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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:
return x.reshape(no_leading_ones(x.shape))
elif n >= 0:
return x.transpose(np.roll(range(x.ndim), -n))
return x.reshape((1,) * -n + x.shape)
return x.transpose(np.roll(range(x.ndim), -1 * n))
return x.reshape((1,) * abs(n) + x.shape)
def example_dct2(debug=True):

380
wafo/misc.py
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@ -7,14 +7,13 @@ import collections
from wafo import numba_misc
import fractions
import numpy as np
from numpy import (
meshgrid,
amax, logical_and, arange, linspace, atleast_1d,
from numpy import (amax, logical_and, arange, linspace, atleast_1d,
asarray, ceil, floor, frexp, hypot,
sqrt, arctan2, sin, cos, exp, log, log1p, mod, diff,
inf, pi, interp, isscalar, zeros, ones,
sign, unique, hstack, vstack, nonzero, where, extract)
from scipy.special import gammaln
sign, unique, hstack, vstack, nonzero, where, extract,
meshgrid)
from scipy.special import gammaln # pylint: disable=no-name-in-module
from scipy.integrate import trapz, simps
import warnings
from time import strftime, gmtime
@ -25,7 +24,6 @@ try:
except ImportError:
warnings.warn('c_library not found. Check its compilation.')
clib = None
FLOATINFO = np.finfo(float)
_TINY = FLOATINFO.tiny
_EPS = FLOATINFO.eps
@ -41,8 +39,10 @@ __all__ = ['now', 'spaceline', 'narg_smallest', 'args_flat', 'is_numlike',
'meshgrid', 'ndgrid', 'trangood', 'tranproc',
'plot_histgrm', 'num2pistr', 'test_docstrings',
'lazywhere', 'lazyselect',
'valarray', 'lfind',
'moving_average',
'piecewise',
'valarray', 'check_random_state']
'check_random_state']
def xor(a, b):
@ -52,6 +52,41 @@ def xor(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):
"""Turn seed into a np.random.RandomState instance
@ -82,16 +117,10 @@ def check_random_state(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.
"""
if typecode is None:
typecode = bool
out = ones(shape, dtype=typecode) * value
if not isinstance(out, np.ndarray):
out = asarray(out)
return out
return np.full(shape, fill_value=value, dtype=typecode)
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
``x >= 0``.
>>> 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])
>>> np.allclose(piecewise([x < 0, x >= 0], [lambda x: -x, lambda x: x], xi=(x,)),
... [ 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
``x*y >= 0``
>>> X, Y = np.meshgrid(x, x)
>>> piecewise([X * Y < 0, ], [lambda x, y: -x * y, lambda x, y: x * y],
... xi=(X, Y))
array([[ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25],
[ 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],
[ 3.75, 2.25, 0.75, 0.75, 2.25, 3.75],
[ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25]])
>>> np.allclose(piecewise([X * Y < 0, ], [lambda x, y: -x * y,
... lambda x, y: x * y], xi=(X, Y)),
... [[ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25],
... [ 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],
... [ 3.75, 2.25, 0.75, 0.75, 2.25, 3.75],
... [ 6.25, 3.75, 1.25, 1.25, 3.75, 6.25]])
True
"""
def otherwise_condition(condlist):
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)
if len(condlist) == len(funclist) - 1:
condlist.append(otherwise_condition(condlist))
if xi is None:
arrays = ()
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)
shape = arrays[0].shape
out = valarray(shape, fillvalue, dtype)
out = np.full(shape, fillvalue, dtype)
for cond, func in zip(condlist, funclist):
if cond.any():
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])
>>> def f(a, b):
... return a*b
>>> lazywhere(a > 2, (a, b), f, np.nan)
array([ nan, nan, 21., 32.])
>>> r = lazywhere(a > 2, (a, b), f, np.nan)
>>> np.allclose(r[2:], [21., 32.]); np.all(np.isnan(r[:2]))
True
True
>>> def f2(a, b):
... return (a*b)**2
>>> lazywhere(a > 2, (a, b), f, f2=f2)
array([ 25., 144., 21., 32.])
>>> np.allclose(lazywhere(a > 2, (a, b), f, f2=f2),
... [ 25., 144., 21., 32.])
True
Notice it assumes that all `arrays` are of the same shape, or can be
broadcasted together.
@ -250,7 +285,7 @@ def lazywhere(cond, arrays, f, fillvalue=None, f2=None):
arrays = np.broadcast_arrays(*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))
if f2 is not None:
temp = tuple(np.extract(~cond, arr) for arr in arrays)
@ -309,11 +344,11 @@ def rotation_matrix(heading, pitch, roll):
Examples
--------
>>> import numpy as np
>>> rotation_matrix(heading=0, pitch=0, roll=0)
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
>>> np.allclose(rotation_matrix(heading=0, pitch=0, roll=0),
... [[ 1., 0., 0.],
... [ 0., 1., 0.],
... [ 0., 0., 1.]])
True
>>> np.allclose(rotation_matrix(heading=180, pitch=0, roll=0),
... [[ -1., 0., 0.],
... [ 0., -1., 0.],
@ -438,12 +473,20 @@ def spaceline(start_point, stop_point, num=10):
Example
-------
>>> import wafo.misc as pm
>>> pm.spaceline((2,0,0), (3,0,0), num=5)
array([[ 2. , 0. , 0. ],
[ 2.25, 0. , 0. ],
[ 2.5 , 0. , 0. ],
[ 2.75, 0. , 0. ],
[ 3. , 0. , 0. ]])
>>> np.allclose(pm.spaceline((2,0,0), (3,0,0), num=5),
... [[ 2. , 0. , 0. ],
... [ 2.25, 0. , 0. ],
... [ 2.5 , 0. , 0. ],
... [ 2.75, 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)
start, stop = np.atleast_1d(start_point, stop_point)
@ -615,6 +658,8 @@ def is_numlike(obj):
True
>>> is_numlike('1')
False
>>> is_numlike([1])
False
"""
try:
obj + 1
@ -670,13 +715,13 @@ class Bunch(object):
Example
-------
>>> d = Bunch(test1=1,test2=3)
>>> d.test1
1
>>> (d.test1, d.test2)
(1, 3)
>>> sorted(d.keys()) == ['test1', 'test2']
True
>>> d.update(test1=2)
>>> d.test1
2
>>> d.update(test1=5)
>>> (d.test1, d.test2)
(5, 3)
'''
def __init__(self, **kwargs):
@ -703,7 +748,7 @@ def sub_dict_select(somedict, somekeys):
# the keyword exists in options
>>> opt = dict(arg1=2, arg2=3)
>>> 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 == {'arg1': 2, 'arg2': 100}
True
@ -713,7 +758,7 @@ def sub_dict_select(somedict, somekeys):
dict_intersection
'''
# 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):
@ -731,13 +776,91 @@ def parse_kwargs(options, **kwargs):
See also sub_dict_select
'''
newopts = sub_dict_select(kwargs, options.keys())
newopts = sub_dict_select(kwargs, options)
if len(newopts) > 0:
options.update(newopts)
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
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
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
-------
@ -760,11 +885,12 @@ def detrendma(x, L):
>>> import numpy as np
>>> import wafo.misc as wm
>>> exp = np.exp; cos = np.cos; randn = np.random.randn
>>> x = np.linspace(0,1,200)
>>> noise = 0.1*randn(x.size)
>>> noise = 0.1*np.sin(100*x)
>>> y = exp(x)+cos(5*2*pi*x) + noise
>>> y0 = wm.detrendma(y,20)
>>> y0 = wm.detrendma(y, 20)
>>> tr = y-y0
>>> np.allclose(tr[:5],
... [ 1.14134814, 1.14134814, 1.14134814, 1.14134814, 1.14134814])
@ -781,28 +907,11 @@ def detrendma(x, L):
See also
--------
Reconstruct
Reconstruct, moving_average
"""
_assert(0 < L, 'L must be positive')
_assert(L == np.round(L), 'L must be an integer')
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
x1 = np.atleast_1d(x)
trend = moving_average(x1, L, axis)
return x1 - trend
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
'''
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 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
>>> np.allclose(ind, [ 9, 25, 80, 97, 151, 168, 223, 239])
True
>>> ind2 = wm.findcross(x,v,'u')
>>> np.allclose(ind2, [ 9, 80, 151, 223])
True
@ -940,7 +1050,6 @@ def findcross(x, v=0.0, kind=None, method='clib'):
# if kind=='dw' or kind=='tw'
# or that the first is a level v up-crossing
# if kind=='uw' or kind=='cw'
first_is_down_crossing = int(xn[ind[0]] > xn[ind[0] + 1])
if xor(first_is_down_crossing, kind in ('dw', 'tw')):
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
y = y[t_start::]
n = len(y)
NC = np.floor(n / 2) - 1
NC = np.floor(n // 2) - 1
if (NC < 1):
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)
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)
else:
if isinstance(method, str):
@ -1218,25 +1327,23 @@ def rfcfilter(x, h, method=0):
>>> import wafo.misc as wm
>>> x = data.sea()
>>> y = wm.rfcfilter(x[:,1], h=0, method=1)
>>> np.all(np.abs(y[0:5]-np.array([-1.2004945 , 0.83950546, -0.09049454,
... -0.02049454, -0.09049454]))<1e-7)
>>> np.allclose(y[0:5], [-1.2004945 , 0.83950546, -0.09049454, -0.02049454, -0.09049454])
True
>>> np.allclose(y.shape, (2172,))
True
>>> y.shape
(2172,)
# 2. This removes all rainflow cycles with range less than 0.5.
>>> y1 = wm.rfcfilter(x[:,1], h=0.5)
>>> y1.shape
(863,)
>>> np.all(np.abs(y1[0:5]-np.array([-1.2004945 , 0.83950546, -0.43049454,
... 0.34950546, -0.51049454]))<1e-7)
>>> np.allclose(y1.shape, (863,))
True
>>> np.allclose(y1[0:5], [-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454])
True
>>> ind = wm.findtp(x[:,1], h=0.5)
>>> y2 = x[ind,1]
>>> y2[0:5]
array([-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454])
>>> y2[-5::]
array([ 0.83950546, -0.64049454, 0.65950546, -1.0004945 , 0.91950546])
>>> np.allclose(y2[0:5], [-1.2004945 , 0.83950546, -0.43049454, 0.34950546, -0.51049454])
True
>>> np.allclose(y2[-5::], [ 0.83950546, -0.64049454, 0.65950546, -1.0004945 , 0.91950546])
True
See also
--------
@ -1609,10 +1716,10 @@ def common_shape(*args, ** kwds):
>>> A = np.ones((4,1))
>>> B = 2
>>> C = np.ones((1,5))*5
>>> wm.common_shape(A,B,C)
(4, 5)
>>> wm.common_shape(A,B,C,shape=(3,4,1))
(3, 4, 5)
>>> np.allclose(wm.common_shape(A,B,C), (4, 5))
True
>>> np.allclose(wm.common_shape(A,B,C,shape=(3,4,1)), (3, 4, 5))
True
See also
--------
@ -1652,12 +1759,12 @@ def argsreduce(condition, * args):
>>> C = rand((1,5))
>>> cond = np.ones(A.shape)
>>> [A1,B1,C1] = wm.argsreduce(cond,A,B,C)
>>> B1.shape
(20,)
>>> np.allclose(B1.shape, (20,))
True
>>> cond[2,:] = 0
>>> [A2,B2,C2] = wm.argsreduce(cond,A,B,C)
>>> B2.shape
(15,)
>>> np.allclose(B2.shape, (15,))
True
See also
--------
@ -1794,7 +1901,7 @@ def getshipchar(**ship_property):
... 'lengthSTD': 2.0113098831942762,
... 'draught': 9.5999999999999996,
... 'propeller_diameterSTD': 0.20267047566705432,
... 'max_deadweightSTD': 3096.9000000000001,
... 'max_deadweight_std': 3096.9000000000001,
... 'beam': 29.0, 'length': 216.0,
... 'beamSTD': 2.9000000000000004,
... 'service_speed': 10.0,
@ -1818,7 +1925,7 @@ def getshipchar(**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_err = length ** 0.13
@ -1837,18 +1944,16 @@ def getshipchar(**ship_property):
p_diam_err = 0.12 * length_err ** (3.0 / 4.0)
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,
draught=draught, draughtSTD=draught_err,
length=length, lengthSTD=length_err,
max_deadweight=max_deadweight,
max_deadweightSTD=max_deadweightSTD,
propeller_diameter=p_diam,
propeller_diameterSTD=p_diam_err,
max_deadweight=max_deadweight, max_deadweightSTD=max_deadweight_std,
propeller_diameter=p_diam, propeller_diameterSTD=p_diam_err,
service_speed=speed, service_speedSTD=speed_err)
shipchar[propertySTD] = 0
shipchar[property_std] = 0
return shipchar
@ -1874,8 +1979,8 @@ def binomln(z, w):
Example
-------
>>> np.abs(binomln(3,2)- 1.09861229)<1e-7
array([ True], dtype=bool)
>>> np.allclose(binomln(3,2), 1.09861229)
True
See also
--------
@ -1918,12 +2023,11 @@ def betaloge(z, w):
--------
betaln, beta
'''
# y = gammaln(z)+gammaln(w)-gammaln(z+w)
zpw = z + w
return (stirlerr(z) + stirlerr(w) + 0.5 * log(2 * pi) +
(w - 0.5) * log(w) + (z - 0.5) * log(z) - stirlerr(zpw) -
(zpw - 0.5) * log(zpw))
return (stirlerr(z) + stirlerr(w) + 0.5 * log(2 * pi) + (w - 0.5) * log(w)
+ (z - 0.5) * log(z) - stirlerr(zpw) - (zpw - 0.5) * log(zpw))
# y = gammaln(z)+gammaln(w)-gammaln(z+w)
# stirlings approximation:
# (-(zpw-0.5).*log(zpw) +(w-0.5).*log(w)+(z-0.5).*log(z) +0.5*log(2*pi))
# return y
@ -1973,8 +2077,8 @@ def gravity(phi=45):
'''
phir = phi * pi / 180. # change from degrees to radians
return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2. -
0.0000059 * sin(2 * phir) ** 2.)
return 9.78049 * (1. + 0.0052884 * sin(phir) ** 2.
- 0.0000059 * sin(2 * phir) ** 2.)
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])
True
t = plt.plot(x, y, xa, ya, 'r.')
plt.show()
plt.close('all')
@ -2099,7 +2202,6 @@ def _discretize_adaptive(fun, a, b, tol=0.005, n=5):
abserr = np.abs(fy0 - fy)
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(tol, tol * abs(fy))
err = erri.max()
@ -2295,7 +2397,7 @@ def tranproc(x, f, x0, *xi):
x,f : array-like
[x,f(x)], transform function, y = f(x).
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
-------
@ -2337,21 +2439,21 @@ def tranproc(x, f, x0, *xi):
--------
trangood.
"""
def _default_step(xo, N):
def _default_step(xo, num_derivatives):
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 ' +
'tranproc.\n' +
'The sampling of the transformation may be too small.')
warnings.warn(msg)
return hn
def _diff(xo, fo, x0, N):
hn = _default_step(xo, N)
def _diff(xo, fo, x0, num_derivatives):
hn = _default_step(xo, num_derivatives)
# Transform X with the derivatives of f.
fder = vstack((xo, fo))
fxder = zeros((N, x0.size))
for k in range(N): # Derivation of f(x) using a difference method.
fxder = zeros((num_derivatives, x0.size))
for k in range(num_derivatives): # Derivation of f(x) using a difference method.
n = fder.shape[-1]
fder = vstack([(fder[0, 0:n - 1] + fder[0, 1:n]) / 2,
diff(fder[1, :]) / hn])
@ -2386,8 +2488,8 @@ def tranproc(x, f, x0, *xi):
xi = atleast_1d(*xi)
if not isinstance(xi, list):
xi = [xi, ]
N = len(xi) # N = number of derivatives
nmax = ceil((xo.ptp()) * 10 ** (7. / max(N, 1)))
num_derivatives = len(xi) # num_derivatives = number of derivatives
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)
n = f.shape[0]
@ -2400,16 +2502,16 @@ def tranproc(x, f, x0, *xi):
y0 = fo[fi] + (fo[fi + 1] - fo[fi]) * xu
y = y0
if N > 4:
if num_derivatives > 4:
warnings.warn('Transformation of derivatives of order>4 is ' +
'not supported.')
N = 4
if N > 0:
num_derivatives = 4
if num_derivatives > 0:
y = [y0]
fxder = _diff(xo, fo, x0, N)
fxder = _diff(xo, fo, x0, num_derivatives)
# Calculate the transforms of the derivatives of X.
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))
return y
@ -2437,14 +2539,18 @@ def good_bins(data=None, range=None, num_bins=None, odd=False, loose=True): # @
Example
-------
>>> import wafo.misc as wm
>>> wm.good_bins(range=(0,5), num_bins=6)
array([-1., 0., 1., 2., 3., 4., 5., 6.])
>>> wm.good_bins(range=(0,5), num_bins=6, loose=False)
array([ 0., 1., 2., 3., 4., 5.])
>>> wm.good_bins(range=(0,5), num_bins=6, odd=True)
array([-1.5, -0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5])
>>> wm.good_bins(range=(0,5), num_bins=6, odd=True, loose=False)
array([-0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5])
>>> np.allclose(wm.good_bins(range=(0,5), num_bins=6),
... [-1., 0., 1., 2., 3., 4., 5., 6.])
True
>>> np.allclose(wm.good_bins(range=(0,5), num_bins=6, loose=False),
... [ 0., 1., 2., 3., 4., 5.])
True
>>> np.allclose(wm.good_bins(range=(0,5), num_bins=6, odd=True),
... [-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):
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],
... [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-004, 2.54841997e-004, 2.54791032e-004, -2.50000000e-101]],
... [2.54841998e-004, 2.54841997e-004, 2.54791032e-004, -2.500000e-101]],
... atol=0)
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)
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))
# dw = w1-w
# print(dw)
w1 = w + _TINY ** (1. / 10) * (np.sign(w) * np.int_(np.abs(w) < _EPS) + np.int_(w == 0))
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 = 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'):
p_1 = (-2 * w1p2 * (k12 * g ** 2. - w12 ** 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 += _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 -
(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_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 += _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 -
(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
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))
+ tmp3 - 0.5 * tmp1) # OK
@ -825,7 +825,7 @@ class SpecData1D(PlotData):
nt = rate * (n_f - 1)
else: # check if Nt is ok
nt = minimum(nt, rate * (n_f - 1))
# nr, nt = int(nr), int(nt)
spec = self.copy()
spec.resample(dt)
@ -990,10 +990,10 @@ class SpecData1D(PlotData):
iseed : scalar integer
starting seed number for the random number generator
(default none is set)
fnLimit : real scalar
fn_limit : real scalar
normalized upper frequency limit of spectrum for 2'nd order
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).
Generally this should be the same as used in the final
non-linear simulation (see example below).
@ -1066,7 +1066,7 @@ class SpecData1D(PlotData):
max_sim = 30
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'
# switch ftype
# case 'f',
@ -1094,9 +1094,9 @@ class SpecData1D(PlotData):
# Expected maximum amplitude for 10000 waves 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
eps = finfo(float).eps
@ -1105,11 +1105,11 @@ class SpecData1D(PlotData):
SL = S
indZero = nonzero(freq < fLimitLo)[0]
if len(indZero):
SL.data[indZero] = 0
ind_zero = nonzero(freq < f_limit_lo)[0]
if len(ind_zero):
SL.data[ind_zero] = 0
maxS = max(S.data)
max_spec = max(S.data)
# Fs = 2*freq(end)+eps # sampling frequency
for ix in range(max_sim):
@ -1117,12 +1117,12 @@ class SpecData1D(PlotData):
method=method, fnlimit=fn_limit,
output='timeseries')
x2.data -= x1.data # x2(:,2:end) = x2(:,2:end) -x1(:,2:end)
S2 = x2.tospecdata(L)
S1 = x1.tospecdata(L)
S2 = x2.tospecdata(max_lag)
S1 = x1.tospecdata(max_lag)
# TODO: Finish spec.to_linspec
# S2 = dat2spec(x2, L)
# S1 = dat2spec(x1, L)
# S2 = dat2spec(x2, max_lag)
# S1 = dat2spec(x1, max_lag)
# %[tf21,fi] = tfe(x2(:,2),x1(:,2),1024,Fs,[],512)
# %Hw11 = interp1q(fi,tf21.*conj(tf21),freq)
if True:
@ -1144,8 +1144,8 @@ class SpecData1D(PlotData):
SL.data = (Hw1 * S.data)
if len(indZero):
SL.data[indZero] = 0
if len(ind_zero):
SL.data[ind_zero] = 0
# end
k = nonzero(SL.data < 0)[0]
if len(k): # Make sure that the current guess is larger than zero
@ -1176,17 +1176,17 @@ class SpecData1D(PlotData):
# figtile
# end
print('Iteration : %d, Hw12 : %g Hw12/maxS : %g' %
(ix, maxHw12, (maxHw12 / maxS)))
if (maxHw12 < maxS * tolerance) and (Hw1[-1] < Hw2[-1]):
print('Iteration : %d, Hw12 : %g Hw12/max_spec : %g' %
(ix, maxHw12, (maxHw12 / max_spec)))
if (maxHw12 < max_spec * tolerance) and (Hw1[-1] < Hw2[-1]):
break
# end
Hw2 = Hw1
# end
# Hw1(end)
# maxS*1e-3
# if Hw1[-1]*S.data>maxS*1e-3,
# max_spec*1e-3
# if Hw1[-1]*S.data>max_spec*1e-3,
# warning('The Nyquist frequency of the spectrum may be too low')
# end
@ -1837,7 +1837,7 @@ class SpecData1D(PlotData):
# end
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])
except Exception:
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):
"""Return an array of all value.
"""
#out = reshape(repeat([value], product(shape, axis=0), axis=0), shape)
out = ones(shape, dtype=bool) * value
if typecode is not None:
out = out.astype(typecode)
@ -37,7 +36,7 @@ def valarray(shape, value=nan, typecode=None):
return out
def _cdff(self, x, dfn, dfd):
def _cdff(x, dfn, dfd):
return special.fdtr(dfn, dfd, x)
@ -91,17 +90,15 @@ def edf(x, method=2):
z = atleast_1d(x)
z.sort()
N = len(z)
n = len(z)
if method == 1:
Fz1 = arange(0.5, N) / N
e_cdf = arange(0.5, n) / n
elif method == 3:
Fz1 = arange(1, N + 1) / N
e_cdf = arange(1, n + 1) / n
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)')
F.setplotter('step')
return F
return PlotData(e_cdf, z, xlab='x', ylab='F(x)', plotmethod='step')
def edfcnd(x, c=None, method=2):
@ -113,9 +110,9 @@ def edfcnd(x, c=None, method=2):
x : array-like
data vector
method : integer scalar
1. Interpolation so that F(X_(k)) == (k-0.5)/n.
2. Interpolation so that F(X_(k)) == k/(n+1). (default)
3. The empirical distribution. F(X_(k)) = k/n
1. Interpolation so that cdf(X_(k)) == (k-0.5)/n.
2. Interpolation so that cdf(X_(k)) == k/(n+1). (default)
3. The empirical distribution. cdf(X_(k)) = k/n
Example
-------
@ -124,8 +121,8 @@ def edfcnd(x, c=None, method=2):
>>> R = ws.rayleigh.rvs(scale=2,size=100)
>>> Fc = ws.edfcnd(R, 1)
>>> hc = Fc.plot()
>>> F = ws.edf(R)
>>> h = F.plot()
>>> cdf = ws.edf(R)
>>> h = cdf.plot()
See also edf, pdfplot, cumtrapz
"""
@ -133,15 +130,13 @@ def edfcnd(x, c=None, method=2):
if c is None:
c = floor(min(z.min(), 0))
try:
F = edf(z[c <= z], method=method)
except:
ValueError('No data points above c=%d' % int(c))
cdf = edf(z[c <= z], method=method)
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):
nmin = max(nmin, 1)
@ -149,6 +144,7 @@ def _check_nmin(nmin, n):
warnings.warn('nmin possibly too large!')
return nmin
def _check_umin_umax(data, umin, umax, nmin):
sd = np.sort(data)
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)
return umin, umax
def _check_nu(nu, nmin, n):
if nu is None:
nu = min(n - nmin, 100)
return nu
def reslife(data, u=None, umin=None, umax=None, nu=None, nmin=3, alpha=0.05,
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)
# 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)
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
# Approximate P% confidence interval
# Za = -invnorm(alpha2); % known mean
Za = -_invt(alpha2, num - 1) # unknown mean
mrlu = mrl + Za * srl / sqrt(num)
mrll = mrl - Za * srl / sqrt(num)
# options.CI = [mrll,mrlu];
# options.numdata = num;
titleTxt = 'Mean residual life with %d%s CI' % (100 * p, '%')
# z_a = -invnorm(alpha2); % known mean
z_a = -_invt(alpha2, num - 1) # unknown mean
mrlu = mrl + z_a * srl / sqrt(num)
mrll = mrl - z_a * srl / sqrt(num)
title_txt = 'Mean residual life with %d%s CI' % (100 * p, '%')
res = PlotData(mrl, u, xlab='Threshold',
ylab='Mean Excess', title=titleTxt)
ylab='Mean Excess', title=title_txt)
res.workspace = dict(
numdata=num, umin=umin, umax=umax, nu=nu, nmin=nmin, alpha=alpha)
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']
if plotflag:
res.plot()
@ -390,11 +388,11 @@ def dispersion_idx(
b_u, ok_u = _find_appropriate_threshold(u, di, di_low, di_up)
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')
#'caption',ci_txt);
res.workspace = dict(umin=umin, umax=umax, nu=nu, nmin=nmin, alpha=alpha)
res.children = [
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]
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_small[-1]))
@ -759,18 +756,18 @@ class RegLogit(object):
See also regglm, reglm, regnonlm
"""
#% 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,
#% 1992.
# 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,
# 1992.
#
#% Author: Gordon K Smyth <gks@maths.uq.oz.au>,
#% Revised by: pab
#% -renamed from oridinal to reglogit
#% -added predict, summary and compare
#% Description: Ordinal logistic regression
# Author: Gordon K Smyth <gks@maths.uq.oz.au>,
# Revised by: pab
# -renamed from oridinal to reglogit
# -added predict, summary and compare
# Description: Ordinal logistic regression
#
#% Uses the auxiliary functions logistic_regression_derivatives and
#% logistic_regression_likelihood.
# Uses the auxiliary functions logistic_regression_derivatives and
# logistic_regression_likelihood.
def __init__(self, maxiter=500, accuracy=1e-6, alpha=0.05,
deletecolinear=True, verbose=False):
@ -939,7 +936,7 @@ class RegLogit(object):
break
# end %while
#% tidy up output
# tidy up output
theta = tb[:nz, ]
beta = tb[nz:(nz + nx)]
@ -1204,7 +1201,7 @@ class RegLogit(object):
R = np.dot(U, np.dot(np.diag(sqrt(S)), V))
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))
u = np.hstack((one, Xnew))
for i in range(nz):
@ -1317,7 +1314,7 @@ def test_reglogit():
x = np.arange(1, 11).reshape(-1, 1)
b = RegLogit()
b.fit(y, x)
# b.display() #% members and methods
# b.display() # members and methods
b.summary()
[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)
b = RegLogit()
b.fit(y, x)
# b.display() #% members and methods
# b.display() # members and methods
b.summary()
[mu, plo, pup] = b.predict(fulloutput=True)
import matplotlib.pyplot as pl

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