(T, sT)
+plt.hold(True)
+# ws.edf(Hs).plot()
+Nmax = len(Hs)
+N = np.r_[1:Nmax + 1]
+
+plt.plot(Nmax/N, sorted(Hs, reverse=True), '.')
+plt.title('Return values in the Gumbel model')
+plt.xlabel('Return period')
+plt.ylabel('Return value')
+#wafostamp([],'(ER)')
+plt.show()
+#disp('Block = 4'),pause(pstate)
+
+## Section 5.2 Generalized Pareto and Extreme Value distributions
+## Section 5.2.1 Generalized Extreme Value distribution
+
+# Empirical distribution of significant wave-height with estimated
+# Generalized Extreme Value distribution,
+gev = ws.genextreme.fit2(Hs)
+gev.plotfitsummary()
+# wafostamp([],'(ER)')
+# disp('Block = 5a'),pause(pstate)
+
+plt.clf()
+x = np.linspace(0,14,200)
+kde = wk.TKDE(Hs, L2=0.5)(x, output='plot')
+kde.plot()
+plt.hold(True)
+plt.plot(x, gev.pdf(x),'--')
+# disp('Block = 5b'),pause(pstate)
+
+# Analysis of yura87 wave data.
+# Wave data interpolated (spline) and organized in 5-minute intervals
+# Normalized to mean 0 and std = 1 to get stationary conditions.
+# maximum level over each 5-minute interval analysed by GEV
+xn = wd.yura87()
+XI = np.r_[1:len(xn):0.25] - .99
+N = len(XI)
+N = N - np.mod(N, 4*60*5)
+
+YI = si.interp1d(xn[:, 0], xn[:, 1], kind='linear')(XI)
+YI = YI.reshape(4*60*5, N/(4*60*5))  # Each column holds 5 minutes of
+                                     # interpolated data.
+Y5 = (YI - YI.mean(axis=0)) / YI.std(axis=0)
+Y5M = Y5.maximum(axis=0)
+Y5gev = ws.genextreme.fit2(Y5M,method='mps')
+Y5gev.plotfitsummary()
+#wafostamp([],'(ER)')
+#disp('Block = 6'),pause(pstate)
+
+## Section 5.2.2 Generalized Pareto distribution
+
+# Exceedances of significant wave-height data over level 3,
+gpd3 = ws.genpareto.fit2(Hs[Hs>3]-3, floc=0)
+gpd3.plotfitsummary()
+#wafostamp([],'(ER)')
+
+##
+plt.figure()
+# Exceedances of significant wave-height data over level 7,
+gpd7 = ws.genpareto.fit2(Hs(Hs>7), floc=7)
+gpd7.plotfitsummary()
+# wafostamp([],'(ER)')
+# disp('Block = 6'),pause(pstate)
+
+##
+#Simulates 100 values from the GEV distribution with parameters (0.3, 1, 2),
+# then estimates the parameters using two different methods and plots the
+# estimated distribution functions together with the empirical distribution.
+Rgev = ws.genextreme.rvs(0.3,1,2,size=100)
+gp = ws.genextreme.fit2(Rgev, method='mps');
+gm = ws.genextreme.fit2(Rgev, *gp.par.tolist(), method='ml')
+gm.plotfitsummary()
+
+gp.plotecdf()
+plt.hold(True)
+plt.plot(x, gm.cdf(x), '--')
+plt.hold(False)
+#wafostamp([],'(ER)')
+#disp('Block =7'),pause(pstate)
+
+##
+# ;
+Rgpd = ws.genpareto.rvs(0.4,0, 1,size=100)
+gp = ws.genpareto.fit2(Rgpd, method='mps')
+gml = ws.genpareto.fit2(Rgpd, method='ml')
+
+gp.plotecdf()
+x = sorted(Rgpd)
+plt.hold(True)
+plt.plot(x, gml.cdf(x))
+# gm = fitgenpar(Rgpd,'method','mom','plotflag',0);
+# plot(x,cdfgenpar(x,gm),'g--')
+#gw = fitgenpar(Rgpd,'method','pwm','plotflag',0);
+#plot(x,cdfgenpar(x,gw),'g:')
+#gml = fitgenpar(Rgpd,'method','ml','plotflag',0);
+#plot(x,cdfgenpar(x,gml),'--')
+#gmps = fitgenpar(Rgpd,'method','mps','plotflag',0);
+#plot(x,cdfgenpar(x,gmps),'r-.')
+plt.hold(False)
+#wafostamp([],'(ER)')
+#disp('Block = 8'),pause(pstate)
+
+##
+# Return values for the GEV distribution
+T = np.logspace(1, 5, 10);
+#[sT, sTlo, sTup] = invgev(1./T,Y5gev,'lowertail',false,'proflog',true);
+
+#T = 2:100000;
+#k=Y5gev.params(1); mu=Y5gev.params(3); sigma=Y5gev.params(2);
+#sT1 = invgev(1./T,Y5gev,'lowertail',false);
+#sT=mu + sigma/k*(1-(-log(1-1./T)).^k);
+plt.clf()
+#plt.semilogx(T,sT,T,sTlo,'r',T,sTup,'r')
+#plt.hold(True)
+#N = np.r_[1:len(Y5M)]
+#Nmax = max(N);
+#plot(Nmax./N, sorted(Y5M,reverse=True), '.')
+#plt.title('Return values in the GEV model')
+#plt.xlabel('Return priod')
+#plt.ylabel('Return value')
+#plt.grid(True)
+#disp('Block = 9'),pause(pstate)
+
+## Section 5.3 POT-analysis
+
+# Estimated expected exceedance over level u as function of u.
+plt.clf()
+
+mrl = ws.reslife(Hs,'umin',2,'umax',10,'Nu',200);
+mrl.plot()
+#wafostamp([],'(ER)')
+#disp('Block = 10'),pause(pstate)
+
+##
+# Estimated distribution functions of monthly maxima
+#with the POT method (solid),
+# fitting a GEV (dashed) and the empirical distribution.
+
+# POT- method
+gpd7 = ws.genpareto.fit2(Hs(Hs>7)-7, method='mps', floc=0)
+khat, loc, sigmahat = gpd7.par
+
+muhat = len(Hs[Hs>7])/(7*3*2)
+bhat = sigmahat/muhat**khat
+ahat = 7-(bhat-sigmahat)/khat
+x = np.linspace(5,15,200);
+plt.plot(x,ws.genextreme.cdf(x, khat,bhat,ahat))
+# disp('Block = 11'),pause(pstate)
+
+##
+# Since we have data to compute the monthly maxima mm over
+#42 months we can also try to fit a
+# GEV distribution directly:
+mm = np.zeros((1,41))
+for i in range(41):
+    mm[i] = max(Hs[((i-1)*14+1):i*14])
+
+
+gev = ws.genextreme.fit2(mm)
+
+
+plt.hold(True)
+gev.plotecdf()
+
+plt.hold(False)
+#wafostamp([],'(ER)')
+#disp('Block = 12, Last block'),pause(pstate)
+

wafo/doc/tutorial_scripts/rainflow_example.py

@@ -0,0 +1,176 @@
+from tutor_init import *
+import itertools
+# import sys
+log = logging.getLogger(__name__)
+log.setLevel(logging.DEBUG)
+
+MARKERS = ('o', 'x', '+', '.', '<', '>', '^', 'v')
+
+
+def plot_varying_symbols(x, y, color='red', size=5):
+    """
+    Create a plot with varying symbols
+    Parameters
+    ----------
+    x : numpy array with x data of the points
+    y : numpy array with y data of the points
+    color : color of the symbols
+
+    Returns
+    -------
+
+    """
+    markers = itertools.cycle(MARKERS)
+    for q, p in zip(x, y):
+        plt.plot(q, p, marker=markers.next(), linestyle='', color=color,
+                 markersize=size)
+
+
+def damage_vs_S(S, beta, K):
+    """
+    Calculate the damage 1/N for a given stress S
+
+    Parameters
+    ----------
+    S       : Stress [Pa]
+    beta    : coefficient, typically 3
+    K       : constant
+
+    Returns
+    -------
+
+    """
+    return K * np.power(S, beta)
+
+# Section 4.3.1 Crossing intensity
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+import wafo.data as wd
+import wafo.objects as wo
+import wafo.misc as wm
+
+xx_sea = wd.sea()
+
+Tlength = xx_sea[-1, 0] - xx_sea[0, 0]
+beta = 3
+K1 = 6.5e-31
+Np = 200
+Tp = Tlength / Np
+A = 100e6
+log.info("setting sin wave with Tp={} and T={}".format(Tp, Tlength))
+Nc = 1.0 / damage_vs_S(A, beta, K1)
+damage = float(Np) / float(Nc)
+log.info("budget at S={} N={}: damage = {} ".format(A, Nc, damage))
+#xx_sea[:, 1] = A * np.cos(2 * np.pi * xx_sea[:, 0]/Tp)
+xx_sea[:, 1] *= 500e6
+
+log.info("loaded sea time series {}".format(xx_sea.shape))
+ts = wo.mat2timeseries(xx_sea)
+
+tp = ts.turning_points()
+mM = tp.cycle_pairs(kind='min2max')
+Mm = tp.cycle_pairs(kind='max2min')
+lc = mM.level_crossings(intensity=True)
+T_sea = ts.args[-1] - ts.args[0]
+
+# for i in dir(mM):
+#    print(i)
+
+
+ts1 = wo.mat2timeseries(xx_sea[:, :])
+tp1 = ts1.turning_points()
+sig_tp = ts.turning_points(h=0, wavetype='astm')
+try:
+    sig_cp = sig_tp.cycle_astm()
+    log.info("Successfully used cycle_astm")
+except AttributeError:
+    log.warning("Could use cycle_astm")
+    sig_cp = None
+tp1 = ts1.turning_points()
+tp2 = ts1.turning_points(wavetype='Mw')
+mM1 = tp1.cycle_pairs(kind='min2max')
+Mm1 = tp1.cycle_pairs(kind='max2min')
+
+tp_rfc = tp1.rainflow_filter(h=100e6)
+mM_rfc = tp_rfc.cycle_pairs()
+try:
+    mM_rfc_a = tp1.cycle_astm()
+except AttributeError:
+    mM_rfc_a = None
+tc1 = ts1.trough_crest()
+min_to_max = True
+rfc_plot = True
+if min_to_max:
+    m1, M1 = mM1.get_minima_and_maxima()
+    i_min_start = 0
+else:
+    m1, M1 = Mm1.get_minima_and_maxima()
+    i_min_start = 2
+
+m_rfc, M_rfc = mM_rfc.get_minima_and_maxima()
+# m_rfc_a, M_rfc_a = mM_rfc_a.get_minima_and_maxima()
+ts1.plot('b-')
+if rfc_plot:
+    plot_varying_symbols(tp_rfc.args[0::2], m_rfc, color='red', size=10)
+    plot_varying_symbols(tp_rfc.args[1::2], M_rfc, color='green', size=10)
+else:
+    plot_varying_symbols(tp.args[i_min_start::2], m1, color='red', size=10)
+    plot_varying_symbols(tp.args[1::2], M1, color='green', size=10)
+
+set_windows_title("Sea time series", log)
+
+plt.figure()
+plt.subplot(122),
+mM.plot()
+plt.title('min-max cycle pairs')
+plt.subplot(121),
+mM_rfc.plot()
+
+title = 'Rainflow filtered cycles'
+plt.title(title)
+set_windows_title(title)
+
+
+# Min-max and rainflow cycle distributions
+#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# import wafo.misc as wm
+ampmM_sea = mM.amplitudes()
+ampRFC_sea = mM_rfc.amplitudes()
+plt.figure()
+title = "s_n_curve"
+set_windows_title(title)
+S = np.linspace(1e6, 1000e6)
+plt.loglog(S, damage_vs_S(S, beta, K1))
+plt.figure()
+plt.subplot(121)
+stress_range = (1, 1e9)
+n_bins = 100
+wm.plot_histgrm(ampmM_sea, bins=n_bins, range=stress_range)
+plt.xlim(stress_range)
+ylim = plt.gca().get_ylim()
+plt.title('min-max amplitude distribution')
+plt.subplot(122)
+if sig_cp is not None:
+    wm.plot_histgrm(sig_cp[:, 0], bins=n_bins, range=stress_range)
+    plt.gca().set_ylim(ylim)
+    title = 'Rainflow amplitude distribution'
+    plt.title(title)
+    plt.semilogy
+    set_windows_title(title)
+
+    hist, bin_edges = np.histogram(
+        sig_cp[
+            :, 0], bins=n_bins, range=stress_range)
+
+    plt.figure()
+    title = "my_bins"
+    plt.title(title)
+    plt.title(title)
+    set_windows_title(title)
+    plt.semilogy
+    plt.bar(bin_edges[:-1], hist, width=stress_range[1] / n_bins)
+
+    print("damage min/max : {}".format(mM_rfc.damage([beta], K1)))
+
+    damage_rfc = K1 * np.sum(sig_cp[:, 0] ** beta)
+    print("damage rfc : {}".format(damage_rfc))
+plt.show('hold')

wafo/doc/tutorial_scripts/tutor_init.py

@@ -0,0 +1,27 @@
+import logging
+import scipy as sp
+import numpy as np
+from numpy import pi, reshape
+import matplotlib.pyplot as plt
+import matplotlib
+matplotlib.use('Qt4Agg')
+from matplotlib import rcParams
+rcParams.update({"font.size": 10})
+
+
+try:
+    from win32api import LoadResource
+except ImportError:
+    pass
+
+log = logging.basicConfig(
+    format="%(asctime)s - %(name)s - %(levelname)s - %(message)s",
+    level=logging.DEBUG)
+
+
+def set_windows_title(title, log=None):
+    if log is not None:
+        log.info("Set windows title {}".format(title))
+    fig = plt.gcf()
+    fig.canvas.set_window_title(title)
+    plt.show()

wafo/f2py_tools.py

@@ -0,0 +1,65 @@
+# -*- coding: utf-8 -*-
+"""
+f2py c_library.pyf c_functions.c -c
+
+See also http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW
+"""
+import os
+import sys
+
+
+def which(program):
+    """
+    Return filepath to program if it exists
+
+    In order to test if a certain executable exists, it will search for the
+    program name in the environment variables.
+    If program is a full path to an executable, it will check it exists
+
+    Copied from:
+    http://stackoverflow.com/questions/377017/test-if-executable-exists-in-python/
+    It is supposed to mimic the UNIX command "which"
+    """
+
+    def is_exe(fpath):
+        return os.path.exists(fpath) and os.access(fpath, os.X_OK)
+
+    fpath, unused_fname = os.path.split(program)
+    if fpath:
+        if is_exe(program):
+            return program
+    else:
+        for path in os.environ["PATH"].split(os.pathsep):
+            exe_file = os.path.join(path, program)
+            if is_exe(exe_file):
+                return exe_file
+
+    return None
+
+
+def f2py_call_str():
+    '''Return which f2py callable is in the path regardless of platform'''
+
+    # define possible options:
+    # on Arch Linux, python and f2py are the calls corresponding to python 3
+    # and python2/f2py2 for python 2
+    # other Linux versions might still use python/f2py for python 2
+
+    if os.path.basename(sys.executable).endswith('2'):
+        options = ('f2py2', 'f2py2.6', 'f2py2.7',)
+    else:  # on Windows and other Linux using python/f2py
+        options = ('f2py.exe', 'f2py.bat', 'f2py', 'f2py2.6', 'f2py2.7',
+                   'f2py.py',)
+    for k in options:
+        if which(k):
+            # Found the f2py path, no need to look further
+            f2py_call = k
+            f2py_path = which(k)
+            break
+
+    try:
+        print('found f2py in:', f2py_path)
+        return f2py_call
+    except NameError:
+        raise UserWarning('Couldn\'t locate f2py. '
+                          'Should be part of NumPy installation.')

wafo/fig.py

@@ -0,0 +1,908 @@
+# /usr/bin/env python
+'''
+Module FIG
+------------
+Module for manipulating windows/figures created using
+pylab or enthought.mayavi.mlab on the windows platform.
+
+Figure manipulation involves
+maximization, minimization, hiding, closing, stacking or tiling.
+
+It is assumed that the figures are uniquely numbered in the following way:
+Figure 1
+Figure 2
+....
+or
+TVTK scene 1
+TVTK scene 2
+TVTK scene 3
+...
+
+Example
+-------
+>>> import pylab as p
+>>> import wafo.fig as fig
+>>> for ix in range(6):
+...     f = p.figure(ix)
+>>> fig.stack('all')
+>>> fig.stack(1,2)
+>>> fig.hide(1)
+>>> fig.restore(1)
+>>> fig.tile()
+>>> fig.pile()
+>>> fig.maximize(4)
+>>> fig.close('all')
+'''
+
+from __future__ import absolute_import, division, print_function
+# import win32api
+import win32gui
+import win32con
+import wx
+import numpy
+
+from win32gui import (EnumWindows, MoveWindow, GetWindowRect, FindWindow,
+                      ShowWindow, BringWindowToTop)
+
+__all__ = ['close', 'cycle', 'hide', 'keep', 'maximize', 'minimize', 'pile',
+           'restore', 'stack', 'tile', 'find_all_figure_numbers', 'set_size']
+
+# Figure format strings to recognize in window title
+FIGURE_TITLE_FORMATS = ('Figure', 'TVTK Scene', 'Chaco Plot Window: Figure')
+_SCREENSIZE = None
+
+
+class CycleDialog(wx.Dialog):
+
+    def _get_buttons(self):
+        hbox = wx.BoxSizer(wx.HORIZONTAL)
+        buttons = ['Forward', 'Back', 'Cancel']
+        callbacks = [self.on_forward, self.on_backward, self.on_cancel]
+        for button, callback in zip(buttons, callbacks):
+            button = wx.Button(self, -1, button, size=(70, 30))
+            self.Bind(wx.EVT_BUTTON, callback, button)
+            hbox.Add(button, 1, wx.ALIGN_CENTER)
+        return hbox
+
+    def _get_message(self):
+        label = ('Press back or forward to display previous or next figure(s),'
+                 ' respectively. Press cancel to quit.')
+        message = wx.StaticText(self, label=label, size=(240, 25))
+        return message
+
+    def __init__(self, parent, interval=None, title='Cycle dialog'):
+        super(CycleDialog, self).__init__(parent, title=title, size=(260, 130))
+        if isinstance(interval, (float, int)):
+            self.interval_milli_sec = interval * 1000
+        else:
+            self.interval_milli_sec = 30
+
+        self.timer = wx.Timer(self)
+        self.Bind(wx.EVT_TIMER, self.on_forward, self.timer)
+
+        vbox = wx.BoxSizer(wx.VERTICAL)
+        vbox.Add(self._get_message(), 0, wx.ALIGN_CENTER | wx.TOP, 20)
+        vbox.Add(self._get_buttons(), 1, wx.ALIGN_CENTER | wx.TOP | wx.BOTTOM, 10)
+        self.SetSizer(vbox)
+
+    def ShowModal(self, *args, **kwargs):
+        self.timer.Start(self.interval_milli_sec, oneShot=True)
+        return super(CycleDialog, self).ShowModal(*args, **kwargs)
+
+    def on_forward(self, evt):
+        self.EndModal(wx.ID_FORWARD)
+
+    def on_backward(self, evt):
+        self.EndModal(wx.ID_BACKWARD)
+
+    def on_cancel(self, evt):
+        self.EndModal(wx.ID_CANCEL)
+
+
+def _get_cycle_dialog(parent=None, interval=None):
+    app = wx.GetApp()
+    if not app:
+        app = wx.App(redirect=False)
+        frame = wx.Frame(None)
+        app.SetTopWindow(frame)
+    dlg = CycleDialog(parent, interval)
+    return dlg
+
+
+def get_window_position_and_size(window_handle):
+    pos = GetWindowRect(window_handle)
+    return pos[0], pos[1], pos[2] - pos[0], pos[3] - pos[1]
+
+
+def get_screen_position_and_size(window_handles):
+    """Return screen position; X, Y and size; width, height.
+
+    Parameters
+    ----------
+    window_handles: list of handles to open window figures
+      (Note: only needed the first time)
+
+    Returns
+    --------
+    X : coordinate of the left side of the screen.
+    Y : coordinate of the top of the screen.
+    width : screen horizontal size
+    height : screen vertical size
+
+    """
+    # pylint: disable=global-statement
+    global _SCREENSIZE
+    if _SCREENSIZE is None:
+        window_handle = window_handles[0]
+        pos = get_window_position_and_size(window_handle)
+        _show_windows((window_handle,), win32con.SW_SHOWMAXIMIZED)
+        _SCREENSIZE = get_window_position_and_size(window_handle)
+        MoveWindow(window_handle, pos[0], pos[1], pos[2], pos[3], 1)
+    return _SCREENSIZE
+
+
+def _get_screen_size(wnds):
+    screen_width, screen_height = get_screen_position_and_size(wnds)[2:4]
+    return screen_width, screen_height
+
+
+def _windowEnumerationHandler(handle, result_list):
+    """Pass to win32gui.EnumWindows() to generate list of window handle, window
+    text tuples."""
+    # pylint: disable=no-member
+    if win32gui.IsWindowVisible(handle):
+        result_list.append((handle, win32gui.GetWindowText(handle)))
+
+
+def _find_window_handles_and_titles(wantedTitle=None):
+    """Return list of window handle and window title tuples.
+
+    Parameter
+    ---------
+    wantedTitle:
+
+    """
+    handles_n_titles = []
+    EnumWindows(_windowEnumerationHandler, handles_n_titles)
+    if wantedTitle is None:
+        return handles_n_titles
+    else:
+        return [(handle, title)
+                for handle, title in handles_n_titles
+                if title.startswith(wantedTitle)]
+
+
+def find_figure_handles(*figure_numbers):
+    """Find figure handles from figure numbers."""
+    wnd_handles = []
+    for figure_number in _parse_figure_numbers(*figure_numbers):
+        for format_ in FIGURE_TITLE_FORMATS:
+            winTitle = format_ + ' %d' % figure_number
+            handle = FindWindow(None, winTitle)
+            if not handle == 0:
+                wnd_handles.append(handle)
+    return wnd_handles
+
+
+def find_all_figure_numbers():
+    """Return list of all figure numbers.
+
+    Example
+    -------
+    >>> import fig
+    >>> import pylab as p
+    >>> for ix in range(5):
+    ...     f = p.figure(ix)
+    ...     p.draw()
+
+    fig.find_all_figure_numbers()
+    [0, 1, 2, 3, 4]
+
+    >>> fig.close()
+
+    """
+    figure_numbers = []
+    for wantedTitle in FIGURE_TITLE_FORMATS:
+        handles_n_titles = _find_window_handles_and_titles(wantedTitle)
+        for _handle, title in handles_n_titles:
+            try:
+                number = int(title.split()[-1])
+                figure_numbers.append(number)
+            except (TypeError, ValueError):
+                pass
+    # pylint: disable=no-member
+    return numpy.unique(figure_numbers).tolist()
+
+
+def _parse_figure_numbers(*args):
+    figure_numbers = []
+    for arg in args:
+        if isinstance(arg, (list, tuple, set)):
+            for val in arg:
+                figure_numbers.append(int(val))
+        elif isinstance(arg, int):
+            figure_numbers.append(arg)
+        elif arg == 'all':
+            figure_numbers = find_all_figure_numbers()
+            break
+        else:
+            raise TypeError('Only integers arguments accepted!')
+
+    if len(figure_numbers) == 0:
+        figure_numbers = find_all_figure_numbers()
+    return figure_numbers
+
+
+def _show_figure(figure_numbers, command):
+    """Sets the specified figure's show state.
+
+    Parameters
+    ----------
+    figure_numbers: list of figure numbers
+    command: one of following commands:
+    SW_FORCEMINIMIZE:
+        Minimizes a window, even if the thread that owns the window is not
+        responding. This flag should only be used when minimizing windows
+        from a different thread.
+    SW_HIDE:
+        Hides the window and activates another window.
+    SW_MAXIMIZE:
+        Maximizes the specified window.
+    SW_MINIMIZE:
+        Minimizes the specified window and activates the next top-level window
+        in the Z order.
+    SW_RESTORE:
+        Activates and displays the window. If the window is minimized or
+        maximized, the system restores it to its original size and position.
+        An application should specify this flag when restoring a minimized
+        window.
+    SW_SHOW:
+        Activates the window and displays it in its current size and position.
+    SW_SHOWDEFAULT:
+        Sets the show state based on the SW_ value specified in the STARTUPINFO
+        structure passed to the CreateProcess function by the program that
+        started the application.
+    SW_SHOWMAXIMIZED:
+        Activates the window and displays it as a maximized window.
+    SW_SHOWMINIMIZED:
+        Activates the window and displays it as a minimized window.
+    SW_SHOWMINNOACTIVE:
+        Displays the window as a minimized window. This value is similar to
+        SW_SHOWMINIMIZED, except the window is not activated.
+    SW_SHOWNA:
+        Displays the window in its current size and position. This value is
+        similar to SW_SHOW, except the window is not activated.
+    SW_SHOWNOACTIVATE:
+        Displays a window in its most recent size and position. This value is
+        similar to SW_SHOWNORMAL, except the window is not actived.
+    SW_SHOWNORMAL:
+        Activates and displays a window. If the window is minimized or
+        maximized, the system restores it to its original size and position.
+        An application should specify this flag when displaying the window for
+        the first time.
+
+    """
+    for number in _parse_figure_numbers(*figure_numbers):
+        for format_ in FIGURE_TITLE_FORMATS:
+            title = format_ + ' %d' % number
+            handle = FindWindow(None, title)
+            if not handle == 0:
+                BringWindowToTop(handle)
+                ShowWindow(handle, command)
+
+
+def _show_windows(handles, command, redraw_now=False):
+    """Sets the specified window's show state.
+
+    Parameters
+    ----------
+    handles: list of window handles
+    command: one of following commands:
+    SW_FORCEMINIMIZE:
+        Minimizes a window, even if the thread that owns the window is not
+        responding. This flag should only be used when minimizing windows
+        from a different thread.
+    SW_HIDE:
+        Hides the window and activates another window.
+    SW_MAXIMIZE:
+        Maximizes the specified window.
+    SW_MINIMIZE:
+        Minimizes the specified window and activates the next top-level window
+        in the Z order.
+    SW_RESTORE:
+        Activates and displays the window. If the window is minimized or
+        maximized, the system restores it to its original size and position.
+        An application should specify this flag when restoring a minimized
+                    window.
+    SW_SHOW:
+        Activates the window and displays it in its current size and position.
+    SW_SHOWDEFAULT:
+        Sets the show state based on the SW_ value specified in the STARTUPINFO
+        structure passed to the CreateProcess function by the program that
+        started the application.
+    SW_SHOWMAXIMIZED:
+        Activates the window and displays it as a maximized window.
+    SW_SHOWMINIMIZED:
+        Activates the window and displays it as a minimized window.
+    SW_SHOWMINNOACTIVE:
+        Displays the window as a minimized window. This value is similar to
+        SW_SHOWMINIMIZED, except the window is not activated.
+    SW_SHOWNA:
+        Displays the window in its current size and position. This value is
+        similar to SW_SHOW, except the window is not activated.
+    SW_SHOWNOACTIVATE:
+        Displays a window in its most recent size and position. This value is
+        similar to SW_SHOWNORMAL, except the window is not actived.
+    SW_SHOWNORMAL:
+        Activates and displays a window. If the window is minimized or
+        maximized, the system restores it to its original size and position.
+        An application should specify this flag when displaying the window for
+        the first time.
+
+    redraw_now :
+
+    """
+    # pylint: disable=no-member
+    for handle in handles:
+        if not handle == 0:
+            BringWindowToTop(handle)
+            ShowWindow(handle, command)
+            if redraw_now:
+                rect = GetWindowRect(handle)
+                win32gui.RedrawWindow(handle, rect, None, win32con.RDW_UPDATENOW)
+
+
+def keep(*figure_numbers):
+    """Keeps figure windows of your choice and closes the rest.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers specifying which figures to keep.
+
+    Example:
+    --------
+    # keep only figures 1,2,3,5 and 7
+    >>> import pylab as p
+    >>> import wafo.fig as fig
+    >>> for ix in range(10):
+    ...     f = p.figure(ix)
+    >>> fig.keep( range(1,4),  5, 7)
+
+    or
+        fig.keep([range(1,4),  5, 7])
+    >>> fig.close()
+
+    See also
+    --------
+    fig.close
+
+    """
+    figs2keep = []
+    for fig in figure_numbers:
+        if isinstance(fig, (list, tuple, set)):
+            for val in fig:
+                figs2keep.append(int(val))
+        elif isinstance(fig, int):
+            figs2keep.append(fig)
+        else:
+            raise TypeError('Only integers arguments accepted!')
+
+    if len(figs2keep) > 0:
+        allfigs = set(find_all_figure_numbers())
+        figs2delete = allfigs.difference(figs2keep)
+        close(figs2delete)
+
+
+def close(*figure_numbers):
+    """  Close figure window(s)
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to close (default 'all').
+
+    Examples
+    --------
+    >>> import pylab as p
+    >>> import wafo.fig as fig
+    >>> for ix in range(5):
+    ...     f = p.figure(ix)
+    >>> fig.close(3,4)   # close figure 3 and 4
+    >>> fig.close('all') # close all remaining figures
+
+    or even simpler
+    fig.close() # close all remaining figures
+
+    See also
+    --------
+    fig.keep
+
+    """
+    # pylint: disable=no-member
+    for handle in find_figure_handles(*figure_numbers):
+        if win32gui.SendMessage(handle, win32con.WM_CLOSE, 0, 0):
+            win32gui.SendMessage(handle, win32con.WM_DESTROY, 0, 0)
+
+
+def restore(*figure_numbers):
+    """Restore figures window size and position to its default value.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to restor (default 'all').
+
+    Description
+    -----------
+    RESTORE Activates and displays the window. If the window is minimized
+    or maximized, the system restores it to its original size and position.
+
+    Examples
+    ---------
+      >>> import pylab as p
+      >>> import wafo.fig as fig
+      >>> for ix in range(5):
+    ...     f = p.figure(ix)
+      >>> fig.restore('all')   #Restores all figures
+      >>> fig.restore()        #same as restore('all')
+      >>> fig.restore(p.gcf().number)   #Restores the current figure
+      >>> fig.restore(3)       #Restores figure 3
+      >>> fig.restore([2, 4])   #Restores figures 2 and 4
+
+       or alternatively
+          fig.restore(2, 4)
+      >>> fig.close()
+
+    See also
+    --------
+    fig.close,
+    fig.keep
+
+    """
+    SW_RESTORE = win32con.SW_RESTORE
+    # SW_RESTORE = win32con.SW_SHOWDEFAULT
+    # SW_RESTORE = win32con.SW_SHOWNORMAL
+    _show_figure(figure_numbers, SW_RESTORE)
+
+
+def hide(*figure_numbers):
+    """hide figure(s) window.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to hide (default 'all').
+
+    Examples:
+    --------
+    >>> import wafo.fig as fig
+     >>> import pylab as p
+    >>> for ix in range(5):
+    ...     f = p.figure(ix)
+     >>> fig.hide('all')   #hides all unhidden figures
+     >>> fig.hide()        #same as hide('all')
+     >>> fig.hide(p.gcf().number)   #hides the current figure
+     >>> fig.hide(3)       #hides figure 3
+     >>> fig.hide([2, 4])   #hides figures 2 and 4
+
+     or alternatively
+         fig.hide(2, 4)
+    >>> fig.restore(list(range(5)))
+     >>> fig.close()
+
+     See also
+     --------
+    fig.cycle,
+    fig.keep,
+    fig.restore
+
+    """
+    _show_figure(figure_numbers, win32con.SW_HIDE)
+
+
+def minimize(*figure_numbers):
+    """Minimize figure(s) window size.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to minimize (default 'all').
+
+    Examples:
+    ---------
+     >>> import wafo.fig as fig
+     >>> import pylab as p
+     >>> for ix in range(5):
+     ...     f = p.figure(ix)
+     >>> fig.minimize('all')   #Minimizes all unhidden figures
+     >>> fig.minimize()        #same as minimize('all')
+     >>> fig.minimize(p.gcf().number)   #Minimizes the current figure
+     >>> fig.minimize(3)       #Minimizes figure 3
+     >>> fig.minimize([2, 4])   #Minimizes figures 2 and 4
+
+     or alternatively
+         fig.minimize(2, 4)
+     >>> fig.close()
+
+     See also
+     --------
+     fig.cycle,
+     fig.keep,
+     fig.restore
+
+    """
+    _show_figure(figure_numbers, win32con.SW_SHOWMINIMIZED)
+
+
+def maximize(*figure_numbers):
+    """Maximize figure(s) window size.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to maximize (default 'all').
+
+    Examples:
+    ---------
+     >>> import pylab as p
+     >>> import wafo.fig as fig
+     >>> for ix in range(5):
+     ...     f = p.figure(ix)
+     >>> fig.maximize('all')   #Maximizes all unhidden figures
+     >>> fig.maximize()        #same as maximize('all')
+     >>> fig.maximize(p.gcf().number)   #Maximizes the current figure
+     >>> fig.maximize(3)       #Maximizes figure 3
+     >>> fig.maximize([2, 4])   #Maximizes figures 2 and 4
+
+     or alternatively
+         fig.maximize(2, 4)
+     >>> fig.close()
+
+     See also
+     --------
+     fig.cycle,
+     fig.keep,
+     fig.restore
+
+    """
+    _show_figure(figure_numbers, win32con.SW_SHOWMAXIMIZED)
+
+
+def pile(*figure_numbers, **kwds):
+    """Pile figure windows.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to pile (default 'all').
+    kwds : dict with the following keys
+        position :
+        width  :
+        height :
+
+    Description
+    -------------
+       PILE piles all open figure windows on top of eachother
+       with complete overlap. PILE(FIGS) can be used to specify which
+       figures that should be piled. Figures are not sorted when specified.
+
+     Example:
+     --------
+     >>> import pylab as p
+     >>> import wafo.fig as fig
+     >>> for ix in range(7):
+     ...     f = p.figure(ix)
+     >>> fig.pile()                # pile all open figures
+     >>> fig.pile(range(1,4), 5, 7)  # pile figure 1,2,3,5 and 7
+     >>> fig.close()
+
+     See also
+     --------
+     fig.cycle, fig.keep, fig.maximize, fig.restore,
+             fig.stack, fig.tile
+
+    """
+    wnds = find_figure_handles(*figure_numbers)
+    numfigs = len(wnds)
+    if numfigs > 0:
+        screen_width, screen_height = _get_screen_size(wnds)
+        pos = kwds.get(
+            'position', (int(screen_width / 5), int(screen_height / 4)))
+        width = kwds.get('width', int(screen_width / 2.5))
+        height = kwds.get('height', int(screen_height / 2))
+
+        for wnd in wnds:
+            MoveWindow(wnd, pos[0], pos[1], width, height, 1)
+            BringWindowToTop(wnd)
+
+
+def set_size(*figure_numbers, **kwds):
+    """Set size for figure windows.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to pile (default 'all').
+    kwds : dict with the following keys
+        width  :
+        height :
+
+    Description
+    -------------
+    Set size sets the size of all open figure windows. SET_SIZE(FIGS)
+    can be used to specify which figures that should be resized.
+    Figures are not sorted when specified.
+
+     Example:
+     --------
+     >>> import pylab as p
+     >>> import fig
+     >>> for ix in range(7):
+     ...     f = p.figure(ix)
+     >>> fig.set_size(7, width=150, height=100)
+     >>> fig.set_size(range(1,4), 5,width=250, height=170)
+     >>> fig.close()
+
+     See also
+     --------
+     fig.cycle, fig.keep, fig.maximize, fig.restore,
+             fig.stack, fig.tile
+
+    """
+    handles = find_figure_handles(*figure_numbers)
+    numfigs = len(handles)
+    if numfigs > 0:
+        screen_width, screen_height = _get_screen_size(handles)
+        width = kwds.get('width', int(screen_width / 2.5))
+        height = kwds.get('height', int(screen_height / 2))
+        new_pos = kwds.get('position', None)
+        pos = new_pos
+        for handle in handles:
+            if not new_pos:
+                pos = get_window_position_and_size(handle)
+            MoveWindow(handle, pos[0], pos[1], width, height, 1)
+            BringWindowToTop(handle)
+
+
+def stack(*figure_numbers, **kwds):
+    """Stack figure windows.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to stack (default 'all').
+    kwds : dict with the following keys
+        figs_per_stack :
+            number of figures per stack (default depends on screenheight)
+
+    Description
+    -----------
+       STACK stacks all open figure windows on top of eachother
+       with maximum overlap. STACK(FIGS) can be used to specify which
+       figures that should be stacked. Figures are not sorted when specified.
+
+     Example:
+     --------
+     >>> import pylab as p
+     >>> import wafo.fig as fig
+     >>> for ix in range(7):
+     ...     f = p.figure(ix)
+     >>> fig.stack()                # stack all open figures
+     >>> fig.stack(range(1,4), 5, 7)  # stack figure 1,2,3,5 and 7
+     >>> fig.close()
+
+     See also
+     --------
+      fig.cycle, fig.keep, fig.maximize, fig.restore,
+             fig.pile, fig.tile
+
+    """
+    wnds = find_figure_handles(*figure_numbers)
+    numfigs = len(wnds)
+    if numfigs > 0:
+        screenpos = get_screen_position_and_size(wnds)
+        y_step = 25
+        x_step = border = 5
+
+        figs_per_stack = kwds.get(
+            'figs_per_stack',
+            int(numpy.fix(0.7 * (screenpos[3] - border) / y_step)))
+
+        for iy in range(numfigs):
+            pos = get_window_position_and_size(wnds[iy])
+            # print('[x, y, w, h] = ', pos)
+            ix = iy % figs_per_stack
+            ypos = int(screenpos[1] + ix * y_step + border)
+            xpos = int(screenpos[0] + ix * x_step + border)
+            MoveWindow(wnds[iy], xpos, ypos, pos[2], pos[3], 1)
+            BringWindowToTop(wnds[iy])
+
+
+def tile(*figure_numbers, **kwds):
+    """Tile figure windows.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to tile (default 'all').
+    kwds : dict with key pairs
+        specifying how many pairs of figures that are tiled at a time
+
+    Description
+    -----------
+       TILE places all open figure windows around on the screen with no
+       overlap. TILE(FIGS) can be used to specify which figures that
+       should be tiled. Figures are not sorted when specified.
+
+     Example:
+     --------
+     >>> import pylab as p
+     >>> import wafo.fig as fig
+     >>> for ix in range(7):
+     ...     f = p.figure(ix)
+     >>> fig.tile()             # tile all open figures
+     >>> fig.tile( range(1,4), 5, 7)    # tile figure 1,2,3,5 and 7
+     >>> fig.tile(range(1,11), pairs=2) # tile figure 1 to 10 two at a time
+     >>> fig.tile(range(1,11), pairs=3) # tile figure 1 to 10 three at a time
+     >>> fig.close()
+
+     See also
+     --------
+     fig.cycle, fig.keep, fig.maximize, fig.minimize
+     fig.restore, fig.pile, fig.stack
+
+    """
+    wnds = find_figure_handles(*figure_numbers)
+
+    nfigs = len(wnds)
+    # Number of windows.
+
+    if nfigs > 0:
+        nfigspertile = kwds.get('pairs', nfigs)
+
+        ceil = numpy.ceil
+        sqrt = numpy.sqrt
+        maximum = numpy.maximum
+
+        nlayers = int(ceil(nfigs / nfigspertile))
+
+        # Number of figures horisontally.
+        nh = maximum(int(ceil(sqrt(nfigspertile))), 2)
+        # Number of figures vertically.
+        nv = maximum(int(ceil(nfigspertile / nh)), 2)
+
+        screenpos = get_screen_position_and_size(wnds)
+        screen_width, screen_heigth = screenpos[2:4]
+
+        hspc = 10            # Horisontal space.
+        topspc = 20            # Space above top figure.
+        medspc = 10            # Space between figures.
+        botspc = 20            # Space below bottom figure.
+
+        figwid = (screen_width - (nh + 1) * hspc) / nh
+        fighgt = (screen_heigth - (topspc + botspc) - (nv - 1) * medspc) / nv
+
+        figwid = int(numpy.round(figwid))
+        fighgt = int(numpy.round(fighgt))
+
+        idx = 0
+        for unused_ix in range(nlayers):
+            for row in range(nv):
+                figtop = int(screenpos[1] + topspc + row * (fighgt + medspc))
+                for col in range(nh):
+                    if (row) * nh + col < nfigspertile:
+                        if idx < nfigs:
+                            figlft = int(
+                                screenpos[0] + (col + 1) * hspc + col * figwid)
+                            fighnd = wnds[idx]
+                            MoveWindow(fighnd, figlft, figtop, figwid, fighgt,
+                                       1)
+                            # Set position.
+                            BringWindowToTop(fighnd)
+                        idx += 1
+
+
+class _CycleGenerator(object):
+
+    """Cycle through figure windows.
+
+    Parameters
+    ----------
+    figure_numbers : list of integers or string
+        specifying which figures to cycle through (default 'all').
+    kwds : dict with the following keys
+        pairs : number of figures to cycle in pairs (default 1)
+        maximize: If True maximize figure when viewing (default False)
+        interval : pause interval in seconds
+
+    Description
+    -----------
+       CYCLE brings up all open figure in ascending order and pauses after
+       each figure. Press escape to quit cycling, backspace to display previous
+       figure(s) and press any other key to display next figure(s)
+       When done, the figures are sorted in ascending order.
+
+    CYCLE(maximize=True) does the same thing, except figures are maximized.
+       CYCLE(pairs=2)   cycle through all figures in pairs of 2.
+
+     Examples:
+     >>> import pylab as p
+     >>> import wafo.fig as fig
+     >>> for ix in range(4):
+     ...     f = p.figure(ix)
+
+     fig.cycle(range(3), interval=1)  # Cycle trough figure 0 to 2
+
+     # Cycle trough figure 0 to 2 with figures maximized
+     fig.cycle(range(3), maximize=True, interval=1)
+     fig.cycle(interval=1)            # Cycle through all figures one at a time
+     fig.tile(pairs=2, interval=1)
+     fig.cycle(pairs=2, interval=2)   # Cycle through all figures two at a time
+
+     fig.cycle(pairs=2)      # Manually cycle through all figures two at a time
+     >>> fig.close()
+
+    See also
+    --------
+     fig.keep, fig.maximize, fig.restore, fig.pile,
+            fig.stack, fig.tile
+
+    """
+    escape_key = chr(27)
+    backspace_key = chr(8)
+
+    def __init__(self, **kwds):
+        self.dialog = None
+        maximize = kwds.get('maximize', False)
+        pairs = kwds.get('pairs', 1)
+        self.interval = kwds.get('interval', 'user_defined')
+        self.nfigspercycle = 1
+        if maximize:
+            self.command = win32con.SW_SHOWMAXIMIZED
+        else:
+            self.command = win32con.SW_SHOWNORMAL
+            if pairs is not None:
+                self.nfigspercycle = pairs
+
+    def _set_options(self, kwds):
+        self.__init__(**kwds)
+
+    def _iterate(self, handles):
+        i = 0
+        numfigs = len(handles)
+        self.dialog = _get_cycle_dialog(parent=None, interval=self.interval)
+        while 0 <= i and i < numfigs:
+            iu = min(i + self.nfigspercycle, numfigs)
+            yield handles[i:iu]
+            i = self.next_index(i)
+        self.dialog.Destroy()
+        raise StopIteration
+
+    def next_index(self, i):
+        result = self.dialog.ShowModal()
+        if result == wx.ID_FORWARD:
+            i += self.nfigspercycle
+        elif result == wx.ID_BACKWARD:
+            i -= self.nfigspercycle
+        else:
+            i = -1
+        return i
+
+    def __call__(self, *figure_numbers, **kwds):
+        handles = find_figure_handles(*figure_numbers)
+        numfigs = len(handles)
+        if numfigs > 0:
+            self._set_options(kwds)
+            for handle in self._iterate(handles):
+                _show_windows(handle, self.command, redraw_now=True)
+
+            _show_windows(handles, win32con.SW_SHOWNORMAL)
+
+cycle = _CycleGenerator()
+
+
+if __name__ == '__main__':
+    from wafo.testing import test_docstrings
+    import matplotlib
+    matplotlib.interactive(True)
+    test_docstrings(__file__)

wafo/integrate_oscillating.py

@@ -0,0 +1,538 @@
+"""
+Created on 20. aug. 2015
+
+@author: pab
+"""
+from __future__ import division
+from collections import namedtuple
+import warnings
+import numdifftools as nd
+import numdifftools.nd_algopy as nda
+from numdifftools.extrapolation import dea3
+from numdifftools.limits import Limit
+import numpy as np
+from numpy import linalg
+from numpy.polynomial.chebyshev import chebval, Chebyshev
+from numpy.polynomial import polynomial
+from wafo.misc import piecewise, findcross, ecross
+
+_FINFO = np.finfo(float)
+EPS = _FINFO.eps
+_EPS = EPS
+_TINY = _FINFO.tiny
+_HUGE = _FINFO.max
+
+
+def _assert(cond, msg):
+    if not cond:
+        raise ValueError(msg)
+
+
+def _assert_warn(cond, msg):
+    if not cond:
+        warnings.warn(msg)
+
+
+class PolyBasis(object):
+    @staticmethod
+    def _derivative(c, m):
+        return polynomial.polyder(c, m)
+
+    @staticmethod
+    def eval(t, c):
+        return polynomial.polyval(t, c)
+
+    @staticmethod
+    def _coefficients(k):
+        c = np.zeros(k + 1)
+        c[k] = 1
+        return c
+
+    def derivative(self, t, k, n=1):
+        c = self._coefficients(k)
+        d_c = self._derivative(c, m=n)
+        return self.eval(t, d_c)
+
+    def __call__(self, t, k):
+        return t**k
+
+
+poly_basis = PolyBasis()
+
+
+class ChebyshevBasis(PolyBasis):
+
+    @staticmethod
+    def _derivative(c, m):
+        cheb = Chebyshev(c)
+        dcheb = cheb.deriv(m=m)
+        return dcheb.coef
+
+    @staticmethod
+    def eval(t, c):
+        return chebval(t, c)
+
+    def __call__(self, t, k):
+        c = self._coefficients(k)
+        return self.eval(t, c)
+
+
+chebyshev_basis = ChebyshevBasis()
+
+
+def richardson(q_val, k):
+    # license BSD
+    # Richardson extrapolation with parameter estimation
+    c = np.real((q_val[k - 1] - q_val[k - 2]) / (q_val[k] - q_val[k - 1])) - 1.
+    # The lower bound 0.07 admits the singularity x.^-0.9
+    c = max(c, 0.07)
+    return q_val[k] + (q_val[k] - q_val[k - 1]) / c
+
+
+def evans_webster_weights(omega, g, d_g, x, basis, *args, **kwds):
+
+    def psi(t, k):
+        return d_g(t, *args, **kwds) * basis(t, k)
+
+    j_w = 1j * omega
+    n = len(x)
+    a_matrix = np.zeros((n, n), dtype=complex)
+    rhs = np.zeros((n,), dtype=complex)
+
+    dbasis = basis.derivative
+    lim_g = Limit(g)
+    b_1 = np.exp(j_w * lim_g(1, *args, **kwds))
+    if np.isnan(b_1):
+        b_1 = 0.0
+    a_1 = np.exp(j_w * lim_g(-1, *args, **kwds))
+    if np.isnan(a_1):
+        a_1 = 0.0
+
+    lim_psi = Limit(psi)
+    for k in range(n):
+        rhs[k] = basis(1, k) * b_1 - basis(-1, k) * a_1
+        a_matrix[k] = (dbasis(x, k, n=1) + j_w * lim_psi(x, k))
+
+    solution = linalg.lstsq(a_matrix, rhs)
+    return solution[0]
+
+
+def osc_weights(omega, g, d_g, x, basis, a_b, *args, **kwds):
+    def _g(t):
+        return g(scale * t + offset, *args, **kwds)
+
+    def _d_g(t):
+        return scale * d_g(scale * t + offset, *args, **kwds)
+
+    w = []
+
+    for a, b in zip(a_b[::2], a_b[1::2]):
+        scale = (b - a) / 2
+        offset = (a + b) / 2
+
+        w.append(evans_webster_weights(omega, _g, _d_g, x, basis))
+
+    return np.asarray(w).ravel()
+
+
+class _Integrator(object):
+    info = namedtuple('info', ['error_estimate', 'n'])
+
+    def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=1,
+                 precision=10, endpoints=True, full_output=False):
+        self.f = f
+        self.g = g
+        self.dg = nd.Derivative(g) if dg is None else dg
+        self.basis = basis
+        self.a = a
+        self.b = b
+        self.s = s
+        self.endpoints = endpoints
+        self.precision = precision
+        self.full_output = full_output
+
+
+class QuadOsc(_Integrator):
+    def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=15,
+                 precision=10, endpoints=False, full_output=False, maxiter=17):
+        self.maxiter = maxiter
+        super(QuadOsc, self).__init__(f, g, dg=dg, a=a, b=b, basis=basis, s=s,
+                                      precision=precision, endpoints=endpoints,
+                                      full_output=full_output)
+
+    @staticmethod
+    def _change_interval_to_0_1(f, g, d_g, a, _b):
+        def f_01(t, *args, **kwds):
+            den = 1 - t
+            return f(a + t / den, *args, **kwds) / den ** 2
+
+        def g_01(t, *args, **kwds):
+            return g(a + t / (1 - t), *args, **kwds)
+
+        def d_g_01(t, *args, **kwds):
+            den = 1 - t
+            return d_g(a + t / den, *args, **kwds) / den ** 2
+        return f_01, g_01, d_g_01, 0., 1.
+
+    @staticmethod
+    def _change_interval_to_m1_0(f, g, d_g, _a, b):
+        def f_m10(t, *args, **kwds):
+            den = 1 + t
+            return f(b + t / den, *args, **kwds) / den ** 2
+
+        def g_m10(t, *args, **kwds):
+            return g(b + t / (1 + t), *args, **kwds)
+
+        def d_g_m10(t, *args, **kwds):
+            den = 1 + t
+            return d_g(b + t / den, *args, **kwds) / den ** 2
+        return f_m10, g_m10, d_g_m10, -1.0, 0.0
+
+    @staticmethod
+    def _change_interval_to_m1_1(f, g, d_g, _a, _b):
+        def f_m11(t, *args, **kwds):
+            den = (1 - t**2)
+            return f(t / den, *args, **kwds) * (1 + t**2) / den ** 2
+
+        def g_m11(t, *args, **kwds):
+            den = (1 - t**2)
+            return g(t / den, *args, **kwds)
+
+        def d_g_m11(t, *args, **kwds):
+            den = (1 - t**2)
+            return d_g(t / den, *args, **kwds) * (1 + t**2) / den ** 2
+        return f_m11, g_m11, d_g_m11, -1., 1.
+
+    def _get_functions(self):
+        a, b = self.a, self.b
+        reverse = np.real(a) > np.real(b)
+        if reverse:
+            a, b = b, a
+        f, g, dg = self.f, self.g, self.dg
+
+        if a == b:
+            pass
+        elif np.isinf(a) | np.isinf(b):
+            # Check real limits
+            if ~np.isreal(a) | ~np.isreal(b) | np.isnan(a) | np.isnan(b):
+                raise ValueError('Infinite intervals must be real.')
+            # Change of variable
+            if np.isfinite(a) & np.isinf(b):
+                f, g, dg, a, b = self._change_interval_to_0_1(f, g, dg, a, b)
+            elif np.isinf(a) & np.isfinite(b):
+                f, g, dg, a, b = self._change_interval_to_m1_0(f, g, dg, a, b)
+            else:  # -inf to inf
+                f, g, dg, a, b = self._change_interval_to_m1_1(f, g, dg, a, b)
+
+        return f, g, dg, a, b, reverse
+
+    def __call__(self, omega, *args, **kwds):
+        f, g, dg, a, b, reverse = self._get_functions()
+
+        val, err = self._quad_osc(f, g, dg, a, b, omega, *args, **kwds)
+
+        if reverse:
+            val = -val
+        if self.full_output:
+            return val, err
+        return val
+
+    @staticmethod
+    def _get_best_estimate(k, q_0, q_1, q_2):
+        if k >= 5:
+            q_v = np.hstack((q_0[k], q_1[k], q_2[k]))
+            q_w = np.hstack((q_0[k - 1], q_1[k - 1], q_2[k - 1]))
+        elif k >= 3:
+            q_v = np.hstack((q_0[k], q_1[k]))
+            q_w = np.hstack((q_0[k - 1], q_1[k - 1]))
+        else:
+            q_v = np.atleast_1d(q_0[k])
+            q_w = q_0[k - 1]
+        errors = np.atleast_1d(abs(q_v - q_w))
+        j = np.nanargmin(errors)
+        return q_v[j], errors[j]
+
+    def _extrapolate(self, k, q_0, q_1, q_2):
+        if k >= 4:
+            q_1[k] = dea3(q_0[k - 2], q_0[k - 1], q_0[k])[0]
+            q_2[k] = dea3(q_1[k - 2], q_1[k - 1], q_1[k])[0]
+        elif k >= 2:
+            q_1[k] = dea3(q_0[k - 2], q_0[k - 1], q_0[k])[0]
+        #         # Richardson extrapolation
+        #         if k >= 4:
+        #             q_1[k] = richardson(q_0, k)
+        #             q_2[k] = richardson(q_1, k)
+        #         elif k >= 2:
+        #             q_1[k] = richardson(q_0, k)
+        q, err = self._get_best_estimate(k, q_0, q_1, q_2)
+        return q, err
+
+    def _quad_osc(self, f, g, dg, a, b, omega, *args, **kwds):
+        if a == b:
+            q_val = b - a
+            err = np.abs(b - a)
+            return q_val, err
+
+        abseps = 10**-self.precision
+        max_iter = self.maxiter
+        basis = self.basis
+        if self.endpoints:
+            x_n = chebyshev_extrema(self.s)
+        else:
+            x_n = chebyshev_roots(self.s)
+            # x_n = tanh_sinh_open_nodes(self.s)
+
+        # One interval
+        hh = (b - a) / 2
+        x = (a + b) / 2 + hh * x_n      # Nodes
+
+        dtype = complex
+        val0 = np.zeros((max_iter, 1), dtype=dtype)  # Quadrature
+        val1 = np.zeros((max_iter, 1), dtype=dtype)  # First extrapolation
+        val2 = np.zeros((max_iter, 1), dtype=dtype)  # Second extrapolation
+
+        lim_f = Limit(f)
+        a_b = np.hstack([a, b])
+        wq = osc_weights(omega, g, dg, x_n, basis, a_b, *args, **kwds)
+        val0[0] = hh * np.sum(wq * lim_f(x, *args, **kwds))
+
+        # Successive bisection of intervals
+        nq = len(x_n)
+        n = nq
+        for k in range(1, max_iter):
+            n += nq * 2**k
+
+            hh = hh / 2
+            x = np.hstack([x + a, x + b]) / 2
+            a_b = np.hstack([a_b + a, a_b + b]) / 2
+            wq = osc_weights(omega, g, dg, x_n, basis, a_b, *args, **kwds)
+
+            val0[k] = hh * np.sum(wq * lim_f(x, *args, **kwds))
+
+            q_val, err = self._extrapolate(k, val0, val1, val2)
+
+            converged = (err <= abseps) | ~np.isfinite(q_val)
+            if converged:
+                break
+        _assert_warn(converged, 'Max number of iterations reached '
+                     'without convergence.')
+        _assert_warn(np.isfinite(q_val),
+                     'Integral approximation is Infinite or NaN.')
+
+        # The error estimate should not be zero
+        err += 2 * np.finfo(q_val).eps
+        return q_val, self.info(err, n)
+
+
+def adaptive_levin_points(m, delta):
+    m_1 = m - 1
+    prm = 0.5
+    while prm * m_1 / delta >= 1:
+        delta = 2 * delta
+    k = np.arange(m)
+    x = piecewise([k < prm * m_1, k == np.ceil(prm * m_1)],
+                  [-1 + k / delta, 0 * k, 1 - (m_1 - k) / delta])
+    return x
+
+
+def open_levin_points(m, delta):
+    return adaptive_levin_points(m + 2, delta)[1:-1]
+
+
+def chebyshev_extrema(m, delta=None):
+    k = np.arange(m)
+    x = np.cos(k * np.pi / (m - 1))
+    return x
+
+
+def tanh_sinh_nodes(m, delta=None, tol=_EPS):
+    tmax = np.arcsinh(np.arctanh(1 - _EPS) * 2 / np.pi)
+    # tmax = 3.18
+    m_1 = int(np.floor(-np.log2(tmax / max(m - 1, 1)))) - 1
+    h = 2.0**-m_1
+    t = np.arange((m + 1) // 2 + 1) * h
+    x = np.tanh(np.pi / 2 * np.sinh(t))
+    k = np.flatnonzero(np.abs(x - 1) <= 10 * tol)
+    y = x[:k[0] + 1] if len(k) else x
+    return np.hstack((-y[:0:-1], y))
+
+
+def tanh_sinh_open_nodes(m, delta=None, tol=_EPS):
+    return tanh_sinh_nodes(m + 1, delta, tol)[1:-1]
+
+
+def chebyshev_roots(m, delta=None):
+    k = np.arange(1, 2 * m, 2) * 0.5
+    x = np.cos(k * np.pi / m)
+    return x
+
+
+class AdaptiveLevin(_Integrator):
+    """Return integral for the Levin-type and adaptive Levin-type methods"""
+
+    @staticmethod
+    def _a_levin(omega, f, g, d_g, x, s, basis, *args, **kwds):
+
+        def psi(t, k):
+            return d_g(t, *args, **kwds) * basis(t, k)
+
+        j_w = 1j * omega
+        nu = np.ones((len(x),), dtype=int)
+        nu[0] = nu[-1] = s
+        S = np.cumsum(np.hstack((nu, 0)))
+        S[-1] = 0
+        n = int(S[-2])
+        a_matrix = np.zeros((n, n), dtype=complex)
+        rhs = np.zeros((n,))
+        dff = Limit(nda.Derivative(f))
+        d_psi = Limit(nda.Derivative(psi))
+        dbasis = basis.derivative
+        for r, t in enumerate(x):
+            for j in range(S[r - 1], S[r]):
+                order = ((j - S[r - 1]) % nu[r])  # derivative order
+                dff.fun.n = order
+                rhs[j] = dff(t, *args, **kwds)
+                d_psi.fun.n = order
+                for k in range(n):
+                    a_matrix[j, k] = (dbasis(t, k, n=order + 1) +
+                                      j_w * d_psi(t, k))
+        k1 = np.flatnonzero(1 - np.isfinite(rhs))
+        if k1.size > 0:  # Remove singularities
+            warnings.warn('Singularities detected! ')
+            a_matrix[k1] = 0
+            rhs[k1] = 0
+        solution = linalg.lstsq(a_matrix, rhs)
+        v = basis.eval([-1, 1], solution[0])
+
+        lim_g = Limit(g)
+        g_b = np.exp(j_w * lim_g(1, *args, **kwds))
+        if np.isnan(g_b):
+            g_b = 0
+        g_a = np.exp(j_w * lim_g(-1, *args, **kwds))
+        if np.isnan(g_a):
+            g_a = 0
+        return v[1] * g_b - v[0] * g_a
+
+    def _get_integration_limits(self, omega, args, kwds):
+        a, b = self.a, self.b
+        M = 30
+        ab = [a]
+        scale = (b - a) / 2
+        n = 30
+        x = np.linspace(a, b, n + 1)
+        dg_x = np.asarray([scale * omega * self.dg(xi, *args, **kwds)
+                           for xi in x])
+        i10 = findcross(dg_x, M)
+        i1 = findcross(dg_x, 1)
+        i0 = findcross(dg_x, 0)
+        im1 = findcross(dg_x, -1)
+        im10 = findcross(dg_x, -M)
+        x10 = ecross(x, dg_x, i10, M) if len(i10) else ()
+        x1 = ecross(x, dg_x, i1, 1) if len(i1) else ()
+        x0 = ecross(x, dg_x, i0, 0) if len(i0) else ()
+        xm1 = ecross(x, dg_x, im1, -1) if len(im1) else ()
+        xm10 = ecross(x, dg_x, im10, -M) if len(im10) else ()
+
+        for i in np.unique(np.hstack((x10, x1, x0, xm1, xm10))):
+            if x[0] < i < x[n]:
+                ab.append(i)
+        ab.append(b)
+        return ab
+
+    def __call__(self, omega, *args, **kwds):
+        ab = self._get_integration_limits(omega, args, kwds)
+        s = self.s
+        val = 0
+        n = 0
+        err = 0
+        for ai, bi in zip(ab[:-1], ab[1:]):
+            vali, infoi = self._QaL(s, ai, bi, omega, *args, **kwds)
+            val += vali
+            err += infoi.error_estimate
+            n += infoi.n
+        if self.full_output:
+            info = self.info(err, n)
+            return val, info
+        return val
+
+    @staticmethod
+    def _get_num_points(s, prec, betam):
+        return 1 if s > 1 else int(prec / max(np.log10(betam + 1), 1) + 1)
+
+    def _QaL(self, s, a, b, omega, *args, **kwds):
+        """if s>1,the integral is computed by Q_s^L"""
+        scale = (b - a) / 2
+        offset = (a + b) / 2
+        prec = self.precision  # desired precision
+
+        def ff(t, *args, **kwds):
+            return scale * self.f(scale * t + offset, *args, **kwds)
+
+        def gg(t, *args, **kwds):
+            return self.g(scale * t + offset, *args, **kwds)
+
+        def dgg(t, *args, **kwds):
+            return scale * self.dg(scale * t + offset, *args, **kwds)
+        dg_a = abs(omega * dgg(-1, *args, **kwds))
+        dg_b = abs(omega * dgg(1, *args, **kwds))
+        g_a = abs(omega * gg(-1, *args, **kwds))
+        g_b = abs(omega * gg(1, *args, **kwds))
+        delta, alpha = min(dg_a, dg_b), min(g_a, g_b)
+
+        betam = delta   # * scale
+        if self.endpoints:
+            if delta < 10 or alpha <= 10 or s > 1:
+                points = chebyshev_extrema
+            else:
+                points = adaptive_levin_points
+        elif delta < 10 or alpha <= 10 or s > 1:
+            points = chebyshev_roots
+        else:
+            points = open_levin_points  # tanh_sinh_open_nodes
+
+        m = self._get_num_points(s, prec, betam)
+        abseps = 10 * 10.0**-prec
+        num_collocation_point_list = m * 2**np.arange(1, 5) + 1
+        basis = self.basis
+
+        q_val = 1e+300
+        num_function_evaluations = 0
+        n = 0
+        for num_collocation_points in num_collocation_point_list:
+            n_old = n
+            q_old = q_val
+            x = points(num_collocation_points, betam)
+            n = len(x)
+            if n > n_old:
+                q_val = self._a_levin(omega, ff, gg, dgg, x, s, basis, *args,
+                                      **kwds)
+                num_function_evaluations += n
+                err = np.abs(q_val - q_old)
+                if err <= abseps:
+                    break
+        info = self.info(err, num_function_evaluations)
+        return q_val, info
+
+
+class EvansWebster(AdaptiveLevin):
+    """Return integral for the Evans Webster method"""
+
+    def __init__(self, f, g, dg=None, a=-1, b=1, basis=chebyshev_basis, s=8,
+                 precision=10, endpoints=False, full_output=False):
+        super(EvansWebster,
+              self).__init__(f, g, dg=dg, a=a, b=b, basis=basis, s=s,
+                             precision=precision, endpoints=endpoints,
+                             full_output=full_output)
+
+    def _a_levin(self, omega, ff, gg, dgg, x, s, basis, *args, **kwds):
+        w = evans_webster_weights(omega, gg, dgg, x, basis, *args, **kwds)
+
+        f = Limit(ff)(x, *args, **kwds)
+        return np.sum(f * w)
+
+    def _get_num_points(self, s, prec, betam):
+        return 8 if s > 1 else int(prec / max(np.log10(betam + 1), 1) + 1)
+
+
+if __name__ == '__main__':
+    tanh_sinh_nodes(16)

wafo/kdetools/demo.py

@@ -9,10 +9,10 @@ import numpy as np
 import warnings
 from wafo.plotbackend import plotbackend as plt
 from wafo.kdetools import Kernel, TKDE, KDE, KRegression, BKRegression
-# try:
+try:
-#     from wafo import fig
+    from wafo import fig
-# except ImportError:
+except ImportError:
-#     warnings.warn('fig import only supported on Windows')
+    warnings.warn('fig import only supported on Windows')
 
 __all__ = ['kde_demo1', 'kde_demo2', 'kde_demo3', 'kde_demo4', 'kde_demo5',
            'kreg_demo1', ]

wafo/misc.py

@@ -19,11 +19,11 @@ import warnings
 from time import strftime, gmtime
 from wafo.plotbackend import plotbackend as plt
 import numbers
-# try:
+try:
-#     from wafo import c_library as clib  # @UnresolvedImport
+    from wafo import c_library as clib  # @UnresolvedImport
-# except ImportError:
+except ImportError:
-#     warnings.warn('c_library not found. Check its compilation.')
+    warnings.warn('c_library not found. Check its compilation.')
-#     clib = None
+    clib = None
 FLOATINFO = np.finfo(float)
 _TINY = FLOATINFO.tiny
 _EPS = FLOATINFO.eps

wafo/numba_misc.py

@@ -441,7 +441,7 @@ def disufq(rA, iA, w, kw, h, g, nmin, nmax, m, n):
     return rvec, ivec
 
 
-# @jit(int32[:](float64[:], float64[:], float64[:, :]))
+@jit(int32[:](float64[:], float64[:], float64[:, :]))
 def _findrfc3_astm(array_ext, a, array_out):
     """
     Rain flow without time analysis
@@ -489,7 +489,7 @@ def _findrfc3_astm(array_ext, a, array_out):
     return c_nr1, c_nr2
 
 
-# @jit(int32[:](float64[:], float64[:], float64[:], float64[:], float64[:, :]))
+@jit(int32[:](float64[:], float64[:], float64[:], float64[:], float64[:, :]))
 def _findrfc5_astm(array_ext, array_t, a, t, array_out):
     """
     Rain flow with time analysis

wafo/objects.py

@@ -13,15 +13,15 @@
 
 
 from __future__ import absolute_import, division
-# from wafo.transform.core import TrData
+from wafo.transform.core import TrData
-# from wafo.transform.estimation import TransformEstimator
+from wafo.transform.estimation import TransformEstimator
-# from wafo.stats import distributions
+from wafo.stats import distributions
 from wafo.misc import (nextpow2, findtp, findrfc, findtc, findcross,
                        ecross, JITImport, DotDict, gravity, findrfc_astm,
                        detrendma)
-# from wafo.interpolate import stineman_interp
+from wafo.interpolate import stineman_interp
 from wafo.containers import PlotData
-# from wafo.plotbackend import plotbackend as plt
+from wafo.plotbackend import plotbackend as plt
 from scipy.integrate import trapz
 from scipy.signal import welch, lfilter
 from scipy.signal.windows import get_window  # @UnusedImport

wafo/padua.py

@@ -0,0 +1,532 @@
+'''
+
+All the software  contained in this library  is protected by copyright.
+Permission  to use, copy, modify, and  distribute this software for any
+purpose without fee is hereby granted, provided that this entire notice
+is included  in all copies  of any software which is or includes a copy
+or modification  of this software  and in all copies  of the supporting
+documentation for such software.
+
+THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+WARRANTY. IN NO EVENT, NEITHER  THE AUTHORS, NOR THE PUBLISHER, NOR ANY
+MEMBER  OF THE EDITORIAL BOARD OF  THE JOURNAL  "NUMERICAL ALGORITHMS",
+NOR ITS EDITOR-IN-CHIEF, BE  LIABLE FOR ANY ERROR  IN THE SOFTWARE, ANY
+MISUSE  OF IT  OR ANY DAMAGE ARISING OUT OF ITS USE. THE ENTIRE RISK OF
+USING THE SOFTWARE LIES WITH THE PARTY DOING SO.
+
+ANY USE OF THE SOFTWARE  CONSTITUTES  ACCEPTANCE  OF THE TERMS  OF THE
+ABOVE STATEMENT.
+
+
+AUTHORS:
+Per A Brodtkorb
+Python code Based on matlab code written by:
+
+Marco Caliari
+University of Verona, Italy
+E-mail: marco.caliari@univr.it
+
+Stefano de Marchi, Alvise Sommariva, Marco Vianello
+University of Padua, Italy
+E-mail: demarchi@math.unipd.it, alvise@math.unipd.it,
+        marcov@math.unipd.it
+
+Reference
+---------
+Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
+NUMERICAL ALGORITHMS, 56 (2011), PP. 45-60
+
+
+Padua module
+------------
+In polynomial interpolation of two variables, the Padua points are the first
+known example (and up to now the only one) of a unisolvent point set
+(that is, the interpolating polynomial is unique) with minimal growth of their
+Lebesgue constant, proven to be O(log2 n).
+This module provides all the functions needed to perform interpolation and
+cubature at the Padua points, together with the functions and the demos used
+in the paper.
+
+pdint.m                 : main function for interpolation at the Padua points
+pdcub.m                 : main function for cubature at the Padua points
+pdpts.m                 : function for the computation of the Padua points
+padua_fit.m              : function for the computation of the interpolation
+                          coefficients by FFT (recommended)
+pdcfsMM.m               : function for the computation of the interpolation
+                          coefficients by matrix multiplications
+pdval.m                 : function for the evaluation of the interpolation
+                          polynomial
+pdwtsFFT.m              : function for the computation of the cubature
+                          weights by FFT
+pdwtsMM.m               : function for the computation of the cubature
+                          weights by matrix multiplications (recommended)
+funct.m                 : function containing some test functions
+demo_pdint.m            : demo script for pdint
+demo_cputime_pdint.m    : demo script for the computation of CPU time for
+                          interpolation
+demo_errors_pdint.m     : demo script for the comparison of interpolation with
+                          coefficients computed by FFT or by matrix
+                          multiplications
+demo_pdcub              : demo script for pdcub
+demo_cputime_pdcub.m    : demo script for the computation of CPU time for
+                          cubature
+demo_errors_pdcub.m     : demo script for the comparison of cubature with
+                          weights computed by FFT or by matrix multiplications
+demo_errors_pdcub_gl.m  : demo script for the comparison of different cubature
+                          formulas
+cubature_square.m       : function for the computation of some cubature
+                          formulas for the square
+omelyan_solovyan_rule.m : function for the computation of Omelyan-Solovyan
+                          cubature points and weights
+Contents.m              : Contents file for Matlab
+
+
+'''
+from __future__ import absolute_import, division
+import numpy as np
+from numpy.fft import fft
+from wafo.dctpack import dct
+from wafo.polynomial import map_from_interval, map_to_interval
+# from scipy.fftpack.realtransforms import dct
+
+
+class _ExampleFunctions(object):
+    '''
+    Computes test function in the points (x, y)
+
+    Parameters
+    ----------
+    x,y : array-like
+        evaluate the function in the points (x,y)
+    i : scalar int (default 0)
+        defining which test function to use. Options are
+        0: franke
+        1: half_sphere
+        2: poly_degree20
+        3: exp_fun1
+        4: exp_fun100
+        5: cos30
+        6: constant
+        7: exp_xy
+        8: runge
+        9: abs_cubed
+        10: gauss
+        11: exp_inv
+
+    Returns
+    -------
+    z : array-like
+        value of the function in the points (x,y)
+    '''
+    @staticmethod
+    def franke(x, y):
+        '''Franke function.
+
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500, is
+        2.1547794245591083e+000 with an estimated absolute error of 8.88e-016.
+
+        The value of the definite integral on the square [0,1] x [0,1],
+        obtained using a Padua Points cubature formula of degree 500, is
+        4.06969589491556e-01 with an estimated absolute error of 8.88e-016.
+
+        Maple: 0.40696958949155611906
+        '''
+        def _exp(x, y, loc, scale, p2=2):
+            return np.exp(- (x - loc[0])**2 / scale[0] - (y - loc[1])**p2 / scale[1])
+        # exp = np.exp
+        x9, y9 = 9. * x, 9. * y
+        return (3. / 4 * _exp(x9, y9, [2, 2], [4, 4]) +
+                3. / 4 * _exp(x9, y9, [-1, -1], [49, 10], p2=1) +
+                1. / 2 * _exp(x9, y9, [7, 3], [4, 4]) -
+                1. / 5 * _exp(x9, y9, [4, 7], [1, 1]))
+
+    @staticmethod
+    def half_sphere(x, y):
+        '''The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 2000, is
+        3.9129044444568244e+000 with an estimated absolute error of 3.22e-010.
+        '''
+        return ((x - 0.5)**2 + (y - 0.5)**2)**(1. / 2)
+
+    @staticmethod
+    def poly_degree20(x, y):
+        ''''Bivariate polynomial having moderate degree.
+        The value of the definite integral on the square [-1,1] x
+        [-1,1], up to machine precision, is 18157.16017316017 (see ref. 6).
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500,
+        is 1.8157160173160162e+004.
+
+        2D modification of an example by L.N.Trefethen (see ref. 7), f(x)=x^20.
+        '''
+        return (x + y)**20
+
+    @staticmethod
+    def exp_fun1(x, y):
+        ''' The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 2000,
+        is 2.1234596326670683e+001 with an estimated absolute error of
+        7.11e-015.
+        '''
+        return np.exp((x - 0.5)**2 + (y - 0.5)**2)
+
+    @staticmethod
+    def exp_fun100(x, y):
+        '''The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 2000,
+        is 3.1415926535849605e-002 with an estimated absolute error of
+        3.47e-017.
+        '''
+        return np.exp(-100 * ((x - 0.5)**2 + (y - 0.5)**2))
+
+    @staticmethod
+    def cos30(x, y):
+        ''' The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500,
+        is 4.3386955120336568e-003 with an estimated absolute error of
+        2.95e-017.
+        '''
+        return np.cos(30 * (x + y))
+
+    @staticmethod
+    def constant(x, y):
+        '''Constant.
+        To test interpolation and cubature at degree 0.
+        The value of the definite integral on the square [-1,1] x [-1,1]
+        is 4.
+        '''
+        return np.ones(np.shape(x + y))
+
+    @staticmethod
+    def exp_xy(x, y):
+        '''The value of the definite integral on the square [-1,1] x [-1,1]
+        is up to machine precision is 5.524391382167263 (see ref. 6).
+        2. The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500,
+        is 5.5243913821672628e+000 with an estimated absolute error of
+        0.00e+000.
+        2D modification of an example by L.N.Trefethen (see ref. 7),
+        f(x)=exp(x).
+        '''
+        return np.exp(x + y)
+
+    @staticmethod
+    def runge(x, y):
+        ''' Bivariate Runge function: as 1D complex function is analytic
+        in a neighborhood of [-1; 1] but not throughout the complex plane.
+
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        up to machine precision, is 0.597388947274307 (see ref. 6).
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500,
+        is 5.9738894727430725e-001 with an estimated absolute error of
+        0.00e+000.
+
+        2D modification of an example by L.N.Trefethen (see ref. 7),
+        f(x)=1/(1+16*x^2).
+        '''
+        return 1. / (1 + 16 * (x**2 + y**2))
+
+    @staticmethod
+    def abs_cubed(x, y):
+        '''Low regular function.
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        up to machine precision, is 2.508723139534059 (see ref. 6).
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500,
+        is 2.5087231395340579e+000 with an estimated absolute error of
+        0.00e+000.
+
+        2D modification of an example by L.N.Trefethen (see ref. 7),
+        f(x)=abs(x)^3.
+        '''
+        return (x**2 + y**2)**(3 / 2)
+
+    @staticmethod
+    def gauss(x, y):
+        '''Bivariate gaussian: smooth function.
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        up to machine precision, is 2.230985141404135 (see ref. 6).
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 500,
+        is 2.2309851414041333e+000 with an estimated absolute error of
+        2.66e-015.
+
+        2D modification of an example by L.N.Trefethen (see ref. 7),
+        f(x)=exp(-x^2).
+        '''
+        return np.exp(-x**2 - y**2)
+
+    @staticmethod
+    def exp_inv(x, y):
+        '''Bivariate example stemming from a 1D C-infinity function.
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        up to machine precision, is 0.853358758654305 (see ref. 6).
+        The value of the definite integral on the square [-1,1] x [-1,1],
+        obtained using a Padua Points cubature formula of degree 2000,
+        is 8.5335875865430544e-001 with an estimated absolute error of
+        3.11e-015.
+
+        2D modification of an example by L.N.Trefethen (see ref. 7),
+        f(x)=exp(-1/x^2).
+        '''
+        arg_z = (x**2 + y**2)
+        # Avoid cases in which "arg_z=0", setting only in those instances
+        # "arg_z=eps".
+        arg_z = arg_z + (1 - np.abs(np.sign(arg_z))) * 1.e-100
+        arg_z = 1. / arg_z
+        return np.exp(-arg_z)
+
+    def __call__(self, x, y, i=0):
+        s = self
+        test_function = [s.franke, s.half_sphere, s.poly_degree20, s.exp_fun1,
+                         s.exp_fun100, s.cos30, s.constant, s.exp_xy, s.runge,
+                         s.abs_cubed, s.gauss, s.exp_inv]
+        return test_function[i](x, y)
+
+
+example_functions = _ExampleFunctions()
+
+
+def _find_m(n):
+    ix = np.r_[1:(n + 1) * (n + 2):2]
+    if np.mod(n, 2) == 0:
+        n2 = n // 2
+        offset = np.array([[0, 1] * n2 + [0, ]] * (n2 + 1))
+        ix = ix - offset.ravel(order='F')
+    return ix
+
+
+def padua_points(n, domain=(-1, 1, -1, 1)):
+    ''' Return Padua points
+
+    Parameters
+    ----------
+    n : scalar integer
+         interpolation degree
+    domain : vector [a,b,c,d]
+        defining the rectangle [a,b] x [c,d]. (default domain = (-1,1,-1,1))
+
+    Returns
+    -------
+    pad : array of shape (2 x (n+1)*(n+2)/2) such that
+        (pad[0,:], pad[1,: ]) defines the Padua points in the domain
+        rectangle [a,b] x [c,d].
+    or
+     X1,Y1,X2,Y2 : arrays
+         Two subgrids X1,Y1 and X2,Y2 defining the Padua points
+    -------------------------------------------------------------------------------
+    '''
+    a, b, c, d = domain
+    t0 = [np.pi] if n == 0 else np.linspace(0, np.pi, n + 1)
+    t1 = np.linspace(0, np.pi, n + 2)
+    zn = map_to_interval(np.cos(t0), a, b)
+    zn1 = map_to_interval(np.cos(t1), c, d)
+
+    Pad1, Pad2 = np.meshgrid(zn, zn1)
+    ix = _find_m(n)
+    return np.vstack((Pad1.ravel(order='F')[ix],
+                      Pad2.ravel(order='F')[ix]))
+
+
+def error_estimate(C0f):
+    ''' Return interpolation error estimate from Padua coefficients
+    '''
+    n = C0f.shape[1]
+    C0f2 = np.fliplr(C0f)
+    errest = sum(np.abs(np.diag(C0f2)))
+    if (n >= 1):
+        errest = errest + sum(np.abs(np.diag(C0f2, -1)))
+        if (n >= 2):
+            errest = errest + sum(np.abs(np.diag(C0f2, -2)))
+    return 2 * errest
+
+
+def padua_fit(Pad, fun, *args):
+    '''
+    Computes the Chebyshevs coefficients
+
+    so that f(x, y) can be approximated by:
+
+           f(x, y) = sum cjk*Tjk(x, y)
+
+    Parameters
+    ----------
+    Pad : array-like
+        Padua points, as computed  with padua_points function.
+    fun : function to be interpolated in the form
+        fun(x, y, *args), where *args are optional arguments for fun.
+
+    Returns
+    -------
+    coefficents: coefficient matrix
+    abs_err   : interpolation error estimate
+
+    Example
+    ------
+    >>> import numpy as np
+    >>> import wafo.padua as wp
+    >>> domain = [0, 1, 0, 1]
+    >>> a, b, c, d = domain
+    >>> points = wp.padua_points(21, domain)
+    >>> C0f, abs_error = wp.padua_fit(points, wp.example_functions.franke)
+    >>> x1 = np.linspace(a, b, 100)
+    >>> x2 = np.linspace(c, d, 101)
+    >>> val = wp.padua_val(x1, x2, C0f, domain, use_meshgrid=True)
+    >>> X1, X2 = np.meshgrid(x1, x2)
+    >>> true_val = wp.example_functions.franke(X1, X2)
+
+    >>> np.allclose(val, true_val, atol=10*abs_error)
+    True
+    >>> np.allclose(np.abs(val-true_val).max(), 0.0073174614275738296)
+    True
+    >>> np.allclose(abs_error, 0.0022486904061664046)
+    True
+
+    import matplotlib.pyplot as  plt
+    plt.contour(x1, x2, val)
+
+    '''
+
+    N = np.shape(Pad)[1]
+    # recover the degree n from N = (n+1)(n+2)/2
+    n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2)
+    C0f = fun(Pad[0], Pad[1], *args)
+    if (n > 0):
+        ix = _find_m(n)
+        GfT = np.zeros((n + 2) * (n + 1))
+        GfT[ix] = C0f * 2 / (n * (n + 1))
+        GfT = GfT.reshape(n + 1, n + 2)
+        GfT = GfT.T
+        GfT[0] = GfT[0] / 2
+        GfT[n + 1] = GfT[n + 1] / 2
+        GfT[:, 0] = GfT[:, 0] / 2
+        GfT[:, n] = GfT[:, n] / 2
+        Gf = GfT.T
+        # compute the interpolation coefficient matrix C0f by FFT
+        Gfhat = np.real(fft(Gf, 2 * n, axis=0))
+        Gfhathat = np.real(fft(Gfhat[:n + 1, :], 2 * (n + 1), axis=1))
+        C0f = 2 * Gfhathat[:, 0:n + 1]
+        C0f[0] = C0f[0, :] / np.sqrt(2)
+        C0f[:, 0] = C0f[:, 0] / np.sqrt(2)
+        C0f = np.fliplr(np.triu(np.fliplr(C0f)))
+        C0f[n] = C0f[n] / 2
+
+    return C0f, error_estimate(C0f)
+
+
+def paduavals2coefs(f):
+    m = len(f)
+    n = int(round(-1.5 + np.sqrt(.25 + 2 * m)))
+    x = padua_points(n)
+    idx = _find_m(n)
+    w = 0 * x[0] + 1. / (n * (n + 1))
+    idx1 = np.all(np.abs(x) == 1, axis=0)
+    w[idx1] = .5 * w[idx1]
+    idx2 = np.all(np.abs(x) != 1, axis=0)
+    w[idx2] = 2 * w[idx2]
+
+    G = np.zeros(idx.max() + 1)
+    G[idx] = 4 * w * f
+
+    use_dct = 100 < n
+    if use_dct:
+        C = np.rot90(dct(dct(G.T).T))  # , axis=1)
+    else:
+        t1 = np.r_[0:n + 1].reshape(-1, 1)
+        Tn1 = np.cos(t1 * t1.T * np.pi / n)
+        t2 = np.r_[0:n + 2].reshape(-1, 1)
+        Tn2 = np.cos(t2 * t2.T * np.pi / (n + 1))
+        C = np.dot(Tn2, np.dot(G, Tn1))
+
+    C[0] = .5 * C[0]
+    C[:, 1] = .5 * C[:, 1]
+    C[0, -1] = .5 * C[0, -1]
+    del C[-1]
+
+    # Take upper-left triangular part:
+    return np.fliplr(np.triu(np.fliplr(C)))
+    # C = triu(C(:,end:-1:1));
+    # C = C(:,end:-1:1);
+
+
+# TODO: padua_fit2 does not work correctly yet.
+def padua_fit2(Pad, fun, *args):
+    # N = np.shape(Pad)[1]
+    # recover the degree n from N = (n+1)(n+2)/2
+    # _n = int(round(-3 + np.sqrt(1 + 8 * N)) / 2)
+    C0f = fun(Pad[0], Pad[1], *args)
+    return paduavals2coefs(C0f)
+
+
+def _compute_moments(n):
+    k = np.r_[0:n:2]
+    mom = 2 * np.sqrt(2) / (1 - k ** 2)
+    mom[0] = 2
+    return mom
+
+
+def padua_cubature(coefficients, domain=(-1, 1, -1, 1)):
+    '''
+    Compute the integral through the coefficient matrix.
+    '''
+    n = coefficients.shape[1]
+    mom = _compute_moments(n)
+    M1, M2 = np.meshgrid(mom, mom)
+    M = M1 * M2
+    C0fM = coefficients[0:n:2, 0:n:2] * M
+    a, b, c, d = domain
+    integral = (b - a) * (d - c) * C0fM.sum() / 4
+    return integral
+
+
+def padua_val(X, Y, coefficients, domain=(-1, 1, -1, 1), use_meshgrid=False):
+    '''
+    Evaluate polynomial in padua form at X, Y.
+
+     Evaluate the interpolation polynomial defined through its coefficient
+     matrix coefficients at the target points X(:,1),X(:,2) or at the
+     meshgrid(X1,X2)
+
+    Parameters
+    ----------
+    X, Y: array-like
+        evaluation points.
+    coefficients : array-like
+         coefficient matrix
+    domain : a vector [a,b,c,d]
+         defining the rectangle [a,b] x [c,d]
+    use_meshgrid: bool
+        If True interpolate at the points meshgrid(X, Y)
+
+    Returns
+    -------
+     fxy : array-like
+         evaluation of the interpolation polynomial at the target points
+    '''
+    def transform(tn, x, a, b):
+        xn = map_from_interval(x, a, b).clip(min=-1, max=1).reshape(1, -1)
+        tx = np.cos(tn * np.arccos(xn)) * np.sqrt(2)
+        tx[0] = 1
+        return tx
+
+    X, Y = np.atleast_1d(X, Y)
+    original_shape = X.shape
+    a, b, c, d = domain
+    n = np.shape(coefficients)[1]
+
+    tn = np.r_[0:n][:, None]
+    tx1 = transform(tn, X.ravel(), a, b)
+    tx2 = transform(tn, Y.ravel(), c, d)
+
+    if use_meshgrid:  # eval on meshgrid points
+        return np.dot(tx1.T, np.dot(coefficients, tx2)).T
+    # scattered points
+    val = np.sum(np.dot(tx1.T, coefficients) * tx2.T, axis=1)
+    return val.reshape(original_shape)
+
+
+if __name__ == '__main__':
+    from wafo.testing import test_docstrings
+    test_docstrings(__file__)

wafo/setup.py

@@ -0,0 +1,18 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Sun Oct 25 14:55:34 2015
+
+@author: dave
+"""
+
+
+def configuration(parent_package='', top_path=None):
+    from numpy.distutils.misc_util import Configuration
+    config = Configuration('wafo', parent_package, top_path)
+    config.add_subpackage('source')
+    config.make_config_py()
+    return config
+
+if __name__ == "__main__":
+    from numpy.distutils.core import setup
+    setup(**configuration(top_path='').todict())

wafo/sg_filter/__init__.py

@@ -0,0 +1,2 @@
+from wafo.sg_filter._core import *  # pylint: disable=wildcard-import
+from wafo.sg_filter import demos

wafo/sg_filter/demos.py

@@ -0,0 +1,488 @@
+import numpy as np
+from scipy.sparse.linalg import expm
+from scipy.signal import medfilt
+from wafo.plotbackend import plotbackend as plt
+from wafo.sg_filter._core import (SavitzkyGolay, smoothn, Kalman,
+                                  HodrickPrescott, HampelFilter)
+
+
+def demo_savitzky_on_noisy_chirp():
+    """
+    Example
+    -------
+    >>> demo_savitzky_on_noisy_chirp()
+
+    >>> plt.close()
+    """
+    plt.figure(figsize=(7, 12))
+
+    # generate chirp signal
+    tvec = np.arange(0, 6.28, .02)
+    true_signal = np.sin(tvec * (2.0 + tvec))
+    true_d_signal = (2 + tvec) * np.cos(tvec * (2.0 + tvec))
+
+    # add noise to signal
+    noise = np.random.normal(size=true_signal.shape)
+    signal = true_signal + .15 * noise
+
+    # plot signal
+    plt.subplot(311)
+    plt.plot(signal)
+    plt.title('signal')
+
+    # smooth and plot signal
+    plt.subplot(312)
+    savgol = SavitzkyGolay(n=8, degree=4)
+    s_signal = savgol.smooth(signal)
+    s2 = smoothn(signal, robust=True)
+    plt.plot(s_signal)
+    plt.plot(s2)
+    plt.plot(true_signal, 'r--')
+    plt.title('smoothed signal')
+
+    # smooth derivative of signal and plot it
+    plt.subplot(313)
+    savgol1 = SavitzkyGolay(n=8, degree=1, diff_order=1)
+
+    dt = tvec[1] - tvec[0]
+    d_signal = savgol1.smooth(signal) / dt
+
+    plt.plot(d_signal)
+    plt.plot(true_d_signal, 'r--')
+    plt.title('smoothed derivative of signal')
+
+
+def demo_kalman_voltimeter():
+    """
+    Example
+    -------
+    >>> demo_kalman_voltimeter()
+
+    >>> plt.close()
+    """
+    V0 = 12
+    h = np.atleast_2d(1)  # voltimeter measure the voltage itself
+    q = 1e-9  # variance of process noise as the car operates
+    r = 0.05 ** 2  # variance of measurement error
+    b = 0  # no system input
+    u = 0  # no system input
+    filt = Kalman(R=r, A=1, Q=q, H=h, B=b)
+
+    # Generate random voltages and watch the filter operate.
+    n = 50
+    truth = np.random.randn(n) * np.sqrt(q) + V0
+    z = truth + np.random.randn(n) * np.sqrt(r)  # measurement
+    x = np.zeros(n)
+
+    for i, zi in enumerate(z):
+        x[i] = filt(zi, u)  # perform a Kalman filter iteration
+
+    _hz = plt.plot(z, 'r.', label='observations')
+    # a-posteriori state estimates:
+    _hx = plt.plot(x, 'b-', label='Kalman output')
+    _ht = plt.plot(truth, 'g-', label='true voltage')
+    plt.legend()
+    plt.title('Automobile Voltimeter Example')
+
+
+def lti_disc(F, L=None, Q=None, dt=1):
+    """LTI_DISC  Discretize LTI ODE with Gaussian Noise.
+
+    Syntax:
+     [A,Q] = lti_disc(F,L,Qc,dt)
+
+    In:
+     F  - NxN Feedback matrix
+     L  - NxL Noise effect matrix        (optional, default identity)
+     Qc - LxL Diagonal Spectral Density  (optional, default zeros)
+     dt - Time Step                      (optional, default 1)
+
+    Out:
+     A - Transition matrix
+     Q - Discrete Process Covariance
+
+    Description:
+     Discretize LTI ODE with Gaussian Noise. The original
+     ODE model is in form
+
+       dx/dt = F x + L w,  w ~ N(0,Qc)
+
+     Result of discretization is the model
+
+       x[k] = A x[k-1] + q, q ~ N(0,Q)
+
+     Which can be used for integrating the model
+     exactly over time steps, which are multiples
+     of dt.
+
+    """
+    n = np.shape(F)[0]
+    if L is None:
+        L = np.eye(n)
+
+    if Q is None:
+        Q = np.zeros((n, n))
+    # Closed form integration of transition matrix
+    A = expm(F * dt)
+
+    # Closed form integration of covariance
+    # by matrix fraction decomposition
+
+    Phi = np.vstack((np.hstack((F, np.dot(np.dot(L, Q), L.T))),
+                     np.hstack((np.zeros((n, n)), -F.T))))
+    AB = np.dot(expm(Phi * dt), np.vstack((np.zeros((n, n)), np.eye(n))))
+    # Q = AB[:n, :] / AB[n:(2 * n), :]
+    Q = np.linalg.solve(AB[n:(2 * n), :].T, AB[:n, :].T)
+    return A, Q
+
+
+def demo_kalman_sine():
+    """Kalman Filter demonstration with sine signal.
+
+    Example
+    -------
+    >>> demo_kalman_sine()
+
+    >>> plt.close()
+    """
+    sd = 0.5
+    dt = 0.1
+    w = 1
+    T = np.arange(0, 30 + dt / 2, dt)
+    n = len(T)
+    X = 3 * np.sin(w * T)
+    Y = X + sd * np.random.randn(n)
+
+    ''' Initialize KF to values
+       x = 0
+       dx/dt = 0
+     with great uncertainty in derivative
+    '''
+    M = np.zeros((2, 1))
+    P = np.diag([0.1, 2])
+    R = sd ** 2
+    H = np.atleast_2d([1, 0])
+    q = 0.1
+    F = np.atleast_2d([[0, 1],
+                       [0, 0]])
+    A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt)
+
+    # Track and animate
+    m = M.shape[0]
+    _MM = np.zeros((m, n))
+    _PP = np.zeros((m, m, n))
+    '''In this demonstration we estimate a stationary sine signal from noisy
+    measurements by using the classical Kalman filter.'
+    '''
+    filt = Kalman(R=R, x=M, P=P, A=A, Q=Q, H=H, B=0)
+
+    # Generate random voltages and watch the filter operate.
+    # n = 50
+    # truth = np.random.randn(n) * np.sqrt(q) + V0
+    # z = truth + np.random.randn(n) * np.sqrt(r)  # measurement
+    truth = X
+    z = Y
+    x = np.zeros((n, m))
+
+    for i, zi in enumerate(z):
+        x[i] = np.ravel(filt(zi, u=0))
+
+    _hz = plt.plot(z, 'r.', label='observations')
+    # a-posteriori state estimates:
+    _hx = plt.plot(x[:, 0], 'b-', label='Kalman output')
+    _ht = plt.plot(truth, 'g-', label='true voltage')
+    plt.legend()
+    plt.title('Automobile Voltimeter Example')
+
+
+#     for k in range(m):
+#         [M,P] = kf_predict(M,P,A,Q);
+#         [M,P] = kf_update(M,P,Y(k),H,R);
+#
+#         MM(:,k) = M;
+#         PP(:,:,k) = P;
+#
+#       %
+#       % Animate
+#       %
+#       if rem(k,10)==1
+#         plot(T,X,'b--',...
+#              T,Y,'ro',...
+#              T(k),M(1),'k*',...
+#              T(1:k),MM(1,1:k),'k-');
+#         legend('Real signal','Measurements','Latest estimate',
+#                'Filtered estimate')
+#         title('Estimating a noisy sine signal with Kalman filter.');
+#         drawnow;
+#
+#         pause;
+#       end
+#     end
+#
+#     clc;
+#     disp('In this demonstration we estimate a stationary sine signal '
+#        'from noisy measurements by using the classical Kalman filter.');
+#     disp(' ');
+#     disp('The filtering results are now displayed sequantially for 10 time '
+#            'step at a time.');
+#     disp(' ');
+#     disp('<push any key to see the filtered and smoothed results together>')
+#     pause;
+#     %
+#     % Apply Kalman smoother
+#     %
+#     SM = rts_smooth(MM,PP,A,Q);
+#     plot(T,X,'b--',...
+#          T,MM(1,:),'k-',...
+#          T,SM(1,:),'r-');
+#     legend('Real signal','Filtered estimate','Smoothed estimate')
+#     title('Filtered and smoothed estimate of the original signal');
+#
+#     clc;
+#     disp('The filtered and smoothed estimates of the signal are now '
+#        'displayed.')
+#     disp(' ');
+#     disp('RMS errors:');
+#     %
+#     % Errors
+#     %
+#     fprintf('KF = %.3f\nRTS = %.3f\n',...
+#             sqrt(mean((MM(1,:)-X(1,:)).^2)),...
+#             sqrt(mean((SM(1,:)-X(1,:)).^2)));
+
+
+def demo_hampel():
+    """
+    Example
+    -------
+    >>> demo_hampel()
+
+    >>> plt.close()
+    """
+    randint = np.random.randint
+    Y = 5000 + np.random.randn(1000)
+    outliers = randint(0, 1000, size=(10,))
+    Y[outliers] = Y[outliers] + randint(1000, size=(10,))
+    YY, res = HampelFilter(dx=3, t=3, fulloutput=True)(Y)
+    YY1, res1 = HampelFilter(dx=1, t=3, adaptive=0.1, fulloutput=True)(Y)
+    YY2, res2 = HampelFilter(dx=3, t=0, fulloutput=True)(Y)  # median
+    plt.figure(1)
+    plot_hampel(Y, YY, res)
+    plt.title('Standard HampelFilter')
+    plt.figure(2)
+    plot_hampel(Y, YY1, res1)
+    plt.title('Adaptive HampelFilter')
+    plt.figure(3)
+    plot_hampel(Y, YY2, res2)
+    plt.title('Median filter')
+
+
+def plot_hampel(Y, YY, res):
+    X = np.arange(len(YY))
+    plt.plot(X, Y, 'b.')  # Original Data
+    plt.plot(X, YY, 'r')  # Hampel Filtered Data
+    plt.plot(X, res['Y0'], 'b--')  # Nominal Data
+    plt.plot(X, res['LB'], 'r--')  # Lower Bounds on Hampel Filter
+    plt.plot(X, res['UB'], 'r--')  # Upper Bounds on Hampel Filter
+    i = res['outliers']
+    plt.plot(X[i], Y[i], 'ks')  # Identified Outliers
+
+
+def demo_tide_filter():
+    """
+    Example
+    -------
+    >>> demo_tide_filter()
+
+    >>> plt.close()
+    """
+    # import statsmodels.api as sa
+    import wafo.spectrum.models as sm
+    sd = 10
+    Sj = sm.Jonswap(Hm0=4. * sd)
+    S = Sj.tospecdata()
+
+    q = (0.1 * sd) ** 2   # variance of process noise s the car operates
+    r = (100 * sd) ** 2  # variance of measurement error
+    b = 0  # no system input
+    u = 0  # no system input
+
+    from scipy.signal import butter, filtfilt, lfilter_zi  # lfilter,
+    freq_tide = 1. / (12 * 60 * 60)
+    freq_wave = 1. / 10
+    freq_filt = freq_wave / 10
+    dt = 1.
+    freq = 1. / dt
+    fn = (freq / 2)
+
+    P = 10 * np.diag([1, 0.01])
+    R = r
+    H = np.atleast_2d([1, 0])
+
+    F = np.atleast_2d([[0, 1],
+                       [0, 0]])
+    A, Q = lti_disc(F, L=None, Q=np.diag([0, q]), dt=dt)
+
+    t = np.arange(0, 60 * 12, 1. / freq)
+    w = 2 * np.pi * freq  # 1 Hz
+    tide = 100 * np.sin(freq_tide * w * t + 2 * np.pi / 4) + 100
+    y = tide + S.sim(len(t), dt=1. / freq)[:, 1].ravel()
+#     lowess = sa.nonparametric.lowess
+#     y2 = lowess(y, t, frac=0.5)[:,1]
+
+    filt = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b)
+    filt2 = Kalman(R=R, x=np.array([[tide[0]], [0]]), P=P, A=A, Q=Q, H=H, B=b)
+    # y = tide + 0.5 * np.sin(freq_wave * w * t)
+    # Butterworth filter
+    b, a = butter(9, (freq_filt / fn), btype='low')
+    # y2 = [lowess(y[max(i-60,0):i + 1], t[max(i-60,0):i + 1], frac=.3)[-1,1]
+    #    for i in range(len(y))]
+    # y2 = [lfilter(b, a, y[:i + 1])[i] for i in range(len(y))]
+    # y3 = filtfilt(b, a, y[:16]).tolist() + [filtfilt(b, a, y[:i + 1])[i]
+    #    for i in range(16, len(y))]
+    # y0 = medfilt(y, 41)
+    _zi = lfilter_zi(b, a)
+    # y2 = lfilter(b, a, y)#, zi=y[0]*zi)  # standard filter
+    y3 = filtfilt(b, a, y)  # filter with phase shift correction
+    y4 = []
+    y5 = []
+    for _i, j in enumerate(y):
+        tmp = np.ravel(filt(j, u=u))
+        tmp = np.ravel(filt2(tmp[0], u=u))
+#         if i==0:
+#             print(filt.x)
+#             print(filt2.x)
+        y4.append(tmp[0])
+        y5.append(tmp[1])
+    _y0 = medfilt(y4, 41)
+    # print(filt.P)
+    # plot
+
+    plt.plot(t, y, 'r.-', linewidth=2, label='raw data')
+    # plt.plot(t, y2, 'b.-', linewidth=2, label='lowess @ %g Hz' % freq_filt)
+    # plt.plot(t, y2, 'b.-', linewidth=2, label='filter @ %g Hz' % freq_filt)
+    plt.plot(t, y3, 'g.-', linewidth=2, label='filtfilt @ %g Hz' % freq_filt)
+    plt.plot(t, y4, 'k.-', linewidth=2, label='kalman')
+    # plt.plot(t, y5, 'k.', linewidth=2, label='kalman2')
+    plt.plot(t, tide, 'y-', linewidth=2, label='True tide')
+    plt.legend(frameon=False, fontsize=14)
+    plt.xlabel("Time [s]")
+    plt.ylabel("Amplitude")
+
+
+def demo_savitzky_on_exponential():
+    """
+    Example
+    -------
+    >>> demo_savitzky_on_exponential()
+
+    >>> plt.close()
+    """
+    t = np.linspace(-4, 4, 500)
+    y = np.exp(-t ** 2) + np.random.normal(0, 0.05, np.shape(t))
+    n = 11
+    ysg = SavitzkyGolay(n, degree=1, diff_order=0)(y)
+    plt.plot(t, y, t, ysg, '--')
+
+
+def demo_smoothn_on_1d_cos():
+    """
+    Example
+    -------
+    >>> demo_smoothn_on_1d_cos()
+
+    >>> plt.close()
+    """
+    x = np.linspace(0, 100, 2 ** 8)
+    y = np.cos(x / 10) + (x / 50) ** 2 + np.random.randn(np.size(x)) / 10
+    y[np.r_[70, 75, 80]] = np.array([5.5, 5, 6])
+    z = smoothn(y)  # Regular smoothing
+    zr = smoothn(y, robust=True)  # Robust smoothing
+    _h0 = plt.subplot(121),
+    _h = plt.plot(x, y, 'r.', x, z, 'k', linewidth=2)
+    plt.title('Regular smoothing')
+    plt.subplot(122)
+    plt.plot(x, y, 'r.', x, zr, 'k', linewidth=2)
+    plt.title('Robust smoothing')
+
+
+def demo_smoothn_on_2d_exp_sin():
+    """
+    Example
+    -------
+    >>> demo_smoothn_on_2d_exp_sin()
+
+    >>> plt.close()
+    """
+    xp = np.arange(0, 1, 0.02)  # np.r_[0:1:0.02]
+    [x, y] = np.meshgrid(xp, xp)
+    f = np.exp(x + y) + np.sin((x - 2 * y) * 3)
+    fn = f + np.random.randn(*f.shape) * 0.5
+    _fs, s = smoothn(fn, fulloutput=True)
+    fs2 = smoothn(fn, s=2 * s)
+    _h = plt.subplot(131),
+    _h = plt.contourf(xp, xp, fn)
+    _h = plt.subplot(132),
+    _h = plt.contourf(xp, xp, fs2)
+    _h = plt.subplot(133),
+    _h = plt.contourf(xp, xp, f)
+
+
+def _cardioid(n=1000):
+    t = np.linspace(0, 2 * np.pi, n)
+    x0 = 2 * np.cos(t) * (1 - np.cos(t))
+    y0 = 2 * np.sin(t) * (1 - np.cos(t))
+    x = x0 + np.random.randn(x0.size) * 0.1
+    y = y0 + np.random.randn(y0.size) * 0.1
+    return x, y, x0, y0
+
+
+def demo_smoothn_on_cardioid():
+    """
+    Example
+    -------
+    >>> demo_smoothn_on_cardioid()
+
+    >>> plt.close()
+    """
+    x, y, x0, y0 = _cardioid()
+    z = smoothn(x + 1j * y, robust=False)
+    plt.plot(x0, y0, 'y',
+             x, y, 'r.',
+             np.real(z), np.imag(z), 'k', linewidth=2)
+
+
+def demo_hodrick_on_cardioid():
+    """
+    Example
+    -------
+    >>> demo_hodrick_on_cardioid()
+
+    >>> plt.close()
+    """
+    x, y, x0, y0 = _cardioid()
+
+    smooth = HodrickPrescott(w=20000)
+    # smooth = HampelFilter(adaptive=50)
+    xs, ys = smooth(x), smooth(y)
+    plt.plot(x0, y0, 'y',
+             x, y, 'r.',
+             xs, ys, 'k', linewidth=2)
+
+
+if __name__ == '__main__':
+    from wafo.testing import test_docstrings
+    test_docstrings(__file__)
+    # demo_savitzky_on_noisy_chirp()
+    # plt.show('hold')  # show plot
+    # demo_kalman_sine()
+    # demo_tide_filter()
+    # demo_hampel()
+    # demo_kalman_voltimeter()
+    # demo_savitzky_on_exponential()
+#     plt.figure(1)
+#     demo_hodrick_on_cardioid()
+#     plt.figure(2)
+#     # demo_smoothn_on_1d_cos()
+#     demo_smoothn_on_cardioid()
+#     plt.show('hold')

wafo/sg_filter/tests/conftest.py

@@ -0,0 +1,11 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""
+    Dummy conftest.py for wafo.
+
+    If you don't know what this is for, just leave it empty.
+    Read more about conftest.py under:
+    https://pytest.org/latest/plugins.html
+"""
+from __future__ import print_function, absolute_import, division
+import pytest  # @UnusedImport

wafo/source/c_library/build_all.py

@@ -0,0 +1,25 @@
+"""
+f2py c_library.pyf c_functions.c -c
+
+See also http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW
+"""
+import os
+import sys
+from wafo.f2py_tools import f2py_call_str
+
+def compile_all():
+    f2py_call = f2py_call_str()
+    print '=' * 75
+    print 'compiling c_codes'
+    print '=' * 75
+
+    compile_format = f2py_call + ' %s %s -c'
+
+    pyfs = ('c_library.pyf',)
+    files = ('c_functions.c',)
+
+    for pyf, file_ in zip(pyfs, files):
+        os.system(compile_format % (pyf, file_))
+
+if __name__ == '__main__':
+    compile_all()

wafo/source/c_library/c_functions.c

@@ -0,0 +1,779 @@
+#include "math.h"
+/*
+*  Install gfortran and run the following to build the module on windows:
+ *   f2py c_library.pyf c_functions.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71
+ */
+
+/*
+ * findrfc.c -
+ *
+ *  Returns indices to RFC turningpoints of a vector
+ *  of turningpoints
+ *
+ * 1998 by Per Andreas Brodtkorb.
+ */
+
+void findrfc(double *y1,double hmin, int *ind, int n,int *info) {
+   double xminus, xplus, Tpl, Tmi, *y, Tstart;
+   int i, j, ix=0, NC, iy;
+   info[0] = 0;
+   if (*(y1+0)> *(y1+1)){
+   /* if first is a max , ignore the first max*/
+      y=&(*(y1+1));
+      NC=floor((n-1)/2);
+      Tstart=1;
+   }
+   else {
+      y=y1;
+      NC=floor(n/2);
+      Tstart=0;
+   }
+
+   if (NC<1){
+      return; /* No RFC cycles*/
+   }
+
+
+   if (( *(y+0) > *(y+1)) && ( *(y+1) > *(y+2)) ){
+      info[0] = -1;
+      return; /*This is not a sequence of turningpoints, exit */
+   }
+   if ((*(y+0) < *(y+1)) && (*(y+1)< *(y+2))){
+      info[0]=-1;
+      return; /*This is not a sequence of turningpoints, exit */
+   }
+
+
+   for (i=0; i<NC; i++) {
+
+      Tmi=Tstart+2*i;
+      Tpl=Tstart+2*i+2;
+      xminus=*(y+2*i);
+      xplus=*(y+2*i+2);
+
+      if(i!=0){
+     j=i-1;
+     while((j>=0) && (*(y+2*j+1)<=*(y+2*i+1))){
+        if( (*(y+2*j)<xminus) ){
+           xminus=*(y+2*j);
+           Tmi=Tstart+2*j;
+        } /*if */
+        j--;
+     } /*while j*/
+      } /*if i */
+      if ( xminus >= xplus){
+     if ( (*(y+2*i+1)-xminus) >= hmin){
+        *(ind+ix)=Tmi;
+        ix++;
+        *(ind+ix)=(Tstart+2*i+1);
+        ix++;
+     } /*if*/
+     goto L180;
+      }
+
+      j=i+1;
+      while((j<NC) ) {
+     if (*(y+2*j+1) >= *(y+2*i+1)) goto L170;
+     if( (*(y+2*j+2) <= xplus) ){
+        xplus=*(y+2*j+2);
+        Tpl=(Tstart+2*j+2);
+     }/*if*/
+        j++;
+      } /*while*/
+
+
+      if ( (*(y+2*i+1)-xminus) >= hmin) {
+     *(ind+ix)=Tmi;
+     ix++;
+     *(ind+ix)=(Tstart+2*i+1);
+     ix++;
+
+      } /*if*/
+      goto L180;
+   L170:
+      if (xplus <= xminus ) {
+     if ( (*(y+2*i+1)-xminus) >= hmin){
+        *(ind+ix)=Tmi;
+        ix++;
+        *(ind+ix)=(Tstart+2*i+1);
+        ix++;
+     } /*if*/
+     /*goto L180;*/
+      }
+      else{
+     if ( (*(y+2*i+1)-xplus) >= hmin) {
+        *(ind+ix)=(Tstart+2*i+1);
+        ix++;
+        *(ind+ix)=Tpl;
+        ix++;
+     } /*if*/
+      } /*elseif*/
+   L180:
+     iy=i;
+   }  /* for i */
+   info[0] = ix;
+  return ;
+}
+
+
+
+/*
+ * findcross.c -
+ *
+ *  Returns indices to level v crossings of argument vector
+ *
+ * 1998 by Per Andreas Brodtkorb. last modified 23.06-98
+ */
+
+
+void findcross(double *y, double v, int *ind, int n, int *info)
+{ int i,start, ix=0,dcross=0;
+    start=0;
+    if  ( y[0]< v){
+        dcross=-1; /* first is a up-crossing*/
+    }
+    else if  ( y[0]> v){
+        dcross=1;  /* first is a down-crossing*/
+    }
+    else if  ( y[0]== v){
+        /* Find out what type of crossing we have next time.. */
+        for (i=1; i<n; i++) {
+            start=i;
+            if  ( y[i]< v){
+                ind[ix] = i-1; /* first crossing is a down crossing*/
+                ix++;
+                dcross=-1; /* The next crossing is a up-crossing*/
+                goto L120;
+            }
+            else if  ( y[i]> v){
+                ind[ix] = i-1; /* first crossing is a up-crossing*/
+                ix++;
+                dcross=1;  /*The next crossing is a down-crossing*/
+                goto L120;
+            }
+        }
+    }
+    L120:
+    for (i=start; i<n-1; i++) {
+        if (( (dcross==-1) && (y[i]<=v) && (y[i+1] > v)  )  || ((dcross==1 ) && (y[i]>=v) && (y[i+1] < v) ) )  {
+
+            ind[ix] = i;
+            ix++;
+            dcross=-dcross;
+        }
+    }
+    info[0] = ix;
+    return;
+}
+
+
+/*
+ * DISUFQ  Is an internal function to spec2nlsdat
+ *
+ *  CALL:  disufq(rvec,ivec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
+ *
+ * rvec, ivec = real and imaginary parts of the resultant  (size m X n).
+ * rA, iA     = real and imaginary parts of the amplitudes (size m X n).
+ * w          = vector with angular frequencies (w>=0)
+ * kw         = vector with wavenumbers (kw>=0)
+ * h          = water depth             (h >=0)
+ * g          = constant acceleration of gravity
+ * nmin       = minimum index where rA(:,nmin) and iA(:,nmin) is
+ *              greater than zero.
+ * nmax       = maximum index where rA(:,nmax) and iA(:,nmax) is
+ *              greater than zero.
+ * m          = size(rA,1),size(iA,1)
+ * n          = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
+ *
+ * DISUFQ returns the summation of difference frequency and sum
+ * frequency effects in the vector vec = rvec +sqrt(-1)*ivec.
+ * The 2'nd order contribution to the Stokes wave is then calculated by
+ * a simple 1D Fourier transform, real(FFT(vec)).
+ *
+ *  Install gfortran and run the following to build the module:
+ *   f2py diffsumfunq.pyf disufq1.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71
+ *
+ * by Per Andreas Brodtkorb 15.08.2001
+ * revised pab 14.03.2002, 01.05.2002 22.07.2002, oct 2008
+ */
+
+void disufq(double *rvec, double *ivec,
+       double *rA,   double *iA,
+       double *w,    double *kw,
+       double h,     double g,
+       int nmin, int nmax,
+       int m,    int n)
+{
+  double Epij, Edij;
+  double tmp1, tmp2, tmp3, tmp4, kfact;
+  double w1, w2, kw1, kw2, Cg;
+  double rrA, iiA, riA, irA;
+  int i,jy,ix,iz1,iv1,ixi,jyi;
+  //int iz2, iv2;
+  //Initialize rvec and ivec to zero
+  for (ix=0;ix<n*m;ix++) {
+    rvec[ix] = 0.0;
+    ivec[ix] = 0.0;
+  }
+
+  // kfact is set to 2 in order to exploit the symmetry.
+  // If you set kfact to 1, you must uncomment all statements
+  // including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].
+
+  kfact = 2.0;
+  if (h>10000){ /* deep water /Inifinite water depth */
+    for (ix = nmin-1;ix<nmax;ix++) {
+      ixi = ix*m;
+      iz1 = 2*ixi;
+      //iz2 = n*m-ixi;
+      kw1  = kw[ix];
+      Epij = kw1;
+      for (i=0;i<m;i++,ixi++,iz1++) {
+          rrA = rA[ixi]*rA[ixi]; ///
+          iiA = iA[ixi]*iA[ixi]; ///
+          riA = rA[ixi]*iA[ixi]; ///
+
+          /// Sum frequency effects along the diagonal
+          tmp1 = kfact*(rrA-iiA)*Epij;
+          tmp2 = kfact*2.0*riA*Epij;
+          rvec[iz1] += tmp1;
+          ivec[iz1] += tmp2;
+
+          //rvec[iz2] += tmp1;
+          //ivec[iz2] -= tmp2;
+          //iz2++;
+
+          /// Difference frequency effects are zero along the diagonal
+          /// and are thus not contributing to the mean.
+      }
+      for (jy = ix+1;jy<nmax;jy++){
+          kw2  = kw[jy];
+          Epij = 0.5*(kw2 + kw1);
+          Edij = -0.5*(kw2 - kw1);
+          //printf("Edij = %f Epij = %f \n", Edij,Epij);
+
+          ixi = ix*m;
+          jyi = jy*m;
+          iz1 = ixi+jyi;
+          iv1 = jyi-ixi;
+          //iz2 = (n*m-iz1);
+          //iv2 = (n*m-iv1);
+          for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
+
+              rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
+              iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
+              riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
+              irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
+
+              /* Sum frequency effects */
+              tmp1 = kfact*2.0*(rrA-iiA)*Epij;
+              tmp2 = kfact*2.0*(riA+irA)*Epij;
+              rvec[iz1] += tmp1;///rvec[i][ix+jy] += tmp1;
+              ivec[iz1] += tmp2;///ivec[i][ix+jy] += tmp2;
+              //rvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] +=  tmp1;
+              //ivec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] -=  tmp2;
+              // iz2++;
+
+              /* Difference frequency effects */
+              tmp1 = kfact*2.0*(rrA+iiA)*Edij;
+              tmp2 = kfact*2.0*(riA-irA)*Edij;
+
+              rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
+              ivec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
+
+              //rvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
+              //ivec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
+              //iv2++;
+          }
+      }
+    }
+  }
+  else{ /* Finite water depth */
+    for (ix = nmin-1;ix<nmax;ix++) {
+     kw1  = kw[ix];
+     w1   = w[ix];
+     tmp1 = tanh(kw1*h);
+     /// Cg, wave group velocity
+     Cg   = 0.5*g*(tmp1 + kw1*h*(1.0- tmp1*tmp1))/w1; /// OK
+     tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
+     tmp2 = 0.5*w1*w1/g;
+     tmp3 = g*kw1/(w1*Cg);
+
+     if (kw1*h<300.0){
+       tmp4 = kw1/sinh(2.0*kw1*h);
+     }
+     else{ // To ensure sinh does not overflow.
+       tmp4 = 0.0;
+     }
+     // Difference frequency effects finite water depth
+     Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
+
+     // Sum frequency effects finite water depth
+     Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
+     //printf("Edij = %f Epij = %f \n", Edij,Epij);
+
+     ixi = ix*m;
+     iz1 = 2*ixi;
+     //iz2 = n*m-ixi;
+     for (i=0;i<m;i++,ixi++,iz1++) {
+
+       rrA = rA[ixi]*rA[ixi]; ///
+       iiA = iA[ixi]*iA[ixi]; ///
+       riA = rA[ixi]*iA[ixi]; ///
+
+
+       /// Sum frequency effects along the diagonal
+       rvec[iz1] +=  kfact*(rrA-iiA)*Epij;
+       ivec[iz1] +=  kfact*2.0*riA*Epij;
+       //rvec[iz2] +=  kfact*(rrA-iiA)*Epij;
+       //ivec[iz2] -=  kfact*2.0*riA*Epij;
+       //iz2++;
+
+       /// Difference frequency effects along the diagonal
+       /// are only contributing to the mean
+       rvec[i] +=  2.0*(rrA+iiA)*Edij;
+     }
+     for (jy = ix+1;jy<nmax;jy++) {
+       // w1  = w[ix];
+       // kw1 = kw[ix];
+       w2   = w[jy];
+       kw2  = kw[jy];
+       tmp1 = g*(kw1/w1)*(kw2/w2);
+       tmp2 = 0.5/g*(w1*w1+w2*w2+w1*w2);
+       tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
+       tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
+       Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
+
+       tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
+       tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
+       tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
+       Edij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
+       //printf("Edij = %f Epij = %f \n", Edij,Epij);
+
+       ixi = ix*m;
+       jyi = jy*m;
+       iz1 = ixi+jyi;
+       iv1 = jyi-ixi;
+       //       iz2 = (n*m-iz1);
+       //       iv2 = n*m-iv1;
+       for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
+     rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
+     iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
+     riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
+     irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
+
+     /* Sum frequency effects */
+     tmp1 = kfact*2.0*(rrA-iiA)*Epij;
+     tmp2 = kfact*2.0*(riA+irA)*Epij;
+     rvec[iz1] += tmp1;///rvec[i][jy+ix] += tmp1;
+     ivec[iz1] += tmp2;///ivec[i][jy+ix] += tmp2;
+     //rvec[iz2] += tmp1;///rvec[i][n*m-(jy+ix)] += tmp1;
+     //ivec[iz2] -= tmp2;///ivec[i][n*m-(jy+ix)] -= tmp2;
+     //iz2++;
+
+     /* Difference frequency effects */
+     tmp1 = kfact*2.0*(rrA+iiA)*Edij;
+     tmp2 = kfact*2.0*(riA-irA)*Edij;
+     rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
+     ivec[iv1] += tmp2;///ivec[i][jy-ix] -= tmp2;
+
+     //rvec[iv2] += tmp1;
+     //ivec[iv2] -= tmp2;
+     //iv2++;
+       }
+     }
+   }
+  }
+  //return i;
+}
+/*
+ * DISUFQ2  Is an internal function to spec2nlsdat
+ *
+ *  CALL:  disufq2(rsvec,isvec,rdvec,idvec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
+ *
+ * rsvec, isvec = real and imaginary parts of the sum frequency
+ *                effects  (size m X n).
+ * rdvec, idvec = real and imaginary parts of the difference frequency
+ *                effects  (size m X n).
+ * rA, iA     = real and imaginary parts of the amplitudes (size m X n).
+ * w          = vector with angular frequencies (w>=0)
+ * kw         = vector with wavenumbers (kw>=0)
+ * h          = water depth             (h >=0)
+ * g          = constant acceleration of gravity
+ * nmin       = minimum index where rA(:,nmin) and iA(:,nmin) is
+ *              greater than zero.
+ * nmax       = maximum index where rA(:,nmax) and iA(:,nmax) is
+ *              greater than zero.
+ * m          = size(rA,1),size(iA,1)
+ * n          = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
+ *
+ * DISUFQ2 returns the summation of sum and difference frequency
+ * frequency effects in the vectors svec = rsvec +sqrt(-1)*isvec and
+ * dvec =  rdvec +sqrt(-1)*idvec.
+ * The 2'nd order contribution to the Stokes wave is then calculated by
+ * a simple 1D Fourier transform, real(FFT(svec+dvec)).
+ *
+ *
+ * This is a MEX-file for MATLAB.
+ * by Per Andreas Brodtkorb 15.08.2001
+ * revised pab 14.03.2002, 01.05.2002
+ */
+
+void disufq2(double *rsvec, double *isvec,
+        double *rdvec, double *idvec,
+        double *rA,   double *iA,
+        double *w,    double *kw,
+        double h,     double g,
+        int nmin, int nmax,
+        int m,    int n)
+{
+  double Epij, Edij;
+  double tmp1, tmp2, tmp3, tmp4, kfact;
+  double w1, w2, kw1, kw2, Cg;
+  double rrA, iiA, riA, irA;
+  int i,jy,ix,iz1,iv1,ixi,jyi;
+  //int iz2,iv2
+
+  //Initialize rvec and ivec to zero
+  for (ix=0;ix<n*m;ix++) {
+    rsvec[ix] = 0.0;
+    isvec[ix] = 0.0;
+    rdvec[ix] = 0.0;
+    idvec[ix] = 0.0;
+  }
+
+  // kfact is set to 2 in order to exploit the symmetry.
+  // If you set kfact to 1, you must uncomment all statements
+  // including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].
+
+  kfact = 2.0;
+  if (h>10000){ /* deep water /Inifinite water depth */
+    for (ix = nmin-1;ix<nmax;ix++) {
+      ixi = ix*m;
+      iz1 = 2*ixi;
+      //iz2 = n*m-ixi;
+      kw1  = kw[ix];
+      Epij = kw1;
+      for (i=0;i<m;i++,ixi++,iz1++) {
+    rrA = rA[ixi]*rA[ixi]; ///
+    iiA = iA[ixi]*iA[ixi]; ///
+    riA = rA[ixi]*iA[ixi]; ///
+
+    /// Sum frequency effects along the diagonal
+    tmp1 = kfact*(rrA-iiA)*Epij;
+    tmp2 = kfact*2.0*riA*Epij;
+    rsvec[iz1] += tmp1;
+    isvec[iz1] += tmp2;
+
+    //rsvec[iz2] += tmp1;
+    //isvec[iz2] -= tmp2;
+    //iz2++;
+
+    /// Difference frequency effects are zero along the diagonal
+    /// and are thus not contributing to the mean.
+      }
+      for (jy = ix+1;jy<nmax;jy++){
+    kw2  = kw[jy];
+    Epij = 0.5*(kw2 + kw1);
+    Edij = -0.5*(kw2 - kw1);
+    //printf("Edij = %f Epij = %f \n", Edij,Epij);
+
+    ixi = ix*m;
+    jyi = jy*m;
+    iz1 = ixi+jyi;
+    iv1 = jyi-ixi;
+    //iz2 = (n*m-iz1);
+    //iv2 = (n*m-iv1);
+    for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
+
+      rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
+      iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
+      riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
+      irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
+
+     /* Sum frequency effects */
+      tmp1 = kfact*2.0*(rrA-iiA)*Epij;
+      tmp2 = kfact*2.0*(riA+irA)*Epij;
+      rsvec[iz1] += tmp1;  ///rvec[i][ix+jy] += tmp1;
+      isvec[iz1] += tmp2;  ///ivec[i][ix+jy] += tmp2;
+      //rsvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
+      //isvec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] += tmp2;
+      //iz2++;
+
+      /* Difference frequency effects */
+      tmp1 = kfact*2.0*(rrA+iiA)*Edij;
+      tmp2 = kfact*2.0*(riA-irA)*Edij;
+
+      rdvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
+      idvec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
+
+      //rdvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
+      //idvec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
+      //  iv2++;
+    }
+      }
+   }
+  }
+  else{ /* Finite water depth */
+    for (ix = nmin-1;ix<nmax;ix++) {
+     kw1  = kw[ix];
+     w1   = w[ix];
+     tmp1 = tanh(kw1*h);
+     /// Cg, wave group velocity
+     Cg   = 0.5*g*(tmp1 + kw1*h*(1.0- tmp1*tmp1))/w1; /// OK
+     tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
+     tmp2 = 0.5*w1*w1/g;
+     tmp3 = g*kw1/(w1*Cg);
+
+     if (kw1*h<300.0){
+       tmp4 = kw1/sinh(2.0*kw1*h);
+     }
+     else{ // To ensure sinh does not overflow.
+       tmp4 = 0.0;
+     }
+     // Difference frequency effects finite water depth
+     Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
+
+     // Sum frequency effects finite water depth
+     Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
+     //printf("Edij = %f Epij = %f \n", Edij,Epij);
+
+     ixi = ix*m;
+     iz1 = 2*ixi;
+     //iz2 = n*m-ixi;
+     for (i=0;i<m;i++,ixi++,iz1++) {
+
+       rrA = rA[ixi]*rA[ixi]; ///
+       iiA = iA[ixi]*iA[ixi]; ///
+       riA = rA[ixi]*iA[ixi]; ///
+
+
+       /// Sum frequency effects along the diagonal
+       rsvec[iz1] +=  kfact*(rrA-iiA)*Epij;
+       isvec[iz1] +=  kfact*2.0*riA*Epij;
+       //rsvec[iz2] +=  kfact*(rrA-iiA)*Epij;
+       //isvec[iz2] -=  kfact*2.0*riA*Epij;
+
+       /// Difference frequency effects along the diagonal
+       /// are only contributing to the mean
+       //printf(" %f \n",2.0*(rrA+iiA)*Edij);
+       rdvec[i] +=  2.0*(rrA+iiA)*Edij;
+     }
+     for (jy = ix+1;jy<nmax;jy++) {
+       // w1  = w[ix];
+       // kw1 = kw[ix];
+       w2   = w[jy];
+       kw2  = kw[jy];
+       tmp1 = g*(kw1/w1)*(kw2/w2);
+       tmp2 = 0.5/g*(w1*w1+w2*w2+w1*w2);
+       tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
+       tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
+       Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
+
+       tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
+       tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
+       tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
+       Edij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
+       //printf("Edij = %f Epij = %f \n", Edij,Epij);
+
+       ixi = ix*m;
+       jyi = jy*m;
+       iz1 = ixi+jyi;
+       iv1 = jyi-ixi;
+       //       iz2 = (n*m-iz1);
+       //       iv2 = (n*m-iv1);
+       for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
+     rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
+     iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
+     riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
+     irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
+
+     /* Sum frequency effects */
+     tmp1 = kfact*2.0*(rrA-iiA)*Epij;
+     tmp2 = kfact*2.0*(riA+irA)*Epij;
+     rsvec[iz1] += tmp1;///rsvec[i][jy+ix] += tmp1;
+     isvec[iz1] += tmp2;///isvec[i][jy+ix] += tmp2;
+     //rsvec[iz2] += tmp1;///rsvec[i][n*m-(jy+ix)] += tmp1;
+     //isvec[iz2] -= tmp2;///isvec[i][n*m-(jy-ix)] += tmp2;
+     //iz2++;
+
+     /* Difference frequency effects */
+     tmp1 = kfact*2.0*(rrA+iiA)*Edij;
+     tmp2 = kfact*2.0*(riA-irA)*Edij;
+     rdvec[iv1] += tmp1;
+     idvec[iv1] += tmp2;
+
+     //rdvec[iv2] += tmp1;
+     //idvec[iv2] -= tmp2;
+     // iv2++;
+       }
+     }
+   }
+  }
+ // return i;
+}
+
+
+/* ++++++++++ BEGIN RF3 [ampl ampl_mean nr_of_cycle] */
+/* ++++++++++ Rain flow without time analysis */
+//By Adam Nieslony
+//Visit the MATLAB Central File Exchange for latest version
+//http://www.mathworks.com/matlabcentral/fileexchange/3026
+void findrfc3_astm(double *array_ext, double *array_out, int n, int *nout) {
+
+    double *pr, *po, a[16384], ampl, mean;
+    int tot_num, index, j, cNr1, cNr2;
+
+    tot_num = n;
+
+    // pointers to the first element of the arrays
+    pr = &array_ext[0];
+    po = &array_out[0];
+
+    // The original rainflow counting by Nieslony, unchanged
+    j = -1;
+    cNr1 = 1;
+    for (index=0; index<tot_num; index++) {
+        a[++j]=*pr++;
+        while ( (j >= 2) && (fabs(a[j-1]-a[j-2]) <= fabs(a[j]-a[j-1])) ) {
+            ampl=fabs( (a[j-1]-a[j-2])/2 );
+            switch(j) {
+                case 0: { break; }
+                case 1: { break; }
+                case 2: {
+                    mean=(a[0]+a[1])/2;
+                    a[0]=a[1];
+                    a[1]=a[2];
+                    j=1;
+                    if (ampl > 0) {
+                        *po++=ampl;
+                        *po++=mean;
+                        *po++=0.50;
+                    }
+                    break;
+                }
+                default: {
+                    mean=(a[j-1]+a[j-2])/2;
+                    a[j-2]=a[j];
+                    j=j-2;
+                    if (ampl > 0) {
+                        *po++=ampl;
+                        *po++=mean;
+                        *po++=1.00;
+                        cNr1++;
+                    }
+                    break;
+                }
+            }
+        }
+    }
+    cNr2 = 1;
+    for (index=0; index<j; index++) {
+        ampl=fabs(a[index]-a[index+1])/2;
+        mean=(a[index]+a[index+1])/2;
+        if (ampl > 0){
+            *po++=ampl;
+            *po++=mean;
+            *po++=0.50;
+            cNr2++;
+        }
+    }
+    // array of ints nout is outputted
+    nout[0] = cNr1;
+    nout[1] = cNr2;
+}
+/* ++++++++++ END RF3 */
+
+
+// ++ BEGIN RF5 [ampl ampl_mean nr_of_cycle cycle_begin_time cycle_period_time]
+/* ++++++++++ Rain flow with time analysis */
+//By Adam Nieslony
+//Visit the MATLAB Central File Exchange for latest version
+//http://www.mathworks.com/matlabcentral/fileexchange/3026
+void
+findrfc5_astm(double *array_ext, double *array_t, double *array_out, int n, int *nout) {
+    double *pr, *pt, *po, a[16384], t[16384], ampl, mean, period, atime;
+    int tot_num, index, j, cNr1, cNr2;
+
+
+//    tot_num = mxGetM(array_ext) * mxGetN(array_ext);
+    tot_num = n;
+
+    // pointers to the first element of the arrays
+    pr = &array_ext[0];
+    pt = &array_t[0];
+    po = &array_out[0];
+
+//    array_out = mxCreateDoubleMatrix(5, tot_num-1, mxREAL);
+
+    // The original rainflow counting by Nieslony, unchanged
+    j = -1;
+    cNr1 = 1;
+    for (index=0; index<tot_num; index++) {
+        a[++j]=*pr++;
+        t[j]=*pt++;
+        while ( (j >= 2) && (fabs(a[j-1]-a[j-2]) <= fabs(a[j]-a[j-1])) ) {
+            ampl=fabs( (a[j-1]-a[j-2])/2 );
+            switch(j)
+{
+                case 0: { break; }
+                case 1: { break; }
+                case 2: {
+                    mean=(a[0]+a[1])/2;
+                    period=(t[1]-t[0])*2;
+                    atime=t[0];
+                    a[0]=a[1];
+                    a[1]=a[2];
+                    t[0]=t[1];
+                    t[1]=t[2];
+                    j=1;
+                    if (ampl > 0) {
+                        *po++=ampl;
+                        *po++=mean;
+                        *po++=0.50;
+                        *po++=atime;
+                        *po++=period;
+                    }
+                    break;
+                }
+                default: {
+                    mean=(a[j-1]+a[j-2])/2;
+                    period=(t[j-1]-t[j-2])*2;
+                    atime=t[j-2];
+                    a[j-2]=a[j];
+                    t[j-2]=t[j];
+                    j=j-2;
+                    if (ampl > 0) {
+                        *po++=ampl;
+                        *po++=mean;
+                        *po++=1.00;
+                        *po++=atime;
+                        *po++=period;
+                        cNr1++;
+                    }
+                    break;
+                }
+            }
+        }
+    }
+    cNr2 = 1;
+    for (index=0; index<j; index++) {
+        ampl=fabs(a[index]-a[index+1])/2;
+        mean=(a[index]+a[index+1])/2;
+        period=(t[index+1]-t[index])*2;
+        atime=t[index];
+        if (ampl > 0){
+            *po++=ampl;
+            *po++=mean;
+            *po++=0.50;
+            *po++=atime;
+            *po++=period;
+            cNr2++;
+        }
+    }
+//  /* free the memeory !!!*/
+//    mxSetN(array_out, tot_num - cNr);
+    nout[0] = cNr1;
+    nout[1] = cNr2;
+}
+/* ++++++++++ END RF5 */

wafo/source/c_library/c_library rf3 rf5 license.txt

@@ -0,0 +1,24 @@
+Copyright (c) 2003, Adam Niesłony
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without 
+modification, are permitted provided that the following conditions are 
+met:
+
+    * Redistributions of source code must retain the above copyright 
+      notice, this list of conditions and the following disclaimer.
+    * Redistributions in binary form must reproduce the above copyright 
+      notice, this list of conditions and the following disclaimer in 
+      the documentation and/or other materials provided with the distribution
+      
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
+ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
+POSSIBILITY OF SUCH DAMAGE.

wafo/source/c_library/c_library.pyf

@@ -0,0 +1,86 @@
+! File c_code.pyf
+python module c_library
+interface
+  subroutine findrfc(y1, hmin, ind, n, info) 
+    intent(c) findrfc              ! findrfc is a C function
+    intent(c)                     ! all findrfc arguments are considered as C based                                  
+    integer intent(hide), depend(y1) :: n=len(y1)
+	double precision dimension(n), intent(in) :: y1    ! input array 
+	double precision intent(in) :: hmin    
+    integer dimension(n), intent(out) :: ind         ! output array,
+	integer dimension(1), intent(out) :: info
+  end subroutine findrfc
+  subroutine findcross(y, v, ind, n, info)
+    intent(c) findcross           ! findcross is a C function
+    intent(c)                     ! all findcross arguments are considered as C based                                  
+    integer intent(hide), depend(y) :: n=len(y)
+	double precision dimension(n), intent(in) :: y    ! input array 
+	double precision intent(in) :: v    
+    integer dimension(n), intent(out) :: ind         ! output array,
+	integer dimension(1),intent(out) :: info
+  end subroutine findcross
+  subroutine disufq(rvec, ivec, rA, iA, w, kw, h, g,nmin,nmax, m, n)
+    intent(c) disufq              ! disufq is a C function
+    intent(c)                     ! all disufq arguments are considered as C based                                  
+    !integer intent(hide), depend(rA),check(n*m==len(iA)) :: n=len(rA)/m
+	!integer intent(hide), depend(rA), check(m==shape(iA,1)) :: m=shape(rA,1)
+    double precision dimension(n*m), intent(in) :: rA, iA    ! input array 
+	double precision dimension(n/2+1), intent(in) :: w, kw    ! input array 
+	double precision intent(in) :: h, g    
+	integer intent(in) :: nmin, nmax
+    double precision dimension(n*m), intent(out) :: rvec, ivec         ! output array,                              
+  end subroutine disufq
+  subroutine disufq2(rsvec, isvec,rdvec, idvec, rA, iA, w, kw, h, g,nmin,nmax, m, n)
+    intent(c) disufq2              ! disufq2 is a C function
+    intent(c)                     ! all disufq2 arguments are considered as C based                                  
+    !integer intent(hide), depend(rA),check(n*m==len(iA)) :: n=len(rA)/m
+	!integer intent(hide), depend(rA), check(m==shape(iA,1)) :: m=shape(rA,1)
+    double precision dimension(n*m), intent(in) :: rA, iA    ! input array 
+	double precision dimension(n/2+1), intent(in) :: w, kw    ! input array 
+	double precision intent(in) :: h, g    
+	integer intent(in) :: nmin, nmax
+    double precision dimension(n*m), intent(out) :: rsvec, isvec, rdvec, idvec         ! output array,                                                  
+  end subroutine disufq2
+
+    ! ===== START NIESLONY RAINFLOW FUNCTIONS
+    !  RAINFLOW Revision: 1.1
+    !  by Adam Nieslony, 2009     
+    subroutine findrfc3_astm(array_ext, array_out, n, nout)
+        intent(c) findrfc3_astm       ! rf3 is a C function
+        intent(c)                     ! all rf3 arguments are 
+                                      ! considered as C based
+        
+        ! n is the length of the input array array_ext
+        integer intent(hide), depend(array_ext) :: n=len(array_ext)
+        
+        ! of input array x
+        double precision intent(in) :: array_ext(n)
+        
+        ! the output array
+        double precision intent(out) :: array_out(n,3)
+        
+        ! nout array, to output additional ints
+        integer dimension(2), intent(out) :: nout        
+    end subroutine findrfc3_astm
+
+    subroutine findrfc5_astm(array_ext, array_t, array_out, n, nout)
+        intent(c) findrfc5_astm       ! rf5 is a C function
+        intent(c)                     ! all rf5 arguments are 
+                                      ! considered as C based
+        
+        ! n is the length of the input array array_ext
+        integer intent(hide), depend(array_ext) :: n=len(array_ext)
+        
+        ! of input array x
+        double precision intent(in) :: array_ext(n), array_t(n)
+        
+        ! the output array
+        double precision intent(out) :: array_out(n,5)
+        
+        ! nout array, to output additional ints
+        integer dimension(2), intent(out) :: nout        
+    end subroutine findrfc5_astm
+    ! ===== END NIESLONY RAINFLOW FUNCTIONS
+
+end interface
+end python module c_library

wafo/source/c_library/setup.py

@@ -0,0 +1,18 @@
+'''
+python setup.py build_src build_ext --inplace
+
+See also http://www.scipy.org/Cookbook/CompilingExtensionsOnWindowsWithMinGW
+'''
+# File setup.py
+
+
+def configuration(parent_package='', top_path=None):
+    from numpy.distutils.misc_util import Configuration
+    config = Configuration('', parent_package, top_path)
+
+    config.add_extension('c_library',
+                         sources=['c_library.pyf', 'c_functions.c'])
+    return config
+if __name__ == "__main__":
+    from numpy.distutils.core import setup
+    setup(**configuration(top_path='').todict())

wafo/source/cov2XXXpdf/bounds/cov2acdfb.f

@@ -0,0 +1,450 @@
+      PROGRAM sp2Acdf1
+C***********************************************************************
+C     This program computes upper and lower bounds for:                *
+C                                                                      *
+C     density of     T_i, for Ac <=h, in a gaussian process i.e.       *
+C                                                                      *
+C     half wavelength (up-crossing to downcrossing) for crests <h      *
+C    or  half wavelength (down-crossing to upcrossing) for trough >h   * 
+C    I.R. 27 Dec. 1999                                                 *
+C***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansrup
+      double precision, dimension(:,:),allocatable :: ansrlo
+      double precision, dimension(:  ),allocatable :: ex,CY
+      double precision, dimension(:,:),allocatable :: xc,fxind
+      double precision, dimension(:  ),allocatable :: h
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable  :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size,icy
+      integer ::it1,it2,status
+      double precision :: ds,dT ! lag spacing for covariances
+! f90  sp2Acdf1.f rind50.f
+
+      CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,Nx,dT)
+      !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      if (abs(def).GT.1) THEN
+        allocate(R3(1:Ntime+1))
+        allocate(R4(1:Ntime+1))
+        !CALL INIT_AMPLITUDES(h,def,Nx)
+      endif
+      allocate(h(1:Nx))
+      CALL INIT_AMPLITUDES(h,def,Nx)
+      CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+   
+      NI=4; Nd=2
+      Nc=3; Mb=2
+      
+      Nj=0
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+                                                      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      
+      allocate(CY(1:Nx)) 
+      do icy=1,Nx
+        CY(icy)=exp(-0.5*h(icy)*h(icy)/100)/(10*sqrt(twopi))
+      enddo 
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) 
+         if (status.ne.0) then 
+             print *,'can not allocate BIG' 
+         end if 
+      allocate(ex(1:Ntime+Nc),stat=status)          
+         if (status.ne.0) then 
+             print *,'can not allocate ex' 
+         end if
+      allocate(ansrup(1:Ntime,1:Nx))
+      allocate(ansrlo(1:Ntime,1:Nx))
+      ansrup=0.d0
+      ansrlo=0.d0
+      allocate(fxind(1:Nx,1:2))    
+      fxind=0.d0 !this is not needed
+      allocate(xc(1:Nc,1:Nx))
+ 
+ 
+      allocate(a_up(Mb,NI-1)) 
+      allocate(a_lo(Mb,NI-1)) 
+        a_up=0.d0 
+        a_lo=0.d0
+        xc(1,1:Nx)=h(1:Nx)
+        xc(2,1:Nx)=u
+        xc(3,1:Nx)=u 
+        
+      if (def.GT.0) then
+         a_up(1,1)=0.d0 
+         a_lo(1,1)=u
+         a_up(1,2)=XdInf
+         a_lo(1,3)=-XdInf 
+         a_up(2,1)=1.d0      
+      else
+         a_up(1,1)=u 
+         a_lo(1,1)=0.d0
+         a_lo(1,2)=-XdInf
+         a_up(1,3)= XdInf  
+         a_lo(2,1)=1.d0 
+      endif
+      !print *,'Nstart',Nstart
+      Nstart=MAX(3,Nstart)  
+      
+     
+       if (SCIS.GT.0) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif 
+ 
+      !print *,'loop starts' 
+      do Ntd=Nstart,Ntime 
+ 
+         Ntdc=Ntd+Nc
+         ex=0.d0
+         BIG=0.d0 
+         CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period
+ 
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd; 
+
+          CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) 
+          !print *,'test',fxind/CY(1:Nx) 
+ 
+          do icy=1,Nx        
+            ansrup(Ntd,icy)=fxind(icy,1)*CC/CY(icy)
+            ansrlo(Ntd,icy)=fxind(icy,2)*CC/CY(icy)
+          enddo
+          if (SCIS.GT.0) then
+            write(11,*)  COV(1) ! save coefficient of variation
+          endif
+      if((Nx.gt.4).or.NIT.gt.4) print *,'Ready: ',Ntd,' of ',Ntime
+      enddo 
+      goto 300
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansrup(ts,ph),ansrlo(ts,ph)
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  continue
+      deallocate(BIG) 
+      deallocate(ex)
+      deallocate(fxind)
+      deallocate(ansrup)
+      deallocate(ansrlo)
+      deallocate(xc)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)  
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+
+      if (allocated(R3)) then
+        deallocate(R3)
+        deallocate(R4)
+        deallocate(h)
+      ENDIF
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,def,Ntime,Nstart,NIT,speed,Nx,dT)
+      IMPLICIT NONE
+      integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) def
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed 
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+     
+      if (abs(def).GT.1) then
+        READ (14,*) dT
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      else
+        if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      endif
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,def,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: def
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      !if (def.LT.0) THEN
+      !   H=-H
+      !endif      
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime,def
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+       enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      if (abs(def).GT.1) then      
+        open (unit=4, file='Cd3.in',STATUS='unknown')
+        open (unit=5, file='Cd4.in',STATUS='unknown')
+
+        do i=1,Ntime
+          read(4,*) R3(i)
+          read(5,*) R4(i)
+        enddo
+
+        close(4)
+        close(5)
+      endif
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,shft,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! For ts>1:
+! X(t2)..X(ts),..X(tn-1) X''(ts) X'(t1) X'(tn) X(ts) X(t1) X(tn) X'(ts) 
+! = [Xt                          Xd                    Xc]
+!
+! For ts<=1: 
+! X(t2)..,..X(tn-1)  X'(t1) X'(tn) Y X(t1) X(tn)  
+! = [Xt              Xd            Xc]
+!Add Y Condition : Y=h
+
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+      if (ts.LE.1) THEN
+	       Ntd1=tn
+          N=Ntd1+Nc;
+          shft=0  ! def=1 want only crest period Tc
+      else
+          Ntd1=tn+1
+          N=Ntd1+4
+          shft=1  ! def=2 or 3 want Tc Ac or Tcf, Ac
+      endif
+
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)
+	 BIG(i      ,Ntd1+1+shft) = 0.d0            !cov(X(ti+1),Y)   
+         BIG(i      ,Ntd1+2+shft) = R0(i+1)         !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+3+shft) = R0(i+1)         !cov(X(t.. ),X(tn))  
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)         =-R1(i+1)         !cov(X(ti+1),X' (t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X' (tn)) 
+      enddo
+      !call echo(big(1:tn,1:tn),tn)
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)     !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+
+!cov(Xc)
+      !print *,'t'
+      BIG(Ntd1+1+shft,Ntd1+1+shft) = 100.d0!100.d0         ! cov(Y,Y) 
+      BIG(Ntd1+1+shft,Ntd1+2+shft) = 0.d0
+      BIG(Ntd1+1+shft,Ntd1+3+shft) = 0.d0
+      BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+2+shft,Ntd1+3+shft) = R0(tn)       ! cov(X(t1),X (tn))
+      BIG(Ntd1+3+shft,Ntd1+3+shft) = R0(1)        ! cov(X(tn),X (tn))
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1+shft) = 0.d0            !cov(X'(tn),Y)     
+      BIG(Ntd1  ,Ntd1+2+shft) = R1(tn)       !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+3+shft) = 0.d0         !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+1+shft) = 0.d0         !cov(X'(t1),Y)
+      BIG(Ntd1-1,Ntd1+2+shft) = 0.d0         !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+3+shft) =-R1(tn)       !cov(X'(t1),X(tn))
+
+
+      !call echo(big(1:N,1:N),N) 
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+           BIG(i,j)=tmp
+        enddo
+        !call echo(big(1:N,1:N),N) 
+      enddo
+      !if (tn.eq.3) then
+      !do j=1,N
+      !  do i=j,N
+      !      print *,'test',j,i,BIG(j,i)
+      !  enddo
+        !call echo(big(1:N,1:N),N) 
+      !enddo
+      !endif
+      !call echo(big(1:N,1:N),N) 
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2Acdf1
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/bounds/cov2mmpdfb.f

@@ -0,0 +1,356 @@
+      PROGRAM sp2mM1
+C***********************************************************************************
+C     Computes upper lower bounds for density of maximum and the following minimum * 
+C***********************************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansrup
+      double precision, dimension(:,:),allocatable :: ansrlo
+      double precision, dimension(:  ),allocatable :: ex,h
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:,:),allocatable :: fxind
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable  :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nstart,Ntime,tn,ts,speed,seed1,seed_size
+      integer :: status,i,j,ij,Nx1
+      double precision :: ds,dT ! lag spacing for covariances
+ 
+! f90  sp2AmM1.f rind52.f 
+
+      CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,Nx1,dT) 
+      Nx=Nx1*(Nx1-1)/2 
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+ 
+      CALL INITDATA(speed)  
+ 
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      allocate(R3(1:Ntime+1))
+      allocate(R4(1:Ntime+1))
+      allocate(h(1:Nx1)) 
+
+      CALL INIT_AMPLITUDES(h,Nx1)
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) 
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Y=  X'(t2)...X'(tn-1)||X''(t1) X''(tn)||X(t1) X(tn) X'(t1) X'(tn)          !!
+! = [       Xt                   Xd                    Xc            ]       !!
+!                                                                            !!
+! Nt=tn-2, Nd=2, Nc=4                                                        !!
+!                                                                            !!
+! Xt= contains Nt time points in the indicator function                      !!
+! Xd=    "     Nd    derivatives                                             !!
+! Xc=    "     Nc    variables to condition on                               !!
+!                                                                            !!
+! There are 3 ( NI=4) regions with constant bariers:                         !!
+! (indI(1)=0);     for i\in (indI(1),indI(2)]    Y(i)<0.                     !!
+! (indI(2)=Nt)  ;  for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1))     !!
+! (indI(3)=Nt+1);  for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn))     !!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+
+      NI=4; Nd=2
+      Nc=4; Mb=1
+      
+      Nj=0
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(R4(1))
+      XtInf=10.d0*SQRT(-R2(1))
+                                                      ! normalizing constant
+      CC=TWOPI*SQRT(-R2(1)/R4(1))
+ 
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) 
+         if (status.ne.0) then 
+             print *,'can not allocate BIG' 
+         end if 
+      allocate(ex(1:Ntime+Nc),stat=status)          
+         if (status.ne.0) then 
+             print *,'can not allocate ex' 
+         end if
+      allocate(ansrup(1:Nx1,1:Nx1))
+      ansrup=0.d0
+      allocate(ansrlo(1:Nx1,1:Nx1))
+      ansrlo=0.d0
+      allocate(fxind(1:Nx,1:2))    
+      fxind=0.d0 !this is not needed
+      allocate(xc(1:Nc,1:Nx))
+ 
+ 
+      allocate(a_up(Mb,NI-1)) 
+      allocate(a_lo(Mb,NI-1)) 
+ 
+        a_up=0.d0 
+        a_lo=0.d0 
+ 
+        ij=0 
+        do i=2,Nx1 
+           do j=1,i-1 
+             ij=ij+1
+             xc(1,ij)=h(i)
+             xc(2,ij)=h(j) 
+           enddo 
+        enddo
+        xc(3,1:Nx)=0.d0
+        xc(4,1:Nx)=0.d0 
+        
+        a_lo(1,1)=-Xtinf
+        a_lo(1,2)=-XdInf
+        a_up(1,3)=+XdInf 
+             
+ 
+      Nstart=MAX(2,Nstart)  
+      
+     
+       if (SCIS.GT.0) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif 
+ 
+      do Ntd=Nstart,Ntime 
+ 
+         Ntdc=Ntd+Nc
+         ex=0.d0
+         BIG=0.d0 
+         CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,R0,R1,R2,R3,R4) ! positive wave period
+ 
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd; 
+
+          CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) 
+          ij=0 
+          do i=2,Nx1 
+             do j=1,i-1 
+                 ij=ij+1  
+                 ansrup(i,j)=ansrup(i,j)+fxind(ij,1)*CC*dt
+                 ansrlo(i,j)=ansrlo(i,j)+fxind(ij,2)*CC*dt
+             enddo 
+          enddo
+ 
+          if (SCIS.GT.0) then
+            write(11,*)  COV(1) ! save coefficient of variation
+          endif       
+          print *,'Ready: ',Ntd,' of ',Ntime
+      enddo 
+      goto 300
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+      do i=1,Nx1 
+        do j=1,Nx1 
+           write(11,*)  ansrup(i,j),ansrlo(i,j)
+        enddo 
+      enddo
+      close(11)
+ 900  continue
+      deallocate(BIG) 
+      deallocate(ex)
+      deallocate(fxind)
+      deallocate(ansrup)
+      deallocate(ansrlo)
+      deallocate(xc)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)  
+      deallocate(R3)
+      deallocate(R4)
+      deallocate(h)
+ 
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (Ntime,Nstart,NIT,speed,Nx,dT)
+      IMPLICIT NONE
+      integer, intent(out):: Ntime,Nstart,NIT,speed,Nx
+      double precision ,intent(out) :: dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed 
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+      READ (14,*) dT
+     
+      if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+      end if
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      open (unit=4, file='Cd3.in',STATUS='unknown')
+      open (unit=5, file='Cd4.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+         read(4,*) R3(i)
+         read(5,*) R4(i)
+       enddo
+      close(1)
+      close(2)
+      close(3)
+      close(3)
+      close(5)
+      return
+      END SUBROUTINE INIT_COVARIANCES
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn
+      integer :: i,j,N 
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+!    X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X(t1),X(tn),X'(t1),X'(tn) 
+! = [          Xt               |      Xd       |          Xc             ]
+!
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+ 
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+       
+      N=tn+4
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1))
+         enddo
+      !cov(Xt,Xc)
+         BIG(i      ,tn+1) =  R1(i+1)         !cov(X'(ti+1),X(t1))  
+         BIG(tn-1-i ,tn+2) = -R1(i+1)         !cov(X'(ti+1),X(tn))  
+         BIG(i      ,tn+3) = -R2(i+1)         !cov(X'(ti+1),X'(t1))  
+         BIG(tn-1-i ,tn+4) = -R2(i+1)         !cov(X'(ti+1),X'(tn))  
+      !Cov(Xt,Xd)
+         BIG(i,tn-1)       = R3(i+1)          !cov(X'(ti+1),X''(t1))  
+         BIG(tn-1-i,tn)    =-R3(i+1)          !cov(X'(ti+1),X''(tn)) 
+      enddo
+      
+!cov(Xd)
+      BIG(tn-1  ,tn-1  ) = R4(1)
+      BIG(tn-1,tn      ) = R4(tn)     !cov(X''(t1),X''(tn))
+      BIG(tn    ,tn    ) = R4(1)
+
+!cov(Xc)
+      BIG(tn+1,tn+1) = R0(1)        ! cov(X(t1),X(t1))
+      BIG(tn+1,tn+2) = R0(tn)       ! cov(X(t1),X(tn))
+      BIG(tn+1,tn+3) = 0.d0         ! cov(X(t1),X'(t1))
+      BIG(tn+1,tn+4) = R1(tn)       ! cov(X(t1),X'(tn))
+      BIG(tn+2,tn+2) = R0(1)        ! cov(X(tn),X(tn))
+      BIG(tn+2,tn+3) =-R1(tn)       ! cov(X(tn),X'(t1))
+      BIG(tn+2,tn+4) = 0.d0         ! cov(X(tn),X'(tn)) 
+      BIG(tn+3,tn+3) =-R2(1)        ! cov(X'(t1),X'(t1))
+      BIG(tn+3,tn+4) =-R2(tn)       ! cov(X'(t1),X'(tn))
+      BIG(tn+4,tn+4) =-R2(1)       ! cov(X'(tn),X'(tn))
+!Xc=X(t1),X(tn),X'(t1),X'(tn) 
+!Xd=X''(t1),X''(tn)
+!cov(Xd,Xc)
+      BIG(tn-1  ,tn+1) = R2(1)           !cov(X''(t1),X(t1))     
+      BIG(tn-1  ,tn+2) = R2(tn)          !cov(X''(t1),X(tn))     
+      BIG(tn-1  ,tn+3) = 0.d0            !cov(X''(t1),X'(t1))     
+      BIG(tn-1  ,tn+4) = R3(tn)          !cov(X''(t1),X'(tn))     
+      BIG(tn    ,tn+1) = R2(tn)          !cov(X''(tn),X(t1))     
+      BIG(tn    ,tn+2) = R2(1)           !cov(X''(tn),X(tn))     
+      BIG(tn    ,tn+3) =-R3(tn)          !cov(X''(tn),X'(t1))     
+      BIG(tn    ,tn+4) = 0.d0            !cov(X''(tn),X'(tn))     
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+           BIG(i,j)=tmp
+        enddo
+      enddo
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+
+      END  PROGRAM  sp2mM1
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/bounds/cov2tccpdfb.f

@@ -0,0 +1,504 @@
+      PROGRAM sp2tccpdf1 
+C*********************************************************************** 
+C     This program computes upper and lower bounds for the:            * 
+C                                                                      * 
+C     density of     T=  T_1+T_2 in a gaussian process i.e.            * 
+C                                                                      * 
+C      wavelengthes for crests <h1 and troughs >h2                     *     
+C                                                                      * 
+C     Sylvie  and Igor 7 dec. 1999                                    * 
+C*********************************************************************** 
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb, 
+     &   NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV 
+      use rind 
+      IMPLICIT NONE 
+      double precision, dimension(:,:),allocatable :: BIG 
+      double precision, dimension(:,:),allocatable :: ansrup 
+      double precision, dimension(:,:),allocatable :: ansrlo 
+      double precision, dimension(:  ),allocatable :: ex,CY1,CY2 
+      double precision, dimension(:,:),allocatable :: xc 
+      double precision, dimension(:,:),allocatable ::fxind 
+      double precision, dimension(:  ),allocatable :: h1,h2 
+      double precision, dimension(:  ),allocatable :: hh1,hh2 
+      double precision, dimension(:  ),allocatable :: R0,R1,R2 
+      double precision             ::CC,U,XddInf,XdInf,XtInf   
+      double precision, dimension(:,:),allocatable :: a_up,a_lo 
+      integer         , dimension(:  ),allocatable :: seed 
+      integer ,dimension(7) :: indI 
+      integer :: Ntime,N0,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2 
+      integer :: icy,icy2 
+      double precision :: ds,dT ! lag spacing for covariances  
+! DIGITAL: 
+! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf.exe rind48.f sp2tthpdf.f 
+! SOLARIS: 
+!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind48.f sp2tthpdf.f 
+ 
+      !print *,'enter sp2thpdf' 
+      CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) 
+       
+      !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT' 
+      !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT 
+      !Nx1=1 
+      !Nx2=1 
+ 
+      Nx=Nx1*Nx2 
+      !print *,'NN',Nx1,Nx2,Nx 
+       
+       
+      !XSPLT=1.5d0 
+      if (SCIS.GT.0) then 
+        allocate(COV(1:Nx)) 
+        call random_seed(SIZE=seed_size)  
+        allocate(seed(seed_size))  
+        call random_seed(GET=seed(1:seed_size))  ! get current seed 
+        seed(1)=seed1                            ! change seed 
+        call random_seed(PUT=seed(1:seed_size))  
+        deallocate(seed) 
+      endif 
+      CALL INITDATA(speed)   
+      !print *,ntime,speed,u,NIT 
+      allocate(R0(1:Ntime+1)) 
+      allocate(R1(1:Ntime+1)) 
+      allocate(R2(1:Ntime+1)) 
+       
+      allocate(h1(1:Nx1)) 
+      allocate(h2(1:Nx2)) 
+      CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2) 
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2) 
+       
+ 
+      allocate(hh1(1:Nx)) 
+      allocate(hh2(1:Nx)) 
+      !h transformation 
+      do icy=1,Nx1 
+         do icy2=1,Nx2 
+         hh1((icy-1)*Nx2+icy2)=h1(icy); 
+         hh2((icy-1)*Nx2+icy2)=h2(icy2);  
+         enddo  
+      enddo 
+ 
+      Nj=0 
+      indI(1)=0 
+ 
+C     ***** The bound 'infinity' is set to 10*sigma ***** 
+      XdInf=10.d0*SQRT(-R2(1)) 
+      XtInf=10.d0*SQRT(R0(1)) 
+      !h1(1)=XtInf 
+      !h2(1)=XtInf 
+      ! normalizing constant 
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) ) 
+      allocate(CY1(1:Nx))  
+      allocate(CY2(1:Nx))  
+      do icy=1,Nx 
+        CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi)) 
+        CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi)) 
+      enddo 
+      !print *,CY1 
+      allocate(ansrup(1:Ntime,1:Nx)) 
+      allocate(ansrlo(1:Ntime,1:Nx)) 
+      ansrup=0.d0 
+      ansrlo=0.d0 
+      allocate(fxind(1:Nx,1:2))     
+      !fxind=0.d0 this is not needed 
+    
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
+! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !! 
+! = [Xt                          Xd                    Xc]                   !! 
+!                                                                            !! 
+! Nt=tn-2, Nd=3, Nc=2+3                                                      !! 
+!                                                                            !! 
+! Xt= contains Nt time points in the indicator function                      !! 
+! Xd=    "     Nd    derivatives                                             !! 
+! Xc=    "     Nc    variables to condition on                               !! 
+! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd     !! 
+!                                                                            !! 
+! There are 6 ( NI=7) regions with constant bariers:                         !! 
+! (indI(1)=0);     for i\in (indI(1),indI(2)] u<Y(i)<h1                      !! 
+! (indI(2)=ts-2);  for i\in (indI(2),indI(2)], inf<Y(i)<inf (no restr.)      !! 
+! (indI(3)=ts-1);  for i\in (indI(3),indI(4)], h2 <Y(i)<u                    !! 
+! (indI(4)=Nt)  ;  for i\in (indI(4),indI(5)], Y(i)<0 (deriv. X'(ts))        !! 
+! (indI(5)=Nt+1);  for i\in (indI(5),indI(6)], Y(i)>0 (deriv. X'(t1))        !! 
+! (indI(6)=Nt+2);  for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn))        !! 
+! (indI(7)=Nt+3);  NI=7.                                                     !! 
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
+ 
+       
+      NI=7; Nd=3 
+      Nc=5; Mb=3 
+      allocate(a_up(1:Mb,1:(NI-1))) 
+      allocate(a_lo(1:Mb,1:(NI-1))) 
+      a_up=0.d0 
+      a_lo=0.d0 
+      allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1)))  
+      ALLOCATE(xc(1:Nc,1:Nx)) 
+      allocate(ex(1:(Ntime+Nc+1))) 
+      !print *,size(ex),Ntime 
+      ex=0.d0 
+      !print *,size(ex),ex 
+      xc(1,1:Nx)=hh1(1:Nx) 
+      xc(2,1:Nx)=hh2(1:Nx) 
+      xc(3,1:Nx)=u 
+      xc(4,1:Nx)=u 
+      xc(5,1:Nx)=u 
+         ! upp- down- upp-crossings at t1,ts,tn 
+        
+        a_lo(1,1)=u 
+        a_up(1,2)=XtInf   ! X(ts) is redundant   
+        a_lo(1,2)=-Xtinf 
+        a_up(1,3)=u 
+    
+  
+        a_lo(1,4)=-XdInf 
+        a_up(1,5)= XdInf 
+        a_up(1,6)= XdInf   
+ 
+        a_up(2,1)=1.d0 
+        a_lo(3,3)=1.d0 !signe a voir!!!!!! 
+!        print *,a_up 
+!        print *,a_lo 
+      do tn=N0,Ntime,1 
+!      do tn=Ntime,Ntime,1 
+        Ntd=tn+1 
+        Nt=Ntd-Nd 
+        Ntdc=Ntd+Nc 
+        indI(4)=Nt 
+        indI(5)=Nt+1 
+        indI(6)=Nt+2 
+        indI(7)=Ntd 
+        if (SCIS.gt.0) then 
+           if (SCIS.EQ.2) then            
+              Nj=max(Nt,0) 
+           else 
+              Nj=min(max(Nt-5, 0),0) 
+           endif 
+        endif 
+        do ts=3,tn-2 
+         !print *,'ts,tn' ,ts,tn,Ntdc 
+         CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period 
+         indI(2)=ts-2 
+         indI(3)=ts-1 
+          
+ 
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc), 
+     &              xc,indI,a_lo,a_up) 
+          
+        ds=dt 
+         do icy=1,Nx 
+         ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2) 
+         ansrup(tn,icy)=ansrup(tn,icy)+fxind(icy,1)*CC*ds 
+     &                          /(CY1(icy)*CY2(icy)) 
+         ansrlo(tn,icy)=ansrlo(tn,icy)+fxind(icy,2)*CC*ds 
+     &                          /(CY1(icy)*CY2(icy)) 
+         enddo 
+        enddo ! ts 
+        print *,'Ready: ',tn,' of ',Ntime 
+ 
+      enddo !tn 
+   
+ 300  open (unit=11, file='dens.out',  STATUS='unknown') 
+    
+      do ts=1,Ntime 
+         do ph=1,Nx 
+            !write(11,*)  ansrup(ts,ph),ansrlo(ts,ph) 
+            write(11,111)  ansrup(ts,ph),ansrlo(ts,ph) 
+         enddo 
+      enddo 
+ 111  FORMAT(2x,F12.8,2x,F12.8)   
+      close(11) 
+ 900  deallocate(big) 
+      deallocate(fxind) 
+      deallocate(ansrup) 
+      deallocate(ansrlo) 
+      deallocate(xc) 
+      deallocate(ex) 
+      deallocate(R0) 
+      deallocate(R1) 
+      deallocate(R2) 
+      if (allocated(COV) ) then 
+         deallocate(COV) 
+      endif 
+        deallocate(h1) 
+        deallocate(h2) 
+        deallocate(hh1) 
+        deallocate(hh2) 
+        deallocate(a_up) 
+        deallocate(a_lo) 
+      stop 
+      !return 
+ 
+      CONTAINS 
+       
+     
+             
+      SUBROUTINE INIT_LEVELS 
+     & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT) 
+      IMPLICIT NONE 
+      integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1 
+      double precision ,intent(out) :: U,dT 
+      
+ 
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') 
+      READ (14,*) U 
+      READ (14,*) Ntime 
+      READ (14,*) N0 
+      READ (14,*) NIT 
+      READ (14,*) speed    
+      READ (14,*) SCIS    
+      READ (14,*) seed1    
+ 
+ 
+        READ (14,*) Nx1,Nx2 
+        READ (14,*) dT 
+        if (Ntime.lt.5) then 
+           print *,'The number of wavelength points is too small, stop' 
+           stop 
+        end if 
+       
+      CLOSE(UNIT=14) 
+        
+      RETURN 
+      END SUBROUTINE INIT_LEVELS 
+  
+C****************************************************** 
+      SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2)       
+      IMPLICIT NONE 
+      double precision, dimension(:), intent(out) :: h1,h2     
+      integer, intent(in) :: Nx1,Nx2 
+      integer :: ix 
+       
+  
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN') 
+ 
+C 
+C Reading in amplitudes 
+C 
+      do ix=1,Nx1 
+        READ (4,*) H1(ix) 
+      enddo 
+      do ix=1,Nx2 
+        READ (4,*) H2(ix) 
+      enddo 
+      CLOSE(UNIT=4) 
+       
+      RETURN 
+      END SUBROUTINE INIT_AMPLITUDES 
+ 
+C************************************************** 
+ 
+C*********************************************************************** 
+C*********************************************************************** 
+        
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2) 
+      IMPLICIT NONE 
+      double precision, dimension(:),intent(out) :: R0,R1,R2 
+      integer,intent(in) :: Ntime 
+      integer :: i 
+      open (unit=1, file='Cd0.in',STATUS='unknown') 
+      open (unit=2, file='Cd1.in',STATUS='unknown') 
+      open (unit=3, file='Cd2.in',STATUS='unknown') 
+ 
+      do i=1,Ntime 
+         read(1,*) R0(i) 
+         read(2,*) R1(i) 
+         read(3,*) R2(i) 
+      enddo 
+      close(1) 
+      close(2) 
+      close(3) 
+       
+      return 
+      END SUBROUTINE INIT_COVARIANCES 
+       
+C*********************************************************************** 
+C*********************************************************************** 
+ 
+C********************************************************************** 
+ 
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2) 
+      IMPLICIT NONE 
+      double precision, dimension(:,:),intent(inout) :: BIG 
+      double precision, dimension(:),intent(in) :: R0,R1,R2 
+      integer ,intent(in) :: tn,ts 
+      integer :: i,j,Ntd1,N !=Ntdc 
+      double precision :: tmp  
+! the order of the variables in the covariance matrix 
+! are organized as follows:  
+!  
+! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)||  
+! = [Xt                          Xd                    Xc] 
+! where  
+! 
+! Xt= time points in the indicator function 
+! Xd= derivatives 
+! Xc=variables to condition on 
+ 
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s), 
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have 
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result). 
+! 
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|) 
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|) 
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|) 
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|) 
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|) 
+ 
+      Ntd1=tn+1 
+      N=Ntd1+Nc 
+      do i=1,tn-2 
+      !cov(Xt) 
+         do j=i,tn-2 
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1)) 
+         enddo 
+      !cov(Xt,Xc) 
+	 BIG(i      ,Ntd1+1) = 0.d0          !cov(X(ti+1),Y1)   
+         BIG(i      ,Ntd1+2) = 0.d0          !cov(X(ti+1),Y2)   
+         BIG(i      ,Ntd1+4) = R0(i+1)       !cov(X(ti+1),X(t1))   
+         BIG(tn-1-i ,Ntd1+5) = R0(i+1)       !cov(X(t.. ),X(tn))   
+ 
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj) 
+         BIG(i,Ntd1-1)   =-R1(i+1)         !cov(X(ti+1),X'(t1))   
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X'(tn))  
+      enddo 
+!cov(Xd) 
+      BIG(Ntd1  ,Ntd1  ) = -R2(1) 
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)        !cov(X'(t1),X'(tn)) 
+      BIG(Ntd1-1,Ntd1-1) = -R2(1) 
+      BIG(Ntd1-2,Ntd1-1) = -R2(ts)        !cov(X'(ts),X'(t1)) 
+      BIG(Ntd1-2,Ntd1-2) = -R2(1) 
+      BIG(Ntd1-2,Ntd1  ) = -R2(tn+1-ts)   !cov(X'(ts),X'(tn)) 
+ 
+!cov(Xc) 
+      BIG(Ntd1+1,Ntd1+1) = 100.d0        ! cov(Y1 Y1)  
+      BIG(Ntd1+1,Ntd1+2) = 0.d0          ! cov(Y1 Y2)  
+      BIG(Ntd1+1,Ntd1+3) = 0.d0          ! cov(Y1 X(ts))  
+      BIG(Ntd1+1,Ntd1+4) = 0.d0          ! cov(Y1 X(t1))  
+      BIG(Ntd1+1,Ntd1+5) = 0.d0          ! cov(Y1 X(tn)) 
+      BIG(Ntd1+2,Ntd1+2) = 100.d0        ! cov(Y2 Y2)  
+      BIG(Ntd1+2,Ntd1+3) = 0.d0          ! cov(Y2 X(ts))  
+      BIG(Ntd1+2,Ntd1+4) = 0.d0          ! cov(Y2 X(t1))  
+      BIG(Ntd1+2,Ntd1+5) = 0.d0          ! cov(Y2 X(tn)) 
+ 
+      BIG(Ntd1+3,Ntd1+3) = R0(1)        ! cov(X(ts),X (ts) 
+      BIG(Ntd1+3,Ntd1+4) = R0(ts)       ! cov(X(ts),X (t1)) 
+      BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts)  ! cov(X(ts),X (tn)) 
+      BIG(Ntd1+4,Ntd1+4) = R0(1)        ! cov(X(t1),X (t1))  
+      BIG(Ntd1+4,Ntd1+5) = R0(tn)       ! cov(X(t1),X (tn)) 
+      BIG(Ntd1+5,Ntd1+5) = R0(1)        ! cov(X(tn),X (tn)) 
+   
+ 
+!cov(Xd,Xc) 
+      BIG(Ntd1  ,Ntd1+1) = 0.d0        !cov(X'(tn),Y1)  
+      BIG(Ntd1  ,Ntd1+2) = 0.d0        !cov(X'(tn),Y2)  
+      BIG(Ntd1-1  ,Ntd1+1) = 0.d0        !cov(X'(t1),Y1)  
+      BIG(Ntd1-1  ,Ntd1+2) = 0.d0        !cov(X'(t1),Y2)  
+      BIG(Ntd1-2  ,Ntd1+1) = 0.d0        !cov(X'(ts),Y1)  
+      BIG(Ntd1-2  ,Ntd1+2) = 0.d0        !cov(X'(ts),Y2)  
+   
+      BIG(Ntd1  ,Ntd1+4) = R1(tn)        !cov(X'(tn),X(t1))      
+      BIG(Ntd1  ,Ntd1+5) = 0.d0          !cov(X'(tn),X(tn)) 
+      BIG(Ntd1-1,Ntd1+4) = 0.d0          !cov(X'(t1),X(t1)) 
+      BIG(Ntd1-1,Ntd1+5) =-R1(tn)        !cov(X'(t1),X(tn)) 
+      BIG(Ntd1  ,Ntd1+3) = R1(tn+1-ts)   !cov(X'(tn),X (ts))   
+      BIG(Ntd1-1,Ntd1+3) =-R1(ts)        !cov(X'(t1),X (ts))    
+      BIG(Ntd1-2,Ntd1+3) = 0.d0          !cov(X'(ts),X (ts) 
+      BIG(Ntd1-2,Ntd1+4) = R1(ts)        !cov(X'(ts),X (t1)) 
+      BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts)  !cov(X'(ts),X (tn)) 
+ 
+ 
+        do i=1,tn-2 
+          j=abs(i+1-ts) 
+!cov(Xt,Xc) 
+          BIG(i,Ntd1+3)   = R0(j+1)      !cov(X(ti+1),X(ts))           
+!Cov(Xt,Xd) 
+          if ((i+1-ts).lt.0) then 
+              BIG(i,Ntd1-2)  =  R1(j+1) 
+            else                         !cov(X(ti+1),X'(ts))   
+              BIG(i,Ntd1-2)  = -R1(j+1) 
+          endif 
+      enddo 
+     
+! make lower triangular part equal to upper  
+      do j=1,N-1 
+        do i=j+1,N 
+           tmp =BIG(j,i) 
+ 
+           BIG(i,j)=tmp 
+        enddo 
+      enddo 
+ 
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) 
+C 10  format(6F8.4) 
+      RETURN 
+      END  SUBROUTINE COV_INPUT 
+ 
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2) 
+      IMPLICIT NONE 
+      double precision, dimension(:,:), intent(out) :: BIG 
+      double precision, dimension(:), intent(in) ::  R0,R1,R2 
+      integer :: pt,i,j 
+! the order of the variables in the covariance matrix 
+! are organized as follows; 
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc] 
+!  
+! where Xd is the derivatives  
+! 
+! Xt= time points in the indicator function 
+! Xd= derivatives 
+! Xc=variables to condition on 
+ 
+!cov(Xc) 
+      BIG(pt+2,pt+2) = R0(1) 
+      BIG(pt+1,pt+1) = R0(1) 
+      BIG(pt+1,pt+2) = R0(pt) 
+!cov(Xd) 
+      BIG(pt,pt)     = -R2(1) 
+      BIG(pt-1,pt-1) = -R2(1) 
+      BIG(pt-1,pt)   = -R2(pt) 
+!cov(Xd,Xc) 
+      BIG(pt,pt+2)   =  0.d0 
+      BIG(pt,pt+1)   = R1(pt) 
+      BIG(pt-1,pt+2) = -R1(pt) 
+      BIG(pt-1,pt+1) =  0.d0 
+  
+      if (pt.GT.2) then 
+!cov(Xt) 
+         do i=1,pt-2 
+           do j=i,pt-2 
+              BIG(i,j) = R0(j-i+1) 
+           enddo 
+        enddo 
+!cov(Xt,Xc) 
+        do i=1,pt-2 
+           BIG(i,pt+1)      = R0(i+1) 
+           BIG(pt-1-i,pt+2) = R0(i+1) 
+        enddo 
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj)) 
+        do i=1,pt-2 
+           BIG(i,pt-1)   = -R1(i+1) 
+           BIG(pt-1-i,pt)=  R1(i+1) 
+        enddo 
+      endif 
+ 
+ 
+      ! make lower triangular part equal to upper  
+      do j=1,pt+1 
+         do i=j+1,pt+2 
+            BIG(i,j)=BIG(j,i) 
+         enddo 
+      enddo 
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6) 
+C 10   format(6F8.4) 
+      RETURN 
+      END  SUBROUTINE COV_INPUT2  
+ 
+ 
+      END  PROGRAM  sp2tccpdf1 
+        
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 

wafo/source/cov2XXXpdf/bounds/cov2tthpdfb.f

@@ -0,0 +1,497 @@
+      PROGRAM sp2tthpdf1
+C***********************************************************************
+C     This program computes:                                           *
+C                                                                      *
+C     density of     T=  T_1+T_2 in a gaussian process i.e.            *
+C                                                                      *
+C      wavelengthes for crests <h1 and troughs >h2                     *    
+C                                                                      *
+C     Sylvie  and Igor 7 dec. 1999                                    *
+C***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &   NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex,CY1,CY2
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h1,h2
+      double precision, dimension(:  ),allocatable :: hh1,hh2
+      double precision, dimension(:  ),allocatable :: R0,R1,R2
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Ntime,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2,N0
+      integer :: icy,icy2
+      double precision :: ds,dT ! lag spacing for covariances 
+! DIGITAL:
+! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf1.exe rind49.f sp2tthpdf1.f
+! SOLARIS:
+!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind49.f sp2tthpdf1.f
+
+      !print *,'enter sp2thpdf'
+      CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
+      
+      !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT
+      !Nx1=1
+      !Nx2=1
+
+      Nx=Nx1*Nx2
+      !print *,'NN',Nx1,Nx2,Nx
+      
+      
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      
+      allocate(h1(1:Nx1))
+      allocate(h2(1:Nx2))
+      CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2)
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2)
+      
+
+      allocate(hh1(1:Nx))
+      allocate(hh2(1:Nx))
+      !h transformation
+      do icy=1,Nx1
+         do icy2=1,Nx2
+         hh1((icy-1)*Nx2+icy2)=h1(icy);
+         hh2((icy-1)*Nx2+icy2)=h2(icy2); 
+         enddo 
+      enddo
+
+      Nj=0
+      indI(1)=0
+
+C     ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+      !h1(1)=XtInf
+      !h2(1)=XtInf
+      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      allocate(CY1(1:Nx)) 
+      allocate(CY2(1:Nx)) 
+      do icy=1,Nx
+        CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi))
+        CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi))
+      enddo
+      !print *,CY1
+      allocate(ansr(1:Ntime,1:Nx))
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      fxind=0.d0 
+   
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !!
+! = [Xt                          Xd                    Xc]                   !!
+!                                                                            !!
+! Nt=tn-2, Nd=3, Nc=2+3                                                      !!
+!                                                                            !!
+! Xt= contains Nt time points in the indicator function                      !!
+! Xd=    "     Nd    derivatives                                             !!
+! Xc=    "     Nc    variables to condition on                               !!
+! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd     !!
+!                                                                            !!
+! There are 6 ( NI=7) regions with constant bariers:                         !!
+! (indI(1)=0);     for i\in (indI(1),indI(2)] u<Y(i)<h1                      !!
+! (indI(2)=ts-2);  for i\in (indI(2),indI(2)], inf<Y(i)<inf (no restr.)      !!
+! (indI(3)=ts-1);  for i\in (indI(3),indI(4)], h2 <Y(i)<u                    !!
+! (indI(4)=Nt)  ;  for i\in (indI(4),indI(5)], Y(i)<0 (deriv. X'(ts))        !!
+! (indI(5)=Nt+1);  for i\in (indI(5),indI(6)], Y(i)>0 (deriv. X'(t1))        !!
+! (indI(6)=Nt+2);  for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn))        !!
+! (indI(7)=Nt+3);  NI=7.                                                     !!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+      
+      NI=7; Nd=3
+      Nc=5; Mb=3
+      allocate(a_up(1:Mb,1:(NI-1)))
+      allocate(a_lo(1:Mb,1:(NI-1)))
+      a_up=0.d0
+      a_lo=0.d0
+      allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) 
+      ALLOCATE(xc(1:Nc,1:Nx))
+      allocate(ex(1:(Ntime+Nc+1)))
+      !print *,size(ex),Ntime
+      ex=0.d0
+      !print *,size(ex),ex
+      xc(1,1:Nx)=hh1(1:Nx)
+      xc(2,1:Nx)=hh2(1:Nx)
+      xc(3,1:Nx)=u
+      xc(4,1:Nx)=u
+      xc(5,1:Nx)=u
+         ! upp- down- upp-crossings at t1,ts,tn
+       
+        a_lo(1,1)=u
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf
+        a_up(1,3)=u
+   
+ 
+        a_lo(1,4)=-XdInf
+        a_up(1,5)= XdInf
+        a_up(1,6)= XdInf  
+
+        a_up(2,1)=1.d0
+        a_lo(3,3)=1.d0 !signe a voir!!!!!!
+!        print *,a_up
+!        print *,a_lo
+      do tn=N0,Ntime,1
+!      do tn=Ntime,Ntime,1
+        Ntd=tn+1
+        Nt=Ntd-Nd
+        Ntdc=Ntd+Nc
+        indI(4)=Nt
+        indI(5)=Nt+1
+        indI(6)=Nt+2
+        indI(7)=Ntd
+        if (SCIS.gt.0) then
+           if (SCIS.EQ.2) then           
+              Nj=max(Nt,0)
+           else
+              Nj=min(max(Nt-5, 0),0)
+           endif
+        endif
+        do ts=3,tn-2
+         !print *,'ts,tn' ,ts,tn,Ntdc
+         CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period
+         indI(2)=ts-2
+         indI(3)=ts-1
+         
+
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
+     &              xc,indI,a_lo,a_up)
+         
+        ds=dt
+         do icy=1,Nx
+         ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2)
+         ansr(tn,icy)=ansr(tn,icy)+fxind(icy)*CC*ds/(CY1(icy)*CY2(icy))
+         enddo
+        enddo ! ts
+        print *,'Ready: ',tn,' of ',Ntime
+
+      enddo !tn
+      !print *,'ansr',ansr
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+      !print *, ansr
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansr(ts,ph),hh1(ph),hh2(ph)
+            ! write(11,111)  ansr(ts,ph)
+
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  deallocate(big)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(ex)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+        deallocate(h1)
+        deallocate(h2)
+        deallocate(hh1)
+        deallocate(hh2)
+        deallocate(a_up)
+        deallocate(a_lo)
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
+      IMPLICIT NONE
+      integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) Ntime
+      READ (14,*) N0
+      READ (14,*) NIT
+      READ (14,*) speed   
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+
+
+        READ (14,*) Nx1,Nx2
+        READ (14,*) dT
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h1,h2    
+      integer, intent(in) :: Nx1,Nx2
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx1
+        READ (4,*) H1(ix)
+      enddo
+      do ix=1,Nx2
+        READ (4,*) H2(ix)
+      enddo
+      CLOSE(UNIT=4)
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      integer,intent(in) :: Ntime
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+      enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! 
+! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| 
+! = [Xt                          Xd                    Xc]
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+
+      Ntd1=tn+1
+      N=Ntd1+Nc
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)
+	 BIG(i      ,Ntd1+1) = 0.d0          !cov(X(ti+1),Y1)  
+         BIG(i      ,Ntd1+2) = 0.d0          !cov(X(ti+1),Y2)  
+         BIG(i      ,Ntd1+4) = R0(i+1)       !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+5) = R0(i+1)       !cov(X(t.. ),X(tn))  
+
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)   =-R1(i+1)         !cov(X(ti+1),X'(t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X'(tn)) 
+      enddo
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)        !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+      BIG(Ntd1-2,Ntd1-1) = -R2(ts)        !cov(X'(ts),X'(t1))
+      BIG(Ntd1-2,Ntd1-2) = -R2(1)
+      BIG(Ntd1-2,Ntd1  ) = -R2(tn+1-ts)   !cov(X'(ts),X'(tn))
+
+!cov(Xc)
+      BIG(Ntd1+1,Ntd1+1) = 100.d0        ! cov(Y1 Y1) 
+      BIG(Ntd1+1,Ntd1+2) = 0.d0          ! cov(Y1 Y2) 
+      BIG(Ntd1+1,Ntd1+3) = 0.d0          ! cov(Y1 X(ts)) 
+      BIG(Ntd1+1,Ntd1+4) = 0.d0          ! cov(Y1 X(t1)) 
+      BIG(Ntd1+1,Ntd1+5) = 0.d0          ! cov(Y1 X(tn))
+      BIG(Ntd1+2,Ntd1+2) = 100.d0        ! cov(Y2 Y2) 
+      BIG(Ntd1+2,Ntd1+3) = 0.d0          ! cov(Y2 X(ts)) 
+      BIG(Ntd1+2,Ntd1+4) = 0.d0          ! cov(Y2 X(t1)) 
+      BIG(Ntd1+2,Ntd1+5) = 0.d0          ! cov(Y2 X(tn))
+
+      BIG(Ntd1+3,Ntd1+3) = R0(1)        ! cov(X(ts),X (ts)
+      BIG(Ntd1+3,Ntd1+4) = R0(ts)       ! cov(X(ts),X (t1))
+      BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts)  ! cov(X(ts),X (tn))
+      BIG(Ntd1+4,Ntd1+4) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+4,Ntd1+5) = R0(tn)       ! cov(X(t1),X (tn))
+      BIG(Ntd1+5,Ntd1+5) = R0(1)        ! cov(X(tn),X (tn))
+  
+
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1) = 0.d0        !cov(X'(tn),Y1) 
+      BIG(Ntd1  ,Ntd1+2) = 0.d0        !cov(X'(tn),Y2) 
+      BIG(Ntd1-1  ,Ntd1+1) = 0.d0        !cov(X'(t1),Y1) 
+      BIG(Ntd1-1  ,Ntd1+2) = 0.d0        !cov(X'(t1),Y2) 
+      BIG(Ntd1-2  ,Ntd1+1) = 0.d0        !cov(X'(ts),Y1) 
+      BIG(Ntd1-2  ,Ntd1+2) = 0.d0        !cov(X'(ts),Y2) 
+  
+      BIG(Ntd1  ,Ntd1+4) = R1(tn)        !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+5) = 0.d0          !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+4) = 0.d0          !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+5) =-R1(tn)        !cov(X'(t1),X(tn))
+      BIG(Ntd1  ,Ntd1+3) = R1(tn+1-ts)   !cov(X'(tn),X (ts))  
+      BIG(Ntd1-1,Ntd1+3) =-R1(ts)        !cov(X'(t1),X (ts))   
+      BIG(Ntd1-2,Ntd1+3) = 0.d0          !cov(X'(ts),X (ts)
+      BIG(Ntd1-2,Ntd1+4) = R1(ts)        !cov(X'(ts),X (t1))
+      BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts)  !cov(X'(ts),X (tn))
+
+
+        do i=1,tn-2
+          j=abs(i+1-ts)
+!cov(Xt,Xc)
+          BIG(i,Ntd1+3)   = R0(j+1)      !cov(X(ti+1),X(ts))          
+!Cov(Xt,Xd)
+          if ((i+1-ts).lt.0) then
+              BIG(i,Ntd1-2)  =  R1(j+1)
+            else                         !cov(X(ti+1),X'(ts))  
+              BIG(i,Ntd1-2)  = -R1(j+1)
+          endif
+      enddo
+    
+! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+
+           BIG(i,j)=tmp
+        enddo
+      enddo
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2tthpdf1
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2acdf.f

@@ -0,0 +1,445 @@
+      PROGRAM sp2Acdf
+C***********************************************************************
+C     This program computes:                                           *
+C                                                                      *
+C     density of     T_i, for Ac <=h, in a gaussian process i.e.       *
+C                                                                      *
+C     half wavelength (up-crossing to downcrossing) for crests <h      *
+C    or  half wavelength (down-crossing to upcrossing) for trough >h   *
+C***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex,CY
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable  :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size,icy
+      integer ::it1,it2,status
+      double precision :: ds,dT ! lag spacing for covariances
+! f90  sp2Acdf.f rind51.f 
+
+      CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,Nx,dT)
+      !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      if (abs(def).GT.1) THEN
+        allocate(R3(1:Ntime+1))
+        allocate(R4(1:Ntime+1))
+        !CALL INIT_AMPLITUDES(h,def,Nx)
+      endif
+      allocate(h(1:Nx))
+      CALL INIT_AMPLITUDES(h,def,Nx)
+      CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+   
+      NI=4; Nd=2
+      Nc=3; Mb=2
+      
+      Nj=0
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+                                                      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      
+      allocate(CY(1:Nx)) 
+      do icy=1,Nx
+        CY(icy)=exp(-0.5*h(icy)*h(icy)/100)/(10*sqrt(twopi))
+      enddo 
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) 
+         if (status.ne.0) then 
+             print *,'can not allocate BIG' 
+         end if 
+      allocate(ex(1:Ntime+Nc),stat=status)          
+         if (status.ne.0) then 
+             print *,'can not allocate ex' 
+         end if
+      allocate(ansr(1:Ntime,1:Nx))
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      fxind=0.d0 !this is not needed
+      allocate(xc(1:Nc,1:Nx))
+ 
+ 
+      allocate(a_up(Mb,NI-1)) 
+      allocate(a_lo(Mb,NI-1)) 
+        a_up=0.d0 
+        a_lo=0.d0
+        xc(1,1:Nx)=h(1:Nx)
+        xc(2,1:Nx)=u
+        xc(3,1:Nx)=u 
+        
+      if (def.GT.0) then
+         a_up(1,1)=0.d0 
+         a_lo(1,1)=u
+         a_up(1,2)=XdInf
+         a_lo(1,3)=-XdInf 
+         a_up(2,1)=1.d0      
+      else
+         a_up(1,1)=u 
+         a_lo(1,1)=0.d0
+         a_lo(1,2)=-XdInf
+         a_up(1,3)= XdInf  
+         a_lo(2,1)=1.d0 
+      endif
+      !print *,'Nstart',Nstart
+      Nstart=MAX(3,Nstart)  
+      
+     
+       if (SCIS.GT.0) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif 
+ 
+      !print *,'loop starts' 
+      do Ntd=Nstart,Ntime 
+ 
+         Ntdc=Ntd+Nc
+         ex=0.d0
+         BIG=0.d0 
+         CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period
+C         CALL ECHO(BIG(1:2,1:2))
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd; 
+
+          CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) 
+          !print *,'test',fxind/CY(1:Nx) 
+ 
+          do icy=1,Nx        
+            ansr(Ntd,icy)=fxind(icy)*CC/CY(icy)
+          enddo
+          if (SCIS.GT.0) then
+            write(11,*)  COV(1) ! save coefficient of variation
+          endif       
+      if((Nx.gt.4).or.NIT.gt.5) print *,'Ready: ',Ntd,' of ',Ntime
+      enddo 
+      goto 300
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+
+      !print *, ansr
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansr(ts,ph)
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  continue
+      deallocate(BIG) 
+      deallocate(ex)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)  
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+
+      if (allocated(R3)) then
+        deallocate(R3)
+        deallocate(R4)
+        deallocate(h)
+      ENDIF
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,def,Ntime,Nstart,NIT,speed,Nx,dT)
+      IMPLICIT NONE
+      integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) def
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed 
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+     
+      if (abs(def).GT.1) then
+        READ (14,*) dT
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      else
+        if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      endif
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,def,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: def
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      !if (def.LT.0) THEN
+      !   H=-H
+      !endif      
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime,def
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+       enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      if (abs(def).GT.1) then      
+        open (unit=4, file='Cd3.in',STATUS='unknown')
+        open (unit=5, file='Cd4.in',STATUS='unknown')
+
+        do i=1,Ntime
+          read(4,*) R3(i)
+          read(5,*) R4(i)
+        enddo
+
+        close(4)
+        close(5)
+      endif
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,shft,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! For ts>1:
+! X(t2)..X(ts),..X(tn-1) X''(ts) X'(t1) X'(tn) X(ts) X(t1) X(tn) X'(ts) 
+! = [Xt                          Xd                    Xc]
+!
+! For ts<=1: 
+! X(t2)..,..X(tn-1)  X'(t1) X'(tn) Y X(t1) X(tn)  
+! = [Xt              Xd            Xc]
+!Add Y Condition : Y=h
+
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+      if (ts.LE.1) THEN
+	       Ntd1=tn
+          N=Ntd1+Nc;
+          shft=0  ! def=1 want only crest period Tc
+      else
+          Ntd1=tn+1
+          N=Ntd1+4
+          shft=1  ! def=2 or 3 want Tc Ac or Tcf, Ac
+      endif
+
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)
+	 BIG(i      ,Ntd1+1+shft) = 0.d0            !cov(X(ti+1),Y)   
+         BIG(i      ,Ntd1+2+shft) = R0(i+1)         !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+3+shft) = R0(i+1)         !cov(X(t.. ),X(tn))  
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)         =-R1(i+1)         !cov(X(ti+1),X' (t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X' (tn)) 
+      enddo
+      !call echo(big(1:tn,1:tn),tn)
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)     !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+
+!cov(Xc)
+      !print *,'t'
+      BIG(Ntd1+1+shft,Ntd1+1+shft) = 100.d0!100.d0         ! cov(Y,Y) 
+      BIG(Ntd1+1+shft,Ntd1+2+shft) = 0.d0
+      BIG(Ntd1+1+shft,Ntd1+3+shft) = 0.d0
+      BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+2+shft,Ntd1+3+shft) = R0(tn)       ! cov(X(t1),X (tn))
+      BIG(Ntd1+3+shft,Ntd1+3+shft) = R0(1)        ! cov(X(tn),X (tn))
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1+shft) = 0.d0            !cov(X'(tn),Y)     
+      BIG(Ntd1  ,Ntd1+2+shft) = R1(tn)       !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+3+shft) = 0.d0         !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+1+shft) = 0.d0         !cov(X'(t1),Y)
+      BIG(Ntd1-1,Ntd1+2+shft) = 0.d0         !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+3+shft) =-R1(tn)       !cov(X'(t1),X(tn))
+
+
+      !call echo(big(1:N,1:N),N) 
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+           BIG(i,j)=tmp
+        enddo
+        !call echo(big(1:N,1:N),N) 
+      enddo
+      !if (tn.eq.3) then
+      !do j=1,N
+      !  do i=j,N
+      !      print *,'test',j,i,BIG(j,i)
+      !  enddo
+        !call echo(big(1:N,1:N),N) 
+      !enddo
+      !endif
+      !call echo(big(1:N,1:N),N) 
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2Acdf
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2mmpdf.f

@@ -0,0 +1,357 @@
+      PROGRAM cov2mmpdf
+C*******************************************************************************
+C     This program computes joint density of maximum and the following minimum * 
+C*******************************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable  :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nstart,Ntime,tn,ts,speed,seed1,seed_size
+      integer :: status,i,j,ij,Nx1
+      double precision :: ds,dT ! lag spacing for covariances
+ 
+! f90  cov2mmpdf.f rind51.f 
+
+      CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,Nx1,dT) 
+      Nx=Nx1*(Nx1-1)/2 
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+ 
+      CALL INITDATA(speed)  
+ 
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      allocate(R3(1:Ntime+1))
+      allocate(R4(1:Ntime+1))
+      allocate(h(1:Nx1)) 
+
+      CALL INIT_AMPLITUDES(h,Nx1)
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) 
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Y=  X'(t2)...X'(tn-1)||X''(t1) X''(tn)|| X'(t1) X'(tn) X(t1) X(tn)         !!
+! = [       Xt                   Xd                    Xc            ]       !!
+!                                                                            !!
+! Nt=tn-2, Nd=2, Nc=4                                                        !!
+!                                                                            !!
+! Xt= contains Nt time points in the indicator function                      !!
+! Xd=    "     Nd    derivatives                                             !!
+! Xc=    "     Nc    variables to condition on                               !!
+!                                                                            !!
+! There are 3 ( NI=4) regions with constant bariers:                         !!
+! (indI(1)=0);     for i\in (indI(1),indI(2)]    Y(i)<0.                     !!
+! (indI(2)=Nt)  ;  for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1))     !!
+! (indI(3)=Nt+1);  for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn))     !!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+
+      NI=4; Nd=2
+      Nc=4; Mb=1
+      
+      Nj=0
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(R4(1))
+      XtInf=10.d0*SQRT(-R2(1))
+                                                      ! normalizing constant
+      CC=TWOPI*SQRT(-R2(1)/R4(1))
+ 
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc),stat=status) 
+         if (status.ne.0) then 
+             print *,'can not allocate BIG' 
+         end if 
+      allocate(ex(1:Ntime+Nc),stat=status)          
+         if (status.ne.0) then 
+             print *,'can not allocate ex' 
+         end if
+      if (Nx.gt.1) then
+         allocate(ansr(1:Nx1,1:Nx1))
+        else
+         allocate(ansr(1,1:Ntime))
+      end if
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      fxind=0.d0 !this is not needed
+      allocate(xc(1:Nc,1:Nx))
+ 
+ 
+      allocate(a_up(Mb,NI-1)) 
+      allocate(a_lo(Mb,NI-1)) 
+ 
+        a_up=0.d0 
+        a_lo=0.d0 
+ 
+        ij=0 
+        do i=2,Nx1 
+           do j=1,i-1 
+             ij=ij+1
+             xc(3,ij)=h(i)
+             xc(4,ij)=h(j) 
+           enddo 
+        enddo
+        xc(1,1:Nx)=0.d0
+        xc(2,1:Nx)=0.d0 
+        
+        a_lo(1,1)=-Xtinf
+        a_lo(1,2)=-XdInf
+        a_up(1,3)=+XdInf 
+             
+ 
+      Nstart=MAX(2,Nstart)  
+      
+     
+       if (SCIS.GT.0) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif 
+ 
+      do Ntd=Nstart,Ntime 
+ 
+         Ntdc=Ntd+Nc
+         ex=0.d0
+         BIG=0.d0 
+         CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,R0,R1,R2,R3,R4) ! positive wave period
+ 
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd; 
+
+          CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) 
+          ij=0
+          if (Nx .gt. 1) then
+          do i=2,Nx1 
+             do j=1,i-1 
+                 ij=ij+1  
+                 ansr(i,j)=ansr(i,j)+fxind(ij)*CC*dt
+             enddo 
+          enddo
+          else
+             ansr(1,Ntd)=fxind(1)*CC
+          end if
+ 
+          if (SCIS.GT.0) then
+            write(11,*)  COV(1) ! save coefficient of variation
+          endif       
+          print *,'Ready: ',Ntd,' of ',Ntime
+      enddo 
+      goto 300
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+      if (Nx.gt.1) then
+      do i=1,Nx1 
+        do j=1,Nx1 
+           write(11,*)  ansr(i,j)
+        enddo 
+      enddo
+      else
+        do j=1,Ntime
+           write(11,*)  ansr(1,j)
+        enddo
+      end if
+      close(11)
+ 900  continue
+      deallocate(BIG) 
+      deallocate(ex)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)  
+      deallocate(R3)
+      deallocate(R4)
+      deallocate(h)
+ 
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (Ntime,Nstart,NIT,speed,Nx,dT)
+      IMPLICIT NONE
+      integer, intent(out):: Ntime,Nstart,NIT,speed,Nx
+      double precision ,intent(out) :: dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed 
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+      READ (14,*) dT
+     
+      if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+      end if
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      open (unit=4, file='Cd3.in',STATUS='unknown')
+      open (unit=5, file='Cd4.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+         read(4,*) R3(i)
+         read(5,*) R4(i)
+       enddo
+      close(1)
+      close(2)
+      close(3)
+      close(3)
+      close(5)
+      return
+      END SUBROUTINE INIT_COVARIANCES
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn
+      integer :: i,j,N 
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+!    X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn) 
+! = [          Xt               |      Xd       |          Xc             ]
+!
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+ 
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+       
+      N=tn+4
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = -R2(j-i+1) ! cov(X'(ti+1),X'(tj+1))
+         enddo
+      !cov(Xt,Xc)
+         BIG(i      ,tn+3) =  R1(i+1)         !cov(X'(ti+1),X(t1))  
+         BIG(tn-1-i ,tn+4) = -R1(i+1)         !cov(X'(ti+1),X(tn))  
+         BIG(i      ,tn+1) = -R2(i+1)         !cov(X'(ti+1),X'(t1))  
+         BIG(tn-1-i ,tn+2) = -R2(i+1)         !cov(X'(ti+1),X'(tn))  
+      !Cov(Xt,Xd)
+         BIG(i,tn-1)       = R3(i+1)          !cov(X'(ti+1),X''(t1))  
+         BIG(tn-1-i,tn)    =-R3(i+1)          !cov(X'(ti+1),X''(tn)) 
+      enddo
+      
+!cov(Xd)
+      BIG(tn-1  ,tn-1  ) = R4(1)
+      BIG(tn-1,tn      ) = R4(tn)     !cov(X''(t1),X''(tn))
+      BIG(tn    ,tn    ) = R4(1)
+
+!cov(Xc)
+      BIG(tn+3,tn+3) = R0(1)        ! cov(X(t1),X(t1))
+      BIG(tn+3,tn+4) = R0(tn)       ! cov(X(t1),X(tn))
+      BIG(tn+1,tn+3) = 0.d0         ! cov(X(t1),X'(t1))
+      BIG(tn+2,tn+3) = R1(tn)       ! cov(X(t1),X'(tn))
+      BIG(tn+4,tn+4) = R0(1)        ! cov(X(tn),X(tn))
+      BIG(tn+1,tn+4) =-R1(tn)       ! cov(X(tn),X'(t1))
+      BIG(tn+2,tn+4) = 0.d0         ! cov(X(tn),X'(tn)) 
+      BIG(tn+1,tn+1) =-R2(1)        ! cov(X'(t1),X'(t1))
+      BIG(tn+1,tn+2) =-R2(tn)       ! cov(X'(t1),X'(tn))
+      BIG(tn+2,tn+2) =-R2(1)       ! cov(X'(tn),X'(tn))
+!Xc=X(t1),X(tn),X'(t1),X'(tn) 
+!Xd=X''(t1),X''(tn)
+!cov(Xd,Xc)
+      BIG(tn-1  ,tn+3) = R2(1)           !cov(X''(t1),X(t1))     
+      BIG(tn-1  ,tn+4) = R2(tn)          !cov(X''(t1),X(tn))     
+      BIG(tn-1  ,tn+1) = 0.d0            !cov(X''(t1),X'(t1))     
+      BIG(tn-1  ,tn+2) = R3(tn)          !cov(X''(t1),X'(tn))     
+      BIG(tn    ,tn+3) = R2(tn)          !cov(X''(tn),X(t1))     
+      BIG(tn    ,tn+4) = R2(1)           !cov(X''(tn),X(tn))     
+      BIG(tn    ,tn+1) =-R3(tn)          !cov(X''(tn),X'(t1))     
+      BIG(tn    ,tn+2) = 0.d0            !cov(X''(tn),X'(tn))     
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+           BIG(i,j)=tmp
+        enddo
+      enddo
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+
+      END  PROGRAM  cov2mmpdf
+       

wafo/source/cov2XXXpdf/cov2mmtpdf.f

@@ -0,0 +1,769 @@
+      PROGRAM sp2mmt
+C*******************************************************************************
+C     This program computes joint density of the  maximum and the following    *
+C     minimum or level u separated maxima and minima + period/wavelength       * 
+C*******************************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),  allocatable :: BIG
+      double precision, dimension(:,:,:),allocatable :: ansr
+      double precision, dimension(:  ),  allocatable :: ex
+      double precision, dimension(:,:),  allocatable :: xc
+      double precision, dimension(:  ),  allocatable :: fxind,h
+      double precision, dimension(:  ),  allocatable :: R0,R1,R2,R3,R4
+      double precision             :: CC,U,XdInf,XtInf  
+      double precision, dimension(1,4)               :: a_up,a_lo      ! size Mb X NI-1
+      integer         , dimension(:  ),  allocatable :: seed
+      integer ,dimension(5) :: indI = 0                                ! length NI
+      integer :: Nstart,Ntime,ts,tn,speed,seed1,seed_size
+      integer :: status,i,j,ij,Nx0,Nx1,DEF,isOdd !,TMP
+      LOGICAL :: SYMMETRY=.FALSE.
+      double precision :: dT ! lag spacing for covariances
+ 
+! f90  -gline -fieee -Nl126 -C -o  intmodule.f rind60.f sp2mmt.f
+
+      CALL INIT_LEVELS(Ntime,Nstart,NIT,speed,SCIS,SEED1,Nx1,dT,u,def) 
+      CALL INITDATA(speed)  
+      
+      if (SCIS.GT.0) then
+        !allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+        if (ALLOCATED(COV)) then
+           open (unit=11, file='COV.out',  STATUS='unknown') 
+           write(11,*) 0.d0
+        endif 
+      endif
+
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      allocate(R3(1:Ntime+1))
+      allocate(R4(1:Ntime+1))
+
+      Nx0 = Nx1 ! just plain Mm
+      IF (def.GT.1) Nx0=2*Nx1   ! level v separated max2min densities wanted     
+      
+       
+      allocate(h(1:Nx0)) 
+      
+      CALL INIT_AMPLITUDES(h,Nx0)
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4) 
+! For DEF = 0,1 : (Maxima, Minima and period/wavelength)
+!         = 2,3 : (Level v separated Maxima and Minima and period/wavelength between them)
+!      If Nx==1 then the conditional  density for  period/wavelength between Maxima and Minima 
+!      given the Max and Min is returned
+!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
+! Y=  X'(t2)..X'(ts)..X'(tn-1)||X''(t1) X''(tn)|| X'(t1) X'(tn)  X(t1) X(tn) 
+! = [       Xt                   Xd                    Xc            ]  
+!                                                                       
+! Nt = tn-2, Nd = 2, Nc = 4
+!                                                                       
+! Xt= contains Nt time points in the indicator function                 
+! Xd=    "     Nd    derivatives in Jacobian
+! Xc=    "     Nc    variables to condition on                          
+!                                                                       
+! There are 3 (NI=4) regions with constant barriers:                    
+! (indI(1)=0);     for i\in (indI(1),indI(2)]    Y(i)<0.                
+! (indI(2)=Nt)  ;  for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1)) 
+! (indI(3)=Nt+1);  for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn))  
+! 
+!
+! For DEF = 4,5 (Level v separated Maxima and Minima and period/wavelength from Max to crossing)
+!     If Nx==1 then the conditional joint density for  period/wavelength between Maxima, Minima and Max to 
+!              level v crossing given the Max and the min is returned
+!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+! Y=  X'(t2)..X'(ts)..X'(tn-1)||X''(t1) X''(tn) X'(ts)|| X'(t1) X'(tn)  X(t1) X(tn) X(ts)
+! = [       Xt                      Xd                     Xc            ]
+!                                                                         
+! Nt = tn-2, Nd = 3, Nc = 5
+!                                                                         
+! Xt= contains Nt time points in the indicator function                      
+! Xd=    "     Nd    derivatives                                             
+! Xc=    "     Nc    variables to condition on                               
+!                                                                            
+! There are 4 (NI=5) regions with constant barriers:                        
+! (indI(1)=0);     for i\in (indI(1),indI(2)]    Y(i)<0.                    
+! (indI(2)=Nt)  ;  for i\in (indI(2)+1,indI(3)], Y(i)<0 (deriv. X''(t1))    
+! (indI(3)=Nt+1);  for i\in (indI(3)+1,indI(4)], Y(i)>0 (deriv. X''(tn))
+! (indI(4)=Nt+2);  for i\in (indI(4)+1,indI(5)], Y(i)<0 (deriv. X'(ts))    
+! 
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+!
+!Revised pab 22.04.2000
+! - added mean separated min/max + (Tdm, TMd) period distributions
+! - added scis 
+
+
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf = 10.d0*SQRT(R4(1))
+      XtInf = 10.d0*SQRT(-R2(1))
+
+      Nc = 4
+      NI=4; Nd=2; 
+      Mb=1 ; 
+      Nj = 0
+      indI(1) = 0
+      Nstart=MAX(2,Nstart) 
+
+      isOdd = MOD(Nx1,2)
+      IF (def.LE.1) THEN ! just plain Mm 
+         Nx = Nx1*(Nx1-1)/2
+         IJ = (Nx1+isOdd)/2         
+         IF (H(1)+H(Nx1).EQ.0.AND.
+     &        (H(IJ).EQ.0.OR.H(IJ)+H(IJ+1).EQ.0) ) THEN
+            SYMMETRY=.FALSE.
+            PRINT *,' Integration region symmetric'
+            ! May save Nx1-isOdd integrations in each time step 
+            ! This is not implemented yet.
+            !Nx = Nx1*(Nx1-1)/2-Nx1+isOdd
+         ENDIF
+        
+         CC = TWOPI*SQRT(-R2(1)/R4(1)) ! normalizing constant = 1/ expected number of zero-up-crossings of X' 
+         
+      ELSE  ! level u separated Mm
+         Nx = (Nx1-1)*(Nx1-1)
+         IF ( ABS(u).LE.1D-8.AND.H(1)+H(Nx1+1).EQ.0.AND.
+     &        (H(Nx1)+H(2*Nx1).EQ.0) ) THEN
+            SYMMETRY=.FALSE. 
+            PRINT *,' Integration region symmetric'
+            ! Not implemented for DEF <= 3
+            !IF (DEF.LE.3) Nx = (Nx1-1)*(Nx1-2)/2 
+         ENDIF
+         
+         IF (DEF.GT.3) THEN
+            Nstart = MAX(Nstart,3)
+            Nc = 5
+            NI=5; Nd=3;
+         ENDIF
+         CC = TWOPI*SQRT(-R0(1)/R2(1))*exp(0.5D0*u*u/R0(1)) ! normalizing constant= 1/ expected number of u-up-crossings of X
+      ENDIF
+
+      !print *,'def',def
+      IF (Nx.GT.1) THEN
+         IF ((DEF.EQ.0.OR.DEF.EQ.2)) THEN ! (M,m) or (M,m)v distribution wanted
+            allocate(ansr(Nx1,Nx1,1),stat=status)
+         ELSE                             ! (M,m,TMm), (M,m,TMm)v  (M,m,TMd)v or (M,M,Tdm)v distributions wanted 
+            allocate(ansr(Nx1,Nx1,Ntime),stat=status)
+         ENDIF
+      ELSEIF (DEF.GT.3) THEN              ! Conditional distribution for (TMd,TMm)v or (Tdm,TMm)v given (M,m)  wanted 
+         allocate(ansr(1,Ntime,Ntime),stat=status)
+      ELSE                                ! Conditional distribution for  (TMm) or (TMm)v given (M,m) wanted
+         allocate(ansr(1,1,Ntime),stat=status)
+      ENDIF
+      if (status.ne.0) print *,'can not allocate ansr'
+      allocate(BIG(Ntime+Nc+1,Ntime+Nc+1),stat=status) 
+      if (status.ne.0) print *,'can not allocate BIG'       
+      allocate(ex(1:Ntime+Nc+1),stat=status)          
+      if (status.ne.0) print *,'can not allocate ex' 
+      allocate(fxind(Nx),xc(Nc,Nx))
+      
+
+! Initialization
+!~~~~~~~~~~~~~~~~~
+      
+      BIG  = 0.d0
+      ex   = 0.d0
+      ansr = 0.d0
+      a_up = 0.d0 
+      a_lo = 0.d0 
+ 
+      xc(:,:) = 0.d0
+      !xc(:,1:Nx) = 0.d0
+      !xc(2,1:Nx) = 0.d0 
+      
+      a_lo(1,1) = -Xtinf
+      a_lo(1,2) = -XdInf
+      a_up(1,3) = +XdInf 
+      a_lo(1,4) = -Xtinf
+      ij = 0 
+      IF (DEF.LE.1) THEN     ! Max2min and period/wavelength
+         do I=2,Nx1
+            J = IJ+I-1
+            xc(3,IJ+1:J) =  h(I)    
+            xc(4,IJ+1:J) =  h(1:I-1) 
+            IJ = J
+         enddo
+      ELSE
+         ! Level u separated Max2min
+         xc(Nc,:) = u
+         ! H(1) = H(Nx1+1)= u => start do loop at I=2 since by definition we must have:  minimum<u-level<Maximum
+         do i=2,Nx1                
+            J = IJ+Nx1-1
+            xc(3,IJ+1:J) =  h(i)              ! Max > u
+            xc(4,IJ+1:J) =  h(Nx1+2:2*Nx1)    ! Min < u
+            IJ = J
+         enddo
+         
+         !CALL ECHO(transpose(xc(3:5,:)))
+         if (DEF.GT.3) GOTO 200
+      ENDIF
+      do Ntd = Nstart,Ntime 
+         !Ntd=tn
+         Ntdc = Ntd+Nc
+         Nt = Ntd-Nd;
+         indI(2) = Nt;
+         indI(3) = Nt+1;
+         indI(4) = Ntd;
+         CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),Ntd,0,R0,R1,R2,R3,R4) ! positive wave period            
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up)
+         IF (Nx.LT.2) THEN
+! Density of TMm given the Max and the Min. Note that the density is not scaled to unity
+            ansr(1,1,Ntd) = fxind(1)*CC 
+            GOTO 100
+         ENDIF
+         IJ = 0
+         SELECT CASE (DEF)
+         CASE(:0)  
+! joint density of (M,m)
+!~~~~~~~~~~~~~~~~~~~~~~~~
+            do  i = 2, Nx1 
+               J = IJ+i-1
+               ansr(1:i-1,i,1) = ansr(1:i-1,i,1)+fxind(ij+1:J)*CC*dt
+               IJ=J
+            enddo 
+         CASE (1) 
+! joint density of (M,m,TMm)
+            do  i = 2, Nx1
+               J = IJ+i-1
+               ansr(1:i-1,i,Ntd) = fxind(ij+1:J)*CC
+               IJ = J
+            enddo
+         CASE (2)
+ ! joint density of level v separated (M,m)v
+            do  i = 2,Nx1
+               J = IJ+Nx1-1
+               ansr(2:Nx1,i,1) = ansr(2:Nx1,i,1)+fxind(ij+1:J)*CC*dt
+               IJ = J
+            enddo 
+         CASE (3:) 
+ ! joint density of level v separated (M,m,TMm)v
+            do  i = 2,Nx1 
+               J = IJ+Nx1-1
+               ansr(2:Nx1,i,Ntd) = ansr(2:Nx1,i,Ntd)+fxind(ij+1:J)*CC
+               IJ = J
+            enddo 
+         END SELECT   
+          
+ 100     if (ALLOCATED(COV)) then
+            write(11,*)  COV(:) ! save coefficient of variation
+         endif       
+         print *,'Ready: ',Ntd,' of ',Ntime
+      enddo
+      
+      goto 800
+
+ 200  do tn = Nstart,Ntime 
+         Ntd = tn+1
+         Ntdc = Ntd + Nc
+         Nt   = Ntd - Nd;
+         indI(2) = Nt;
+         indI(3) = Nt + 1;
+         indI(4) = Nt + 2;
+         indI(5) = Ntd;
+         !CALL COV_INPUT2(BIG(1:Ntdc,1:Ntdc),tn,-2,R0,R1,R2,R3,R4) ! positive wave period
+         IF (SYMMETRY) GOTO 300
+        
+         do ts = 2,tn-1       
+            CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period
+            !print *,'Big='
+            !CALL ECHO(BIG(1:Ntdc,1:MIN(Ntdc,10)))
+            CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) 
+           
+            SELECT CASE (def)
+            CASE (:4) 
+               IF (Nx.EQ.1) THEN
+! Joint density (TMd,TMm) given the Max and the min. Note the density is not scaled to unity
+                  ansr(1,ts,tn) = fxind(1)*CC
+         
+               ELSE
+! 4,  gives level u separated Max2min and wave period from Max to the crossing of level u (M,m,TMd).
+                  ij = 0
+                  do  i = 2,Nx1 
+                     J = IJ+Nx1-1 
+                     ansr(2:Nx1,i,ts) = ansr(2:Nx1,i,ts)+
+     &                    fxind(ij+1:J)*CC*dt
+                     IJ = J
+                  enddo 
+               ENDIF
+            CASE (5:)
+               IF (Nx.EQ.1) THEN
+! Joint density (Tdm,TMm) given the Max and the min. Note the density is not scaled to unity
+                  ansr(1,tn-ts+1,tn) = fxind(1)*CC
+               ELSE   
+               
+! 5,  gives level u separated Max2min and wave period from the crossing of level u to the min (M,m,Tdm).
+               ij = 0
+               do  i = 2,Nx1 
+                  J = IJ+Nx1-1
+                  ansr(2:Nx1,i,tn-ts+1)=ansr(2:Nx1,i,tn-ts+1)+
+     &                 fxind(ij+1:J)*CC*dt
+                  IJ = J
+               enddo 
+               ENDIF
+            END SELECT
+            if (ALLOCATED(COV)) then
+               write(11,*)  COV(:) ! save coefficient of variation
+            endif       
+         enddo
+         GOTO 400
+ 300     do ts = 2,FLOOR(DBLE(Ntd)/2.d0)     ! Using the symmetry since U = 0 and the transformation is linear
+            CALL COV_INPUT(BIG(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period
+                                !print *,'Big='
+                                !CALL ECHO(BIG(1:Ntdc,1:Ntdc))
+            CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex,xc,indI,a_lo,a_up) 
+            IF (Nx.EQ.1) THEN
+! Joint density of (TMd,TMm),(Tdm,TMm) given the max and the min. Note that the density is not scaled to unity
+               ansr(1,ts,tn) = fxind(1)*CC
+               IF (ts.LT.tn-ts+1) THEN
+                  ansr(1,tn-ts+1,tn) = fxind(1)*CC
+               ENDIF
+               GOTO 350
+            ENDIF
+            IJ = 0 
+            SELECT CASE (def)
+            CASE (:4) 
+              
+! 4,  gives level u separated Max2min and wave period from Max to the crossing of level u (M,m,TMd).
+               do  i = 2,Nx1 
+                  j = ij+Nx1-1  
+                  ansr(2:Nx1,i,ts) = ansr(2:Nx1,i,ts)+
+     &                 fxind(ij+1:J)*CC*dt
+                  IF (ts.LT.tn-ts+1) THEN
+                     ansr(i,2:Nx1,tn-ts+1) =  
+     &                    ansr(i,2:Nx1,tn-ts+1)+fxind(ij+1:J)*CC*dt ! exploiting the symmetry
+                  ENDIF
+                  IJ = J
+               enddo 
+            CASE (5:)
+! 5,   gives level u separated Max2min and wave period from the crossing of level u to min (M,m,Tdm).
+               do  i = 2,Nx1 
+                  J = IJ+Nx1-1
+                  
+                  ansr(2:Nx1,i,tn-ts+1)=ansr(2:Nx1,i,tn-ts+1)+
+     &                 fxind(ij+1:J)*CC*dt
+                  IF (ts.LT.tn-ts+1) THEN
+                     ansr(i,2:Nx1,ts) = ansr(i,2:Nx1,ts)+
+     &                    fxind(ij+1:J)*CC*dt ! exploiting the symmetry
+                  ENDIF
+                  IJ = J
+               enddo 
+            END SELECT 
+ 350     enddo
+ 400     print *,'Ready: ',tn,' of ',Ntime
+      enddo
+      
+
+      
+      
+ 800  open (unit=11, file='dens.out',  STATUS='unknown')
+      !print *,'ans, IJ,def', shape(ansr),IJ,DEF
+      if (Nx.GT.1) THEN
+         ij = 1
+         IF (DEF.GT.2.OR.DEF.EQ.1) IJ = Ntime
+                                !print *,'ans, IJ,def', size(ansr),IJ,DEF
+         do ts = 1,ij
+            do j=1,Nx1 
+               do i=1,Nx1 
+                  write(11,*)  ansr(i,j,ts)
+               enddo 
+            enddo
+         enddo
+      ELSE
+         ij = 1
+         IF (DEF.GT.3) IJ = Ntime
+                                !print *,'ans, IJ,def', size(ansr),IJ,DEF
+         do ts = 1,Ntime
+            do j = 1,ij 
+               write(11,*)  ansr(1,j,ts)
+            enddo 
+         enddo
+      ENDIF
+      close(11)
+ 900  continue
+      deallocate(BIG) 
+      deallocate(ex)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)  
+      deallocate(R3)
+      deallocate(R4)
+      deallocate(h)
+      
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+      stop
+                                !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (Ntime,Nstart,NIT,speed,SCIS,SEED1,Nx,dT,u,def)
+      IMPLICIT NONE
+      integer, intent(out):: Ntime,Nstart,NIT,speed,Nx,DEF,SCIS,SEED1
+      double precision ,intent(out) :: dT,U
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed 
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+      READ (14,*) dT
+      READ (14,*) U
+      READ (14,*) DEF
+     
+      if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+      end if
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      open (unit=4, file='Cd3.in',STATUS='unknown')
+      open (unit=5, file='Cd4.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+         read(4,*) R3(i)
+         read(5,*) R4(i)
+      enddo
+      close(1)
+      close(2)
+      close(3)
+      close(3)
+      close(5)
+      return
+      END SUBROUTINE INIT_COVARIANCES
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT2(BIG,tn,ts,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,N,shft 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! for ts <= 1:
+!    X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn)  X'(t1),X'(tn),X(t1),X(tn) 
+! = [          Xt               |      Xd       |          Xc             ]
+!
+! for ts > =2:
+!    X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(t1),X'(tn),X(t1),X(tn) X(ts) 
+! = [          Xt               |      Xd       |          Xc             ]
+!
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+ 
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+      
+      if (ts.GT.1) THEN
+         ! Assumption: a previous call to covinput has been made
+         ! need only to update the last row and column of big:
+         N=tn+5
+           !Cov(Xt,Xc)
+         do i=1,tn-2
+            j=abs(i+1-ts)
+            BIG(i,N)  = -sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X'(ti+1),X(ts)) 
+         enddo
+  !Cov(Xc)
+         BIG(N    ,N) =  R0(1)       ! cov(X(ts),X(ts))
+         BIG(tn+3 ,N) =  R0(ts)      ! cov(X(t1),X(ts))
+         BIG(tn+4 ,N) =  R0(tn-ts+1) ! cov(X(tn),X(ts))
+         BIG(tn+1 ,N) = -R1(ts)      ! cov(X'(t1),X(ts))
+         BIG(tn+2 ,N) =  R1(tn-ts+1) ! cov(X'(tn),X(ts))
+  !Cov(Xd,Xc)
+         BIG(tn-1 ,N) =  R2(ts)      !cov(X''(t1),X(ts))     
+         BIG(tn   ,N) =  R2(tn-ts+1) !cov(X''(tn),X(ts))
+
+                                ! make lower triangular part equal to upper 
+         do j=1,N-1
+            BIG(N,j) = BIG(j,N)
+         enddo
+         return
+      endif
+      IF (ts.LT.0) THEN
+         shft = 1
+         N=tn+5;
+      ELSE
+         shft = 0
+         N=tn+4;
+      ENDIF
+      
+      
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = -R2(j-i+1)              ! cov(X'(ti+1),X'(tj+1))
+         enddo
+      !cov(Xt,Xc)
+         BIG(i      ,tn+3) =  R1(i+1)         !cov(X'(ti+1),X(t1))  
+         BIG(tn-1-i ,tn+4) = -R1(i+1)         !cov(X'(ti+1),X(tn))  
+         BIG(i      ,tn+1) = -R2(i+1)         !cov(X'(ti+1),X'(t1))  
+         BIG(tn-1-i ,tn+2) = -R2(i+1)         !cov(X'(ti+1),X'(tn))  
+      !Cov(Xt,Xd)
+         BIG(i,tn-1)       = R3(i+1)          !cov(X'(ti+1),X''(t1))  
+         BIG(tn-1-i,tn)    =-R3(i+1)          !cov(X'(ti+1),X''(tn)) 
+      enddo
+      
+!cov(Xd)
+      BIG(tn-1  ,tn-1  ) = R4(1)
+      BIG(tn-1  ,tn    ) = R4(tn)     !cov(X''(t1),X''(tn))
+      BIG(tn    ,tn    ) = R4(1)
+
+!cov(Xc)
+      BIG(tn+3 ,tn+3) = R0(1)        ! cov(X(t1),X(t1))
+      BIG(tn+3 ,tn+4) = R0(tn)       ! cov(X(t1),X(tn))
+      BIG(tn+1 ,tn+3) = 0.d0         ! cov(X(t1),X'(t1))
+      BIG(tn+2 ,tn+3) = R1(tn)       ! cov(X(t1),X'(tn))
+      BIG(tn+4 ,tn+4) = R0(1)        ! cov(X(tn),X(tn))
+      BIG(tn+1 ,tn+4) =-R1(tn)       ! cov(X(tn),X'(t1))
+      BIG(tn+2 ,tn+4) = 0.d0         ! cov(X(tn),X'(tn)) 
+      BIG(tn+1 ,tn+1) =-R2(1)        ! cov(X'(t1),X'(t1))
+      BIG(tn+1 ,tn+2) =-R2(tn)       ! cov(X'(t1),X'(tn))
+      BIG(tn+2 ,tn+2) =-R2(1)        ! cov(X'(tn),X'(tn))
+!Xc=X(t1),X(tn),X'(t1),X'(tn) 
+!Xd=X''(t1),X''(tn)
+!cov(Xd,Xc)
+      BIG(tn-1  ,tn+3) = R2(1)           !cov(X''(t1),X(t1))     
+      BIG(tn-1  ,tn+4) = R2(tn)          !cov(X''(t1),X(tn))     
+      BIG(tn-1  ,tn+1) = 0.d0            !cov(X''(t1),X'(t1))     
+      BIG(tn-1  ,tn+2) = R3(tn)          !cov(X''(t1),X'(tn))     
+      BIG(tn    ,tn+3) = R2(tn)          !cov(X''(tn),X(t1))     
+      BIG(tn    ,tn+4) = R2(1)           !cov(X''(tn),X(tn))     
+      BIG(tn    ,tn+1) =-R3(tn)          !cov(X''(tn),X'(t1))     
+      BIG(tn    ,tn+2) = 0.d0            !cov(X''(tn),X'(tn))
+      
+     
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           BIG(i,j) = BIG(j,i)
+        enddo
+      enddo
+      RETURN
+      END  SUBROUTINE COV_INPUT2
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,N,shft, tnold = 0  
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! for  ts <= 1:
+!    X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn)  X'(t1),X'(tn),X(t1),X(tn) 
+! = [          Xt               |      Xd       |          Xc             ]
+!
+! for ts > =2:
+!    X'(t2)..X'(ts),...,X'(tn-1) X''(t1),X''(tn) X'(ts)  X'(t1),X'(tn),X(t1),X(tn) X(ts) 
+! = [          Xt               |      Xd               |          Xc             ]
+!
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+ 
+! Computations of all covariances follows simple rules: Cov(X(t),X(s)) = r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  = sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   = r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+      SAVE tnold
+    
+      if (ts.GT.1) THEN
+         shft = 1  
+         N=tn+5+shft
+           !Cov(Xt,Xc)
+         do i=1,tn-2
+            j=abs(i+1-ts)
+            BIG(i,N)  = -sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X'(ti+1),X(ts)) 
+         enddo
+  !Cov(Xc)
+         BIG(N         ,N) =  R0(1)       ! cov(X(ts),X(ts))
+         BIG(tn+shft+3 ,N) =  R0(ts)      ! cov(X(t1),X(ts))
+         BIG(tn+shft+4 ,N) =  R0(tn-ts+1) ! cov(X(tn),X(ts))
+         BIG(tn+shft+1 ,N) = -R1(ts)      ! cov(X'(t1),X(ts))
+         BIG(tn+shft+2 ,N) =  R1(tn-ts+1) ! cov(X'(tn),X(ts))
+  !Cov(Xd,Xc)
+         BIG(tn-1 ,N) =  R2(ts)      !cov(X''(t1),X(ts))     
+         BIG(tn   ,N) =  R2(tn-ts+1) !cov(X''(tn),X(ts))
+ 
+                                !ADD a level u crossing  at ts
+
+           !Cov(Xt,Xd)
+         do i = 1,tn-2
+            j = abs(i+1-ts)
+            BIG(i,tn+shft)  = -R2(j+1) !cov(X'(ti+1),X'(ts)) 
+         enddo
+       !Cov(Xd)  
+         BIG(tn+shft,tn+shft) = -R2(1)  !cov(X'(ts),X'(ts))
+         BIG(tn-1   ,tn+shft) =  R3(ts) !cov(X''(t1),X'(ts))
+         BIG(tn     ,tn+shft) = -R3(tn-ts+1)  !cov(X''(tn),X'(ts))
+
+        !Cov(Xd,Xc)
+         BIG(tn+shft ,N       ) =  0.d0        !cov(X'(ts),X(ts)) 
+         BIG(tn+shft,tn+shft+3) =  R1(ts)      ! cov(X'(ts),X(t1))
+         BIG(tn+shft,tn+shft+4) = -R1(tn-ts+1) ! cov(X'(ts),X(tn))
+         BIG(tn+shft,tn+shft+1) = -R2(ts)      ! cov(X'(ts),X'(t1))
+         BIG(tn+shft,tn+shft+2) = -R2(tn-ts+1) ! cov(X'(ts),X'(tn))
+                 
+                                 
+         
+         IF (tnold.EQ.tn) THEN  ! A previous call to covinput with tn==tnold has been made
+                                ! need only to update  row and column N and tn+1 of big:
+                                ! make lower triangular part equal to upper and then return
+            do j=1,tn+shft
+               BIG(N,j) = BIG(j,N)
+               BIG(tn+shft,j) = BIG(j,tn+shft)   
+            enddo
+             do j=tn+shft+1,N-1
+               BIG(N,j) = BIG(j,N)
+               BIG(j,tn+shft) = BIG(tn+shft,j)   
+            enddo
+            return
+         ENDIF
+         tnold = tn
+      ELSE
+         N = tn+4
+         shft = 0
+      endif
+          
+      
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = -R2(j-i+1)              ! cov(X'(ti+1),X'(tj+1))
+         enddo
+      !cov(Xt,Xc)
+         BIG(i      ,tn+shft+3) =  R1(i+1)         !cov(X'(ti+1),X(t1))  
+         BIG(tn-1-i ,tn+shft+4) = -R1(i+1)         !cov(X'(ti+1),X(tn))  
+         BIG(i      ,tn+shft+1) = -R2(i+1)         !cov(X'(ti+1),X'(t1))  
+         BIG(tn-1-i ,tn+shft+2) = -R2(i+1)         !cov(X'(ti+1),X'(tn))  
+      !Cov(Xt,Xd)
+         BIG(i,tn-1)       = R3(i+1)          !cov(X'(ti+1),X''(t1))  
+         BIG(tn-1-i,tn)    =-R3(i+1)          !cov(X'(ti+1),X''(tn)) 
+      enddo
+      
+!cov(Xd)
+      BIG(tn-1  ,tn-1  ) = R4(1)
+      BIG(tn-1  ,tn    ) = R4(tn)     !cov(X''(t1),X''(tn))
+      BIG(tn    ,tn    ) = R4(1)
+
+!cov(Xc)
+      BIG(tn+shft+3 ,tn+shft+3) = R0(1)        ! cov(X(t1),X(t1))
+      BIG(tn+shft+3 ,tn+shft+4) = R0(tn)       ! cov(X(t1),X(tn))
+      BIG(tn+shft+1 ,tn+shft+3) = 0.d0         ! cov(X(t1),X'(t1))
+      BIG(tn+shft+2 ,tn+shft+3) = R1(tn)       ! cov(X(t1),X'(tn))
+      BIG(tn+shft+4 ,tn+shft+4) = R0(1)        ! cov(X(tn),X(tn))
+      BIG(tn+shft+1 ,tn+shft+4) =-R1(tn)       ! cov(X(tn),X'(t1))
+      BIG(tn+shft+2 ,tn+shft+4) = 0.d0         ! cov(X(tn),X'(tn)) 
+      BIG(tn+shft+1 ,tn+shft+1) =-R2(1)        ! cov(X'(t1),X'(t1))
+      BIG(tn+shft+1 ,tn+shft+2) =-R2(tn)       ! cov(X'(t1),X'(tn))
+      BIG(tn+shft+2 ,tn+shft+2) =-R2(1)        ! cov(X'(tn),X'(tn))
+!Xc=X(t1),X(tn),X'(t1),X'(tn) 
+!Xd=X''(t1),X''(tn)
+!cov(Xd,Xc)
+      BIG(tn-1  ,tn+shft+3) = R2(1)           !cov(X''(t1),X(t1))     
+      BIG(tn-1  ,tn+shft+4) = R2(tn)          !cov(X''(t1),X(tn))     
+      BIG(tn-1  ,tn+shft+1) = 0.d0            !cov(X''(t1),X'(t1))     
+      BIG(tn-1  ,tn+shft+2) = R3(tn)          !cov(X''(t1),X'(tn))     
+      BIG(tn    ,tn+shft+3) = R2(tn)          !cov(X''(tn),X(t1))     
+      BIG(tn    ,tn+shft+4) = R2(1)           !cov(X''(tn),X(tn))     
+      BIG(tn    ,tn+shft+1) =-R3(tn)          !cov(X''(tn),X'(t1))     
+      BIG(tn    ,tn+shft+2) = 0.d0            !cov(X''(tn),X'(tn))
+      
+     
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           BIG(i,j) = BIG(j,i)
+        enddo
+      enddo
+      RETURN
+      END  SUBROUTINE COV_INPUT
+      END  PROGRAM  sp2mmt
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2tccpdf.f

@@ -0,0 +1,498 @@
+      PROGRAM sp2tccpdf
+C***********************************************************************
+C     This program computes:                                           *
+C                                                                      *
+C     density of     T=  T_1+T_2 in a gaussian process i.e.            *
+C                                                                      *
+C      wavelengthes for crests <h1 and troughs >h2                     *    
+C                                                                      *
+C     Sylvie  and Igor 7 dec. 1999                                    *
+C***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &   NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex,CY1,CY2
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h1,h2
+      double precision, dimension(:  ),allocatable :: hh1,hh2
+      double precision, dimension(:  ),allocatable :: R0,R1,R2
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Ntime,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2,N0
+      integer :: icy,icy2
+      double precision :: ds,dT ! lag spacing for covariances 
+! DIGITAL:
+! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf1.exe rind49.f sp2tthpdf1.f
+! SOLARIS:
+!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind49.f sp2tthpdf1.f
+
+      !print *,'enter sp2thpdf'
+      CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
+      
+      !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT
+      !Nx1=1
+      !Nx2=1
+
+      Nx=Nx1*Nx1 
+      !print *,'NN',Nx1,Nx2,Nx
+      
+      
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      
+      allocate(h1(1:Nx1))
+      allocate(h2(1:Nx2))
+      CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2)
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2)
+      
+
+      allocate(hh1(1:Nx))
+      allocate(hh2(1:Nx))
+      !h transformation
+      do icy=1,Nx1
+         do icy2=1,Nx2
+         hh1((icy-1)*Nx2+icy2)=h1(icy);
+         hh2((icy-1)*Nx2+icy2)=h2(icy2); 
+         enddo 
+      enddo
+
+      Nj=0
+      indI(1)=0
+
+C     ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+      !h1(1)=XtInf
+      !h2(1)=XtInf
+      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      allocate(CY1(1:Nx)) 
+      allocate(CY2(1:Nx)) 
+      do icy=1,Nx
+        CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi))
+        CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi))
+      enddo
+      !print *,CY1
+      allocate(ansr(1:Ntime,1:Nx))
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      fxind=0.d0 
+   
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !!
+! = [Xt                          Xd                    Xc]                   !!
+!                                                                            !!
+! Nt=tn-2, Nd=3, Nc=2+3                                                      !!
+!                                                                            !!
+! Xt= contains Nt time points in the indicator function                      !!
+! Xd=    "     Nd    derivatives                                             !!
+! Xc=    "     Nc    variables to condition on                               !!
+! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd     !!
+!                                                                            !!
+! There are 6 ( NI=7) regions with constant bariers:                         !!
+! (indI(1)=0);     for i\in (indI(1),indI(2)] u<Y(i)<h1                      !!
+! (indI(2)=ts-2);  for i\in (indI(2),indI(2)], inf<Y(i)<inf (no restr.)      !!
+! (indI(3)=ts-1);  for i\in (indI(3),indI(4)], h2 <Y(i)<u                    !!
+! (indI(4)=Nt)  ;  for i\in (indI(4),indI(5)], Y(i)<0 (deriv. X'(ts))        !!
+! (indI(5)=Nt+1);  for i\in (indI(5),indI(6)], Y(i)>0 (deriv. X'(t1))        !!
+! (indI(6)=Nt+2);  for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn))        !!
+! (indI(7)=Nt+3);  NI=7.                                                     !!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+      
+      NI=7; Nd=3
+      Nc=5; Mb=3
+      allocate(a_up(1:Mb,1:(NI-1)))
+      allocate(a_lo(1:Mb,1:(NI-1)))
+      a_up=0.d0
+      a_lo=0.d0
+      allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) 
+      ALLOCATE(xc(1:Nc,1:Nx))
+      allocate(ex(1:(Ntime+Nc+1)))
+      !print *,size(ex),Ntime
+      ex=0.d0
+      !print *,size(ex),ex
+      xc(1,1:Nx)=hh1(1:Nx)
+      xc(2,1:Nx)=hh2(1:Nx)
+      xc(3,1:Nx)=u
+      xc(4,1:Nx)=u
+      xc(5,1:Nx)=u
+         ! upp- down- upp-crossings at t1,ts,tn
+       
+        a_lo(1,1)=u
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf
+        a_up(1,3)=u
+   
+ 
+        a_lo(1,4)=-XdInf
+        a_up(1,5)= XdInf
+        a_up(1,6)= XdInf  
+
+        a_up(2,1)=1.d0
+        a_lo(3,3)=1.d0 !signe a voir!!!!!!
+!        print *,a_up
+!        print *,a_lo
+      do tn=N0,Ntime,1
+!      do tn=Ntime,Ntime,1
+        Ntd=tn+1
+        Nt=Ntd-Nd
+        Ntdc=Ntd+Nc
+        indI(4)=Nt
+        indI(5)=Nt+1
+        indI(6)=Nt+2
+        indI(7)=Ntd
+        if (SCIS.gt.0) then
+           if (SCIS.EQ.2) then           
+              Nj=max(Nt,0)
+           else
+              Nj=min(max(Nt-5, 0),0)
+           endif
+        endif
+        do ts=3,tn-2
+         !print *,'ts,tn' ,ts,tn,Ntdc
+         CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period
+         indI(2)=ts-2
+         indI(3)=ts-1
+         
+
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
+     &              xc,indI,a_lo,a_up)
+         
+        ds=dt
+         do icy=1,Nx
+         ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2)
+         ansr(tn,icy)=ansr(tn,icy)+fxind(icy)*CC*ds/(CY1(icy)*CY2(icy))
+         enddo
+        enddo ! ts
+        print *,'Ready: ',tn,' of ',Ntime
+
+      enddo !tn
+      !print *,'ansr',ansr
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+      !print *, ansr
+      do ts=1,Ntime
+         do ph=1,Nx
+            !write(11,*)  ansr(ts,ph),hh1(ph),hh2(ph)
+            write(11,111)  ansr(ts,ph)
+
+         enddo
+      enddo
+ 111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  deallocate(big)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(ex)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+        deallocate(h1)
+        deallocate(h2)
+        deallocate(hh1)
+        deallocate(hh2)
+        deallocate(a_up)
+        deallocate(a_lo)
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
+      IMPLICIT NONE
+      integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN') 
+      
+      READ (14,*) U
+      READ (14,*) Ntime
+      READ (14,*) N0
+      READ (14,*) NIT
+      READ (14,*) speed   
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+
+
+        READ (14,*) Nx1,Nx2
+        READ (14,*) dT
+        if (Ntime.lt.5) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h1,h2    
+      integer, intent(in) :: Nx1,Nx2
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx1
+        READ (4,*) H1(ix)
+      enddo
+      do ix=1,Nx2
+        READ (4,*) H2(ix)
+      enddo
+      CLOSE(UNIT=4)
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      integer,intent(in) :: Ntime
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+      enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! 
+! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| 
+! = [Xt                          Xd                    Xc]
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+
+      Ntd1=tn+1
+      N=Ntd1+Nc
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)
+	 BIG(i      ,Ntd1+1) = 0.d0          !cov(X(ti+1),Y1)  
+         BIG(i      ,Ntd1+2) = 0.d0          !cov(X(ti+1),Y2)  
+         BIG(i      ,Ntd1+4) = R0(i+1)       !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+5) = R0(i+1)       !cov(X(t.. ),X(tn))  
+
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)   =-R1(i+1)         !cov(X(ti+1),X'(t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X'(tn)) 
+      enddo
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)        !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+      BIG(Ntd1-2,Ntd1-1) = -R2(ts)        !cov(X'(ts),X'(t1))
+      BIG(Ntd1-2,Ntd1-2) = -R2(1)
+      BIG(Ntd1-2,Ntd1  ) = -R2(tn+1-ts)   !cov(X'(ts),X'(tn))
+
+!cov(Xc)
+      BIG(Ntd1+1,Ntd1+1) = 100.d0        ! cov(Y1 Y1) 
+      BIG(Ntd1+1,Ntd1+2) = 0.d0          ! cov(Y1 Y2) 
+      BIG(Ntd1+1,Ntd1+3) = 0.d0          ! cov(Y1 X(ts)) 
+      BIG(Ntd1+1,Ntd1+4) = 0.d0          ! cov(Y1 X(t1)) 
+      BIG(Ntd1+1,Ntd1+5) = 0.d0          ! cov(Y1 X(tn))
+      BIG(Ntd1+2,Ntd1+2) = 100.d0        ! cov(Y2 Y2) 
+      BIG(Ntd1+2,Ntd1+3) = 0.d0          ! cov(Y2 X(ts)) 
+      BIG(Ntd1+2,Ntd1+4) = 0.d0          ! cov(Y2 X(t1)) 
+      BIG(Ntd1+2,Ntd1+5) = 0.d0          ! cov(Y2 X(tn))
+
+      BIG(Ntd1+3,Ntd1+3) = R0(1)        ! cov(X(ts),X (ts)
+      BIG(Ntd1+3,Ntd1+4) = R0(ts)       ! cov(X(ts),X (t1))
+      BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts)  ! cov(X(ts),X (tn))
+      BIG(Ntd1+4,Ntd1+4) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+4,Ntd1+5) = R0(tn)       ! cov(X(t1),X (tn))
+      BIG(Ntd1+5,Ntd1+5) = R0(1)        ! cov(X(tn),X (tn))
+  
+
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1) = 0.d0        !cov(X'(tn),Y1) 
+      BIG(Ntd1  ,Ntd1+2) = 0.d0        !cov(X'(tn),Y2) 
+      BIG(Ntd1-1  ,Ntd1+1) = 0.d0        !cov(X'(t1),Y1) 
+      BIG(Ntd1-1  ,Ntd1+2) = 0.d0        !cov(X'(t1),Y2) 
+      BIG(Ntd1-2  ,Ntd1+1) = 0.d0        !cov(X'(ts),Y1) 
+      BIG(Ntd1-2  ,Ntd1+2) = 0.d0        !cov(X'(ts),Y2) 
+  
+      BIG(Ntd1  ,Ntd1+4) = R1(tn)        !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+5) = 0.d0          !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+4) = 0.d0          !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+5) =-R1(tn)        !cov(X'(t1),X(tn))
+      BIG(Ntd1  ,Ntd1+3) = R1(tn+1-ts)   !cov(X'(tn),X (ts))  
+      BIG(Ntd1-1,Ntd1+3) =-R1(ts)        !cov(X'(t1),X (ts))   
+      BIG(Ntd1-2,Ntd1+3) = 0.d0          !cov(X'(ts),X (ts)
+      BIG(Ntd1-2,Ntd1+4) = R1(ts)        !cov(X'(ts),X (t1))
+      BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts)  !cov(X'(ts),X (tn))
+
+
+        do i=1,tn-2
+          j=abs(i+1-ts)
+!cov(Xt,Xc)
+          BIG(i,Ntd1+3)   = R0(j+1)      !cov(X(ti+1),X(ts))          
+!Cov(Xt,Xd)
+          if ((i+1-ts).lt.0) then
+              BIG(i,Ntd1-2)  =  R1(j+1)
+            else                         !cov(X(ti+1),X'(ts))  
+              BIG(i,Ntd1-2)  = -R1(j+1)
+          endif
+      enddo
+    
+! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+
+           BIG(i,j)=tmp
+        enddo
+      enddo
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2tccpdf
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2tcpdf.f

@@ -0,0 +1,440 @@
+      PROGRAM sp2tcpdf
+C***********************************************************************
+C     This program computes:                                           *
+C                                                                      *
+C     density of     T_i, for Ac <=h, in a gaussian process i.e.       *
+C                                                                      *
+C     half wavelength (up-crossing to downcrossing) for crests <h      *
+C    or  half wavelength (down-crossing to upcrossing) for trough >h   *
+C***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex,CY
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(2,6) :: a_up=0.d0,a_lo=0.d0
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size,icy
+      integer ::it1,it2
+      double precision :: ds,dT ! lag spacing for covariances 
+! DIGITAL:
+! f90  -o ~/WAT/V1/sp2tcpdf.exe rind44.f sp2tcpdf.f
+
+      !print *,'enter sp2thpdf'
+      CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,Nx,dT)
+      !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      if (abs(def).GT.1) THEN
+        !allocate(h(1:Nx))
+        allocate(R3(1:Ntime+1))
+        allocate(R4(1:Ntime+1))
+        !CALL INIT_AMPLITUDES(h,def,Nx)
+      endif
+      allocate(h(1:Nx))
+      CALL INIT_AMPLITUDES(h,def,Nx)
+      CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+
+      print *,'Nx',Nx
+      
+      Nj=0
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+      print *,'XdInf,XtInf'
+      print *,XdInf,XtInf
+      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      !fy(h)
+      allocate(CY(1:Nx)) 
+      do icy=1,Nx
+        CY(icy)=exp(-0.5*h(icy)*h(icy)/100)/(10*sqrt(twopi))
+      enddo
+
+      allocate(ansr(1:Ntime,1:Nx))
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      fxind=0.d0 !this is not needed
+   
+      NI=4; Nd=2
+      Nc=3; Mb=2
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc))
+      allocate(xc(1:Nc,1:Nx))
+      allocate(ex(1:Ntime+Nc)) 
+      ex=0.d0
+      !print *,'nc',Nc,Nx 
+        xc(1,1:Nx)=h(1:Nx)
+        print *,'xc',h(1)         
+        print *,'test',def;
+        xc(2,1:Nx)=u
+        xc(3,1:Nx)=u
+      if (def.GT.0) then
+         a_up(1,1)=u     !+XtInf 
+         a_lo(1,1)=u
+         a_up(1,2)=XdInf
+         a_lo(1,3)=-XdInf 
+         a_up(2,1)=1.d0      
+      else
+         a_up(1,1)=u 
+         a_lo(1,1)=u      !-XtInf
+         a_lo(1,2)=-XdInf
+         a_up(1,3)= XdInf  
+         a_lo(2,1)=1.d0  
+         print *,'a_lo',a_lo(2,1)
+      endif
+      !print *,'Nstart',Nstart
+      Nstart=MAX(3,Nstart)  
+      !print *,'Nstart',Nstart
+      if (SCIS.GT.0) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif
+      do Ntd=Nstart,Ntime
+         !CALL COV_INPUT2(BIG,Ntd, R0,R1,R2)
+         Ntdc=Ntd+Nc;
+         CALL COV_INPUT(BIG,Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd;
+         !Ntdc=Ntd+Nc;
+ 
+          CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
+     &              xc,indI,a_lo,a_up) 
+         ! print *,'test',fxind/CY(1:Nx)
+          do icy=1,Nx        
+            ansr(Ntd,icy)=fxind(icy)*CC/CY(icy)
+          enddo
+          if (SCIS.GT.0) then
+            write(11,*)  COV(1) ! save coefficient of variation
+          endif       
+          print *,'Ready: ',Ntd,' of ',Ntime
+      enddo 
+      goto 300
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+
+      !print *, ansr
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansr(ts,ph)
+            ! write(11,111)  ansr(ts,ph)
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  deallocate(big)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(ex)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)  
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+
+      if (allocated(R3)) then
+        deallocate(R3)
+        deallocate(R4)
+        deallocate(h)
+      ENDIF
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,def,Ntime,Nstart,NIT,speed,Nx,dT)
+      IMPLICIT NONE
+      integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) def
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed 
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+      print *,'def',def
+      if (abs(def).GT.1) then
+        READ (14,*) dT
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      else
+        if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      endif
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,def,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: def
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      !if (def.LT.0) THEN
+      !   H=-H
+      !endif      
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime,def
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+       enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      if (abs(def).GT.1) then      
+        open (unit=4, file='Cd3.in',STATUS='unknown')
+        open (unit=5, file='Cd4.in',STATUS='unknown')
+
+        do i=1,Ntime
+          read(4,*) R3(i)
+          read(5,*) R4(i)
+        enddo
+
+        close(4)
+        close(5)
+      endif
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,shft,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! For ts>1:
+! X(t2)..X(ts),..X(tn-1) X''(ts) X'(t1) X'(tn) X(ts) X(t1) X(tn) X'(ts) 
+! = [Xt                          Xd                    Xc]
+!
+! For ts<=1: 
+! X(t2)..,..X(tn-1)  X'(t1) X'(tn) Y X(t1) X(tn)  
+! = [Xt              Xd            Xc]
+!Add Y Condition : Y=h
+
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+      if (ts.LE.1) THEN
+	       Ntd1=tn
+          N=Ntd1+Nc;
+          shft=0  ! def=1 want only crest period Tc
+      else
+          Ntd1=tn+1
+          N=Ntd1+4
+          shft=1  ! def=2 or 3 want Tc Ac or Tcf, Ac
+      endif
+
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)
+	 BIG(i      ,Ntd1+1+shft) = 0.d0            !cov(X(ti+1),Y)   
+         BIG(i      ,Ntd1+2+shft) = R0(i+1)         !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+3+shft) = R0(i+1)         !cov(X(t.. ),X(tn))  
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)         =-R1(i+1)         !cov(X(ti+1),X' (t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X' (tn)) 
+      enddo
+      !call echo(big(1:tn,1:tn),tn)
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)     !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+
+!cov(Xc)
+      !print *,'t'
+      BIG(Ntd1+1+shft,Ntd1+1+shft) = 100.d0!100.d0         ! cov(Y,Y) 
+      BIG(Ntd1+1+shft,Ntd1+2+shft) = 0.d0
+      BIG(Ntd1+1+shft,Ntd1+3+shft) = 0.d0
+      BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+2+shft,Ntd1+3+shft) = R0(tn)       ! cov(X(t1),X (tn))
+      BIG(Ntd1+3+shft,Ntd1+3+shft) = R0(1)        ! cov(X(tn),X (tn))
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1+shft) = 0.d0            !cov(X'(tn),Y)     
+      BIG(Ntd1  ,Ntd1+2+shft) = R1(tn)       !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+3+shft) = 0.d0         !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+1+shft) = 0.d0         !cov(X'(t1),Y)
+      BIG(Ntd1-1,Ntd1+2+shft) = 0.d0         !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+3+shft) =-R1(tn)       !cov(X'(t1),X(tn))
+
+
+      !call echo(big(1:N,1:N),N) 
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+           BIG(i,j)=tmp
+        enddo
+        !call echo(big(1:N,1:N),N) 
+      enddo
+      !if (tn.eq.3) then
+      !do j=1,N
+      !  do i=j,N
+      !      print *,'test',j,i,BIG(j,i)
+      !  enddo
+        !call echo(big(1:N,1:N),N) 
+      !enddo
+      !endif
+      !call echo(big(1:N,1:N),N) 
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2tcpdf
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2thpdf.f

@@ -0,0 +1,569 @@
+      PROGRAM sp2thpdf
+!***********************************************************************
+!     This program computes:                                           *
+!                                                                      *
+!     density of         S_i,Hi,T_i in a gaussian process i.e.         *
+!                                                                      *
+!      quart wavelength (up-crossing to crest) and crest amplitude     *    
+!  
+! def = 1,  gives half wave period, Tc (default).
+!      -1,  gives half wave period, Tt.
+!       2,  gives half wave period and wave crest amplitude (Tc,Ac).
+!      -2,  gives half wave period and wave trough amplitude (Tt,At).
+!       3,  gives crest front period and wave crest amplitude (Tcf,Ac).
+!      -3,  gives trough back period and wave trough amplitude (Ttb,At).
+!       4,  gives minimum of crest front/back period and wave crest 
+!                                           amplitude (max(Tcf,Tcb),Ac).
+!      -4,  gives minimum of trough front/back period and wave trough 
+!                                           amplitude (max(Ttf,Ttb),At).
+!***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &   NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(2,6) :: a_up=0.d0,a_lo=0.d0
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size
+      double precision :: ds,dT ! lag spacing for covariances 
+! DIGITAL:
+! f90 -g2 -C -automatic -o ../wave/alpha/sp2thpdf.exe rind44.f sp2thpdf.f
+! SOLARIS:
+!f90 -g -O -w3 -Bdynamic -fixed -o ../wave/sol2/sp2thpdf.exe rind44.f sp2thpdf.f
+! linux:
+! f90 -gline -Nl126 -C -o sp2thpdf.exe rind45.f sp2thpdf.f
+! HP700
+!f90 -g -C -o ../exec/hp700/sp2thpdf.exe rind45.f sp2thpdf.f
+!f90 -g -C +check=all +FPVZID -o ../exec/hp700/sp2thpdf2.exe rind45.f sp2thpdf.f
+
+
+      !print *,'enter sp2thpdf'
+      CALL INIT_LEVELS(U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT)
+      !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT
+
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      if (abs(def).GT.1) THEN
+        allocate(h(1:Nx))
+        allocate(R3(1:Ntime+1))
+        allocate(R4(1:Ntime+1))
+        
+        CALL INIT_AMPLITUDES(h,def,Nx)
+      endif
+      CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+
+      !print *,'Nx',Nx
+      
+      Nj=0
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+      !print *,'XdInf,XtInf'
+      !print *,XdInf,XtInf
+      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      if (abs(def).EQ.4) CC=2.d0*CC
+      allocate(ansr(1:Ntime,1:Nx))
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      !fxind=0.d0 this is not needed
+   
+      if (abs(def).GT.1) then 
+        GOTO 200
+      endif
+      NI=4; Nd=2
+      Nc=2; Mb=1
+      Nx=1
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc))
+      allocate(xc(1:Nc,1:Nx))
+      allocate(ex(1:Ntime+Nc)) 
+      ex=0.d0 
+      xc(1,1)=u
+      xc(2,1)=u
+
+      if (def.GT.0) then
+         a_up(1,1)=u+XtInf 
+         a_lo(1,1)=u
+         a_up(1,2)=XdInf
+         a_lo(1,3)=-XdInf       
+      else
+         a_up(1,1)=u 
+         a_lo(1,1)=u-XtInf
+         a_lo(1,2)=-XdInf
+         a_up(1,3)= XdInf      
+      endif
+      !print *,'Nstart',Nstart
+      Nstart=MAX(2,Nstart)  
+      !print *,'Nstart',Nstart
+      if (SCIS.GT.0) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif
+      do Ntd=Nstart,Ntime
+         !CALL COV_INPUT2(BIG,Ntd, R0,R1,R2)
+         CALL COV_INPUT(BIG,Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd;
+         Ntdc=Ntd+Nc;
+         !if (SCIS.gt.0) then
+         !  if (SCIS.EQ.2) then           
+         !     Nj=max(Nt,0)
+         !  else
+         !     Nj=min(max(Nt-5, 0),0)
+         !  endif
+         !endif
+         !Ex=0.d0
+         !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc)
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
+     &              xc,indI,a_lo,a_up)         
+         ansr(Ntd,1)=fxind(1)*CC
+         if (SCIS.GT.0) then
+            write(11,*)  COV(1) ! save coefficient of variation
+         endif       
+         print *,'Ready: ',Ntd,' of ',Ntime
+      enddo
+      if (SCIS.GT.0) then
+        close(11) 
+      endif
+      goto 300
+200   continue 
+      XddInf=10.d0*SQRT(R4(1))
+      NI=7; Nd=3
+      Nc=4; Mb=2
+      allocate(BIG(1:Ntime+Nc+1,1:Ntime+Nc+1)) 
+      ALLOCATE(xc(1:Nc,1:Nx))
+      allocate(ex(1:Ntime+Nc+1))
+      
+      ex=0.d0 
+      xc(1,1:Nx)=h
+      xc(2,1:Nx)=u
+      xc(3,1:Nx)=u
+      xc(4,1:Nx)=0.d0
+      
+      if (def.GT.0) then
+        a_up(2,1)=1.d0   !*h 
+        a_lo(1,1)=u
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf 
+        a_up(2,2)=1.d0   ! *h
+        a_lo(2,2)=1.d0   ! *h
+        a_up(2,3)=1.d0   !*h 
+        a_lo(1,3)=u
+
+        a_lo(1,4)=-XddInf
+        a_up(1,5)= XdInf
+        a_lo(1,6)=-XdInf       
+      else !def<0
+        a_up(1,1)=u   
+        a_lo(2,1)=1.d0 !*h
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf 
+        a_up(2,2)=1.d0          ! *h
+        a_lo(2,2)=1.d0          ! *h
+        a_up(1,3)=u   
+        a_lo(2,3)=1.d0 !*h
+
+        a_up(1,4)=XddInf
+        a_lo(1,5)=-XdInf
+        a_up(1,6)=XdInf
+      endif 
+      
+      Nstart=MAX(Nstart,3)
+      do tn=Nstart,Ntime,1
+        Ntd=tn+1
+        Nt=Ntd-Nd
+        Ntdc=Ntd+Nc
+        indI(4)=Nt
+        indI(5)=Nt+1
+        indI(6)=Nt+2
+        indI(7)=Ntd
+        if (SCIS.gt.0) then
+           if (SCIS.EQ.2) then           
+              Nj=max(Nt,0)
+           else
+              Nj=min(max(Nt-5, 0),0)
+           endif
+        endif
+        do ts=2,FLOOR(DBLE(tn+1)/2.d0)
+         !print *,'ts,tn' ,ts,tn
+         CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period
+         indI(2)=ts-2
+         indI(3)=ts-1          
+         !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc)
+         !print *,'sp call rind'
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
+     &              xc,indI,a_lo,a_up)
+         !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc)
+         !print *,'sp rind finished',fxind
+         !goto 900
+         if (abs(def).LT.3) THEN
+            if (ts .EQ.tn-ts+1) then
+               ds=dt
+            else 
+               ds=2.d0*dt
+            endif
+            ansr(tn,1:Nx)=ansr(tn,1:Nx)+fxind*CC*ds
+         else 
+            ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*dT
+           if ((ts.LT.tn-ts+1).and. (abs(def).lt.4)) THEN
+             ansr(tn-ts+1,1:Nx)=ansr(tn-ts+1,1:Nx)+fxind*CC*dT ! exploiting the symmetry
+           endif
+         endif
+        enddo ! ts
+        print *,'Ready: ',tn,' of ',Ntime
+
+      enddo !tn
+      !print *,'ansr',ansr
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+      !print *, ansr
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansr(ts,ph)
+            ! write(11,111)  ansr(ts,ph)
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  deallocate(big)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(ex)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+      if (allocated(R3)) then
+        deallocate(R3)
+        deallocate(R4)
+        deallocate(h)
+      ENDIF
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT)
+      IMPLICIT NONE
+      integer, intent(out):: def,Ntime,Nstart,NIT,speed,Nx,SCIS,seed1
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) def
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed   
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+
+      if (abs(def).GT.1) then
+        READ (14,*) Nx
+        READ (14,*) dT
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      else
+        Nx=1
+        if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      endif
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,def,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: def
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      !if (def.LT.0) THEN
+      !   H=-H
+      !endif      
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime,def
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+      enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      if (abs(def).GT.1) then      
+        open (unit=4, file='Cd3.in',STATUS='unknown')
+        open (unit=5, file='Cd4.in',STATUS='unknown')
+
+        do i=1,Ntime
+          read(4,*) R3(i)
+          read(5,*) R4(i)
+        enddo
+
+        close(4)
+        close(5)
+      endif
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,shft,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! For ts>1:
+! ||X(t2)..X(ts),..X(tn-1)||X''(ts) X'(t1) X'(tn)||X(ts) X(t1) X(tn) X'(ts)|| 
+! = [Xt                          Xd                    Xc]
+!
+! For ts<=1: 
+! ||X(t2)..,..X(tn-1)||X'(t1) X'(tn)||X(t1) X(tn)||  
+! = [Xt              Xd            Xc]
+
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+      if (ts.LE.1) THEN
+	  Ntd1=tn
+          N=Ntd1+2;
+          shft=0  ! def=1 want only crest period Tc
+      else
+          Ntd1=tn+1
+          N=Ntd1+4
+          shft=1  ! def=2 or 3 want Tc Ac or Tcf, Ac
+      endif
+
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)	
+         BIG(i      ,Ntd1+1+shft) = R0(i+1)         !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+2+shft) = R0(i+1)         !cov(X(t.. ),X(tn))  
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)         =-R1(i+1)         !cov(X(ti+1),X' (t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X' (tn)) 
+      enddo
+      !call echo(big(1:tn,1:tn),tn)
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)     !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+
+!cov(Xc)
+      BIG(Ntd1+1+shft,Ntd1+1+shft) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+1+shft,Ntd1+2+shft) = R0(tn)      ! cov(X(t1),X (tn))
+      BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1)        ! cov(X(tn),X (tn))
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1+shft) = R1(tn)       !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+2+shft) = 0.d0         !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+1+shft) = 0.d0         !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+2+shft) =-R1(tn)      !cov(X'(t1),X(tn))
+
+
+      if (ts.GT.1) then 
+
+! 
+!cov(Xc)
+        BIG(Ntd1+1,Ntd1+1) = R0(1)        ! cov(X(ts),X (ts)
+        BIG(Ntd1+1,Ntd1+2) = R0(ts)       ! cov(X(ts),X (t1))
+        BIG(Ntd1+1,Ntd1+3) = R0(tn+1-ts)  ! cov(X(ts),X (tn))
+        BIG(Ntd1+1,Ntd1+4) = 0.d0         ! cov(X(ts),X'(ts))
+
+        BIG(Ntd1+2,Ntd1+4) = R1(ts)       ! cov(X(t1),X'(ts))
+        BIG(Ntd1+3,Ntd1+4) = -R1(tn+1-ts)  !cov(X(tn),X'(ts))
+        BIG(Ntd1+4,Ntd1+4) = -R2(1)       ! cov(X'(ts),X'(ts))
+
+!cov(Xd)
+        BIG(Ntd1-2,Ntd1-1) = -R3(ts)      !cov(X''(ts),X'(t1))
+        BIG(Ntd1-2,Ntd1-2) = R4(1)
+        BIG(Ntd1-2,Ntd1  ) = R3(tn+1-ts)   !cov(X''(ts),X'(tn))
+!cov(Xd,Xc)
+        BIG(Ntd1  ,Ntd1+4) =-R2(tn+1-ts)   !cov(X'(tn),X'(ts))  
+        BIG(Ntd1  ,Ntd1+1) = R1(tn+1-ts)   !cov(X'(tn),X (ts))  
+
+        BIG(Ntd1-1,Ntd1+4) =-R2(ts)       !cov(X'(t1),X'(ts))     
+        BIG(Ntd1-1,Ntd1+1) =-R1(ts)       !cov(X'(t1),X (ts))  
+ 
+        BIG(Ntd1-2,Ntd1+1) = R2(1)        !cov(X''(ts),X (ts)
+        BIG(Ntd1-2,Ntd1+2) = R2(ts)       !cov(X''(ts),X (t1))
+        BIG(Ntd1-2,Ntd1+3) = R2(tn+1-ts)   !cov(X''(ts),X (tn))
+        BIG(Ntd1-2,Ntd1+4) = 0.d0         !cov(X''(ts),X'(ts))
+!cov(Xt,Xc)
+        do i=1,tn-2
+          j=abs(i+1-ts)
+          BIG(i,Ntd1+1)   = R0(j+1) !cov(X(ti+1),X(ts))  
+          BIG(i,Ntd1+4)   = sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X(ti+1),X'(ts))   ! check this
+        
+!Cov(Xt,Xd)=cov(X(ti+1),X(ts))       
+          BIG(i,Ntd1-2)    = R2(j+1) !cov(X(ti+1),X''(ts))  
+        enddo
+      endif ! ts>1
+
+      !call echo(big(1:N,1:N),N) 
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+
+           BIG(i,j)=tmp
+        enddo
+        !call echo(big(1:N,1:N),N) 
+
+      enddo
+      !call echo(big(1:N,1:N),N) 
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2thpdf
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2thpdfalan.f

@@ -0,0 +1,632 @@
+      PROGRAM sp2thpdf
+!***********************************************************************
+!     This program computes:                                           *
+!                                                                      *
+!     density of         S_i,Hi,T_i in a gaussian process i.e.         *
+!                                                                      *
+!      quart wavelength (up-crossing to crest) and crest amplitude     *    
+!  
+! def = 1,  gives half wave period, Tc (default).
+!      -1,  gives half wave period, Tt.
+!       2,  gives half wave period and wave crest amplitude (Tc,Ac).
+!      -2,  gives half wave period and wave trough amplitude (Tt,At).
+!       3,  gives crest front period and wave crest amplitude (Tcf,Ac).
+!      -3,  gives trough back period and wave trough amplitude (Ttb,At).
+!       4,  gives minimum of crest front/back period and wave crest 
+!                                           amplitude (min(Tcf,Tcb),Ac).
+!      -4,  gives minimum of trough front/back period and wave trough 
+!                                           amplitude (min(Ttf,Ttb),At).
+!***********************************************************************
+!History:
+! revised Per A. Brodtkorb 04.04.2000
+!   - 
+! revised Per A. Brodtkorb 23.11.99
+!   - fixed a bug in calculating pdf for def = +/- 4
+! revised Per A. Brodtkorb 03.11.99
+!   - added def = +/-4 
+! revised Per A. Brodtkorb 23.09.99
+!   - minor changes to covinput
+!   - removed the calculation of the transformation to spec2thpdf.m
+! by Igor Rychlik
+
+
+      use GLOBALDATA, only : rateLHD,SCIS,NSIMmax,COV,ABSEPS
+      use globalconst
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansr
+      double precision, dimension(:  ),allocatable :: ex
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:  ),allocatable :: fxind,h
+      double precision, dimension(:  ),allocatable :: R0,R1,R2,R3,R4
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(2,6) :: a_up=0.d0,a_lo=0.d0
+      integer, dimension(6)            :: INFIN=2
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Nx,Nt,Nc,Nd,NI,Mb,Ntd, Ntdc
+      integer :: Nstart,Ntime,tn,ts,speed,ph,def,seed1,seed_size
+      double precision :: dT, EPSOLD ! lag spacing for covariances 
+      LOGICAL :: init=.TRUE.
+! DIGITAL:
+! f90 -g2 -C -automatic -o ../wave/alpha/sp2thpdf.exe rind44.f sp2thpdf.f
+! SOLARIS:
+!f90 -g -O -w3 -Bdynamic -fixed -o ../wave/sol2/sp2thpdf.exe rind44.f sp2thpdf.f
+! linux:
+! f90  -gline -Nl126 -C -o ../exec/lnx86/sp2thpdf8.exe  intmodule.f rind60.f sp2thpdf.f
+! f90 -gline -Nl126 -C -o sp2thpdf.exe rind45.f sp2thpdf.f
+! f90  -gline -Nl126 -C -o ../exec/lnx86/sp2thpdf3.exe  adaptmodule.f krbvrcmod.f krobovmod.f rcrudemod.f rind55.f sp2thpdf.f
+! HP700
+!f90 -g -C -o ../exec/hp700/sp2thpdf.exe rind45.f sp2thpdf.f
+!f90 -g -C +check=all +FPVZID -o ../exec/hp700/sp2thpdf.exe rind45.f sp2thpdf.f
+! f90 +gprof +extend_source +Oall +Odataprefetch +Ofastaccess +Oinfo +Oprocelim -C +check=all  -o ../exec/hp700/sp2thpdf.exe rind48.f sp2thpdf.f
+
+      !print *,'enter sp2thpdf'
+      
+      CALL INIT_LEVELS(U,def,Ntime,Nstart,speed,SCIS,seed1,
+     &     Nx,dT,rateLHD)
+      !print *,'U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,def,Ntime,Nstart,NIT,speed,SCIS,seed1,Nx,dT
+      
+      
+      if (SCIS.GT.0) then
+        !allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      if (abs(def).GT.1) THEN
+        allocate(h(1:Nx))
+        allocate(R3(1:Ntime+1))
+        allocate(R4(1:Ntime+1))        
+        CALL INIT_AMPLITUDES(h,def,Nx)
+      endif
+      CALL INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+
+      !print *,'Nx',Nx
+      
+      
+      indI(1)=0
+C ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+      !print *,'XdInf,XtInf'
+      !print *,XdInf,XtInf
+      ! normalizing constant
+      CC=TWPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      allocate(ansr(1:Ntime,1:Nx))
+      ansr=0.d0
+      allocate(fxind(1:Nx))    
+      !fxind=0.d0 this is not needed
+   
+      if (abs(def).GT.1)   GOTO 200
+      
+      NI=4; Nd=2
+      Nc=2; Mb=1
+      Nx=1
+      allocate(BIG(1:Ntime+Nc,1:Ntime+Nc))
+      allocate(xc(1:Nc,1:Nx))
+      allocate(ex(1:Ntime+Nc)) 
+      ex=0.d0 
+      xc(1,1)=u
+      xc(2,1)=u
+! INFIN =  INTEGER, array of integration limits flags:  size 1 x Nb     (in)
+!            if INFIN(I) < 0, Ith limits are (-infinity, infinity);
+!            if INFIN(I) = 0, Ith limits are (-infinity, Hup(I)];
+!            if INFIN(I) = 1, Ith limits are [Hlo(I), infinity);
+!            if INFIN(I) = 2, Ith limits are [Hlo(I), Hup(I)].
+
+      if (def.GT.0) then
+         INFIN(1:2) = 1
+         INFIN(3) = 0
+         a_up(1,1)= u+XtInf 
+         a_lo(1,1)= u
+         a_up(1,2)= XdInf
+         a_lo(1,3)=-XdInf       
+      else
+         INFIN(1:2) = 0
+         INFIN(3) = 1
+         a_up(1,1)=u 
+         a_lo(1,1)=u-XtInf
+         a_lo(1,2)=-XdInf
+         a_up(1,3)= XdInf      
+      endif
+      !print *,'Nstart',Nstart
+      Nstart=MAX(2,Nstart)  
+      !print *,'Nstart',Nstart
+      if (ALLOCATED(COV)) then
+         open (unit=11, file='COV.out',  STATUS='unknown') 
+         write(11,*) 0.d0
+      endif
+      do Ntd=Nstart,Ntime
+         !CALL COV_INPUT2(BIG,Ntd, R0,R1,R2)
+         CALL COV_INPUT(BIG,Ntd,-1,R0,R1,R2,R3,R4) ! positive wave period
+         Nt=Ntd-Nd;
+         indI(2)=Nt;
+         indI(3)=Nt+1;
+         indI(4)=Ntd;
+         Ntdc=Ntd+Nc;
+!         IF (Ntd.GT.5.AND.(INIT)) THEN
+!            INIT=.FALSE.
+!            CALL INITDATA(speed)
+!         ENDIF
+         !if (SCIS.gt.1) Nj=Nt
+         !if (SCIS.gt.0) then
+         !  if (SCIS.EQ.2) then           
+         !     Nj=max(Nt,0)
+         !  else
+         !     Nj=min(max(Nt-5, 0),0)
+         !  endif
+         !endif
+         !Ex=0.d0
+         !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc)
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),xc,
+     &        Nt,indI(1:NI),a_lo(1:Mb,1:NI-1),a_up(1:Mb,1:NI-1),
+     &        INFIN(1:NI-1))         
+         ansr(Ntd,1)=fxind(1)*CC
+         if (ALLOCATED(COV)) then  !SCIS.GT.0
+            write(11,*)  COV(1) ! save coefficient of variation
+         endif       
+         print *,'Ready: ',Ntd,' of ',Ntime
+      enddo
+      if (ALLOCATED(COV)) then
+        close(11) 
+      endif
+      goto 300
+200   continue 
+      XddInf=10.d0*SQRT(R4(1))
+      NI=7; Nd=3
+      Nc=4; Mb=2
+      allocate(BIG(1:Ntime+Nc+1,1:Ntime+Nc+1)) 
+      ALLOCATE(xc(1:Nc,1:Nx))
+      allocate(ex(1:Ntime+Nc+1))
+      
+      ex=0.d0 
+      xc(1,1:Nx)=h(1:Nx)
+      xc(2,1:Nx)=u
+      xc(3,1:Nx)=u
+      xc(4,1:Nx)=0.d0
+
+! INFIN =  INTEGER, array of integration limits flags:  size 1 x Nb     (in)
+!            if INFIN(I) < 0, Ith limits are (-infinity, infinity);
+!            if INFIN(I) = 0, Ith limits are (-infinity, Hup(I)];
+!            if INFIN(I) = 1, Ith limits are [Hlo(I), infinity);
+!            if INFIN(I) = 2, Ith limits are [Hlo(I), Hup(I)].      
+      if (def.GT.0) then
+         INFIN(2)=-1
+         INFIN(4)=0
+         INFIN(5)=1
+         INFIN(6)=0
+        a_up(2,1)=1.d0   !*h 
+        a_lo(1,1)=u
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf 
+        a_up(2,2)=1.d0   ! *h
+        a_lo(2,2)=1.d0   ! *h
+        a_up(2,3)=1.d0   !*h 
+        a_lo(1,3)=u
+
+        a_lo(1,4)=-XddInf
+        a_up(1,5)= XdInf
+        a_lo(1,6)=-XdInf       
+      else !def<0
+         INFIN(2)=-1
+         INFIN(4)=1
+         INFIN(5)=0
+         INFIN(6)=1
+        a_up(1,1)=u   
+        a_lo(2,1)=1.d0 !*h
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf 
+        a_up(2,2)=1.d0          ! *h
+        a_lo(2,2)=1.d0          ! *h
+        a_up(1,3)=u   
+        a_lo(2,3)=1.d0 !*h
+        a_up(1,4)=XddInf
+        a_lo(1,5)=-XdInf
+        a_up(1,6)=XdInf
+      endif 
+      EPSOLD=ABSEPS
+      Nstart=MAX(Nstart,3)
+      do tn=Nstart,Ntime,1
+        Ntd=tn+1
+        Nt=Ntd-Nd
+        Ntdc=Ntd+Nc
+        indI(4)=Nt
+        indI(5)=Nt+1
+        indI(6)=Nt+2
+        indI(7)=Ntd
+!        IF (Ntd.GT.5.AND.INIT) THEN
+!           INIT=.FALSE.
+!           CALL INITDATA(speed)
+!        ENDIF
+        !if (SCIS.gt.1) Nj=Nt
+        !if (SCIS.gt.0) then
+        !   if (SCIS.EQ.2) then           
+        !      Nj=max(Nt,0)
+        !   else
+        !      Nj=min(max(Nt-5, 0),0)
+        !   endif
+        !endif
+        ABSEPS=MIN(SQRT(DBLE(tn))*EPSOLD*0.5D0,0.1D0)
+        do ts=2,FLOOR(DBLE(tn+1)/2.d0)
+                                !print *,'ts,tn' ,ts,tn
+           CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2,R3,R4) ! positive wave period
+           indI(2)=ts-2
+           indI(3)=ts-1          
+                                !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc)
+                                !print *,'sp call rind'
+           CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),xc,
+     &          Nt,indI(1:NI),a_lo(1:Mb,1:NI-1),a_up(1:Mb,1:NI-1),
+     &          INFIN(1:NI-1))  
+                                !CALL echo(BIG(1:Ntdc,1:min(7,Ntdc)),Ntdc)
+                                !print *,'sp rind finished',fxind
+                                !goto 900
+           SELECT CASE (ABS(def))
+           CASE (:2) 
+!       2,  gives half wave period and wave crest amplitude (Tc,Ac).
+!      -2,  gives half wave period and wave trough amplitude (Tt,At).
+              if (ts .EQ.tn-ts+1) then
+                 ansr(tn,1:Nx)=ansr(tn,1:Nx)+fxind*CC*dt
+              else 
+                 ansr(tn,1:Nx)=ansr(tn,1:Nx)+fxind*CC*2.d0*dt
+              endif              
+           CASE (3)
+!       3,  gives crest front period and wave crest amplitude (Tcf,Ac).
+!      -3,  gives trough back period and wave trough amplitude (Ttb,At).
+              ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*dT
+              if ((ts.LT.tn-ts+1)) THEN
+                 ansr(tn-ts+1,1:Nx)=ansr(tn-ts+1,1:Nx)+fxind*CC*dT ! exploiting the symmetry
+              endif
+           CASE (4:)
+!       4,  gives minimum of crest front/back period and wave crest amplitude (min(Tcf,Tcb),Ac).
+!      -4,  gives minimum of trough front/back period and wave trough amplitude (min(Ttf,Ttb),At).
+              if (ts .EQ.tn-ts+1) then
+                 ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*dt
+              else 
+                 ansr(ts,1:Nx)=ansr(ts,1:Nx)+fxind*CC*2.0*dt
+              endif
+           end select
+        enddo                   ! ts
+        print *,'Ready: ',tn,' of ',Ntime, ' ABSEPS = ', ABSEPS
+
+      enddo                     !tn
+      !print *,'ansr',ansr
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+      !print *, ansr
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansr(ts,ph)
+            ! write(11,111)  ansr(ts,ph)
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  deallocate(big)
+      deallocate(fxind)
+      deallocate(ansr)
+      deallocate(xc)
+      deallocate(ex)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+      if (allocated(R3)) then
+        deallocate(R3)
+        deallocate(R4)
+        deallocate(h)
+      ENDIF
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,def,Ntime,Nstart,speed,SCIS,seed1,Nx,dT,rateLHD)
+      IMPLICIT NONE
+      integer, intent(out):: def,Ntime,Nstart,speed,Nx,SCIS,seed1,
+     &  rateLHD
+      double precision ,intent(out) :: U,dT
+      double precision :: XSPLT
+      integer :: NIT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) def
+      READ (14,*) Ntime
+      READ (14,*) Nstart
+      READ (14,*) NIT
+      READ (14,*) speed   
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+      READ (14,*) Nx
+      READ (14,*) dT
+      READ (14,*) rateLHD
+      READ (14,*) XSPLT
+      if (abs(def).GT.1) then
+       
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      else
+        Nx=1
+        if (Ntime.lt.2) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      endif
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h,def,Nx)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h    
+      integer, intent(in) :: def
+      integer, intent(in) :: Nx
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx
+        READ (4,*) H(ix)
+      enddo
+      CLOSE(UNIT=4)
+      !if (def.LT.0) THEN
+      !   H=-H
+      !endif      
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,def,R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      double precision, dimension(:),intent(out) :: R3,R4
+      integer,intent(in) :: Ntime,def
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+      
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+      enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      if (abs(def).GT.1) then      
+        open (unit=4, file='Cd3.in',STATUS='unknown')
+        open (unit=5, file='Cd4.in',STATUS='unknown')
+
+        do i=1,Ntime
+          read(4,*) R3(i)
+          read(5,*) R4(i)
+        enddo
+
+        close(4)
+        close(5)
+      endif
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2,R3,R4)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      double precision, dimension(:),intent(in) :: R3,R4
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,shft,Ntd1,N !=Ntdc
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! For ts>1:
+! ||X(t2)..X(ts),..X(tn-1)||X''(ts) X'(t1) X'(tn)||X(ts) X(t1) X(tn) X'(ts)|| 
+! = [Xt                          Xd                    Xc]
+!
+! For ts<=1: 
+! ||X(t2)..,..X(tn-1)||X'(t1) X'(tn)||X(t1) X(tn)||  
+! = [Xt              Xd            Xc]
+
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+      if (ts.LE.1) THEN
+          Ntd1=tn
+          N=Ntd1+2;
+          shft=0  ! def=1 want only crest period Tc
+      else
+          Ntd1=tn+1
+          N=Ntd1+4
+          shft=1  ! def=2 or 3 want Tc Ac or Tcf, Ac
+      endif
+
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)	
+         BIG(i      ,Ntd1+1+shft) = R0(i+1)         !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+2+shft) = R0(i+1)         !cov(X(t.. ),X(tn))  
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)         =-R1(i+1)         !cov(X(ti+1),X' (t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X' (tn)) 
+      enddo
+      !call echo(big(1:tn,1:tn),tn)
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)     !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+
+!cov(Xc)
+      BIG(Ntd1+1+shft,Ntd1+1+shft) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+1+shft,Ntd1+2+shft) = R0(tn)      ! cov(X(t1),X (tn))
+      BIG(Ntd1+2+shft,Ntd1+2+shft) = R0(1)        ! cov(X(tn),X (tn))
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1+shft) = R1(tn)       !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+2+shft) = 0.d0         !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+1+shft) = 0.d0         !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+2+shft) =-R1(tn)      !cov(X'(t1),X(tn))
+
+
+      if (ts.GT.1) then 
+
+! 
+!cov(Xc)
+        BIG(Ntd1+1,Ntd1+1) = R0(1)        ! cov(X(ts),X (ts)
+        BIG(Ntd1+1,Ntd1+2) = R0(ts)       ! cov(X(ts),X (t1))
+        BIG(Ntd1+1,Ntd1+3) = R0(tn+1-ts)  ! cov(X(ts),X (tn))
+        BIG(Ntd1+1,Ntd1+4) = 0.d0         ! cov(X(ts),X'(ts))
+
+        BIG(Ntd1+2,Ntd1+4) = R1(ts)       ! cov(X(t1),X'(ts))
+        BIG(Ntd1+3,Ntd1+4) = -R1(tn+1-ts)  !cov(X(tn),X'(ts))
+        BIG(Ntd1+4,Ntd1+4) = -R2(1)       ! cov(X'(ts),X'(ts))
+
+!cov(Xd)
+        BIG(Ntd1-2,Ntd1-1) = -R3(ts)      !cov(X''(ts),X'(t1))
+        BIG(Ntd1-2,Ntd1-2) = R4(1)
+        BIG(Ntd1-2,Ntd1  ) = R3(tn+1-ts)   !cov(X''(ts),X'(tn))
+!cov(Xd,Xc)
+        BIG(Ntd1  ,Ntd1+4) =-R2(tn+1-ts)   !cov(X'(tn),X'(ts))  
+        BIG(Ntd1  ,Ntd1+1) = R1(tn+1-ts)   !cov(X'(tn),X (ts))  
+
+        BIG(Ntd1-1,Ntd1+4) =-R2(ts)       !cov(X'(t1),X'(ts))     
+        BIG(Ntd1-1,Ntd1+1) =-R1(ts)       !cov(X'(t1),X (ts))  
+ 
+        BIG(Ntd1-2,Ntd1+1) = R2(1)        !cov(X''(ts),X (ts)
+        BIG(Ntd1-2,Ntd1+2) = R2(ts)       !cov(X''(ts),X (t1))
+        BIG(Ntd1-2,Ntd1+3) = R2(tn+1-ts)   !cov(X''(ts),X (tn))
+        BIG(Ntd1-2,Ntd1+4) = 0.d0         !cov(X''(ts),X'(ts))
+!cov(Xt,Xc)
+        do i=1,tn-2
+          j=abs(i+1-ts)
+          BIG(i,Ntd1+1)   = R0(j+1) !cov(X(ti+1),X(ts))  
+          BIG(i,Ntd1+4)   = sign(R1(j+1),R1(j+1)*dble(ts-i-1)) !cov(X(ti+1),X'(ts))   ! check this
+        
+!Cov(Xt,Xd)=cov(X(ti+1),X(ts))       
+          BIG(i,Ntd1-2)    = R2(j+1) !cov(X(ti+1),X''(ts))  
+        enddo
+      endif ! ts>1
+
+      !call echo(big(1:N,1:N),N) 
+      ! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           BIG(i,j) =BIG(j,i)
+        enddo
+        !call echo(big(1:N,1:N),N) 
+      enddo
+      !call echo(big(1:N,1:N),N) 
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+      END  PROGRAM  sp2thpdf
+       
+
+
+
+
+
+
+
+

wafo/source/cov2XXXpdf/cov2tthpdf.f

@@ -0,0 +1,505 @@
+      PROGRAM sp2tthpdf
+C***********************************************************************
+C     This program computes upper and lower bounds for the:            *
+C                                                                      *
+C     density of     T=  T_1+T_2 in a gaussian process i.e.            *
+C                                                                      *
+C      wavelengthes for crests <h1 and troughs >h2                     *    
+C                                                                      *
+C     Sylvie  and Igor 7 dec. 1999                                    *
+C***********************************************************************
+      use GLOBALDATA, only : Nt,Nj,Nd,Nc,Ntd,Ntdc,NI,Mb,
+     &   NIT,Nx,TWOPI,XSPLT,SCIS,NSIMmax,COV
+      use rind
+      IMPLICIT NONE
+      double precision, dimension(:,:),allocatable :: BIG
+      double precision, dimension(:,:),allocatable :: ansrup
+      double precision, dimension(:,:),allocatable :: ansrlo
+      double precision, dimension(:  ),allocatable :: ex,CY1,CY2
+      double precision, dimension(:,:),allocatable :: xc
+      double precision, dimension(:,:),allocatable ::fxind
+      double precision, dimension(:  ),allocatable :: h1,h2
+      double precision, dimension(:  ),allocatable :: hh1,hh2
+      double precision, dimension(:  ),allocatable :: R0,R1,R2
+      double precision             ::CC,U,XddInf,XdInf,XtInf  
+      double precision, dimension(:,:),allocatable :: a_up,a_lo
+      integer         , dimension(:  ),allocatable :: seed
+      integer ,dimension(7) :: indI
+      integer :: Ntime,N0,tn,ts,speed,ph,seed1,seed_size,Nx1,Nx2
+      integer :: icy,icy2
+      double precision :: ds,dT ! lag spacing for covariances 
+! DIGITAL:
+! f90 -g2 -C -automatic -o ~/WAT/V4/sp2tthpdf.exe rind48.f sp2tthpdf.f
+! SOLARIS:
+!f90 -g -O -w3 -Bdynamic -fixed -o ../sp2tthpdf.exe rind48.f sp2tthpdf.f
+
+      !print *,'enter sp2thpdf'
+      CALL INIT_LEVELS(U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
+      
+      !print *,'U,Ntime,NIT,speed,SCIS,seed1,Nx,dT'
+      !print *,U,Ntime,NIT,speed,SCIS,seed1,Nx,dT
+      !Nx1=1
+      !Nx2=1
+
+      Nx=Nx1*Nx2
+      !print *,'NN',Nx1,Nx2,Nx
+      
+      
+      !XSPLT=1.5d0
+      if (SCIS.GT.0) then
+        allocate(COV(1:Nx))
+        call random_seed(SIZE=seed_size) 
+        allocate(seed(seed_size)) 
+        call random_seed(GET=seed(1:seed_size))  ! get current seed
+        seed(1)=seed1                            ! change seed
+        call random_seed(PUT=seed(1:seed_size)) 
+        deallocate(seed)
+      endif
+      CALL INITDATA(speed)  
+      !print *,ntime,speed,u,NIT
+      allocate(R0(1:Ntime+1))
+      allocate(R1(1:Ntime+1))
+      allocate(R2(1:Ntime+1))
+      
+      allocate(h1(1:Nx1))
+      allocate(h2(1:Nx2))
+      CALL INIT_AMPLITUDES(h1,Nx1,h2,Nx2)
+      CALL INIT_COVARIANCES(Ntime,R0,R1,R2)
+      
+
+      allocate(hh1(1:Nx))
+      allocate(hh2(1:Nx))
+      !h transformation
+      do icy=1,Nx1
+         do icy2=1,Nx2
+         hh1((icy-1)*Nx2+icy2)=h1(icy);
+         hh2((icy-1)*Nx2+icy2)=h2(icy2); 
+         enddo 
+      enddo
+
+      Nj=0
+      indI(1)=0
+
+C     ***** The bound 'infinity' is set to 10*sigma *****
+      XdInf=10.d0*SQRT(-R2(1))
+      XtInf=10.d0*SQRT(R0(1))
+      !h1(1)=XtInf
+      !h2(1)=XtInf
+      ! normalizing constant
+      CC=TWOPI*SQRT(-R0(1)/R2(1))*exp(u*u/(2.d0*R0(1)) )
+      allocate(CY1(1:Nx)) 
+      allocate(CY2(1:Nx)) 
+      do icy=1,Nx
+        CY1(icy)=exp(-0.5*hh1(icy)*hh1(icy)/100)/(10*sqrt(twopi))
+        CY2(icy)=exp(-0.5*hh2(icy)*hh2(icy)/100)/(10*sqrt(twopi))
+      enddo
+      !print *,CY1
+      allocate(ansrup(1:Ntime,1:Nx))
+      allocate(ansrlo(1:Ntime,1:Nx))
+      ansrup=0.d0
+      ansrlo=0.d0
+      allocate(fxind(1:Nx,1:2))    
+      !fxind=0.d0 this is not needed
+   
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+! Y={X(t2)..,X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)} !!
+! = [Xt                          Xd                    Xc]                   !!
+!                                                                            !!
+! Nt=tn-2, Nd=3, Nc=2+3                                                      !!
+!                                                                            !!
+! Xt= contains Nt time points in the indicator function                      !!
+! Xd=    "     Nd    derivatives                                             !!
+! Xc=    "     Nc    variables to condition on                               !!
+! (Y1,Y2) dummy variables ind. of all other v. inputing h1,h2 into rindd     !!
+!                                                                            !!
+! There are 6 ( NI=7) regions with constant bariers:                         !!
+! (indI(1)=0);     for i\in (indI(1),indI(2)] u<Y(i)<h1                      !!
+! (indI(2)=ts-2);  for i\in (indI(2),indI(2)], inf<Y(i)<inf (no restr.)      !!
+! (indI(3)=ts-1);  for i\in (indI(3),indI(4)], h2 <Y(i)<u                    !!
+! (indI(4)=Nt)  ;  for i\in (indI(4),indI(5)], Y(i)<0 (deriv. X'(ts))        !!
+! (indI(5)=Nt+1);  for i\in (indI(5),indI(6)], Y(i)>0 (deriv. X'(t1))        !!
+! (indI(6)=Nt+2);  for i\in (indI(6),indI(7)], Y(i)>0 (deriv. X'(tn))        !!
+! (indI(7)=Nt+3);  NI=7.                                                     !!
+!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+      
+      NI=7; Nd=3
+      Nc=5; Mb=3
+      allocate(a_up(1:Mb,1:(NI-1)))
+      allocate(a_lo(1:Mb,1:(NI-1)))
+      a_up=0.d0
+      a_lo=0.d0
+      allocate(BIG(1:(Ntime+Nc+1),1:(Ntime+Nc+1))) 
+      ALLOCATE(xc(1:Nc,1:Nx))
+      allocate(ex(1:(Ntime+Nc+1)))
+      !print *,size(ex),Ntime
+      ex=0.d0
+      !print *,size(ex),ex
+      xc(1,1:Nx)=hh1(1:Nx)
+      xc(2,1:Nx)=hh2(1:Nx)
+      xc(3,1:Nx)=u
+      xc(4,1:Nx)=u
+      xc(5,1:Nx)=u
+         ! upp- down- upp-crossings at t1,ts,tn
+       
+        a_lo(1,1)=u
+        a_up(1,2)=XtInf   ! X(ts) is redundant  
+        a_lo(1,2)=-Xtinf
+        a_up(1,3)=u
+   
+ 
+        a_lo(1,4)=-XdInf
+        a_up(1,5)= XdInf
+        a_up(1,6)= XdInf  
+
+        a_up(2,1)=1.d0
+        a_lo(3,3)=1.d0 !signe a voir!!!!!!
+!        print *,a_up
+!        print *,a_lo
+      do tn=N0,Ntime,1
+!      do tn=Ntime,Ntime,1
+        Ntd=tn+1
+        Nt=Ntd-Nd
+        Ntdc=Ntd+Nc
+        indI(4)=Nt
+        indI(5)=Nt+1
+        indI(6)=Nt+2
+        indI(7)=Ntd
+        if (SCIS.gt.0) then
+           if (SCIS.EQ.2) then           
+              Nj=max(Nt,0)
+           else
+              Nj=min(max(Nt-5, 0),0)
+           endif
+        endif
+        do ts=3,tn-2
+         !print *,'ts,tn' ,ts,tn,Ntdc
+         CALL COV_INPUT(Big(1:Ntdc,1:Ntdc),tn,ts,R0,R1,R2)!positive wave period
+         indI(2)=ts-2
+         indI(3)=ts-1
+         
+
+         CALL RINDD(fxind,Big(1:Ntdc,1:Ntdc),ex(1:Ntdc),
+     &              xc,indI,a_lo,a_up)
+         
+        ds=dt
+         do icy=1,Nx
+         ! ansr(tn,:)=ansr(tn,:)+fxind*CC*ds./(CY1.*CY2)
+         ansrup(tn,icy)=ansrup(tn,icy)+fxind(icy,1)*CC*ds
+     &                          /(CY1(icy)*CY2(icy))
+         ansrlo(tn,icy)=ansrlo(tn,icy)+fxind(icy,2)*CC*ds
+     &                          /(CY1(icy)*CY2(icy))
+         enddo
+        enddo ! ts
+        print *,'Ready: ',tn,' of ',Ntime
+
+      enddo !tn
+  
+ 300  open (unit=11, file='dens.out',  STATUS='unknown')
+   
+      do ts=1,Ntime
+         do ph=1,Nx
+            write(11,*)  ansrup(ts,ph),ansrlo(ts,ph)!,hh1(ph),hh2(ph)
+            ! write(11,111)  ansrup(ts,ph),ansrlo(ts,ph)
+
+         enddo
+      enddo
+ !111  FORMAT(2x,F12.8)  
+      close(11)
+ 900  deallocate(big)
+      deallocate(fxind)
+      deallocate(ansrup)
+      deallocate(ansrlo)
+      deallocate(xc)
+      deallocate(ex)
+      deallocate(R0)
+      deallocate(R1)
+      deallocate(R2)
+      if (allocated(COV) ) then
+         deallocate(COV)
+      endif
+        deallocate(h1)
+        deallocate(h2)
+        deallocate(hh1)
+        deallocate(hh2)
+        deallocate(a_up)
+        deallocate(a_lo)
+      stop
+      !return
+
+      CONTAINS
+      
+    
+            
+      SUBROUTINE INIT_LEVELS
+     & (U,Ntime,N0,NIT,speed,SCIS,seed1,Nx1,Nx2,dT)
+      IMPLICIT NONE
+      integer, intent(out):: Ntime,N0,NIT,speed,Nx1,Nx2,SCIS,seed1
+      double precision ,intent(out) :: U,dT
+     
+
+      OPEN(UNIT=14,FILE='reflev.in',STATUS= 'UNKNOWN')
+      READ (14,*) U
+      READ (14,*) Ntime
+      READ (14,*) N0
+      READ (14,*) NIT
+      READ (14,*) speed   
+      READ (14,*) SCIS   
+      READ (14,*) seed1   
+
+
+        READ (14,*) Nx1,Nx2
+        READ (14,*) dT
+        if (Ntime.lt.3) then
+           print *,'The number of wavelength points is too small, stop'
+           stop
+        end if
+      
+      CLOSE(UNIT=14)
+       
+      RETURN
+      END SUBROUTINE INIT_LEVELS
+ 
+C******************************************************
+      SUBROUTINE INIT_AMPLITUDES(h1,Nx1,h2,Nx2)      
+      IMPLICIT NONE
+      double precision, dimension(:), intent(out) :: h1,h2    
+      integer, intent(in) :: Nx1,Nx2
+      integer :: ix
+      
+ 
+      OPEN(UNIT=4,FILE='h.in',STATUS= 'UNKNOWN')
+
+C
+C Reading in amplitudes
+C
+      do ix=1,Nx1
+        READ (4,*) H1(ix)
+      enddo
+      do ix=1,Nx2
+        READ (4,*) H2(ix)
+      enddo
+      CLOSE(UNIT=4)
+      
+      RETURN
+      END SUBROUTINE INIT_AMPLITUDES
+
+C**************************************************
+
+C***********************************************************************
+C***********************************************************************
+       
+      SUBROUTINE INIT_COVARIANCES(Ntime,R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:),intent(out) :: R0,R1,R2
+      integer,intent(in) :: Ntime
+      integer :: i
+      open (unit=1, file='Cd0.in',STATUS='unknown')
+      open (unit=2, file='Cd1.in',STATUS='unknown')
+      open (unit=3, file='Cd2.in',STATUS='unknown')
+
+      do i=1,Ntime
+         read(1,*) R0(i)
+         read(2,*) R1(i)
+         read(3,*) R2(i)
+      enddo
+      close(1)
+      close(2)
+      close(3)
+      
+      return
+      END SUBROUTINE INIT_COVARIANCES
+      
+C***********************************************************************
+C***********************************************************************
+
+C**********************************************************************
+
+      SUBROUTINE COV_INPUT(BIG,tn,ts, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:),intent(inout) :: BIG
+      double precision, dimension(:),intent(in) :: R0,R1,R2
+      integer ,intent(in) :: tn,ts
+      integer :: i,j,Ntd1,N !=Ntdc
+      double precision :: tmp 
+! the order of the variables in the covariance matrix
+! are organized as follows: 
+! 
+! ||X(t2)..X(ts),..X(tn-1)||X'(ts) X'(t1) X'(tn)||Y1 Y2 X(ts) X(t1) X(tn)|| 
+! = [Xt                          Xd                    Xc]
+! where 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+! Computations of all covariances follows simple rules: Cov(X(t),X(s))=r(t,s),
+! then  Cov(X'(t),X(s))=dr(t,s)/dt.  Now for stationary X(t) we have
+! a function r(tau) such that Cov(X(t),X(s))=r(s-t) (or r(t-s) will give the same result).
+!
+! Consequently  Cov(X'(t),X(s))    = -r'(s-t)    = -sign(s-t)*r'(|s-t|)
+!               Cov(X'(t),X'(s))   = -r''(s-t)   = -r''(|s-t|)
+!               Cov(X''(t),X'(s))  =  r'''(s-t)  =  sign(s-t)*r'''(|s-t|)
+!               Cov(X''(t),X(s))   =  r''(s-t)   =   r''(|s-t|)
+!               Cov(X''(t),X''(s)) =  r''''(s-t) = r''''(|s-t|)
+
+      Ntd1=tn+1
+      N=Ntd1+Nc
+      do i=1,tn-2
+      !cov(Xt)
+         do j=i,tn-2
+           BIG(i,j) = R0(j-i+1) ! cov(X(ti+1),X(tj+1))
+         enddo
+      !cov(Xt,Xc)
+	 BIG(i      ,Ntd1+1) = 0.d0          !cov(X(ti+1),Y1)  
+         BIG(i      ,Ntd1+2) = 0.d0          !cov(X(ti+1),Y2)  
+         BIG(i      ,Ntd1+4) = R0(i+1)       !cov(X(ti+1),X(t1))  
+         BIG(tn-1-i ,Ntd1+5) = R0(i+1)       !cov(X(t.. ),X(tn))  
+
+      !Cov(Xt,Xd)=cov(X(ti+1),x(tj)
+         BIG(i,Ntd1-1)   =-R1(i+1)         !cov(X(ti+1),X'(t1))  
+         BIG(tn-1-i,Ntd1)= R1(i+1)         !cov(X(ti+1),X'(tn)) 
+      enddo
+!cov(Xd)
+      BIG(Ntd1  ,Ntd1  ) = -R2(1)
+      BIG(Ntd1-1,Ntd1  ) = -R2(tn)        !cov(X'(t1),X'(tn))
+      BIG(Ntd1-1,Ntd1-1) = -R2(1)
+      BIG(Ntd1-2,Ntd1-1) = -R2(ts)        !cov(X'(ts),X'(t1))
+      BIG(Ntd1-2,Ntd1-2) = -R2(1)
+      BIG(Ntd1-2,Ntd1  ) = -R2(tn+1-ts)   !cov(X'(ts),X'(tn))
+
+!cov(Xc)
+      BIG(Ntd1+1,Ntd1+1) = 100.d0        ! cov(Y1 Y1) 
+      BIG(Ntd1+1,Ntd1+2) = 0.d0          ! cov(Y1 Y2) 
+      BIG(Ntd1+1,Ntd1+3) = 0.d0          ! cov(Y1 X(ts)) 
+      BIG(Ntd1+1,Ntd1+4) = 0.d0          ! cov(Y1 X(t1)) 
+      BIG(Ntd1+1,Ntd1+5) = 0.d0          ! cov(Y1 X(tn))
+      BIG(Ntd1+2,Ntd1+2) = 100.d0        ! cov(Y2 Y2) 
+      BIG(Ntd1+2,Ntd1+3) = 0.d0          ! cov(Y2 X(ts)) 
+      BIG(Ntd1+2,Ntd1+4) = 0.d0          ! cov(Y2 X(t1)) 
+      BIG(Ntd1+2,Ntd1+5) = 0.d0          ! cov(Y2 X(tn))
+
+      BIG(Ntd1+3,Ntd1+3) = R0(1)        ! cov(X(ts),X (ts)
+      BIG(Ntd1+3,Ntd1+4) = R0(ts)       ! cov(X(ts),X (t1))
+      BIG(Ntd1+3,Ntd1+5) = R0(tn+1-ts)  ! cov(X(ts),X (tn))
+      BIG(Ntd1+4,Ntd1+4) = R0(1)        ! cov(X(t1),X (t1)) 
+      BIG(Ntd1+4,Ntd1+5) = R0(tn)       ! cov(X(t1),X (tn))
+      BIG(Ntd1+5,Ntd1+5) = R0(1)        ! cov(X(tn),X (tn))
+  
+
+!cov(Xd,Xc)
+      BIG(Ntd1  ,Ntd1+1) = 0.d0        !cov(X'(tn),Y1) 
+      BIG(Ntd1  ,Ntd1+2) = 0.d0        !cov(X'(tn),Y2) 
+      BIG(Ntd1-1  ,Ntd1+1) = 0.d0        !cov(X'(t1),Y1) 
+      BIG(Ntd1-1  ,Ntd1+2) = 0.d0        !cov(X'(t1),Y2) 
+      BIG(Ntd1-2  ,Ntd1+1) = 0.d0        !cov(X'(ts),Y1) 
+      BIG(Ntd1-2  ,Ntd1+2) = 0.d0        !cov(X'(ts),Y2) 
+  
+      BIG(Ntd1  ,Ntd1+4) = R1(tn)        !cov(X'(tn),X(t1))     
+      BIG(Ntd1  ,Ntd1+5) = 0.d0          !cov(X'(tn),X(tn))
+      BIG(Ntd1-1,Ntd1+4) = 0.d0          !cov(X'(t1),X(t1))
+      BIG(Ntd1-1,Ntd1+5) =-R1(tn)        !cov(X'(t1),X(tn))
+      BIG(Ntd1  ,Ntd1+3) = R1(tn+1-ts)   !cov(X'(tn),X (ts))  
+      BIG(Ntd1-1,Ntd1+3) =-R1(ts)        !cov(X'(t1),X (ts))   
+      BIG(Ntd1-2,Ntd1+3) = 0.d0          !cov(X'(ts),X (ts)
+      BIG(Ntd1-2,Ntd1+4) = R1(ts)        !cov(X'(ts),X (t1))
+      BIG(Ntd1-2,Ntd1+5) = -R1(tn+1-ts)  !cov(X'(ts),X (tn))
+
+
+        do i=1,tn-2
+          j=abs(i+1-ts)
+!cov(Xt,Xc)
+          BIG(i,Ntd1+3)   = R0(j+1)      !cov(X(ti+1),X(ts))          
+!Cov(Xt,Xd)
+          if ((i+1-ts).lt.0) then
+              BIG(i,Ntd1-2)  =  R1(j+1)
+            else                         !cov(X(ti+1),X'(ts))  
+              BIG(i,Ntd1-2)  = -R1(j+1)
+          endif
+      enddo
+    
+! make lower triangular part equal to upper 
+      do j=1,N-1
+        do i=j+1,N
+           tmp =BIG(j,i)
+
+           BIG(i,j)=tmp
+        enddo
+      enddo
+
+C     write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10  format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT
+
+      SUBROUTINE COV_INPUT2(BIG,pt, R0,R1,R2)
+      IMPLICIT NONE
+      double precision, dimension(:,:), intent(out) :: BIG
+      double precision, dimension(:), intent(in) ::  R0,R1,R2
+      integer :: pt,i,j
+! the order of the variables in the covariance matrix
+! are organized as follows;
+! X(t2)...X(tn-1) X'(t1) X'(tn) X(t1) X(tn) = [Xt Xd Xc]
+! 
+! where Xd is the derivatives 
+!
+! Xt= time points in the indicator function
+! Xd= derivatives
+! Xc=variables to condition on
+
+!cov(Xc)
+      BIG(pt+2,pt+2) = R0(1)
+      BIG(pt+1,pt+1) = R0(1)
+      BIG(pt+1,pt+2) = R0(pt)
+!cov(Xd)
+      BIG(pt,pt)     = -R2(1)
+      BIG(pt-1,pt-1) = -R2(1)
+      BIG(pt-1,pt)   = -R2(pt)
+!cov(Xd,Xc)
+      BIG(pt,pt+2)   =  0.d0
+      BIG(pt,pt+1)   = R1(pt)
+      BIG(pt-1,pt+2) = -R1(pt)
+      BIG(pt-1,pt+1) =  0.d0
+ 
+      if (pt.GT.2) then
+!cov(Xt)
+         do i=1,pt-2
+           do j=i,pt-2
+              BIG(i,j) = R0(j-i+1)
+           enddo
+        enddo
+!cov(Xt,Xc)
+        do i=1,pt-2
+           BIG(i,pt+1)      = R0(i+1)
+           BIG(pt-1-i,pt+2) = R0(i+1)
+        enddo
+!Cov(Xt,Xd)=cov(X(ti+1),x(tj))
+        do i=1,pt-2
+           BIG(i,pt-1)   = -R1(i+1)
+           BIG(pt-1-i,pt)=  R1(i+1)
+        enddo
+      endif
+
+
+      ! make lower triangular part equal to upper 
+      do j=1,pt+1
+         do i=j+1,pt+2
+            BIG(i,j)=BIG(j,i)
+         enddo
+      enddo
+C      write (*,10) ((BIG(j,i),i=N+1,N+6),j=N+1,N+6)
+C 10   format(6F8.4)
+      RETURN
+      END  SUBROUTINE COV_INPUT2 
+
+
+      END  PROGRAM  sp2tthpdf
+       
+
+
+
+
+
+
+
+

wafo/source/mreg/build_all.py

@@ -0,0 +1,30 @@
+"""
+f2py c_library.pyf c_functions.c -c
+
+gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -c dsvdc.f mregmodule.f
+
+"""
+import os
+import sys
+from wafo.f2py_tools import f2py_call_str
+
+
+def compile_all():
+    f2py_call = f2py_call_str()
+    print '=' * 75
+    print 'compiling cov2mod'
+    print '=' * 75
+
+    files = ['dsvdc', 'mregmodule', 'intfcmod']
+    compile1_format = 'gfortran -fPIC -c %s.f'
+    format1 = '%s.o ' * len(files)
+    for file_ in files:
+        os.system(compile1_format % file_)
+    file_objects = format1 % tuple(files)
+
+    os.system(f2py_call + ' -m cov2mod  -c %s cov2mmpdfreg_intfc.f' %
+              file_objects)
+
+
+if __name__ == '__main__':
+    compile_all()

wafo/source/mreg/cov2mmpdfreg.f

@@ -0,0 +1,651 @@
+C     Version  1994-X-18 
+
+C     This is a new version of WAMP program computing crest-trough wavelength 
+C     and amplitude  density.
+C     
+C     revised pab 2007
+C     -moved all common blocks into modules
+C     -renamed from minmax to sp2mmpdfreg + fixed some bugs
+C     revised pab July 2007
+!     -renamed from sp2mmpdfreg to cov2mmpdfreg
+
+      PROGRAM cov2mmpdfreg
+      USE SIZEMOD
+      USE EPSMOD
+      USE CHECKMOD
+      USE MREGMOD
+      IMPLICIT NONE
+      real*8 Q0,SQ0,Q1,SQ1, AA, BB, DAI, AI , U,V,VV, XL0, XL2, XL4
+      REAL*8 VDERI, CDER,SDER, DER, CONST, F, HHHH,FM, VALUE
+C	INTEGER, PARAMETER :: MMAX = 5, NMAX = 101, RDIM = 10201
+      REAL*8, DIMENSION(NMAX) :: HHT,T,Ulev,Vlev,VT,UT,Vdd,Udd
+      REAL*8, DIMENSION(RDIM) :: R,R1,R2,R3
+      REAL*8, DIMENSION(5*NMAX) :: COV
+      REAL*8, DIMENSION(NMAX,NMAX) :: UVdens
+C      DIMENSION UVdens(NMAX,NMAX),HHT(NMAX)
+C      DIMENSION T(NMAX),Ulev(NMAX),Vlev(NMAX)
+C      DIMENSION VT(NMAX),UT(NMAX),Vdd(NMAX),Udd(NMAX)
+C      DIMENSION COV(5*NMAX),R(RDIM),R1(RDIM),R2(RDIM),R3(RDIM)
+      DIMENSION AA(MMAX-2,MMAX-2),BB(MMAX+1),DAI(MMAX),AI((MMAX+1)*NMAX)
+
+C
+C   The program computes the joint density of maximum the following minimum
+C   and the distance between Max and min for a zero-mean stationary 
+C   Gaussian process with covariance function defined explicitely with 4 
+C   derivatives. The process should be normalized so that the first and 
+C   the second spectral moments are equal to 1. The values of Max are taken
+C   as the nodes at Hermite-Quadrature and then integrated out so that
+C   the output is a joint density of wavelength T and amplitude H=Max-min.
+C   The Max values are defined by subroutine Gauss_M with the accuracy
+C   input  epsu. The principle is that the integral of the marginal density 
+C   of f_Max is computed with sufficient accuracy.
+C
+      REAL*8, DIMENSION(NMAX) :: B0,DB0,DDB0,B1,DB1,DDB1,DB2,DDB2
+      REAL*8, DIMENSION(NMAX) :: Q,SQ,VDER,DBI,BI
+C      DIMENSION B0(NMAX),DB0(NMAX),DDB0(NMAX)
+C      DIMENSION B1(NMAX),DB1(NMAX),DDB1(NMAX)
+C      DIMENSION DB2(NMAX),DDB2(NMAX)
+C      DIMENSION Q(NMAX),SQ(NMAX),VDER(NMAX),DBI(NMAX),BI(NMAX)
+      INTEGER :: J,I,I1,I2,I3,IU, IV, NU,NV,NG,N,NIT, NNIT, INF
+	  INTEGER ::  fffff
+C	REAL*8 EPS0
+C	INTEGER III01,III11,III21,III31,III41,III51
+C     *,III61,III71,III81,III91,III101 , III0
+C      COMMON/CHECK1/III01,III11,III21,III31,III41,III51
+C     *,III61,III71,III81,III91,III101 
+C      COMMON/CHECKQ/III0 
+C      COMMON /EPS/  EPS,EPSS,CEPSS
+
+C
+C  Initiation of all constants and integration nodes 'INITINTEG'
+C
+      CALL INITINTEG(NIT)
+c
+c   OBS. we are using the variables R,R1,R2 R3 as a temporary storage 
+C   for transformation  g  of the process.
+
+
+
+c
+      CALL INITLEVELS(Ulev,NU,Vlev,NV,T,HHT,N,R1,R2,NG)
+      IF( R1(1) .gt. R1(ng))  then
+      do 13 I=1,ng
+      R3(I)=R1(I)
+      R(I) =R2(I)
+13    continue
+      do 17 i=1,ng
+      R1(i) = R3(ng-i+1)
+      R2(i) = R(ng-i+1)
+17    continue
+      end if
+      if(abs(R1(ng)-R1(1))*abs(R2(ng)-R2(1)).lt.0.01d0) then
+      print *,'The transformation  g is singular, stop'
+      stop
+      end if
+      DO 14 IV=1,Nv
+         V=Vlev(IV)
+         CALL TRANSF(NG,V,R2,R1,VALUE,DER) 
+         VT(IV)=VALUE
+         Vdd(IV)=DER
+14    continue
+      DO 16 IU=1,Nu
+         U = Ulev(IU)
+         CALL TRANSF(NG,U,R2,R1,VALUE,DER) 
+         UT(IU)  = VALUE
+         Udd(IU) = DER
+         do 16 IV=1,Nv
+             UVdens(IU,IV)=0.0d0
+16    CONTINUE
+      
+      
+      CALL COVG(XL0,XL2,XL4,COV,R1,R2,R3,T,N)
+      
+      
+      Q0=XL4
+      IF (Q0.le.1.0D0+EPS) then
+      Print *,'Covariance structure is singular, stop.'
+      stop
+      end if
+      SQ0 = SQRT(Q0)
+      Q1  = XL0-XL2*XL2/XL4
+      IF (Q1.le.eps) then
+      Print *,'Covariance structure is singular, stop.'
+      stop
+      end if
+      SQ1 = SQRT(Q1)
+      DO 10 I=1,N
+        B0(I)  =-COV(I+2*N)
+        DB0(I) =-COV(I+3*N)
+        DDB0(I)=-COV(I+4*N)
+      
+        B1(I)  =COV(I)+COV(I+2*N)*(XL2/XL4)
+        DB1(I) =COV(I+N)+COV(I+3*N)*(XL2/XL4)
+        DDB1(I)=COV(I+2*N)+XL2*(COV(I+4*N)/XL4)
+C
+C       Q(I) contains Var(X(T(i))|X'(0),X''(0),X(0))
+C    VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0))
+C
+        Q(I)=XL0 - COV(I+N)*(COV(I+N)/XL2) - B0(I)*(B0(I)/Q0)
+     1     -B1(I)*(B1(I)/Q1)
+        VDER(I)=XL4 - (COV(I+3*N)*COV(I+3*N))/XL2 - (DDB0(I)*DDB0(I))/Q0
+     1     - (DDB1(I)*DDB1(I))/Q1 
+      
+
+C
+C       DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0))
+C
+        DDB2(I)=-XL2 - (COV(I+N)*COV(I+3*N))/XL2 - DDB0(I)*(B0(I)/Q0)
+     1     -DDB1(I)*(B1(I)/Q1)
+        IF(Q(I).LE.eps) then
+          SQ(i)  =0.0d0
+          DDB2(i)=0.0d0
+        else
+          SQ(I)=SQRT(Q(I))
+C 
+C       VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0),X(T(i))
+C
+      
+          VDER(I)=VDER(I) - (DDB2(I)*DDB2(I))/Q(I)
+        end if
+      
+10    CONTINUE
+      DO 15 I=1,N
+      DO 15 J=1,N
+C      
+C   R1 contains Cov(X(T(I)),X'(T(J))|X'(0),X''(0),X(0)) 
+C
+      R1(J+(I-1)*N)=R1(J+(I-1)*N) -  COV(I+N)*(COV(J+2*N)/XL2) 
+     1 -  (B0(I)*DB0(J)/Q0) -  (B1(I)*DB1(J)/Q1) 
+      
+C      
+C   R2 contains Cov(X'(T(I)),X'(T(J))|X'(0),X''(0),X(0))
+C
+      R2(J+(I-1)*N) = -R2(J+(I-1)*N) - COV(I+2*N)*(COV(J+2*N)/XL2) 
+     1   - DB0(I)*DB0(J)/Q0  - DB1(I)*(DB1(J)/Q1) 
+C      
+C   R3 contains Cov(X''(T(I)),X'(T(J))|X'(0),X''(0),X(0))
+C
+      R3(J+(I-1)*N) = R3(J+(I-1)*N) - COV(I+3*N)*(COV(J+2*N)/XL2) 
+     1   - DB0(J)*(DDB0(I)/Q0)  - DDB1(I)*(DB1(J)/Q1) 
+15    CONTINUE
+
+C  The initiations are finished and we are beginning with 3 loops
+C  on T=T(I), U=Ulevels(IU), V=Ulevels(IV), U>V.
+      
+      DO 20 I=1,N
+
+           NNIT=NIT
+           IF (Q(I).LE.EPS) GO TO 20
+
+         DO 30 I1=1,I
+            DB2(I1)=R1(I1+(I-1)*N) 
+
+C     Cov(X'(T(I1)),X(T(i))|X'(0),X''(0),X(0)) 
+C     DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0))
+
+ 30      CONTINUE
+	
+         DO 50 I3=1,I
+            DBI(I3) = R3(I3+(I-1)*N) - (DDB2(I)*DB2(I3)/Q(I)) 
+            BI(I3)  = R2(I3+(I-1)*N) - (DB2(I)*DB2(I3)/Q(I))
+ 50      CONTINUE
+         DO 51 I3=1,I-1
+            AI(I3)=0.0d0
+            AI(I3+I-1)=DB0(I3)/SQ0 
+            AI(I3+2*(I-1))=DB1(I3)/SQ1
+            AI(I3+3*(I-1))=DB2(I3)/SQ(I)
+ 51      CONTINUE
+         VDERI=VDER(I)
+         DAI(1)=0.0d0
+         DAI(2)=DDB0(I)/SQ0
+         DAI(3)=DDB1(I)/SQ1 
+         DAI(4)=DDB2(I)/SQ(I) 
+         AA(1,1)=DB0(I)/SQ0 
+         AA(1,2)=DB1(I)/SQ1 
+         AA(1,3)=DB2(I)/SQ(I) 
+         AA(2,1)=XL2/SQ0
+         AA(2,2)=SQ1
+         AA(2,3)=0.0d0
+         AA(3,1)=B0(I)/SQ0 
+         AA(3,2)=B1(I)/SQ1 
+         AA(3,3)=SQ(I)
+         IF (BI(I).LE.EPS) NNIT=0
+         IF (NNIT.GT.1) THEN
+            IF(I.LT.1) GO TO 41
+            DO 40 I1=1,I-1
+               DO 40 I2=1,I-1
+
+C   R contains Cov(X'(T(I1)),X'(T(I2))|X'(0),X''(0),X(0),X(I)) 
+
+      R(I2+(I1-1)*(I-1))=R2(I2+(I1-1)*N)-(DB2(I1)*DB2(I2)/Q(I)) 
+
+ 40         CONTINUE
+ 41         CONTINUE
+         END IF
+
+C  Here the covariance of the problem would be innitiated
+
+            INF=0
+            Print *,'   Laps to go:',N-I+1
+         DO 80 IV=1,Nv
+            V=VT(IV)
+!            IF (ABS(V).GT.5.0D0) GO TO 80                  
+            IF (Vdd(IV).LT.EPS0) GO TO 80
+            DO 60 IU=1,Nu
+                  U=UT(IU)
+				IF (U.LE.V) go to 60
+!                  IF (ABS(U).GT.5.0D0) GO TO 60                  
+                  IF (Udd(IU).LT.EPS0) GO TO 60
+                  BB(1)=0.0d0
+                  BB(2)=U
+                  BB(3)=V
+!	if (IV.EQ.2.AND.IU.EQ.1) THEN	
+!	fffff = 10
+!	endif
+                 
+      CALL MREG(F,R,BI,DBI,AA,BB,AI,DAI,VDERI,3,I-1,NNIT,INF)
+             INF=1
+             UVdens(IU,IV) = UVdens(IU,IV) + Udd(IU)*Vdd(IV)*HHT(I)*F
+!	if (F.GT.0.01.AND.U.GT.2.AND.V.LT.-2) THEN  
+! 	if (N-I+1 .eq. 38.and.IV.EQ.26.AND.IU.EQ.16) THEN
+!	if (IV.EQ.32.AND.IU.EQ.8.and.I.eq.11) THEN		
+!          PRINT * ,' R:', R(1:I)
+!	    PRINT * ,' BI:', BI(1:I)
+!		PRINT * ,' DBI:', DBI(1:I)
+!		PRINT * ,' DB2:', DB2(1:I)
+!		PRINT * ,' DB0(1):', DB0(1)
+!		PRINT * ,' DB1(1):', DB1(1)
+!          PRINT * ,' DAI:', DAI
+!		PRINT * ,' BB:', BB
+!	    PRINT * ,' VDERI:', VDERI
+!          PRINT * ,' F    :', F
+!		PRINT * ,' UVDENS :',  UVdens(IU,IV)
+!	    fffff = 10
+!	endif
+
+ 60         CONTINUE
+ 80       continue
+ 20   CONTINUE
+       hhhh=0.0d0
+       do 90 Iu=1,Nu
+       do 90 Iv=1,Nv
+       WRITE(10,300) Ulev(iu),Vlev(iv),UVdens(iu,iv)
+       hhhh=hhhh+UVdens(iu,iv)
+ 90    continue
+      if (nu.gt.1.and.nv.gt.1) then
+      write(11,*) 'SumSum f_uv *du*dv='
+     1,(Ulev(2)-Ulev(1))*(Vlev(2)-Vlev(1))*hhhh
+      end if
+      
+C      sder=sqrt(XL4-XL2*XL2/XL0)
+C      cder=-XL2/sqrt(XL0)
+C      const=1/sqrt(XL0*XL4)
+C      DO 95 IU=1,NU     
+C        U=UT(IU)
+C        FM=Udd(IU)*const*exp(-0.5*U*U/XL0)*PMEAN(-cder*U,sder)
+C        WRITE(9,300) Ulev(IU),FM
+C 95   continue      
+C      DO 105 IV=1,NV     
+C        V=VT(IV)
+C        VV=cder*V
+C        Fm=Vdd(IV)*const*exp(-0.5*V*V/XL0)*PMEAN(VV,sder)
+C        WRITE(8,300) Vlev(IV),Fm
+C 105   continue 
+      if (III0.eq.0) III0=1
+
+      write(11,*) 'Rate of calls RINDT0:',float(iii01)/float(III0)
+      write(11,*) 'Rate of calls RINDT1:',float(iii11)/float(III0)
+      write(11,*) 'Rate of calls RINDT2:',float(iii21)/float(III0)
+      write(11,*) 'Rate of calls RINDT3:',float(iii31)/float(III0)
+      write(11,*) 'Rate of calls RINDT4:',float(iii41)/float(III0)
+      write(11,*) 'Rate of calls RINDT5:',float(iii51)/float(III0)
+      write(11,*) 'Rate of calls RINDT6:',float(iii61)/float(III0)
+      write(11,*) 'Rate of calls RINDT7:',float(iii71)/float(III0)
+      write(11,*) 'Rate of calls RINDT8:',float(iii81)/float(III0)
+      write(11,*) 'Rate of calls RINDT9:',float(iii91)/float(III0)
+      write(11,*) 'Rate of calls RINDT10:',float(iii101)/float(III0)
+      write(11,*) 'Number of calls of RINDT*',III0
+
+      CLOSE(UNIT=8)
+      CLOSE(UNIT=9)
+      CLOSE(UNIT=10)
+      CLOSE(UNIT=11)
+
+ 300  FORMAT(4(3X,F10.6))
+      STOP
+      END
+
+      SUBROUTINE INITLEVELS(ULEVELS,NU,Vlevels,Nv,T,HT,N,TG,XG,NG)
+      USE TBRMOD
+      USE SIZEMOD
+      IMPLICIT NONE
+C	INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201
+C      DIMENSION ULEVELS(1),Vlevels(1),T(1),HT(1),TG(1),XG(1),HH(101)
+      REAL*8, DIMENSION(NMAX), intent(inout) :: ULEVELS,Vlevels,T,HT
+      REAL*8, DIMENSION(RDIM), intent(inout) :: TG,XG
+      INTEGER, intent(inout) :: NG
+      REAL*8 :: UMIN,UMAX,VMIN,VMAX, HU,HV
+      integer :: N, I, NU, NV
+C	REAL*8, DIMENSION(NMAX) :: HH
+C      COMMON/TBR/HH
+      OPEN(UNIT=2,FILE='transf.in')
+      OPEN(UNIT=4,FILE='Mm.in')
+      OPEN(UNIT=3,FILE='t.in')
+      
+
+      NG=1
+ 12   READ (2,*,END=11) TG(NG),XG(NG)
+      NG=NG+1
+      GO TO 12
+ 11   CONTINUE
+      NG=NG-1
+      IF (NG.GT.501) THEN
+      PRINT *,'Vector defining transformation of data > 501, stop'
+      STOP
+      END IF
+
+
+      N=1
+ 32   READ (3,*,END=31) T(N)
+      N=N+1
+      GO TO 32
+ 31   CONTINUE
+      N=N-1      
+      
+      CLOSE(UNIT=3)
+      
+      IF(N.ge.NMAX) then
+      print *,'The number of wavelength points >',NMAX-1, ' stop'
+      stop
+      end if
+      IF(N.lt.2) then
+      print *,'The number of wavelength points < 2, stop'
+      stop
+      end if
+
+      HT(1)=0.5d0*(T(2)-T(1))
+      HT(N)=0.5d0*(T(N)-T(N-1))
+      HH(1)=-100.0d0
+      HH(N)=-100.0d0
+      DO 10 I=2,N-1
+         HT(I)=0.5d0*(T(I+1)-T(I-1))
+         HH(I)=-100.0d0
+10    CONTINUE
+      
+
+      
+      READ(4,*) Umin,Umax,NU
+      READ(4,*) Vmin,Vmax,NV
+
+      IF(NU.gt.NMAX) then
+      print *,'The number of maxima >',NMAX,' stop'
+      stop
+      end if
+      IF(NV.gt.NMAX) then
+      print *,'The number of minima >',NMAX,' stop'
+      stop
+      end if
+
+      IF(NU.LT.1) Then
+      print *,'The number of maxima < 1, stop'
+      stop
+      end if
+      IF(NV.LT.1) Then
+      print *,'The number of minima < 1, stop'
+      stop
+      end if
+
+      Ulevels(1)=Umax
+      IF (NU.lt.2) go to 25
+      HU=(Umax-Umin)/DBLE(NU-1)
+      DO 20 I=1,NU-1
+         ULEVELS(I+1)=Umax-DBLE(I)*HU
+20    CONTINUE
+
+ 25   continue
+      Vlevels(1)=Vmax
+      IF (NV.lt.2) go to 35
+      HV=(Vmax-Vmin)/DBLE(NV-1)
+      DO 30 I=1,Nv-1
+         VLEVELS(I+1)=Vmax-DBLE(I)*HV
+30    CONTINUE
+35    continue
+      CLOSE(UNIT=4)
+      RETURN
+      END
+
+
+      SUBROUTINE TRANSF(N,T,A,TIMEV,VALUE,DER) 
+C
+C N number of data points
+C TIMEV vector of time points
+C A a vector of values of a function G(TIME)
+C T independent time point
+C VALUE is a value of a function at T, i.e. VALUE=G(T).
+c DER=G'(t)
+C
+      USE SIZEMOD
+      IMPLICIT NONE
+      REAL*8, intent(inout):: VALUE, DER,T
+C      INTEGER, PARAMETER :: RDIM = 10201
+      REAL*8, DIMENSION(RDIM), intent(in) :: A,TIMEV
+      integer, intent(in) :: N
+      REAL*8:: T1
+      integer :: I
+      
+      IF (T.LT.TIMEV(1))  then
+      der=(A(2)-A(1))/(TIMEV(2)-TIMEV(1))
+      T1=T-TIMEV(1)
+      VALUE=A(1)+T1*DER
+      return
+      end if
+      IF (T.GT.TIMEV(N)) then
+      der = (A(N)-A(N-1))/(TIMEV(N)-TIMEV(N-1))
+      T1  = T-TIMEV(N)
+      VALUE=A(N)+T1*DER
+      return
+      end if
+      DO 5 I=2,N
+      IF (T.LT.TIMEV(I)) GO TO 10
+5     CONTINUE
+10    I=I-1
+      T1=T-TIMEV(I)
+      DER=(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I))
+      VALUE=A(I)+T1*DER
+      RETURN
+      END
+
+      REAL*8 FUNCTION SPLE(N,T,A,TIMEV)
+C
+C N number of data points
+C TIME vector of time points
+C A a vector of values of a function G(TIME)
+C T independent time point
+C SPLE is a value of a function at T, i.e. SPLE=G(T).
+C
+      USE SIZEMOD
+      IMPLICIT NONE
+      INTEGER, INTENT(IN):: N
+
+      REAL*8, INTENT(IN) :: T
+      REAL*8, DIMENSION(5*NMAX), INTENT(IN) :: A,TIMEV
+      REAL*8 :: T1
+      INTEGER :: I
+      SPLE=-9.9d0
+      IF (T.LT.TIMEV(1) .OR. T.GT.TIMEV(N)) RETURN
+      DO 5 I=2,N
+      IF (T.LT.TIMEV(I)) GO TO 10
+5     CONTINUE
+10    I=I-1
+      T1=T-TIMEV(I)
+      SPLE=A(I)+T1*(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I))
+      RETURN
+      END
+
+
+
+      SUBROUTINE COVG(XL0,XL2,XL4,COV,COV1,COV2,COV3,T,N)
+C
+C  COVG  evaluates: 
+C
+C  XL0,XL2,XL4 - spectral moments.
+C
+C  Covariance function and its four derivatives for a vector T of length N. 
+C  It is saved in a vector COV; COV(1,...,N)=r(T), COV(N+1,...,2N)=r'(T), etc.
+C  The vector COV should be of the length 5*N.
+C
+C  Covariance matrices COV1=r'(T-T), COV2=r''(T-T) and COV3=r'''(T-T) 
+C  Dimension of  COV1, COV2  should be   N*N.
+C
+      USE SIZEMOD
+!	IMPLICIT NONE
+C	INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201
+      REAL*8, PARAMETER:: ZERO = 0.0d0
+      REAL*8, intent(inout) :: XL0,XL2,XL4
+      REAL*8, DIMENSION(5*NMAX), intent(inout) :: COV
+      REAL*8, DIMENSION(5*NMAX) :: A, TIMEV
+      REAL*8, DIMENSION(RDIM), intent(inout) :: COV1,COV2,COV3
+      REAL*8, DIMENSION(NMAX), intent(in) :: T
+      INTEGER, intent(in) :: N
+      integer :: NT, I, J, II
+      REAL*8 :: TT, T0
+      OPEN(UNIT=32,FILE='Cd0.in')
+      OPEN(UNIT=33,FILE='Cd1.in')
+      OPEN(UNIT=34,FILE='Cd2.in')
+      OPEN(UNIT=35,FILE='Cd3.in')
+      OPEN(UNIT=36,FILE='Cd4.in')
+C
+C   COV(Y(T),Y(0))
+C
+
+      NT=1
+ 12   READ (32,*,END=11) TIMEV(NT),A(NT)
+      NT=NT+1
+      GO TO 12
+ 11   CONTINUE
+      NT=NT-1
+      
+      
+      XL0=SPLE(NT,ZERO,A,TIMEV)
+
+      DO 10 I=1,N
+      COV(I)=SPLE(NT,T(I),A,TIMEV)
+10    CONTINUE
+
+C     
+C    DERIVATIVE  COV(Y(T),Y(0))
+C
+
+      NT=1
+ 22   READ (33,*,END=21) TIMEV(NT),A(NT)
+      NT=NT+1
+      GO TO 22
+ 21   CONTINUE
+      NT=NT-1      
+
+      II=0
+      DO 20 I=1,N
+      COV(I+N)=SPLE(NT,T(I),A,TIMEV)
+      DO 20 J=1,N
+      II=II+1
+      T0=T(J)-T(I)
+      TT=ABS(T0)
+      COV1(II)=SPLE(NT,TT,A,TIMEV)
+      IF (T0.LT.0.0d0) COV1(II)=-COV1(II)
+20    CONTINUE
+
+C    2-DERIVATIVE  COV(Y(T),Y(0))
+
+      NT=1
+ 32   READ (34,*,END=31) TIMEV(NT),A(NT)
+      NT=NT+1
+      GO TO 32
+ 31   CONTINUE
+      NT=NT-1      
+
+      II=0
+      XL2=-SPLE(NT,ZERO,A,TIMEV)
+
+      DO 30 I=1,N
+      COV(I+2*N)=SPLE(NT,T(I),A,TIMEV)
+      DO 30 J=1,N
+      II=II+1
+      TT=ABS(T(J)-T(I))
+      COV2(II)=SPLE(NT,TT,A,TIMEV)
+30    CONTINUE
+
+C    3-DERIVATIVE  COV(Y(T),Y(0))
+
+            NT=1
+ 42   READ (35,*,END=41) TIMEV(NT),A(NT)
+      NT=NT+1
+      GO TO 42
+ 41   CONTINUE
+      NT=NT-1      
+
+      
+      II=0
+      DO 40 I=1,N
+      COV(I+3*N)=SPLE(NT,T(I),A,TIMEV)
+      DO 40 J=1,N
+      II=II+1
+      T0=T(J)-T(I)
+      TT=ABS(T0)
+      COV3(II)=SPLE(NT,TT,A,TIMEV)
+      IF (T0.LT.0.0d0) COV3(II)=-COV3(II)
+40    CONTINUE
+
+
+
+C    4-DERIVATIVE  COV(Y(T),Y(0))
+
+      NT=1
+ 52   READ (36,*,END=51) TIMEV(NT),A(NT)
+      NT=NT+1
+      GO TO 52
+ 51   CONTINUE
+      NT=NT-1
+      
+      XL4=SPLE(NT,ZERO,A,TIMEV)
+
+      DO 50 I=1,N
+      COV(I+4*N)=SPLE(NT,T(I),A,TIMEV)
+50    CONTINUE
+      CLOSE(UNIT=32)
+      CLOSE(UNIT=33)
+      CLOSE(UNIT=34)
+      CLOSE(UNIT=35)
+      CLOSE(UNIT=36)
+      RETURN
+      END
+
+      SUBROUTINE INITINTEG(NIT)
+      USE RINTMOD
+      USE EPSMOD
+      USE INFCMOD
+      USE MREGMOD
+!	IMPLICIT NONE
+      INTEGER, intent(inout) :: NIT
+!	INTEGER ISQ1
+C      dimension  INF(10),INFO(10)
+      
+C      COMMON /RINT/   C,FC
+C      COMMON /EPS/    EPS,EPSS,CEPSS
+C      COMMON /INFC/   ISQ,INF,INFO
+      OPEN(UNIT=1,FILE='accur.in')
+      OPEN(UNIT=8,FILE='min.out')
+      OPEN(UNIT=9,FILE='Max.out')
+      OPEN(UNIT=10,FILE='Maxmin.out')
+      OPEN(UNIT=11,FILE='Maxmin.log')
+
+      READ(1,*) NIT,IAC,ISQ
+      READ(1,*) EPS,EPSS,EPS0
+      
+      CLOSE (UNIT=1)
+      
+      FC=FI(C)-FI(-C)
+      CEPSS=1.0d0-EPSS
+
+      RETURN
+      END
+

wafo/source/mreg/cov2mmpdfreg_intfc.f

@@ -0,0 +1,370 @@
+C     Version  1994-X-18
+
+C     This is a new version of WAMP program computing crest-trough wavelength
+C     and amplitude  density.
+C
+C     revised pab 2007
+C     -moved all common blocks into modules
+C     -renamed from minmax to sp2mmpdfreg + fixed some bugs
+C     revised pab July 2007
+!     -renamed from sp2mmpdfreg to cov2mmpdfreg
+! gfortran -W -Wall -pedantic-errors -fbounds-check -Werror -c dsvdc.f  mregmodule.f cov2mmpdfreg.f
+
+      SUBROUTINE INITINTEG(EPS_,EPSS_,EPS0_,C_,IAC_,ISQ_)
+!      Initiation of all constants and integration nodes 'INITINTEG'
+      USE RINTMOD
+      USE EPSMOD
+      USE INFCMOD
+      USE MREGMOD
+      REAL*8 :: EPS_,EPSS_,EPS0_,C_
+      INTEGER :: IAC_,ISQ_
+Cf2py real*8, optional :: EPS_ = 0.01
+Cf2py real*8, optional :: EPSS_ = 0.00005
+Cf2py real*8, optional  :: EPS0_ = 0.00005
+Cf2py real*8, optional  :: C_ = 4.5
+Cf2py integer, optional :: IAC_ = 1
+Cf2py integer, optional :: ISQ_ = 0
+!     IMPLICIT NONE
+C      COMMON /RINT/   C,FC
+C      COMMON /EPS/    EPS,EPSS,CEPSS
+C      COMMON /INFC/   ISQ,INF,INFO
+
+      IAC = IAC_
+      ISQ = ISQ_
+      EPS = EPS_
+      EPSS = EPSS_
+      EPS0 = EPS0_
+      C = C_
+
+      FC = FI(C)-FI(-C)
+!      CEPSS = 1.0d0-EPSS
+      RETURN
+      END SUBROUTINE INITINTEG
+
+      subroutine cov2mmpdfreg(UVdens,t,COV,ULev,VLev,Tg,Xg,Nt,Nu,Nv,Ng,
+     &   NIT)
+      USE SIZEMOD
+      USE EPSMOD
+      USE CHECKMOD
+      USE MREGMOD
+      USE INTFCMOD
+      IMPLICIT NONE
+      INTEGER, INTENT(IN) :: Nt, Nu, Nv, Ng, NIT
+      REAL*8, DIMENSION(Nt,5), intent(in):: COV
+      REAL*8, DIMENSION(Nu,Nv), intent(out):: UVdens
+      REAL*8, DIMENSION(Nu), intent(in):: ULev
+      REAL*8, DIMENSION(Nv), intent(in):: VLev
+      REAL*8, DIMENSION(Ng), intent(in):: Tg, Xg
+      REAL*8, dimension(Nt), intent(in):: T
+Cf2py integer, intent(hide), depend(t) :: Nt = len(t)
+Cf2py integer, intent(hide), depend(Ulev) :: Nu = len(Ulev)
+Cf2py integer, intent(hide), depend(Vlev) :: Nv = len(Vlev)
+Cf2py integer, intent(hide), depend(Tg) :: Ng = len(Tg)
+Cf2py integer, optional :: NIT = 2
+Cf2py real*8, intent(out), depend(Nu,Nv) :: UVdens
+Cf2py depend(Ng)  Xg
+Cf2py depend(Nt,5)  COV
+      real*8 Q0,SQ0,Q1,SQ1, U,V, XL0, XL2, XL4
+      REAL*8 VDERI, DER, F, HHHH, VALUE
+C      REAL*8 VV, CDER,SDER, CONST1, FM
+C     INTEGER, PARAMETER :: MMAX = 5, NMAX = 101, RDIM = 10201
+      REAL*8, DIMENSION(NMAX) :: HHT,VT,UT,Vdd,Udd
+      REAL*8, DIMENSION(RDIM) :: R,R1,R2,R3
+      REAL*8:: AA(MMAX-2,MMAX-2),AI((MMAX+1)*NMAX)
+      REAL*8, DIMENSION(MMAX+1) :: BB, DAI
+C      DIMENSION UVdens(NMAX,NMAX),HHT(NMAX)
+C      DIMENSION T(NMAX),Ulev(NMAX),Vlev(NMAX)
+C      DIMENSION VT(NMAX),UT(NMAX),Vdd(NMAX),Udd(NMAX)
+C      DIMENSION COV(5*NMAX),R(RDIM),R1(RDIM),R2(RDIM),R3(RDIM)
+
+
+C
+C   The program computes the joint density of maximum the following minimum
+C   and the distance between Max and min for a zero-mean stationary
+C   Gaussian process with covariance function defined explicitely with 4
+C   derivatives. The process should be normalized so that the first and
+C   the second spectral moments are equal to 1. The values of Max are taken
+C   as the nodes at Hermite-Quadrature and then integrated out so that
+C   the output is a joint density of wavelength T and amplitude H=Max-min.
+C   The Max values are defined by subroutine Gauss_M with the accuracy
+C   input  epsu. The principle is that the integral of the marginal density
+C   of f_Max is computed with sufficient accuracy.
+C
+      REAL*8, DIMENSION(NMAX) :: B0,DB0,DDB0,B1,DB1,DDB1,DB2,DDB2
+      REAL*8, DIMENSION(NMAX) :: Q,SQ,VDER,DBI,BI
+C      DIMENSION B0(NMAX),DB0(NMAX),DDB0(NMAX)
+C      DIMENSION B1(NMAX),DB1(NMAX),DDB1(NMAX)
+C      DIMENSION DB2(NMAX),DDB2(NMAX)
+C      DIMENSION Q(NMAX),SQ(NMAX),VDER(NMAX),DBI(NMAX),BI(NMAX)
+      INTEGER :: J,I,I1,I2,I3,IU, IV,N, NNIT, INF
+C     INTEGER ::  fffff
+C     REAL*8 EPS0
+C     INTEGER III01,III11,III21,III31,III41,III51
+C     *,III61,III71,III81,III91,III101 , III0
+C      COMMON/CHECK1/III01,III11,III21,III31,III41,III51
+C     *,III61,III71,III81,III91,III101
+C      COMMON/CHECKQ/III0
+C      COMMON /EPS/  EPS,EPSS,CEPSS
+
+C
+C  Initiation of all constants and integration nodes 'INITINTEG'
+C
+!      CALL INITINTEG()
+
+!     OPEN(UNIT=8,FILE='min.out')
+!      OPEN(UNIT=9,FILE='Max.out')
+!      OPEN(UNIT=10,FILE='Maxmin.out')
+!      OPEN(UNIT=11,FILE='Maxmin.log')
+c
+c   OBS. we are using the variables R,R1,R2 R3 as a temporary storage
+C   for transformation  g  of the process.
+
+      N = Nt
+      CALL INITLEVELS(T,HHT,Nt,NU,Nv)
+C      CALL INITLEVELS(Ulev,NU,Vlev,NV,T,HHT,Nt,R1,R2,NG)
+      IF( Tg(1) .gt. Tg(ng))  then
+       print *,'Error Tg must be strictly increasing'
+       return
+      end if
+      if(abs(Tg(ng)-Tg(1))*abs(Xg(ng)-Xg(1)).lt.0.01d0) then
+       print *,'The transformation  g is singular, stop'
+       return
+      end if
+
+!      do IV=1,Nt
+!      print *, 'Cov', COV(IV,:)
+!      end do
+
+      DO IV=1,Nv
+         V=Vlev(IV)
+         CALL TRANSF(NG,V,Xg,Tg,VALUE,DER)
+         VT(IV)=VALUE
+         Vdd(IV)=DER
+      enddo
+      DO IU=1,Nu
+         U = Ulev(IU)
+         CALL TRANSF(NG,U,Xg,Tg,VALUE,DER)
+         UT(IU)  = VALUE
+         Udd(IU) = DER
+         do IV=1,Nv
+             UVdens(IU,IV)=0.0d0
+         enddo
+      enddo
+
+      CALL COVG(XL0,XL2,XL4,R1,R2,R3,COV,T,Nt)
+
+
+      Q0=XL4
+      IF (Q0.le.1.0D0+EPS) then
+      Print *,'Covariance structure is singular, stop.'
+      return
+      end if
+      SQ0 = SQRT(Q0)
+      Q1  = XL0-XL2*XL2/XL4
+      IF (Q1.le.EPS) then
+      Print *,'Covariance structure is singular, stop.'
+      return
+      end if
+      SQ1 = SQRT(Q1)
+      DO I=1,Nt
+        B0(I)  =-COV(I,3)
+        DB0(I) =-COV(I,4)
+        DDB0(I)=-COV(I,5)
+
+        B1(I)  =COV(I,1)+COV(I,3)*(XL2/XL4)
+        DB1(I) =COV(I,2)+COV(I,4)*(XL2/XL4)
+        DDB1(I)=COV(I,3)+XL2*(COV(I,5)/XL4)
+C
+C       Q(I) contains Var(X(T(i))|X'(0),X''(0),X(0))
+C    VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0))
+C
+        Q(I)=XL0 - COV(I,2)*(COV(I,2)/XL2) - B0(I)*(B0(I)/Q0)
+     1     -B1(I)*(B1(I)/Q1)
+        VDER(I)=XL4 - (COV(I,4)*COV(I,4))/XL2 - (DDB0(I)*DDB0(I))/Q0
+     1     - (DDB1(I)*DDB1(I))/Q1
+
+
+C
+C       DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0))
+C
+        DDB2(I)=-XL2 - (COV(I,2)*COV(I,4))/XL2 - DDB0(I)*(B0(I)/Q0)
+     1     -DDB1(I)*(B1(I)/Q1)
+        IF(Q(I).LE.eps) then
+          SQ(i)  =0.0d0
+          DDB2(i)=0.0d0
+        else
+          SQ(I)=SQRT(Q(I))
+C
+C       VDER(I) contains Var(X''(T(i))|X'(0),X''(0),X(0),X(T(i))
+C
+
+          VDER(I)=VDER(I) - (DDB2(I)*DDB2(I))/Q(I)
+        end if
+
+c10    CONTINUE
+      enddo
+      DO I=1,Nt
+      DO J=1,Nt
+C
+C   R1 contains Cov(X(T(I)),X'(T(J))|X'(0),X''(0),X(0))
+C
+      R1(J+(I-1)*N) = R1(J+(I-1)*N) -  COV(I,2)*(COV(J,3)/XL2)
+     1   - (B0(I)*DB0(J)/Q0) -  (B1(I)*DB1(J)/Q1)
+
+C
+C   R2 contains Cov(X'(T(I)),X'(T(J))|X'(0),X''(0),X(0))
+C
+      R2(J+(I-1)*N) = -R2(J+(I-1)*N) - COV(I,3)*(COV(J,3)/XL2)
+     1   - DB0(I)*DB0(J)/Q0  - DB1(I)*(DB1(J)/Q1)
+C
+C   R3 contains Cov(X''(T(I)),X'(T(J))|X'(0),X''(0),X(0))
+C
+      R3(J+(I-1)*N) = R3(J+(I-1)*N) - COV(I,4)*(COV(J,3)/XL2)
+     1   - DB0(J)*(DDB0(I)/Q0)  - DDB1(I)*(DB1(J)/Q1)
+c15    CONTINUE
+      enddo
+      enddo
+
+C  The initiations are finished and we are beginning with 3 loops
+C  on T=T(I), U=Ulevels(IU), V=Ulevels(IV), U>V.
+
+      DO I=1,Nt
+
+           NNIT=NIT
+           IF (Q(I).LE.EPS) GO TO 20
+
+         DO I1=1,I
+            DB2(I1)=R1(I1+(I-1)*N)
+
+C     Cov(X'(T(I1)),X(T(i))|X'(0),X''(0),X(0))
+C     DDB2(I) contains Cov(X''(T(i)),X(T(i))|X'(0),X''(0),X(0))
+
+         enddo
+
+         DO I3=1,I
+            DBI(I3) = R3(I3+(I-1)*N) - (DDB2(I)*DB2(I3)/Q(I))
+            BI(I3)  = R2(I3+(I-1)*N) - (DB2(I)*DB2(I3)/Q(I))
+         enddo
+         DO I3=1,I-1
+            AI(I3)=0.0d0
+            AI(I3+I-1)=DB0(I3)/SQ0
+            AI(I3+2*(I-1))=DB1(I3)/SQ1
+            AI(I3+3*(I-1))=DB2(I3)/SQ(I)
+         enddo
+         VDERI=VDER(I)
+         DAI(1)=0.0d0
+         DAI(2)=DDB0(I)/SQ0
+         DAI(3)=DDB1(I)/SQ1
+         DAI(4)=DDB2(I)/SQ(I)
+         AA(1,1)=DB0(I)/SQ0
+         AA(1,2)=DB1(I)/SQ1
+         AA(1,3)=DB2(I)/SQ(I)
+         AA(2,1)=XL2/SQ0
+         AA(2,2)=SQ1
+         AA(2,3)=0.0d0
+         AA(3,1)=B0(I)/SQ0
+         AA(3,2)=B1(I)/SQ1
+         AA(3,3)=SQ(I)
+         IF (BI(I).LE.EPS) NNIT=0
+         IF (NNIT.GT.1) THEN
+            IF(I.LT.1) GO TO 41
+            DO I1=1,I-1
+               DO I2=1,I-1
+C   R contains Cov(X'(T(I1)),X'(T(I2))|X'(0),X''(0),X(0),X(I))
+      R(I2+(I1-1)*(I-1))=R2(I2+(I1-1)*N)-(DB2(I1)*DB2(I2)/Q(I))
+
+            enddo
+            enddo
+ 41         CONTINUE
+         END IF
+
+C  Here the covariance of the problem would be initiated
+
+            INF=0
+            Print *,'   Laps to go:',Nt-I+1
+         DO IV=1,Nv
+            V=VT(IV)
+!            IF (ABS(V).GT.5.0D0) GO TO 80
+            IF (Vdd(IV).LT.EPS0) GO TO 80
+            DO IU=1,Nu
+                  U=UT(IU)
+                  IF (U.LE.V) go to 60
+!                  IF (ABS(U).GT.5.0D0) GO TO 60
+                  IF (Udd(IU).LT.EPS0) GO TO 60
+                  BB(1)=0.0d0
+                  BB(2)=U
+                  BB(3)=V
+!     if (IV.EQ.2.AND.IU.EQ.1) THEN
+!     fffff = 10
+!     endif
+
+      CALL MREG(F,R,BI,DBI,AA,BB,AI,DAI,VDERI,3,I-1,NNIT,INF)
+             INF=1
+             UVdens(IU,IV) = UVdens(IU,IV) + Udd(IU)*Vdd(IV)*HHT(I)*F
+
+!     if (F.GT.0.01.AND.U.GT.2.AND.V.LT.-2) THEN
+!     if (N-I+1 .eq. 38.and.IV.EQ.26.AND.IU.EQ.16) THEN
+!     if (IV.EQ.32.AND.IU.EQ.8.and.I.eq.11) THEN
+!          PRINT * ,' R:', R(1:I)
+!         PRINT * ,' BI:', BI(1:I)
+!         PRINT * ,' DBI:', DBI(1:I)
+!         PRINT * ,' DB2:', DB2(1:I)
+!         PRINT * ,' DB0(1):', DB0(1)
+!         PRINT * ,' DB1(1):', DB1(1)
+!          PRINT * ,' DAI:', DAI
+!         PRINT * ,' BB:', BB
+!         PRINT * ,' VDERI:', VDERI
+!          PRINT * ,' F    :', F
+!         PRINT * ,' UVDENS :',  UVdens(IU,IV)
+!         fffff = 10
+!     endif
+
+ 60         CONTINUE
+            enddo
+ 80       continue
+          enddo
+ 20   CONTINUE
+      enddo
+
+      hhhh=0.0d0
+      do Iu=1,Nu
+      do Iv=1,Nv
+!       WRITE(10,300) Ulev(iu),Vlev(iv),UVdens(iu,iv)
+        hhhh=hhhh+UVdens(iu,iv)
+      enddo
+      enddo
+      if (nu.gt.1.and.nv.gt.1) then
+      VALUE = (Ulev(2)-Ulev(1))*(Vlev(2)-Vlev(1))*hhhh
+      print *,'SumSum f_uv *du*dv=', VALUE
+      end if
+
+C      sder=sqrt(XL4-XL2*XL2/XL0)
+C      cder=-XL2/sqrt(XL0)
+C      const1=1/sqrt(XL0*XL4)
+C      DO 95 IU=1,NU
+C        U=UT(IU)
+C        FM=Udd(IU)*const1*exp(-0.5*U*U/XL0)*PMEAN(-cder*U,sder)
+C        WRITE(9,300) Ulev(IU),FM
+C 95   continue
+C      DO 105 IV=1,NV
+C        V=VT(IV)
+C        VV=cder*V
+C        Fm=Vdd(IV)*const1*exp(-0.5*V*V/XL0)*PMEAN(VV,sder)
+C        WRITE(8,300) Vlev(IV),Fm
+C 105   continue
+      if (III0.eq.0) III0=1
+
+      PRINT *, 'Rate of calls RINDT0:',float(iii01)/float(III0)
+      PRINT *, 'Rate of calls RINDT1:',float(iii11)/float(III0)
+      PRINT *, 'Rate of calls RINDT2:',float(iii21)/float(III0)
+      PRINT *, 'Rate of calls RINDT3:',float(iii31)/float(III0)
+      PRINT *, 'Rate of calls RINDT4:',float(iii41)/float(III0)
+      PRINT *, 'Rate of calls RINDT5:',float(iii51)/float(III0)
+      PRINT *, 'Rate of calls RINDT6:',float(iii61)/float(III0)
+      PRINT *, 'Rate of calls RINDT7:',float(iii71)/float(III0)
+      PRINT *, 'Rate of calls RINDT8:',float(iii81)/float(III0)
+      PRINT *, 'Rate of calls RINDT9:',float(iii91)/float(III0)
+      PRINT *, 'Rate of calls RINDT10:',float(iii101)/float(III0)
+      PRINT *, 'Number of calls of RINDT*',III0
+      return
+      END subroutine cov2mmpdfreg

wafo/source/mreg/dsvdc.f

@@ -0,0 +1,613 @@
+      MODULE SVD
+      IMPLICIT NONE
+      INTEGER, PARAMETER  :: dp = SELECTED_REAL_KIND(12, 60)
+
+! Based upon routines from the NSWC (Naval Surface Warfare Center),
+! which were based upon LAPACK routines.
+
+! Code converted using TO_F90 by Alan Miller
+! Date: 2003-11-11  Time: 17:50:44
+! Revised pab 2007
+! Converted to fixed form
+
+
+      CONTAINS
+
+
+      SUBROUTINE drotg(da, db, dc, ds)
+ 
+!     DESIGNED BY C.L.LAWSON, JPL, 1977 SEPT 08
+!
+!     CONSTRUCT THE GIVENS TRANSFORMATION
+!
+!         ( DC  DS )
+!     G = (        ) ,    DC**2 + DS**2 = 1 ,
+!         (-DS  DC )
+!
+!     WHICH ZEROS THE SECOND ENTRY OF THE 2-VECTOR  (DA,DB)**T .
+!
+!     THE QUANTITY R = (+/-)SQRT(DA**2 + DB**2) OVERWRITES DA IN
+!     STORAGE.  THE VALUE OF DB IS OVERWRITTEN BY A VALUE Z WHICH
+!     ALLOWS DC AND DS TO BE RECOVERED BY THE FOLLOWING ALGORITHM:
+!           IF Z=1  SET  DC=0.D0  AND  DS=1.D0
+!           IF DABS(Z) < 1  SET  DC=SQRT(1-Z**2)  AND  DS=Z
+!           IF DABS(Z) > 1  SET  DC=1/Z  AND  DS=SQRT(1-DC**2)
+!
+!     NORMALLY, THE SUBPROGRAM DROT(N,DX,INCX,DY,INCY,DC,DS) WILL
+!     NEXT BE CALLED TO APPLY THE TRANSFORMATION TO A 2 BY N MATRIX.
+!
+! ------------------------------------------------------------------
+
+      REAL (dp), INTENT(IN OUT)  :: da
+      REAL (dp), INTENT(IN OUT)  :: db
+      REAL (dp), INTENT(OUT)     :: dc
+      REAL (dp), INTENT(OUT)     :: ds
+
+      REAL (dp)  :: u, v, r
+      IF (ABS(da) <= ABS(db)) GO TO 10
+
+! *** HERE ABS(DA) > ABS(DB) ***
+
+      u = da + da
+      v = db / u
+
+!     NOTE THAT U AND R HAVE THE SIGN OF DA
+
+      r = SQRT(.25D0 + v**2) * u
+
+!     NOTE THAT DC IS POSITIVE
+
+      dc = da / r
+      ds = v * (dc + dc)
+      db = ds
+      da = r
+      RETURN
+
+! *** HERE ABS(DA) <= ABS(DB) ***
+
+   10 IF (db == 0.d0) GO TO 20
+      u = db + db
+      v = da / u
+
+!     NOTE THAT U AND R HAVE THE SIGN OF DB
+!     (R IS IMMEDIATELY STORED IN DA)
+
+      da = SQRT(.25D0 + v**2) * u
+
+!     NOTE THAT DS IS POSITIVE
+
+      ds = db / da
+      dc = v * (ds + ds)
+      IF (dc == 0.d0) GO TO 15
+      db = 1.d0 / dc
+      RETURN
+   15 db = 1.d0
+      RETURN
+
+! *** HERE DA = DB = 0.D0 ***
+
+   20 dc = 1.d0
+      ds = 0.d0
+      RETURN
+
+      END SUBROUTINE drotg
+
+
+      SUBROUTINE dswap1 (n, dx, dy)
+!     INTERCHANGES TWO VECTORS.
+!     USES UNROLLED LOOPS FOR INCREMENTS EQUAL ONE.
+!     JACK DONGARRA, LINPACK, 3/11/78.
+!     This version is for increments = 1.
+
+      INTEGER, INTENT(IN)        :: n
+      REAL (dp), INTENT(IN OUT)  :: dx(*)
+      REAL (dp), INTENT(IN OUT)  :: dy(*)
+
+      REAL (dp)  :: dtemp
+      INTEGER    :: i, m, mp1
+
+      IF(n <= 0) RETURN
+
+!       CODE FOR BOTH INCREMENTS EQUAL TO 1
+!
+!       CLEAN-UP LOOP
+
+      m = MOD(n,3)
+      IF( m == 0 ) GO TO 40
+      DO  i = 1,m
+       dtemp = dx(i)
+       dx(i) = dy(i)
+       dy(i) = dtemp
+      END DO
+      IF( n < 3 ) RETURN
+  40  mp1 = m + 1
+      DO  i = mp1,n,3
+      dtemp = dx(i)
+      dx(i) = dy(i)
+      dy(i) = dtemp
+      dtemp = dx(i + 1)
+      dx(i + 1) = dy(i + 1)
+      dy(i + 1) = dtemp
+      dtemp = dx(i + 2)
+      dx(i + 2) = dy(i + 2)
+      dy(i + 2) = dtemp
+      END DO
+      RETURN
+      END SUBROUTINE  dswap1
+
+
+      SUBROUTINE  drot1 (n, dx, dy, c, s)
+!     APPLIES A PLANE ROTATION.
+!     JACK DONGARRA, LINPACK, 3/11/78.
+!     This version is for increments = 1.
+
+      INTEGER, INTENT(IN)        :: n
+      REAL (dp), INTENT(IN OUT)  :: dx(*)
+      REAL (dp), INTENT(IN OUT)  :: dy(*)
+      REAL (dp), INTENT(IN)      :: c
+      REAL (dp), INTENT(IN)      :: s
+
+      REAL (dp)  :: dtemp
+      INTEGER    :: i
+
+      IF(n <= 0) RETURN
+!       CODE FOR BOTH INCREMENTS EQUAL TO 1
+
+      DO  i = 1,n
+      dtemp = c*dx(i) + s*dy(i)
+      dy(i) = c*dy(i) - s*dx(i)
+      dx(i) = dtemp
+      END DO
+      RETURN
+      END SUBROUTINE  drot1
+
+
+      SUBROUTINE dsvdc(x, n, p, s, e, u, v, job, info)
+
+      INTEGER, INTENT(IN)      :: n
+      INTEGER, INTENT(IN)      :: p
+      REAL (dp), INTENT(IN OUT)  :: x(:,:)
+      REAL (dp), INTENT(OUT)   :: s(:)
+      REAL (dp), INTENT(OUT)   :: e(:)
+      REAL (dp), INTENT(OUT)   :: u(:,:)
+      REAL (dp), INTENT(OUT)   :: v(:,:)
+      INTEGER, INTENT(IN)      :: job
+      INTEGER, INTENT(OUT)         :: info
+
+!     DSVDC IS A SUBROUTINE TO REDUCE A DOUBLE PRECISION NXP MATRIX X
+!     BY ORTHOGONAL TRANSFORMATIONS U AND V TO DIAGONAL FORM.  THE
+!     DIAGONAL ELEMENTS S(I) ARE THE SINGULAR VALUES OF X.  THE
+!     COLUMNS OF U ARE THE CORRESPONDING LEFT SINGULAR VECTORS,
+!     AND THE COLUMNS OF V THE RIGHT SINGULAR VECTORS.
+!
+!     ON ENTRY
+!
+!         X         DOUBLE PRECISION(LDX,P), WHERE LDX.GE.N.
+!                   X CONTAINS THE MATRIX WHOSE SINGULAR VALUE
+!                   DECOMPOSITION IS TO BE COMPUTED.  X IS
+!                   DESTROYED BY DSVDC.
+!
+!         LDX       INTEGER.
+!                   LDX IS THE LEADING DIMENSION OF THE ARRAY X.
+!
+!         N         INTEGER.
+!                   N IS THE NUMBER OF ROWS OF THE MATRIX X.
+!
+!         P         INTEGER.
+!                   P IS THE NUMBER OF COLUMNS OF THE MATRIX X.
+!
+!         LDU       INTEGER.
+!                   LDU IS THE LEADING DIMENSION OF THE ARRAY U.
+!                   (SEE BELOW).
+!
+!         LDV       INTEGER.
+!                   LDV IS THE LEADING DIMENSION OF THE ARRAY V.
+!                   (SEE BELOW).
+!
+!         JOB       INTEGER.
+!                   JOB CONTROLS THE COMPUTATION OF THE SINGULAR
+!                   VECTORS.  IT HAS THE DECIMAL EXPANSION AB
+!                   WITH THE FOLLOWING MEANING
+!
+!                        A.EQ.0    DO NOT COMPUTE THE LEFT SINGULAR VECTORS.
+!                        A.EQ.1    RETURN THE N LEFT SINGULAR VECTORS IN U.
+!                        A.GE.2    RETURN THE FIRST MIN(N,P) SINGULAR
+!                                  VECTORS IN U.
+!                        B.EQ.0    DO NOT COMPUTE THE RIGHT SINGULAR VECTORS.
+!                        B.EQ.1    RETURN THE RIGHT SINGULAR VECTORS IN V.
+!
+!     ON RETURN
+!
+!         S         DOUBLE PRECISION(MM), WHERE MM=MIN(N+1,P).
+!                   THE FIRST MIN(N,P) ENTRIES OF S CONTAIN THE SINGULAR
+!                   VALUES OF X ARRANGED IN DESCENDING ORDER OF MAGNITUDE.
+!
+!         E         DOUBLE PRECISION(P).
+!                   E ORDINARILY CONTAINS ZEROS.  HOWEVER SEE THE
+!                   DISCUSSION OF INFO FOR EXCEPTIONS.
+!
+!         U         DOUBLE PRECISION(LDU,K), WHERE LDU.GE.N.  IF
+!                                   JOBA.EQ.1 THEN K.EQ.N, IF JOBA.GE.2
+!                                   THEN K.EQ.MIN(N,P).
+!                   U CONTAINS THE MATRIX OF LEFT SINGULAR VECTORS.
+!                   U IS NOT REFERENCED IF JOBA.EQ.0.  IF N.LE.P
+!                   OR IF JOBA.EQ.2, THEN U MAY BE IDENTIFIED WITH X
+!                   IN THE SUBROUTINE CALL.
+!
+!         V         DOUBLE PRECISION(LDV,P), WHERE LDV.GE.P.
+!                   V CONTAINS THE MATRIX OF RIGHT SINGULAR VECTORS.
+!                   V IS NOT REFERENCED IF JOB.EQ.0.  IF P.LE.N,
+!                   THEN V MAY BE IDENTIFIED WITH X IN THE
+!                   SUBROUTINE CALL.
+!
+!         INFO      INTEGER.
+!                   THE SINGULAR VALUES (AND THEIR CORRESPONDING SINGULAR
+!                   VECTORS) S(INFO+1),S(INFO+2),...,S(M) ARE CORRECT
+!                   (HERE M=MIN(N,P)).  THUS IF INFO.EQ.0, ALL THE
+!                   SINGULAR VALUES AND THEIR VECTORS ARE CORRECT.
+!                   IN ANY EVENT, THE MATRIX B = TRANS(U)*X*V IS THE
+!                   BIDIAGONAL MATRIX WITH THE ELEMENTS OF S ON ITS DIAGONAL
+!                   AND THE ELEMENTS OF E ON ITS SUPER-DIAGONAL (TRANS(U)
+!                   IS THE TRANSPOSE OF U).  THUS THE SINGULAR VALUES
+!                   OF X AND B ARE THE SAME.
+!
+!     LINPACK. THIS VERSION DATED 03/19/79 .
+!     G.W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB.
+!
+!     DSVDC USES THE FOLLOWING FUNCTIONS AND SUBPROGRAMS.
+!
+!     EXTERNAL DROT
+!     BLAS DAXPY,DDOT,DSCAL,DSWAP,DNRM2,DROTG
+!     FORTRAN DABS,DMAX1,MAX0,MIN0,MOD,DSQRT
+
+!     INTERNAL VARIABLES
+
+      INTEGER :: iter, j, jobu, k, kase, kk, l, ll, lls, lm1, lp1, ls, 
+     & lu, m, maxit,mm, mm1, mp1, nct, nctp1, ncu, nrt, nrtp1
+      REAL (dp) :: t, work(n)
+      REAL (dp) :: b, c, cs, el, emm1, f, g, scale, shift, sl, sm, sn, 
+     & smm1, t1, test, ztest
+      LOGICAL :: wantu, wantv
+
+!     SET THE MAXIMUM NUMBER OF ITERATIONS.
+
+      maxit = 30
+
+!     DETERMINE WHAT IS TO BE COMPUTED.
+
+      wantu = .false.
+      wantv = .false.
+      jobu = MOD(job,100)/10
+      ncu = n
+      IF (jobu > 1) ncu = MIN(n,p)
+      IF (jobu /= 0) wantu = .true.
+      IF (MOD(job,10) /= 0) wantv = .true.
+
+!     REDUCE X TO BIDIAGONAL FORM, STORING THE DIAGONAL ELEMENTS
+!     IN S AND THE SUPER-DIAGONAL ELEMENTS IN E.
+
+      info = 0
+      nct = MIN(n-1, p)
+      s(1:nct+1) = 0.0_dp
+      nrt = MAX(0, MIN(p-2,n))
+      lu = MAX(nct,nrt)
+      IF (lu < 1) GO TO 170
+      DO  l = 1, lu
+        lp1 = l + 1
+        IF (l > nct) GO TO 20
+  
+!           COMPUTE THE TRANSFORMATION FOR THE L-TH COLUMN AND
+!           PLACE THE L-TH DIAGONAL IN S(L).
+  
+        s(l) = SQRT( SUM( x(l:n,l)**2 ) )
+        IF (s(l) == 0.0D0) GO TO 10
+        IF (x(l,l) /= 0.0D0) s(l) = SIGN(s(l), x(l,l))
+        x(l:n,l) = x(l:n,l) / s(l)
+        x(l,l) = 1.0D0 + x(l,l)
+
+  10    s(l) = -s(l)
+
+  20    IF (p < lp1) GO TO 50
+        DO  j = lp1, p
+          IF (l > nct) GO TO 30
+          IF (s(l) == 0.0D0) GO TO 30
+    
+!              APPLY THE TRANSFORMATION.
+    
+          t = -DOT_PRODUCT(x(l:n,l), x(l:n,j)) / x(l,l)
+          x(l:n,j) = x(l:n,j) + t * x(l:n,l)
+    
+!           PLACE THE L-TH ROW OF X INTO  E FOR THE
+!           SUBSEQUENT CALCULATION OF THE ROW TRANSFORMATION.
+    
+   30     e(j) = x(l,j)
+        END DO
+
+   50   IF (.NOT.wantu .OR. l > nct) GO TO 70
+  
+! PLACE THE TRANSFORMATION IN U FOR SUBSEQUENT BACK MULTIPLICATION.
+  
+        u(l:n,l) = x(l:n,l)
+
+   70   IF (l > nrt) CYCLE
+  
+!           COMPUTE THE L-TH ROW TRANSFORMATION AND PLACE THE
+!           L-TH SUPER-DIAGONAL IN E(L).
+  
+        e(l) = SQRT( SUM( e(lp1:p)**2 ) )
+        IF (e(l) == 0.0D0) GO TO 80
+        IF (e(lp1) /= 0.0D0) e(l) = SIGN(e(l), e(lp1))
+        e(lp1:lp1+p-l-1) = e(lp1:p) / e(l)
+        e(lp1) = 1.0D0 + e(lp1)
+
+   80   e(l) = -e(l)
+        IF (lp1 > n .OR. e(l) == 0.0D0) GO TO 120
+  
+!              APPLY THE TRANSFORMATION.
+  
+        work(lp1:n) = 0.0D0
+        DO  j = lp1, p
+          work(lp1:lp1+n-l-1) = work(lp1:lp1+n-l-1) + e(j) * 
+     &    x(lp1:lp1+n-l-1,j)
+        END DO
+        DO  j = lp1, p
+          x(lp1:lp1+n-l-1,j) = x(lp1:lp1+n-l-1,j) - (e(j)/e(lp1)) *
+     &     work(lp1:lp1+n-l-1)
+        END DO
+
+  120   IF (.NOT.wantv) CYCLE
+  
+!              PLACE THE TRANSFORMATION IN V FOR SUBSEQUENT
+!              BACK MULTIPLICATION.
+  
+        v(lp1:p,l) = e(lp1:p)
+      END DO
+
+!     SET UP THE FINAL BIDIAGONAL MATRIX OF ORDER M.
+
+  170 m = MIN(p,n+1)
+      nctp1 = nct + 1
+      nrtp1 = nrt + 1
+      IF (nct < p) s(nctp1) = x(nctp1,nctp1)
+      IF (n < m) s(m) = 0.0D0
+      IF (nrtp1 < m) e(nrtp1) = x(nrtp1,m)
+      e(m) = 0.0D0
+
+!     IF REQUIRED, GENERATE U.
+
+      IF (.NOT.wantu) GO TO 300
+      IF (ncu < nctp1) GO TO 200
+      DO  j = nctp1, ncu
+        u(1:n,j) = 0.0_dp
+        u(j,j) = 1.0_dp
+      END DO
+
+  200 DO  ll = 1, nct
+        l = nct - ll + 1
+        IF (s(l) == 0.0D0) GO TO 250
+        lp1 = l + 1
+        IF (ncu < lp1) GO TO 220
+        DO  j = lp1, ncu
+          t = -DOT_PRODUCT(u(l:n,l), u(l:n,j)) / u(l,l)
+          u(l:n,j) = u(l:n,j) + t * u(l:n,l)
+        END DO
+
+  220   u(l:n,l) = -u(l:n,l)
+        u(l,l) = 1.0D0 + u(l,l)
+        lm1 = l - 1
+        IF (lm1 < 1) CYCLE
+        u(1:lm1,l) = 0.0_dp
+        CYCLE
+
+  250   u(1:n,l) = 0.0_dp
+      u(l,l) = 1.0_dp
+      END DO
+
+!     IF IT IS REQUIRED, GENERATE V.
+
+  300 IF (.NOT.wantv) GO TO 350
+      DO  ll = 1, p
+        l = p - ll + 1
+        lp1 = l + 1
+        IF (l > nrt) GO TO 320
+        IF (e(l) == 0.0D0) GO TO 320
+        DO  j = lp1, p
+        t = -DOT_PRODUCT(v(lp1:lp1+p-l-1,l), 
+     &                v(lp1:lp1+p-l-1,j)) / v(lp1,l)
+        v(lp1:lp1+p-l-1,j) = v(lp1:lp1+p-l-1,j) + t * v(lp1:lp1+p-l-1,l)
+        END DO
+
+  320   v(1:p,l) = 0.0D0
+        v(l,l) = 1.0D0
+      END DO
+
+!     MAIN ITERATION LOOP FOR THE SINGULAR VALUES.
+
+  350 mm = m
+      iter = 0
+
+!        QUIT IF ALL THE SINGULAR VALUES HAVE BEEN FOUND.
+
+!     ...EXIT
+  360 IF (m == 0) GO TO 620
+
+!        IF TOO MANY ITERATIONS HAVE BEEN PERFORMED, SET FLAG AND RETURN.
+
+      IF (iter < maxit) GO TO 370
+      info = m
+!     ......EXIT
+      GO TO 620
+
+!        THIS SECTION OF THE PROGRAM INSPECTS FOR NEGLIGIBLE ELEMENTS
+!        IN THE S AND E ARRAYS.  ON COMPLETION
+!        THE VARIABLES KASE AND L ARE SET AS FOLLOWS.
+!
+!           KASE = 1     IF S(M) AND E(L-1) ARE NEGLIGIBLE AND L < M
+!           KASE = 2     IF S(L) IS NEGLIGIBLE AND L < M
+!           KASE = 3     IF E(L-1) IS NEGLIGIBLE, L < M, AND
+!                        S(L), ..., S(M) ARE NOT NEGLIGIBLE (QR STEP).
+!           KASE = 4     IF E(M-1) IS NEGLIGIBLE (CONVERGENCE).
+
+  370 DO  ll = 1, m
+          l = m - ll
+!        ...EXIT
+          IF (l == 0) EXIT
+          test = ABS(s(l)) + ABS(s(l+1))
+          ztest = test + ABS(e(l))
+          IF (ztest /= test) CYCLE
+          e(l) = 0.0D0
+!        ......EXIT
+          EXIT
+      END DO
+
+      IF (l /= m - 1) GO TO 410
+      kase = 4
+      GO TO 480
+
+  410 lp1 = l + 1
+      mp1 = m + 1
+      DO  lls = lp1, mp1
+      ls = m - lls + lp1
+!           ...EXIT
+      IF (ls == l) EXIT
+      test = 0.0D0
+      IF (ls /= m) test = test + ABS(e(ls))
+      IF (ls /= l + 1) test = test + ABS(e(ls-1))
+      ztest = test + ABS(s(ls))
+      IF (ztest /= test) CYCLE
+      s(ls) = 0.0D0
+!           ......EXIT
+      EXIT
+      END DO
+
+      IF (ls /= l) GO TO 450
+      kase = 3
+      GO TO 480
+
+  450 IF (ls /= m) GO TO 460
+      kase = 1
+      GO TO 480
+
+  460 kase = 2
+      l = ls
+  480 l = l + 1
+
+!        PERFORM THE TASK INDICATED BY KASE.
+
+      SELECT CASE ( kase )
+      CASE (    1)
+      GO TO 490
+      CASE (    2)
+      GO TO 520
+      CASE (    3)
+      GO TO 540
+      CASE (    4)
+      GO TO 570
+      END SELECT
+
+!        DEFLATE NEGLIGIBLE S(M).
+
+  490 mm1 = m - 1
+      f = e(m-1)
+      e(m-1) = 0.0D0
+      DO  kk = l, mm1
+        k = mm1 - kk + l
+        t1 = s(k)
+        CALL drotg(t1, f, cs, sn)
+        s(k) = t1
+        IF (k == l) GO TO 500
+        f = -sn*e(k-1)
+        e(k-1) = cs*e(k-1)
+      
+  500   IF (wantv) CALL drot1(p, v(1:,k), v(1:,m), cs, sn)
+      END DO
+      GO TO 610
+
+!        SPLIT AT NEGLIGIBLE S(L).
+
+  520 f = e(l-1)
+      e(l-1) = 0.0D0
+      DO  k = l, m
+      t1 = s(k)
+      CALL drotg(t1, f, cs, sn)
+      s(k) = t1
+      f = -sn*e(k)
+      e(k) = cs*e(k)
+      IF (wantu) CALL drot1(n, u(1:,k), u(1:,l-1), cs, sn)
+      END DO
+      GO TO 610
+
+!        PERFORM ONE QR STEP.
+!
+!           CALCULATE THE SHIFT.
+ 
+  540 scale = MAX(ABS(s(m)),ABS(s(m-1)),ABS(e(m-1)),ABS(s(l)),ABS(e(l)))
+      sm = s(m)/scale
+      smm1 = s(m-1)/scale
+      emm1 = e(m-1)/scale
+      sl = s(l)/scale
+      el = e(l)/scale
+      b = ((smm1 + sm)*(smm1 - sm) + emm1**2)/2.0D0
+      c = (sm*emm1)**2
+      shift = 0.0D0
+      IF (b == 0.0D0 .AND. c == 0.0D0) GO TO 550
+      shift = SQRT(b**2+c)
+      IF (b < 0.0D0) shift = -shift
+      shift = c/(b + shift)
+
+  550 f = (sl + sm)*(sl - sm) - shift
+      g = sl*el
+
+!           CHASE ZEROS.
+
+      mm1 = m - 1
+      DO  k = l, mm1
+        CALL drotg(f, g, cs, sn)
+        IF (k /= l) e(k-1) = f
+        f = cs*s(k) + sn*e(k)
+        e(k) = cs*e(k) - sn*s(k)
+        g = sn*s(k+1)
+        s(k+1) = cs*s(k+1)
+        IF (wantv) CALL drot1(p, v(1:,k), v(1:,k+1), cs, sn)
+        CALL drotg(f, g, cs, sn)
+        s(k) = f
+        f = cs*e(k) + sn*s(k+1)
+        s(k+1) = -sn*e(k) + cs*s(k+1)
+        g = sn*e(k+1)
+        e(k+1) = cs*e(k+1)
+        IF (wantu .AND. k < n) CALL drot1(n, u(1:,k), u(1:,k+1), cs, sn)
+        END DO
+        e(m-1) = f
+        iter = iter + 1
+       GO TO 610
+
+!        CONVERGENCE.
+
+!           MAKE THE SINGULAR VALUE  POSITIVE.
+
+  570 IF (s(l) >= 0.0D0) GO TO 590
+      s(l) = -s(l)
+      IF (wantv) v(1:p,l) = -v(1:p,l)
+
+!           ORDER THE SINGULAR VALUE.
+
+  590 IF (l == mm) GO TO 600
+!           ...EXIT
+      IF (s(l) >= s(l+1)) GO TO 600
+      t = s(l)
+      s(l) = s(l+1)
+      s(l+1) = t
+      IF (wantv .AND. l < p) CALL dswap1(p, v(1:,l), v(1:,l+1))
+      IF (wantu .AND. l < n) CALL dswap1(n, u(1:,l), u(1:,l+1))
+      l = l + 1
+      GO TO 590
+
+  600 iter = 0
+      m = m - 1
+
+  610 GO TO 360
+
+  620 RETURN
+      END SUBROUTINE dsvdc
+
+      END MODULE SVD

wafo/source/mreg/intfcmod.f

@@ -0,0 +1,189 @@
+      MODULE INTFCMOD
+      IMPLICIT NONE
+      PUBLIC :: INITLEVELS, TRANSF, COVG
+
+      CONTAINS
+      SUBROUTINE INITLEVELS(T,HT,N,NU,Nv)
+      USE TBRMOD
+      USE SIZEMOD
+      IMPLICIT NONE
+C     INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201
+C      DIMENSION ULEVELS(1),Vlevels(1),T(1),HT(1),TG(1),XG(1),HH(101)
+      REAL*8, DIMENSION(:), intent(in) :: T
+      REAL*8, DIMENSION(:), intent(out) :: HT
+C      INTEGER, intent(in) :: NG
+      REAL*8 :: UMIN,UMAX,VMIN,VMAX, HU,HV
+      integer :: N, I, NU, NV
+C     REAL*8, DIMENSION(NMAX) :: HH
+C      COMMON/TBR/HH
+
+C      IF (NG.GT.501) THEN
+C      PRINT *,'Vector defining transformation of data > 501, stop'
+C      STOP
+C      END IF
+
+
+      IF(N.ge.NMAX) then
+      print *,'The number of wavelength points >',NMAX-1, ' stop'
+      stop
+      end if
+      IF(N.lt.2) then
+      print *,'The number of wavelength points < 2, stop'
+      stop
+      end if
+
+      HT(1)=0.5d0*(T(2)-T(1))
+      HT(N)=0.5d0*(T(N)-T(N-1))
+      HH(1)=-100.0d0
+      HH(N)=-100.0d0
+      DO I=2,N-1
+         HT(I)=0.5d0*(T(I+1)-T(I-1))
+         HH(I)=-100.0d0
+c10    CONTINUE
+      enddo
+
+
+      IF(NU.gt.NMAX) then
+      print *,'The number of maxima >',NMAX,' stop'
+      stop
+      end if
+      IF(NV.gt.NMAX) then
+      print *,'The number of minima >',NMAX,' stop'
+      stop
+      end if
+
+      IF(NU.LT.1) Then
+      print *,'The number of maxima < 1, stop'
+      stop
+      end if
+      IF(NV.LT.1) Then
+      print *,'The number of minima < 1, stop'
+      stop
+      end if
+
+      RETURN
+      END SUBROUTINE INITLEVELS
+
+
+      SUBROUTINE TRANSF(N,T,A,TIMEV,VALUE,DER)
+C
+C N number of data points
+C TIMEV vector of time points
+C A a vector of values of a function G(TIME)
+C T independent time point
+C VALUE is a value of a function at T, i.e. VALUE=G(T).
+c DER=G'(t)
+C
+      USE SIZEMOD
+      IMPLICIT NONE
+      REAL*8, intent(inout):: VALUE, DER,T
+C      INTEGER, PARAMETER :: RDIM = 10201
+      REAL*8, DIMENSION(:), intent(in) :: A,TIMEV
+      integer, intent(in) :: N
+      REAL*8:: T1
+      integer :: I
+
+      IF (T.LT.TIMEV(1))  then
+      der=(A(2)-A(1))/(TIMEV(2)-TIMEV(1))
+      T1=T-TIMEV(1)
+      VALUE=A(1)+T1*DER
+      return
+      end if
+      IF (T.GT.TIMEV(N)) then
+      der = (A(N)-A(N-1))/(TIMEV(N)-TIMEV(N-1))
+      T1  = T-TIMEV(N)
+      VALUE=A(N)+T1*DER
+      return
+      end if
+      DO I=2,N
+      IF (T.LT.TIMEV(I)) GO TO 10
+      ENDDO
+ 10   I=I-1
+      T1=T-TIMEV(I)
+      DER=(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I))
+      VALUE=A(I)+T1*DER
+      RETURN
+      END SUBROUTINE TRANSF
+
+      REAL*8 FUNCTION SPLE(N,T,A,TIMEV)
+C
+C N number of data points
+C TIME vector of time points
+C A a vector of values of a function G(TIME)
+C T independent time point
+C SPLE is a value of a function at T, i.e. SPLE=G(T).
+C
+      USE SIZEMOD
+      IMPLICIT NONE
+      INTEGER, INTENT(IN):: N
+
+      REAL*8, INTENT(IN) :: T
+      REAL*8, DIMENSION(:), INTENT(IN) :: A,TIMEV
+      REAL*8 :: T1
+      INTEGER :: I
+      SPLE=-9.9d0
+      IF (T.LT.TIMEV(1) .OR. T.GT.TIMEV(N)) RETURN
+      DO I=2,N
+      IF (T.LT.TIMEV(I)) GO TO 10
+      ENDDO
+ 10   I=I-1
+      T1=T-TIMEV(I)
+      SPLE=A(I)+T1*(A(I+1)-A(I))/(TIMEV(i+1)-TIMEV(I))
+      RETURN
+      END FUNCTION SPLE
+
+      SUBROUTINE COVG(XL0,XL2,XL4,COV1,COV2,COV3,COV,T,N)
+C
+C  Covariance function and its four derivatives for a vector T of length N
+C  is assumed in a vector COV; COV(1,...,N,1)=r(T), COV(1,...,N, 2)=r'(T), etc.
+C  The vector COV should be of the shape N x 5.
+C
+C  COVG  Returns:
+C  XL0,XL2,XL4 - spectral moments.
+C
+C  Covariance matrices COV1=r'(T-T), COV2=r''(T-T) and COV3=r'''(T-T)
+C  Dimension of  COV1, COV2  should be atleast  N*N.
+C
+      USE SIZEMOD
+!     IMPLICIT NONE
+C     INTEGER, PARAMETER:: NMAX = 101, RDIM = 10201
+      REAL*8, PARAMETER:: ZERO = 0.0d0
+      REAL*8, intent(inout) :: XL0,XL2,XL4
+      REAL*8, DIMENSION(N,5), intent(in) :: COV
+      REAL*8, DIMENSION(N), intent(in) :: T
+      REAL*8, DIMENSION(RDIM), intent(inout) :: COV1,COV2,COV3
+      INTEGER, intent(in) :: N
+      integer :: I, J, II
+      REAL*8 :: TT, T0
+C
+C                  COV(Y(T),Y(0)) = COV(:,1)
+C      DERIVATIVE  COV(Y(T),Y(0)) = COV(:,2)
+C    2-DERIVATIVE  COV(Y(T),Y(0)) = COV(:,3)
+C    3-DERIVATIVE  COV(Y(T),Y(0)) = COV(:,4)
+C    4-DERIVATIVE  COV(Y(T),Y(0)) = COV(:,5)
+
+      XL0 = COV(1,1)
+      XL2 = -COV(1,3)
+      XL4 = COV(1,5)
+!     XL0 =  SPLE(NT, ZERO, COV(:,1), T)
+!     XL2 = -SPLE(NT, ZERO, COV(:,3), T)
+!     XL4 =  SPLE(NT, ZERO, COV(:,5), T)
+
+      II=0
+      DO I=1,N
+      DO J=1,N
+      II = II+1
+      T0 = T(J)-T(I)
+      TT = ABS(T0)
+      COV1(II) = SPLE(N, TT, COV(:,2), T)
+      COV2(II) = SPLE(N, TT, COV(:,3), T)
+      COV3(II) = SPLE(N, TT, COV(:,4), T)
+      IF (T0.LT.0.0d0) then
+      COV1(II)=-COV1(II)
+      COV3(II)=-COV3(II)
+      endif
+      enddo
+      enddo
+      RETURN
+      END SUBROUTINE COVG
+      END module intfcmod

wafo/source/mvn/build_all.py

@@ -0,0 +1,20 @@
+"""
+builds mvn.pyd
+"""
+import os
+import sys
+
+
+from wafo.f2py_tools import f2py_call_str
+
+def compile_all():
+    f2py_call = f2py_call_str()
+    print '=' * 75
+    print 'compiling mvn'
+    print '=' * 75
+
+    os.system(f2py_call + ' mvn.pyf mvndst.f -c ')
+
+
+if __name__ == '__main__':
+    compile_all()

wafo/source/mvn/mvn.pyf

@@ -0,0 +1,39 @@
+!    -*- f90 -*-
+! Note: the context of this file is case sensitive.
+
+python module mvn ! in 
+    interface  ! in :mvn
+        subroutine mvnun(d,n,lower,upper,means,covar,maxpts,abseps,releps,value,inform) ! in :mvn:mvndst.f
+            integer intent(hide) :: d=shape(means,0)
+            integer intent(hide) :: n=shape(means,1)
+            double precision dimension(d) :: lower
+            double precision dimension(d) :: upper
+            double precision dimension(d,n) :: means
+            double precision dimension(d,d) :: covar
+            integer intent(optional) :: maxpts=d*1000
+            double precision intent(optional) :: abseps=1e-6
+            double precision intent(optional) :: releps=1e-6
+            double precision intent(out) :: value
+            integer intent(out) :: inform
+        end subroutine mvnun
+
+        subroutine mvndst(n,lower,upper,infin,correl,maxpts,abseps,releps,error,value,inform) ! in :mvn:mvndst.f
+            integer intent(hide) :: n=len(lower)
+            double precision dimension(n) :: lower
+            double precision dimension(n) :: upper
+            integer dimension(n) :: infin
+            double precision dimension(n*(n-1)/2) :: correl
+            integer intent(optional) :: maxpts=2000
+            double precision intent(optional) :: abseps=1e-6
+            double precision intent(optional) :: releps=1e-6
+            double precision intent(out) :: error
+            double precision intent(out) :: value
+            integer intent(out) :: inform
+            integer :: ivls
+            common /dkblck/ ivls
+        end subroutine mvndst
+    end interface 
+end python module mvn
+
+! This file was auto-generated with f2py (version:2.39.235_1752).
+! See http://cens.ioc.ee/projects/f2py2e/