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Added lfind to misc.py

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Replaced call to valarray with np.full
Refactored code from detrendma into a new function moving_average.
Made doctests more robust.
pep8
master
Per A Brodtkorb 6 years ago
parent 75591fcd3e
commit a263988888
4 changed files with 327 additions and 224 deletions
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4
wafo/dctpack.py
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@ -346,8 +346,8 @@ def shiftdim(x, n=None):
if n is None: if n is None:
return x.reshape(no_leading_ones(x.shape)) return x.reshape(no_leading_ones(x.shape))
elif n >= 0: elif n >= 0:
return x.transpose(np.roll(range(x.ndim), -n)) return x.transpose(np.roll(range(x.ndim), -1 * n))
return x.reshape((1,) * -n + x.shape) return x.reshape((1,) * abs(n) + x.shape)
def example_dct2(debug=True): def example_dct2(debug=True):

380
wafo/misc.py
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@ -7,14 +7,13 @@ import collections
from wafo import numba_misc from wafo import numba_misc
import fractions import fractions
import numpy as np import numpy as np
from numpy import ( from numpy import (amax, logical_and, arange, linspace, atleast_1d,
meshgrid,
amax, logical_and, arange, linspace, atleast_1d,
asarray, ceil, floor, frexp, hypot, asarray, ceil, floor, frexp, hypot,
sqrt, arctan2, sin, cos, exp, log, log1p, mod, diff, sqrt, arctan2, sin, cos, exp, log, log1p, mod, diff,
inf, pi, interp, isscalar, zeros, ones, inf, pi, interp, isscalar, zeros, ones,
sign, unique, hstack, vstack, nonzero, where, extract) sign, unique, hstack, vstack, nonzero, where, extract,
from scipy.special import gammaln meshgrid)
from scipy.special import gammaln # pylint: disable=no-name-in-module
from scipy.integrate import trapz, simps from scipy.integrate import trapz, simps
import warnings import warnings
from time import strftime, gmtime from time import strftime, gmtime
@ -25,7 +24,6 @@ try:
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) FLOATINFO = np.finfo(float)
_TINY = FLOATINFO.tiny _TINY = FLOATINFO.tiny
_EPS = FLOATINFO.eps _EPS = FLOATINFO.eps
@ -41,8 +39,10 @@ __all__ = ['now', 'spaceline', 'narg_smallest', 'args_flat', 'is_numlike',
'meshgrid', 'ndgrid', 'trangood', 'tranproc', 'meshgrid', 'ndgrid', 'trangood', 'tranproc',
'plot_histgrm', 'num2pistr', 'test_docstrings', 'plot_histgrm', 'num2pistr', 'test_docstrings',
'lazywhere', 'lazyselect', 'lazywhere', 'lazyselect',
'valarray', 'lfind',
'moving_average',
'piecewise', 'piecewise',
'valarray', 'check_random_state'] 'check_random_state']
def xor(a, b): def xor(a, b):
@ -52,6 +52,41 @@ def xor(a, b):
return a ^ b return a ^ b
def lfind(haystack, needle, maxiter=None):
"""Return indices to the maxiter first needles in the haystack as an iterable generator.
Parameters
----------
haystack: list or tuple of items
needle: item to find
maxiter: scalar integer maximum number of occurences
Returns
-------
indices_gen: generator object
Example
------
>>> haystack = (1, 3, 4, 3, 10, 3, 1, 2, 5, 7, 10)
>>> list(lfind(haystack, 3))
[1, 3, 5]
>>> [i for i in lfind(haystack, 3, 2)]
[1, 3]
>>> [i for i in lfind(haystack, 0, 2)]
[]
"""
maxiter = inf if maxiter is None else maxiter
ix = -1
i = 0
while i < maxiter:
i += 1
try:
ix = haystack.index(needle, ix + 1)
yield ix
except (ValueError, KeyError):
break
def check_random_state(seed): def check_random_state(seed):
"""Turn seed into a np.random.RandomState instance """Turn seed into a np.random.RandomState instance
@ -82,16 +117,10 @@ def check_random_state(seed):
raise ValueError(msg.format(seed)) raise ValueError(msg.format(seed))
def valarray(shape, value=np.NaN, typecode=None): def valarray(shape, value=np.nan, typecode=None):
"""Return an array of all value. """Return an array of all value.
""" """
if typecode is None: return np.full(shape, fill_value=value, dtype=typecode)
typecode = bool
out = ones(shape, dtype=typecode) * value
if not isinstance(out, np.ndarray):
out = asarray(out)
return out
def piecewise(condlist, funclist, xi=None, fillvalue=0.0, args=(), **kw): def piecewise(condlist, funclist, xi=None, fillvalue=0.0, args=(), **kw):
@ -173,20 +202,22 @@ def piecewise(condlist, funclist, xi=None, fillvalue=0.0, args=(), **kw):
Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for
``x >= 0``. ``x >= 0``.
>>> piecewise([x < 0, x >= 0], [lambda x: -x, lambda x: x], xi=(x,)) >>> np.allclose(piecewise([x < 0, x >= 0], [lambda x: -x, lambda x: x], xi=(x,)),
array([ 2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) ... [ 2.5, 1.5, 0.5, 0.5, 1.5, 2.5])
True
Define the absolute value, which is ``-x*y`` for ``x*y <0`` and ``x*y`` for Define the absolute value, which is ``-x*y`` for ``x*y <0`` and ``x*y`` for
``x*y >= 0`` ``x*y >= 0``
>>> X, Y = np.meshgrid(x, x) >>> X, Y = np.meshgrid(x, x)
>>> piecewise([X * Y < 0, ], [lambda x, y: -x * y, lambda x, y: x * y], >>> np.allclose(piecewise([X * Y < 0, ], [lambda x, y: -x * y,
... xi=(X, Y)) ... lambda x, y: x * y], xi=(X, Y)),
array([[ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25], ... [[ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25],
[ 3.75, 2.25, 0.75, 0.75, 2.25, 3.75], ... [ 3.75, 2.25, 0.75, 0.75, 2.25, 3.75],
[ 1.25, 0.75, 0.25, 0.25, 0.75, 1.25], ... [ 1.25, 0.75, 0.25, 0.25, 0.75, 1.25],
[ 1.25, 0.75, 0.25, 0.25, 0.75, 1.25], ... [ 1.25, 0.75, 0.25, 0.25, 0.75, 1.25],
[ 3.75, 2.25, 0.75, 0.75, 2.25, 3.75], ... [ 3.75, 2.25, 0.75, 0.75, 2.25, 3.75],
[ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25]]) ... [ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25]])
True
""" """
def otherwise_condition(condlist): def otherwise_condition(condlist):
return ~np.logical_or.reduce(condlist, axis=0) return ~np.logical_or.reduce(condlist, axis=0)
@ -201,6 +232,7 @@ def piecewise(condlist, funclist, xi=None, fillvalue=0.0, args=(), **kw):
condlist = np.broadcast_arrays(*condlist) condlist = np.broadcast_arrays(*condlist)
if len(condlist) == len(funclist) - 1: if len(condlist) == len(funclist) - 1:
condlist.append(otherwise_condition(condlist)) condlist.append(otherwise_condition(condlist))
if xi is None: if xi is None:
arrays = () arrays = ()
dtype = np.result_type(*funclist) dtype = np.result_type(*funclist)
@ -212,7 +244,7 @@ def piecewise(condlist, funclist, xi=None, fillvalue=0.0, args=(), **kw):
dtype = np.result_type(*arrays) dtype = np.result_type(*arrays)
shape = arrays[0].shape shape = arrays[0].shape
out = valarray(shape, fillvalue, dtype) out = np.full(shape, fillvalue, dtype)
for cond, func in zip(condlist, funclist): for cond, func in zip(condlist, funclist):
if cond.any(): if cond.any():
if isinstance(func, collections.Callable): if isinstance(func, collections.Callable):
@ -231,12 +263,15 @@ def lazywhere(cond, arrays, f, fillvalue=None, f2=None):
>>> a, b = np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8]) >>> a, b = np.array([1, 2, 3, 4]), np.array([5, 6, 7, 8])
>>> def f(a, b): >>> def f(a, b):
... return a*b ... return a*b
>>> lazywhere(a > 2, (a, b), f, np.nan) >>> r = lazywhere(a > 2, (a, b), f, np.nan)
array([ nan, nan, 21., 32.]) >>> np.allclose(r[2:], [21., 32.]); np.all(np.isnan(r[:2]))
True
True
>>> def f2(a, b): >>> def f2(a, b):
... return (a*b)**2 ... return (a*b)**2
>>> lazywhere(a > 2, (a, b), f, f2=f2) >>> np.allclose(lazywhere(a > 2, (a, b), f, f2=f2),
array([ 25., 144., 21., 32.]) ... [ 25., 144., 21., 32.])
True
Notice it assumes that all `arrays` are of the same shape, or can be Notice it assumes that all `arrays` are of the same shape, or can be
broadcasted together. broadcasted together.
@ -250,7 +285,7 @@ def lazywhere(cond, arrays, f, fillvalue=None, f2=None):
arrays = np.broadcast_arrays(*arrays) arrays = np.broadcast_arrays(*arrays)
temp = tuple(np.extract(cond, arr) for arr in arrays) temp = tuple(np.extract(cond, arr) for arr in arrays)
out = valarray(np.shape(arrays[0]), value=fillvalue) out = np.full(np.shape(arrays[0]), fill_value=fillvalue)
np.place(out, cond, f(*temp)) np.place(out, cond, f(*temp))
if f2 is not None: if f2 is not None:
temp = tuple(np.extract(~cond, arr) for arr in arrays) temp = tuple(np.extract(~cond, arr) for arr in arrays)
@ -309,11 +344,11 @@ def rotation_matrix(heading, pitch, roll):
Examples Examples
-------- --------
>>> import numpy as np >>> import numpy as np
>>> rotation_matrix(heading=0, pitch=0, roll=0) >>> np.allclose(rotation_matrix(heading=0, pitch=0, roll=0),
array([[ 1., 0., 0.], ... [[ 1., 0., 0.],
[ 0., 1., 0.], ... [ 0., 1., 0.],
[ 0., 0., 1.]]) ... [ 0., 0., 1.]])
True
>>> np.allclose(rotation_matrix(heading=180, pitch=0, roll=0), >>> np.allclose(rotation_matrix(heading=180, pitch=0, roll=0),
... [[ -1., 0., 0.], ... [[ -1., 0., 0.],
... [ 0., -1., 0.], ... [ 0., -1., 0.],
@ -438,12 +473,20 @@ def spaceline(start_point, stop_point, num=10):
Example Example
------- -------
>>> import wafo.misc as pm >>> import wafo.misc as pm
>>> pm.spaceline((2,0,0), (3,0,0), num=5) >>> np.allclose(pm.spaceline((2,0,0), (3,0,0), num=5),
array([[ 2. , 0. , 0. ], ... [[ 2. , 0. , 0. ],
[ 2.25, 0. , 0. ], ... [ 2.25, 0. , 0. ],
[ 2.5 , 0. , 0. ], ... [ 2.5 , 0. , 0. ],
[ 2.75, 0. , 0. ], ... [ 2.75, 0. , 0. ],
[ 3. , 0. , 0. ]]) ... [ 3. , 0. , 0. ]])
True
>>> np.allclose(pm.spaceline((2,0,0), (0,0,3), num=5),
... [[ 2. , 0. , 0. ],
... [ 1.5 , 0. , 0.75],
... [ 1. , 0. , 1.5 ],
... [ 0.5 , 0. , 2.25],
... [ 0. , 0. , 3. ]])
True
''' '''
num = int(num) num = int(num)
start, stop = np.atleast_1d(start_point, stop_point) start, stop = np.atleast_1d(start_point, stop_point)
@ -615,6 +658,8 @@ def is_numlike(obj):
True True
>>> is_numlike('1') >>> is_numlike('1')
False False
>>> is_numlike([1])
False
""" """
try: try:
obj + 1 obj + 1
@ -670,13 +715,13 @@ class Bunch(object):
Example Example
------- -------
>>> d = Bunch(test1=1,test2=3) >>> d = Bunch(test1=1,test2=3)
>>> d.test1 >>> (d.test1, d.test2)
1 (1, 3)
>>> sorted(d.keys()) == ['test1', 'test2'] >>> sorted(d.keys()) == ['test1', 'test2']
True True
>>> d.update(test1=2) >>> d.update(test1=5)
>>> d.test1 >>> (d.test1, d.test2)
2 (5, 3)
''' '''
def __init__(self, **kwargs): def __init__(self, **kwargs):
@ -703,7 +748,7 @@ def sub_dict_select(somedict, somekeys):
# the keyword exists in options # the keyword exists in options
>>> opt = dict(arg1=2, arg2=3) >>> opt = dict(arg1=2, arg2=3)
>>> kwds = dict(arg2=100,arg3=1000) >>> kwds = dict(arg2=100,arg3=1000)
>>> sub_dict = sub_dict_select(kwds,opt.keys()) >>> sub_dict = sub_dict_select(kwds, opt)
>>> opt.update(sub_dict) >>> opt.update(sub_dict)
>>> opt == {'arg1': 2, 'arg2': 100} >>> opt == {'arg1': 2, 'arg2': 100}
True True
@ -713,7 +758,7 @@ def sub_dict_select(somedict, somekeys):
dict_intersection dict_intersection
''' '''
# slower: validKeys = set(somedict).intersection(somekeys) # slower: validKeys = set(somedict).intersection(somekeys)
return dict((k, somedict[k]) for k in somekeys if k in somedict) return type(somedict)((k, somedict[k]) for k in somekeys if k in somedict)
def parse_kwargs(options, **kwargs): def parse_kwargs(options, **kwargs):
@ -731,13 +776,91 @@ def parse_kwargs(options, **kwargs):
See also sub_dict_select See also sub_dict_select
''' '''
newopts = sub_dict_select(kwargs, options.keys()) newopts = sub_dict_select(kwargs, options)
if len(newopts) > 0: if len(newopts) > 0:
options.update(newopts) options.update(newopts)
return options return options
def detrendma(x, L): def moving_average(x, L, axis=0):
"""
Return moving average from data using a window of size 2*L+1.
If 2*L+1 > len(x) then the mean is returned
Parameters
----------
x : vector or matrix of column vectors
of data
L : scalar, integer
defines the size of the moving average window
axis: scalar integer
axis along which the moving average is computed. Default axis=0.
Returns
-------
y : ndarray
moving average
Examples
--------
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> exp = np.exp; cos = np.cos; randn = np.random.randn
>>> x = np.linspace(0,1,200)
>>> y = exp(x)+cos(5*2*pi*x)+1e-1*randn(x.size)
>>> y0 = moving_average(y, 20)
>>> np.allclose(y0[:4], [ 1.1189971, 1.1189971, 1.1189971, 1.1189971], atol=1e-1)
True
>>> x2 = np.linspace(1, 5, 5)
>>> np.allclose(moving_average(x2, L=1), [2., 2., 3., 4., 4.])
True
>>> np.allclose(moving_average(x2, L=10), [3., 3., 3., 3., 3.])
True
>>> x3 = np.vstack((x2, x2+5))
>>> np.allclose(moving_average(x3, L=1, axis=1), [[2., 2., 3., 4., 4.],
... [7., 7., 8., 9., 9.]])
True
>>> np.allclose(moving_average(x3, L=10, axis=1), [[3., 3., 3., 3., 3.],
... [8., 8., 8., 8., 8.]])
True
h = plt.plot(x, y, x, y0, 'r', x, exp(x), 'k', x, tr, 'm')
plt.close('all')
See also
--------
Reconstruct
"""
_assert(0 < L, 'L must be positive')
_assert(L == np.round(L), 'L must be an integer')
x1 = np.atleast_1d(x)
axes = np.arange(x.ndim)
axes[0] = axis
axes[axis] = 0
x1 = np.transpose(x1, axes)
y = np.empty_like(x1)
n = x1.shape[0]
if n < 2 * L + 1: # only able to remove the mean
y[:] = x1.mean(axis=0)
return np.transpose(y, axes)
mn = x1[0:2 * L + 1].mean(axis=0)
y[0:L + 1] = mn
ix = np.r_[L + 1:(n - L)]
y[ix] = ((x1[ix + L] - x1[ix - L]) / (2 * L)).cumsum(axis=0) + mn
y[n - L::] = y[n - L - 1]
return np.transpose(y, axes)
def detrendma(x, L, axis=0):
""" """
Removes a trend from data using a moving average Removes a trend from data using a moving average
of size 2*L+1. If 2*L+1 > len(x) then the mean is removed of size 2*L+1. If 2*L+1 > len(x) then the mean is removed
@ -748,6 +871,8 @@ def detrendma(x, L):
of data of data
L : scalar, integer L : scalar, integer
defines the size of the moving average window defines the size of the moving average window
axis: scalar integer
axis along which the moving average is computed. Default axis=0.
Returns Returns
------- -------
@ -760,11 +885,12 @@ def detrendma(x, L):
>>> import numpy as np >>> import numpy as np
>>> import wafo.misc as wm >>> import wafo.misc as wm
>>> exp = np.exp; cos = np.cos; randn = np.random.randn >>> exp = np.exp; cos = np.cos; randn = np.random.randn
>>> x = np.linspace(0,1,200) >>> x = np.linspace(0,1,200)
>>> noise = 0.1*randn(x.size) >>> noise = 0.1*randn(x.size)
>>> noise = 0.1*np.sin(100*x) >>> noise = 0.1*np.sin(100*x)
>>> y = exp(x)+cos(5*2*pi*x) + noise >>> y = exp(x)+cos(5*2*pi*x) + noise
>>> y0 = wm.detrendma(y,20) >>> y0 = wm.detrendma(y, 20)
>>> tr = y-y0 >>> tr = y-y0
>>> np.allclose(tr[:5], >>> np.allclose(tr[:5],
... [ 1.14134814, 1.14134814, 1.14134814, 1.14134814, 1.14134814]) ... [ 1.14134814, 1.14134814, 1.14134814, 1.14134814, 1.14134814])
@ -781,28 +907,11 @@ def detrendma(x, L):
See also See also
-------- --------
Reconstruct Reconstruct, moving_average
""" """
_assert(0 < L, 'L must be positive') x1 = np.atleast_1d(x)
_assert(L == np.round(L), 'L must be an integer') trend = moving_average(x1, L, axis)
return x1 - trend
x_1 = np.atleast_1d(x)
if x_1.shape[0] == 1:
x_1 = x_1.ravel()
n = x_1.shape[0]
if n < 2 * L + 1: # only able to remove the mean
return x_1 - x_1.mean(axis=0)
mean = x_1[:2 * L + 1].mean(axis=0)
y = np.empty_like(x_1)
y[:L + 1] = x_1[:L + 1] - mean
i = np.r_[L + 1:(n - L)]
trend = ((x_1[i + L] - x_1[i - L]) / (2 * L)).cumsum(axis=0) + mean
y[i] = x_1[i] - trend
y[n - L::] = x_1[n - L::] - trend[-1]
return y
def ecross(t, f, ind, v=0): def ecross(t, f, ind, v=0):
@ -860,7 +969,7 @@ def _findcross(x, method='numba'):
'''Return indices to zero up and downcrossings of a vector '''Return indices to zero up and downcrossings of a vector
''' '''
if clib is not None and method == 'clib': if clib is not None and method == 'clib':
ind, m = clib.findcross(x, 0.0) ind, m = clib.findcross(x, 0.0) # pylint: disable=no-member
return ind[:int(m)] return ind[:int(m)]
return numba_misc.findcross(x) return numba_misc.findcross(x)
@ -903,6 +1012,7 @@ def findcross(x, v=0.0, kind=None, method='clib'):
>>> ind = wm.findcross(x,v) # all crossings >>> ind = wm.findcross(x,v) # all crossings
>>> np.allclose(ind, [ 9, 25, 80, 97, 151, 168, 223, 239]) >>> np.allclose(ind, [ 9, 25, 80, 97, 151, 168, 223, 239])
True True
>>> ind2 = wm.findcross(x,v,'u') >>> ind2 = wm.findcross(x,v,'u')
>>> np.allclose(ind2, [ 9, 80, 151, 223]) >>> np.allclose(ind2, [ 9, 80, 151, 223])
True True
@ -940,7 +1050,6 @@ def findcross(x, v=0.0, kind=None, method='clib'):
# if kind=='dw' or kind=='tw' # if kind=='dw' or kind=='tw'
# or that the first is a level v up-crossing # or that the first is a level v up-crossing
# if kind=='uw' or kind=='cw' # if kind=='uw' or kind=='cw'
first_is_down_crossing = int(xn[ind[0]] > xn[ind[0] + 1]) first_is_down_crossing = int(xn[ind[0]] > xn[ind[0] + 1])
if xor(first_is_down_crossing, kind in ('dw', 'tw')): if xor(first_is_down_crossing, kind in ('dw', 'tw')):
ind = ind[1::] ind = ind[1::]
@ -1171,7 +1280,7 @@ def findrfc(tp, h=0.0, method='clib'):
t_start = int(y[0] > y[1]) # first is a max, ignore it t_start = int(y[0] > y[1]) # first is a max, ignore it
y = y[t_start::] y = y[t_start::]
n = len(y) n = len(y)
NC = np.floor(n / 2) - 1 NC = np.floor(n // 2) - 1
if (NC < 1): if (NC < 1):
return zeros(0, dtype=np.int) # No RFC cycles*/ return zeros(0, dtype=np.int) # No RFC cycles*/
@ -1182,7 +1291,7 @@ def findrfc(tp, h=0.0, method='clib'):
return zeros(0, dtype=np.int) return zeros(0, dtype=np.int)
if clib is not None and method == 'clib': if clib is not None and method == 'clib':
ind, ix = clib.findrfc(y, h) ind, ix = clib.findrfc(y, h) # pylint: disable=no-member
ix = int(ix) ix = int(ix)
else: else:
if isinstance(method, str): if isinstance(method, str):
@ -1218,25 +1327,23 @@ def rfcfilter(x, h, method=0):
>>> import wafo.misc as wm >>> import wafo.misc as wm
>>> x = data.sea() >>> x = data.sea()
>>> y = wm.rfcfilter(x[:,1], h=0, method=1) >>> y = wm.rfcfilter(x[:,1], h=0, method=1)
>>> np.all(np.abs(y[0:5]-np.array([-1.2004945 , 0.83950546, -0.09049454, >>> np.allclose(y[0:5], [-1.2004945 , 0.83950546, -0.09049454, -0.02049454, -0.09049454])
... -0.02049454, -0.09049454]))<1e-7) True
>>> np.allclose(y.shape, (2172,))
True True
>>> y.shape
(2172,)
# 2. This removes all rainflow cycles with range less than 0.5. # 2. This removes all rainflow cycles with range less than 0.5.
>>> y1 = wm.rfcfilter(x[:,1], h=0.5) >>> y1 = wm.rfcfilter(x[:,1], h=0.5)
>>> y1.shape >>> np.allclose(y1.shape, (863,))
(863,) True
>>> np.all(np.abs(y1[0:5]-np.array([-1.2004945 , 0.83950546, -0.43049454, >>> np.allclose(y1[0:5], [-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454])
... 0.34950546, -0.51049454]))<1e-7)
True True
>>> ind = wm.findtp(x[:,1], h=0.5) >>> ind = wm.findtp(x[:,1], h=0.5)
>>> y2 = x[ind,1] >>> y2 = x[ind,1]
>>> y2[0:5] >>> np.allclose(y2[0:5], [-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454])
array([-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454]) True
>>> y2[-5::] >>> np.allclose(y2[-5::], [ 0.83950546, -0.64049454, 0.65950546, -1.0004945 , 0.91950546])
array([ 0.83950546, -0.64049454, 0.65950546, -1.0004945 , 0.91950546]) True
See also See also
-------- --------
@ -1609,10 +1716,10 @@ def common_shape(*args, ** kwds):
>>> A = np.ones((4,1)) >>> A = np.ones((4,1))
>>> B = 2 >>> B = 2
>>> C = np.ones((1,5))*5 >>> C = np.ones((1,5))*5
>>> wm.common_shape(A,B,C) >>> np.allclose(wm.common_shape(A,B,C), (4, 5))
(4, 5) True
>>> wm.common_shape(A,B,C,shape=(3,4,1)) >>> np.allclose(wm.common_shape(A,B,C,shape=(3,4,1)), (3, 4, 5))
(3, 4, 5) True
See also See also
-------- --------
@ -1652,12 +1759,12 @@ def argsreduce(condition, * args):
>>> C = rand((1,5)) >>> C = rand((1,5))
>>> cond = np.ones(A.shape) >>> cond = np.ones(A.shape)
>>> [A1,B1,C1] = wm.argsreduce(cond,A,B,C) >>> [A1,B1,C1] = wm.argsreduce(cond,A,B,C)
>>> B1.shape >>> np.allclose(B1.shape, (20,))
(20,) True
>>> cond[2,:] = 0 >>> cond[2,:] = 0
>>> [A2,B2,C2] = wm.argsreduce(cond,A,B,C) >>> [A2,B2,C2] = wm.argsreduce(cond,A,B,C)
>>> B2.shape >>> np.allclose(B2.shape, (15,))
(15,) True
See also See also
-------- --------
@ -1794,7 +1901,7 @@ def getshipchar(**ship_property):
... 'lengthSTD': 2.0113098831942762, ... 'lengthSTD': 2.0113098831942762,
... 'draught': 9.5999999999999996, ... 'draught': 9.5999999999999996,
... 'propeller_diameterSTD': 0.20267047566705432, ... 'propeller_diameterSTD': 0.20267047566705432,
... 'max_deadweightSTD': 3096.9000000000001, ... 'max_deadweight_std': 3096.9000000000001,
... 'beam': 29.0, 'length': 216.0, ... 'beam': 29.0, 'length': 216.0,
... 'beamSTD': 2.9000000000000004, ... 'beamSTD': 2.9000000000000004,
... 'service_speed': 10.0, ... 'service_speed': 10.0,
@ -1818,7 +1925,7 @@ def getshipchar(**ship_property):
''' '''
max_deadweight, prop = _get_max_deadweight(**ship_property) max_deadweight, prop = _get_max_deadweight(**ship_property)
propertySTD = prop + 'STD' property_std = prop + 'STD'
length = np.round(3.45 * max_deadweight ** 0.40) length = np.round(3.45 * max_deadweight ** 0.40)
length_err = length ** 0.13 length_err = length ** 0.13
@ -1837,18 +1944,16 @@ def getshipchar(**ship_property):
p_diam_err = 0.12 * length_err ** (3.0 / 4.0) p_diam_err = 0.12 * length_err ** (3.0 / 4.0)
max_deadweight = np.round(max_deadweight) max_deadweight = np.round(max_deadweight)
max_deadweightSTD = 0.1 * max_deadweight max_deadweight_std = 0.1 * max_deadweight
shipchar = dict(beam=beam, beamSTD=beam_err, shipchar = dict(beam=beam, beamSTD=beam_err,
draught=draught, draughtSTD=draught_err, draught=draught, draughtSTD=draught_err,
length=length, lengthSTD=length_err, length=length, lengthSTD=length_err,
max_deadweight=max_deadweight, max_deadweight=max_deadweight, max_deadweightSTD=max_deadweight_std,
max_deadweightSTD=max_deadweightSTD, propeller_diameter=p_diam, propeller_diameterSTD=p_diam_err,
propeller_diameter=p_diam,
propeller_diameterSTD=p_diam_err,
service_speed=speed, service_speedSTD=speed_err) service_speed=speed, service_speedSTD=speed_err)
shipchar[propertySTD] = 0 shipchar[property_std] = 0
return shipchar return shipchar
@ -1874,8 +1979,8 @@ def binomln(z, w):
Example Example
------- -------
>>> np.abs(binomln(3,2)- 1.09861229)<1e-7 >>> np.allclose(binomln(3,2), 1.09861229)
array([ True], dtype=bool) True
See also See also
-------- --------
@ -1918,12 +2023,11 @@ def betaloge(z, w):
-------- --------
betaln, beta betaln, beta
''' '''
# y = gammaln(z)+gammaln(w)-gammaln(z+w)
zpw = z + w zpw = z + w
return (stirlerr(z) + stirlerr(w) + 0.5 * log(2 * pi) + return (stirlerr(z) + stirlerr(w) + 0.5 * log(2 * pi) + (w - 0.5) * log(w)
(w - 0.5) * log(w) + (z - 0.5) * log(z) - stirlerr(zpw) - + (z - 0.5) * log(z) - stirlerr(zpw) - (zpw - 0.5) * log(zpw))
(zpw - 0.5) * log(zpw))
# y = gammaln(z)+gammaln(w)-gammaln(z+w)
# stirlings approximation: # stirlings approximation:
# (-(zpw-0.5).*log(zpw) +(w-0.5).*log(w)+(z-0.5).*log(z) +0.5*log(2*pi)) # (-(zpw-0.5).*log(zpw) +(w-0.5).*log(w)+(z-0.5).*log(z) +0.5*log(2*pi))
# return y # return y
@ -1973,8 +2077,8 @@ def gravity(phi=45):
''' '''
phir = phi * pi / 180. # change from degrees to radians phir = phi * pi / 180. # change from degrees to radians
return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2. - return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2.
0.0000059 * sin(2 * phir) ** 2.) - 0.0000059 * sin(2 * phir) ** 2.)
def nextpow2(x): def nextpow2(x):
@ -2035,7 +2139,6 @@ def discretize(fun, a, b, tol=0.005, n=5, method='linear'):
>>> np.allclose(xa[:5], [0., 0.19634954, 0.39269908, 0.58904862, 0.78539816]) >>> np.allclose(xa[:5], [0., 0.19634954, 0.39269908, 0.58904862, 0.78539816])
True True
t = plt.plot(x, y, xa, ya, 'r.') t = plt.plot(x, y, xa, ya, 'r.')
plt.show() plt.show()
plt.close('all') plt.close('all')
@ -2099,7 +2202,6 @@ def _discretize_adaptive(fun, a, b, tol=0.005, n=5):
abserr = np.abs(fy0 - fy) abserr = np.abs(fy0 - fy)
erri = 0.5 * (abserr / (np.abs(fy0) + np.abs(fy) + _TINY + tol)) erri = 0.5 * (abserr / (np.abs(fy0) + np.abs(fy) + _TINY + tol))
# abserr = np.abs(fy0 - fy)
# converged = abserr <= np.maximum(abseps, releps * abs(fy)) # converged = abserr <= np.maximum(abseps, releps * abs(fy))
# converged = abserr <= np.maximum(tol, tol * abs(fy)) # converged = abserr <= np.maximum(tol, tol * abs(fy))
err = erri.max() err = erri.max()
@ -2295,7 +2397,7 @@ def tranproc(x, f, x0, *xi):
x,f : array-like x,f : array-like
[x,f(x)], transform function, y = f(x). [x,f(x)], transform function, y = f(x).
x0, x1,...,xn : vectors x0, x1,...,xn : vectors
where xi is the i'th time derivative of x0. 0<=N<=4. where xi is the i'th time derivative of x0. 0<=n<=4.
Returns Returns
------- -------
@ -2337,21 +2439,21 @@ def tranproc(x, f, x0, *xi):
-------- --------
trangood. trangood.
""" """
def _default_step(xo, N): def _default_step(xo, num_derivatives):
hn = xo[1] - xo[0] hn = xo[1] - xo[0]
if hn ** N < sqrt(_EPS): if hn ** num_derivatives < sqrt(_EPS):
msg = ('Numerical problems may occur for the derivatives in ' + msg = ('Numerical problems may occur for the derivatives in ' +
'tranproc.\n' + 'tranproc.\n' +
'The sampling of the transformation may be too small.') 'The sampling of the transformation may be too small.')
warnings.warn(msg) warnings.warn(msg)
return hn return hn
def _diff(xo, fo, x0, N): def _diff(xo, fo, x0, num_derivatives):
hn = _default_step(xo, N) hn = _default_step(xo, num_derivatives)
# Transform X with the derivatives of f. # Transform X with the derivatives of f.
fder = vstack((xo, fo)) fder = vstack((xo, fo))
fxder = zeros((N, x0.size)) fxder = zeros((num_derivatives, x0.size))
for k in range(N): # Derivation of f(x) using a difference method. for k in range(num_derivatives): # Derivation of f(x) using a difference method.
n = fder.shape[-1] n = fder.shape[-1]
fder = vstack([(fder[0, 0:n - 1] + fder[0, 1:n]) / 2, fder = vstack([(fder[0, 0:n - 1] + fder[0, 1:n]) / 2,
diff(fder[1, :]) / hn]) diff(fder[1, :]) / hn])
@ -2386,8 +2488,8 @@ def tranproc(x, f, x0, *xi):
xi = atleast_1d(*xi) xi = atleast_1d(*xi)
if not isinstance(xi, list): if not isinstance(xi, list):
xi = [xi, ] xi = [xi, ]
N = len(xi) # N = number of derivatives num_derivatives = len(xi) # num_derivatives = number of derivatives
nmax = ceil((xo.ptp()) * 10 ** (7. / max(N, 1))) nmax = ceil((xo.ptp()) * 10 ** (7. / max(num_derivatives, 1)))
xo, fo = trangood(xo, fo, min_x=min(x0), max_x=max(x0), max_n=nmax) xo, fo = trangood(xo, fo, min_x=min(x0), max_x=max(x0), max_n=nmax)
n = f.shape[0] n = f.shape[0]
@ -2400,16 +2502,16 @@ def tranproc(x, f, x0, *xi):
y0 = fo[fi] + (fo[fi + 1] - fo[fi]) * xu y0 = fo[fi] + (fo[fi + 1] - fo[fi]) * xu
y = y0 y = y0
if N > 4: if num_derivatives > 4:
warnings.warn('Transformation of derivatives of order>4 is ' + warnings.warn('Transformation of derivatives of order>4 is ' +
'not supported.') 'not supported.')
N = 4 num_derivatives = 4
if N > 0: if num_derivatives > 0:
y = [y0] y = [y0]
fxder = _diff(xo, fo, x0, N) fxder = _diff(xo, fo, x0, num_derivatives)
# Calculate the transforms of the derivatives of X. # Calculate the transforms of the derivatives of X.
dfuns = [_der_1, _der_2, _der_3, _der_4] dfuns = [_der_1, _der_2, _der_3, _der_4]
for dfun in dfuns[:N]: for dfun in dfuns[:num_derivatives]:
y.append(dfun(fxder, xi)) y.append(dfun(fxder, xi))
return y return y
@ -2437,14 +2539,18 @@ def good_bins(data=None, range=None, num_bins=None, odd=False, loose=True): # @
Example Example
------- -------
>>> import wafo.misc as wm >>> import wafo.misc as wm
>>> wm.good_bins(range=(0,5), num_bins=6) >>> np.allclose(wm.good_bins(range=(0,5), num_bins=6),
array([-1., 0., 1., 2., 3., 4., 5., 6.]) ... [-1., 0., 1., 2., 3., 4., 5., 6.])
>>> wm.good_bins(range=(0,5), num_bins=6, loose=False) True
array([ 0., 1., 2., 3., 4., 5.]) >>> np.allclose(wm.good_bins(range=(0,5), num_bins=6, loose=False),
>>> wm.good_bins(range=(0,5), num_bins=6, odd=True) ... [ 0., 1., 2., 3., 4., 5.])
array([-1.5, -0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5]) True
>>> wm.good_bins(range=(0,5), num_bins=6, odd=True, loose=False) >>> np.allclose(wm.good_bins(range=(0,5), num_bins=6, odd=True),
array([-0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5]) ... [-1.5, -0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5])
True
>>> np.allclose(wm.good_bins(range=(0,5), num_bins=6, odd=True, loose=False),
... [-0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5])
True
''' '''
def _default_range(range_, x): def _default_range(range_, x):
return range_ if range_ else (x.min(), x.max()) return range_ if range_ else (x.min(), x.max())

60
wafo/spectrum/core.py
Unescape Escape View File

@ -135,7 +135,7 @@ def qtf(w, h=inf, g=9.81, method='winterstein', rtol=1e-7, atol=0):
>>> np.allclose(hd2, [[-2.50000000e-101, 2.54841998e-022, 2.54841998e-012, 2.54841998e-004], >>> np.allclose(hd2, [[-2.50000000e-101, 2.54841998e-022, 2.54841998e-012, 2.54841998e-004],
... [2.54841998e-022, -2.50000000e-101, 2.54836901e-012, 2.54841997e-004], ... [2.54841998e-022, -2.50000000e-101, 2.54836901e-012, 2.54841997e-004],
... [2.54841998e-012, 2.54836901e-012, -2.50000000e-101, 2.54791032e-004], ... [2.54841998e-012, 2.54836901e-012, -2.50000000e-101, 2.54791032e-004],
... [2.54841998e-004, 2.54841997e-004, 2.54791032e-004, -2.50000000e-101]], ... [2.54841998e-004, 2.54841997e-004, 2.54791032e-004, -2.500000e-101]],
... atol=0) ... atol=0)
True True
@ -175,9 +175,8 @@ def qtf(w, h=inf, g=9.81, method='winterstein', rtol=1e-7, atol=0):
h_dii = zeros(num_w) h_dii = zeros(num_w)
return h_s, h_d, h_dii return h_s, h_d, h_dii
w1 = w + _TINY **(1./10) * (np.sign(w) * np.int_(np.abs(w) < _EPS) + np.int_(w==0)) w1 = w + _TINY ** (1. / 10) * (np.sign(w) * np.int_(np.abs(w) < _EPS) + np.int_(w == 0))
# dw = w1-w
# print(dw)
w = w1 w = w1
# k_w += _TINY ** (1./3) * (np.sign(k_w) * np.int_(np.abs(k_w) < _EPS) + np.int_(k_w==0)) # k_w += _TINY ** (1./3) * (np.sign(k_w) * np.int_(np.abs(k_w) < _EPS) + np.int_(k_w==0))
k_w = w2k(w, theta=0, h=h, g=g, rtol=rtol, atol=atol)[0] k_w = w2k(w, theta=0, h=h, g=g, rtol=rtol, atol=atol)[0]
@ -194,10 +193,10 @@ def qtf(w, h=inf, g=9.81, method='winterstein', rtol=1e-7, atol=0):
if method.startswith('langley'): if method.startswith('langley'):
p_1 = (-2 * w1p2 * (k12 * g ** 2. - w12 ** 2.) + p_1 = (-2 * w1p2 * (k12 * g ** 2. - w12 ** 2.) +
w_1 * (w_2 ** 4. - g ** 2 * k_2 ** 2) + w_1 * (w_2 ** 4. - g ** 2 * k_2 ** 2) +
w_2 * (w_1 ** 4 - g * 2. * k_1 ** 2)) / (4. * w12 +_TINY) w_2 * (w_1 ** 4 - g * 2. * k_1 ** 2)) / (4. * w12 + _TINY)
p_2 = w1p2 ** 2. * cosh((k1p2) * h) - g * (k1p2) * sinh((k1p2) * h) p_2 = w1p2 ** 2. * cosh((k1p2) * h) - g * (k1p2) * sinh((k1p2) * h)
p_2 += _TINY * np.int_(p_2==0) p_2 += _TINY * np.int_(p_2 == 0)
h_s = (-p_1 / p_2 * w1p2 * cosh((k1p2) * h) / g - h_s = (-p_1 / p_2 * w1p2 * cosh((k1p2) * h) / g -
(k12 * g ** 2 - w12 ** 2.) / (4 * g * w12 + _TINY) + (k12 * g ** 2 - w12 ** 2.) / (4 * g * w12 + _TINY) +
@ -207,7 +206,7 @@ def qtf(w, h=inf, g=9.81, method='winterstein', rtol=1e-7, atol=0):
w_1 * (w_2 ** 4 - g ** 2 * k_2 ** 2) + w_1 * (w_2 ** 4 - g ** 2 * k_2 ** 2) +
w_2 * (w_1 ** 4 - g ** 2 * k_1 ** 2)) / (4. * w12 + _TINY) w_2 * (w_1 ** 4 - g ** 2 * k_1 ** 2)) / (4. * w12 + _TINY)
p_4 = w1m2 ** 2. * cosh(k1m2 * h) - g * (k1m2) * sinh((k1m2) * h) p_4 = w1m2 ** 2. * cosh(k1m2 * h) - g * (k1m2) * sinh((k1m2) * h)
p_4 += _TINY * np.int_(p_4==0) p_4 += _TINY * np.int_(p_4 == 0)
h_d = (-p_3 / p_4 * (w1m2) * cosh((k1m2) * h) / g - h_d = (-p_3 / p_4 * (w1m2) * cosh((k1m2) * h) / g -
(k12 * g ** 2 + w12 ** 2) / (4 * g * w12 + _TINY) + (k12 * g ** 2 + w12 ** 2) / (4 * g * w12 + _TINY) +
@ -224,7 +223,8 @@ def qtf(w, h=inf, g=9.81, method='winterstein', rtol=1e-7, atol=0):
tiny_diag = _TINY * np.diag(np.ones(num_w)) # Avoid division by zero on diagonal tiny_diag = _TINY * np.diag(np.ones(num_w)) # Avoid division by zero on diagonal
tmp3 = (w_1 ** 2 + w_2 ** 2 - w12) / g # OK tmp3 = (w_1 ** 2 + w_2 ** 2 - w12) / g # OK
numerator = (tmp1 - tmp3 - g * (w_1 * k_2 ** 2 - w_2 * k_1 ** 2) / (w12 * w1m2 + tiny_diag)) numerator = (tmp1 - tmp3 - g * (w_1 * k_2 ** 2
- w_2 * k_1 ** 2) / (w12 * w1m2 + tiny_diag))
h_d = 0.25 * (numerator / (1. - g * h * k1m2 / (w1m2 ** 2. + tiny_diag) * tanh(k1m2)) h_d = 0.25 * (numerator / (1. - g * h * k1m2 / (w1m2 ** 2. + tiny_diag) * tanh(k1m2))
+ tmp3 - 0.5 * tmp1) # OK + tmp3 - 0.5 * tmp1) # OK
@ -825,7 +825,7 @@ class SpecData1D(PlotData):
nt = rate * (n_f - 1) nt = rate * (n_f - 1)
else: # check if Nt is ok else: # check if Nt is ok
nt = minimum(nt, rate * (n_f - 1)) nt = minimum(nt, rate * (n_f - 1))
# nr, nt = int(nr), int(nt)
spec = self.copy() spec = self.copy()
spec.resample(dt) spec.resample(dt)
@ -990,10 +990,10 @@ class SpecData1D(PlotData):
iseed : scalar integer iseed : scalar integer
starting seed number for the random number generator starting seed number for the random number generator
(default none is set) (default none is set)
fnLimit : real scalar fn_limit : real scalar
normalized upper frequency limit of spectrum for 2'nd order normalized upper frequency limit of spectrum for 2'nd order
components. The frequency is normalized with components. The frequency is normalized with
sqrt(gravity*tanh(kbar*water_depth)/Amax)/(2*pi) sqrt(gravity*tanh(kbar*water_depth)/a_max)/(2*pi)
(default sqrt(2), i.e., Convergence criterion). (default sqrt(2), i.e., Convergence criterion).
Generally this should be the same as used in the final Generally this should be the same as used in the final
non-linear simulation (see example below). non-linear simulation (see example below).
@ -1066,7 +1066,7 @@ class SpecData1D(PlotData):
max_sim = 30 max_sim = 30
tolerance = 5e-4 tolerance = 5e-4
L = 200 # maximum lag size of the window function used in estimate max_lag = 200 # maximum lag size of the window function used in estimate
# ftype = self.freqtype #options are 'f' and 'w' and 'k' # ftype = self.freqtype #options are 'f' and 'w' and 'k'
# switch ftype # switch ftype
# case 'f', # case 'f',
@ -1094,9 +1094,9 @@ class SpecData1D(PlotData):
# Expected maximum amplitude for 10000 waves seastate # Expected maximum amplitude for 10000 waves seastate
num_waves = 10000 # Typical number of waves in 30 hour seastate num_waves = 10000 # Typical number of waves in 30 hour seastate
Amax = sqrt(2 * log(num_waves)) * Hm0 / 4 a_max = sqrt(2 * log(num_waves)) * Hm0 / 4
fLimitLo = sqrt(gravity * tanh(kbar * water_depth) * Amax / water_depth ** 3) f_limit_lo = sqrt(gravity * tanh(kbar * water_depth) * a_max / water_depth ** 3)
freq = S.args freq = S.args
eps = finfo(float).eps eps = finfo(float).eps
@ -1105,11 +1105,11 @@ class SpecData1D(PlotData):
SL = S SL = S
indZero = nonzero(freq < fLimitLo)[0] ind_zero = nonzero(freq < f_limit_lo)[0]
if len(indZero): if len(ind_zero):
SL.data[indZero] = 0 SL.data[ind_zero] = 0
maxS = max(S.data) max_spec = max(S.data)
# Fs = 2*freq(end)+eps # sampling frequency # Fs = 2*freq(end)+eps # sampling frequency
for ix in range(max_sim): for ix in range(max_sim):
@ -1117,12 +1117,12 @@ class SpecData1D(PlotData):
method=method, fnlimit=fn_limit, method=method, fnlimit=fn_limit,
output='timeseries') output='timeseries')
x2.data -= x1.data # x2(:,2:end) = x2(:,2:end) -x1(:,2:end) x2.data -= x1.data # x2(:,2:end) = x2(:,2:end) -x1(:,2:end)
S2 = x2.tospecdata(L) S2 = x2.tospecdata(max_lag)
S1 = x1.tospecdata(L) S1 = x1.tospecdata(max_lag)
# TODO: Finish spec.to_linspec # TODO: Finish spec.to_linspec
# S2 = dat2spec(x2, L) # S2 = dat2spec(x2, max_lag)
# S1 = dat2spec(x1, L) # S1 = dat2spec(x1, max_lag)
# %[tf21,fi] = tfe(x2(:,2),x1(:,2),1024,Fs,[],512) # %[tf21,fi] = tfe(x2(:,2),x1(:,2),1024,Fs,[],512)
# %Hw11 = interp1q(fi,tf21.*conj(tf21),freq) # %Hw11 = interp1q(fi,tf21.*conj(tf21),freq)
if True: if True:
@ -1144,8 +1144,8 @@ class SpecData1D(PlotData):
SL.data = (Hw1 * S.data) SL.data = (Hw1 * S.data)
if len(indZero): if len(ind_zero):
SL.data[indZero] = 0 SL.data[ind_zero] = 0
# end # end
k = nonzero(SL.data < 0)[0] k = nonzero(SL.data < 0)[0]
if len(k): # Make sure that the current guess is larger than zero if len(k): # Make sure that the current guess is larger than zero
@ -1176,17 +1176,17 @@ class SpecData1D(PlotData):
# figtile # figtile
# end # end
print('Iteration : %d, Hw12 : %g Hw12/maxS : %g' % print('Iteration : %d, Hw12 : %g Hw12/max_spec : %g' %
(ix, maxHw12, (maxHw12 / maxS))) (ix, maxHw12, (maxHw12 / max_spec)))
if (maxHw12 < maxS * tolerance) and (Hw1[-1] < Hw2[-1]): if (maxHw12 < max_spec * tolerance) and (Hw1[-1] < Hw2[-1]):
break break
# end # end
Hw2 = Hw1 Hw2 = Hw1
# end # end
# Hw1(end) # Hw1(end)
# maxS*1e-3 # max_spec*1e-3
# if Hw1[-1]*S.data>maxS*1e-3, # if Hw1[-1]*S.data>max_spec*1e-3,
# warning('The Nyquist frequency of the spectrum may be too low') # warning('The Nyquist frequency of the spectrum may be too low')
# end # end
@ -1837,7 +1837,7 @@ class SpecData1D(PlotData):
# end # end
try: try:
f.cl, f.pl = qlevels(f.f, [10, 30, 50, 70, 90, 95, 99, 99.9], f.cl, f.pl = qlevels(f.data, [10, 30, 50, 70, 90, 95, 99, 99.9],
f.args[0], f.args[1]) f.args[0], f.args[1])
except Exception: except Exception:
warnings.warn('Singularity likely in pdf') warnings.warn('Singularity likely in pdf')

95
wafo/stats/core.py
Unescape Escape View File

@ -28,7 +28,6 @@ def now():
def valarray(shape, value=nan, typecode=None): def valarray(shape, value=nan, typecode=None):
"""Return an array of all value. """Return an array of all value.
""" """
#out = reshape(repeat([value], product(shape, axis=0), axis=0), shape)
out = ones(shape, dtype=bool) * value out = ones(shape, dtype=bool) * value
if typecode is not None: if typecode is not None:
out = out.astype(typecode) out = out.astype(typecode)
@ -37,7 +36,7 @@ def valarray(shape, value=nan, typecode=None):
return out return out
def _cdff(self, x, dfn, dfd): def _cdff(x, dfn, dfd):
return special.fdtr(dfn, dfd, x) return special.fdtr(dfn, dfd, x)
@ -91,17 +90,15 @@ def edf(x, method=2):
z = atleast_1d(x) z = atleast_1d(x)
z.sort() z.sort()
N = len(z) n = len(z)
if method == 1: if method == 1:
Fz1 = arange(0.5, N) / N e_cdf = arange(0.5, n) / n
elif method == 3: elif method == 3:
Fz1 = arange(1, N + 1) / N e_cdf = arange(1, n + 1) / n
else: else:
Fz1 = arange(1, N + 1) / (N + 1) e_cdf = arange(1, n + 1) / (n + 1)
F = PlotData(Fz1, z, xlab='x', ylab='F(x)') return PlotData(e_cdf, z, xlab='x', ylab='F(x)', plotmethod='step')
F.setplotter('step')
return F
def edfcnd(x, c=None, method=2): def edfcnd(x, c=None, method=2):
@ -113,9 +110,9 @@ def edfcnd(x, c=None, method=2):
x : array-like x : array-like
data vector data vector
method : integer scalar method : integer scalar
1. Interpolation so that F(X_(k)) == (k-0.5)/n. 1. Interpolation so that cdf(X_(k)) == (k-0.5)/n.
2. Interpolation so that F(X_(k)) == k/(n+1). (default) 2. Interpolation so that cdf(X_(k)) == k/(n+1). (default)
3. The empirical distribution. F(X_(k)) = k/n 3. The empirical distribution. cdf(X_(k)) = k/n
Example Example
------- -------
@ -124,8 +121,8 @@ def edfcnd(x, c=None, method=2):
>>> R = ws.rayleigh.rvs(scale=2,size=100) >>> R = ws.rayleigh.rvs(scale=2,size=100)
>>> Fc = ws.edfcnd(R, 1) >>> Fc = ws.edfcnd(R, 1)
>>> hc = Fc.plot() >>> hc = Fc.plot()
>>> F = ws.edf(R) >>> cdf = ws.edf(R)
>>> h = F.plot() >>> h = cdf.plot()
See also edf, pdfplot, cumtrapz See also edf, pdfplot, cumtrapz
""" """
@ -133,15 +130,13 @@ def edfcnd(x, c=None, method=2):
if c is None: if c is None:
c = floor(min(z.min(), 0)) c = floor(min(z.min(), 0))
try: cdf = edf(z[c <= z], method=method)
F = edf(z[c <= z], method=method)
except:
ValueError('No data points above c=%d' % int(c))
if - inf < c: if - inf < c:
F.labels.ylab = 'F(x| X>=%g)' % c cdf.labels.ylab = 'F(x| X>=%g)' % c
return cdf
return F
def _check_nmin(nmin, n): def _check_nmin(nmin, n):
nmin = max(nmin, 1) nmin = max(nmin, 1)
@ -149,6 +144,7 @@ def _check_nmin(nmin, n):
warnings.warn('nmin possibly too large!') warnings.warn('nmin possibly too large!')
return nmin return nmin
def _check_umin_umax(data, umin, umax, nmin): def _check_umin_umax(data, umin, umax, nmin):
sd = np.sort(data) sd = np.sort(data)
sdmax, sdmin = sd[-nmin], sd[0] sdmax, sdmin = sd[-nmin], sd[0]
@ -156,11 +152,13 @@ def _check_umin_umax(data, umin, umax, nmin):
umin = sdmin if umin is None else max(umin, sdmin) umin = sdmin if umin is None else max(umin, sdmin)
return umin, umax return umin, umax
def _check_nu(nu, nmin, n): def _check_nu(nu, nmin, n):
if nu is None: if nu is None:
nu = min(n - nmin, 100) nu = min(n - nmin, 100)
return nu return nu
def reslife(data, u=None, umin=None, umax=None, nu=None, nmin=3, alpha=0.05, def reslife(data, u=None, umin=None, umax=None, nu=None, nmin=3, alpha=0.05,
plotflag=False): plotflag=False):
""" """
@ -227,7 +225,9 @@ def reslife(data, u=None, umin=None, umax=None, nu=None, nmin=3, alpha=0.05,
# srl = valarray(nu) # srl = valarray(nu)
# num = valarray(nu) # num = valarray(nu)
mean_and_std = lambda data1: (data1.mean(), data1.std(), data1.size) def mean_and_std(data1):
return data1.mean(), data1.std(), data1.size
dat = arr(data) dat = arr(data)
tmp = arr([mean_and_std(dat[dat > tresh] - tresh) for tresh in u.tolist()]) tmp = arr([mean_and_std(dat[dat > tresh] - tresh) for tresh in u.tolist()])
@ -236,20 +236,18 @@ def reslife(data, u=None, umin=None, umax=None, nu=None, nmin=3, alpha=0.05,
alpha2 = alpha / 2 alpha2 = alpha / 2
# Approximate P% confidence interval # Approximate P% confidence interval
# Za = -invnorm(alpha2); % known mean # z_a = -invnorm(alpha2); % known mean
Za = -_invt(alpha2, num - 1) # unknown mean z_a = -_invt(alpha2, num - 1) # unknown mean
mrlu = mrl + Za * srl / sqrt(num) mrlu = mrl + z_a * srl / sqrt(num)
mrll = mrl - Za * srl / sqrt(num) mrll = mrl - z_a * srl / sqrt(num)
# options.CI = [mrll,mrlu]; title_txt = 'Mean residual life with %d%s CI' % (100 * p, '%')
# options.numdata = num;
titleTxt = 'Mean residual life with %d%s CI' % (100 * p, '%')
res = PlotData(mrl, u, xlab='Threshold', res = PlotData(mrl, u, xlab='Threshold',
ylab='Mean Excess', title=titleTxt) ylab='Mean Excess', title=title_txt)
res.workspace = dict( res.workspace = dict(
numdata=num, umin=umin, umax=umax, nu=nu, nmin=nmin, alpha=alpha) numdata=num, umin=umin, umax=umax, nu=nu, nmin=nmin, alpha=alpha)
res.children = [ res.children = [
PlotData(vstack([mrll, mrlu]).T, u, xlab='Threshold', title=titleTxt)] PlotData(vstack([mrll, mrlu]).T, u, xlab='Threshold', title=title_txt)]
res.plot_args_children = [':r'] res.plot_args_children = [':r']
if plotflag: if plotflag:
res.plot() res.plot()
@ -390,11 +388,11 @@ def dispersion_idx(
b_u, ok_u = _find_appropriate_threshold(u, di, di_low, di_up) b_u, ok_u = _find_appropriate_threshold(u, di, di_low, di_up)
ci_txt = '{0:d}{1} CI'.format(100 * p, '%') ci_txt = '{0:d}{1} CI'.format(100 * p, '%')
titleTxt = 'Dispersion Index plot' title_txt = 'Dispersion Index plot'
res = PlotData(di, u, title=titleTxt, res = PlotData(di, u, title=title_txt,
labx='Threshold', laby='Dispersion Index') labx='Threshold', laby='Dispersion Index')
#'caption',ci_txt);
res.workspace = dict(umin=umin, umax=umax, nu=nu, nmin=nmin, alpha=alpha) res.workspace = dict(umin=umin, umax=umax, nu=nu, nmin=nmin, alpha=alpha)
res.children = [ res.children = [
PlotData(vstack([di_low * ones(nu), di_up * ones(nu)]).T, u, PlotData(vstack([di_low * ones(nu), di_up * ones(nu)]).T, u,
@ -448,7 +446,6 @@ def decluster(data, t=None, thresh=None, tmin=1):
return data[i], t[i] return data[i], t[i]
def _remove_index_to_data_too_close_to_each_other(ix_e, is_too_small, di_e, ti_e, tmin): def _remove_index_to_data_too_close_to_each_other(ix_e, is_too_small, di_e, ti_e, tmin):
is_too_close = np.hstack((is_too_small[0], is_too_small[:-1] | is_too_small[1:], is_too_close = np.hstack((is_too_small[0], is_too_small[:-1] | is_too_small[1:],
is_too_small[-1])) is_too_small[-1]))
@ -759,18 +756,18 @@ class RegLogit(object):
See also regglm, reglm, regnonlm See also regglm, reglm, regnonlm
""" """
#% Original for MATLAB written by Gordon K Smyth <gks@maths.uq.oz.au>, # Original for MATLAB written by Gordon K Smyth <gks@maths.uq.oz.au>,
#% U of Queensland, Australia, on Nov 19, 1990. Last revision Aug 3, # U of Queensland, Australia, on Nov 19, 1990. Last revision Aug 3,
#% 1992. # 1992.
# #
#% Author: Gordon K Smyth <gks@maths.uq.oz.au>, # Author: Gordon K Smyth <gks@maths.uq.oz.au>,
#% Revised by: pab # Revised by: pab
#% -renamed from oridinal to reglogit # -renamed from oridinal to reglogit
#% -added predict, summary and compare # -added predict, summary and compare
#% Description: Ordinal logistic regression # Description: Ordinal logistic regression
# #
#% Uses the auxiliary functions logistic_regression_derivatives and # Uses the auxiliary functions logistic_regression_derivatives and
#% logistic_regression_likelihood. # logistic_regression_likelihood.
def __init__(self, maxiter=500, accuracy=1e-6, alpha=0.05, def __init__(self, maxiter=500, accuracy=1e-6, alpha=0.05,
deletecolinear=True, verbose=False): deletecolinear=True, verbose=False):
@ -939,7 +936,7 @@ class RegLogit(object):
break break
# end %while # end %while
#% tidy up output # tidy up output
theta = tb[:nz, ] theta = tb[:nz, ]
beta = tb[nz:(nz + nx)] beta = tb[nz:(nz + nx)]
@ -1204,7 +1201,7 @@ class RegLogit(object):
R = np.dot(U, np.dot(np.diag(sqrt(S)), V)) R = np.dot(U, np.dot(np.diag(sqrt(S)), V))
ib = np.r_[0, nz:np1] ib = np.r_[0, nz:np1]
#% Var(eta_i) = var(theta_i+Xnew*b) # Var(eta_i) = var(theta_i+Xnew*b)
vareta = zeros((n, nz)) vareta = zeros((n, nz))
u = np.hstack((one, Xnew)) u = np.hstack((one, Xnew))
for i in range(nz): for i in range(nz):
@ -1317,7 +1314,7 @@ def test_reglogit():
x = np.arange(1, 11).reshape(-1, 1) x = np.arange(1, 11).reshape(-1, 1)
b = RegLogit() b = RegLogit()
b.fit(y, x) b.fit(y, x)
# b.display() #% members and methods # b.display() # members and methods
b.summary() b.summary()
[mu, plo, pup] = b.predict(fulloutput=True) # @UnusedVariable [mu, plo, pup] = b.predict(fulloutput=True) # @UnusedVariable
@ -1331,7 +1328,7 @@ def test_reglogit2():
y = (np.cos(x) > 2 * np.random.rand(n, 1) - 1) y = (np.cos(x) > 2 * np.random.rand(n, 1) - 1)
b = RegLogit() b = RegLogit()
b.fit(y, x) b.fit(y, x)
# b.display() #% members and methods # b.display() # members and methods
b.summary() b.summary()
[mu, plo, pup] = b.predict(fulloutput=True) [mu, plo, pup] = b.predict(fulloutput=True)
import matplotlib.pyplot as pl import matplotlib.pyplot as pl

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