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Merge branch 'master' of https://github.com/wafo-project/pywafo.git

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master
pbrod 9 years ago
parent c4e5bfd66a 52411de937
commit d04c28df0d
4 changed files with 2377 additions and 2362 deletions
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11
wafo/definitions.py
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@ -12,11 +12,12 @@ Examples
--------
In order to view the documentation do the following in an ipython window:
>>> import wafo.definitions as wd
>>> wd.crossings()
import wafo.definitions as wd
wd.crossings()
or
>>> wd.crossings?
wd.crossings?
"""
@ -303,3 +304,7 @@ def waves():
findcross
"""
print(waves.__doc__)
if __name__ == '__main__':
import doctest
doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)

3
wafo/gaussian.py
Unescape Escape View File

@ -598,7 +598,8 @@ def prbnormndpc(rho, a, b, abserr=1e-4, relerr=1e-4, usesimpson=True,
'''
# Call fortran implementation
val, err, ier = mvnprdmod.prbnormndpc(rho, a, b, abserr, relerr, usebreakpoints, usesimpson) # @UndefinedVariable @IgnorePep8
val, err, ier = mvnprdmod.prbnormndpc(rho, a, b, abserr, relerr,
usebreakpoints, usesimpson)
if ier > 0:
warnings.warn('Abnormal termination ier = %d\n\n%s' %

119
wafo/integrate.py
Unescape Escape View File

@ -5,8 +5,9 @@ from numpy import pi, sqrt, ones, zeros # @UnresolvedImport
from scipy import integrate as intg
import scipy.special.orthogonal as ort
from scipy import special as sp
from .plotbackend import plotbackend as plt
from scipy.integrate import simps, trapz
from .plotbackend import plotbackend as plt
from .demos import humps
from .misc import dea3
from .dctpack import dct
@ -48,9 +49,9 @@ def clencurt(fun, a, b, n0=5, trace=False, args=()):
Example
-------
>>> import numpy as np
>>> val,err = clencurt(np.exp,0,2)
>>> abs(val-np.expm1(2))< err, err<1e-10
(array([ True], dtype=bool), array([ True], dtype=bool))
>>> val, err = clencurt(np.exp, 0, 2)
>>> np.allclose(val, np.expm1(2)), err[0] < 1e-10
(True, True)
See also
@ -103,24 +104,20 @@ def clencurt(fun, a, b, n0=5, trace=False, args=()):
f[0, :] = f[0, :] / 2
f[n, :] = f[n, :] / 2
# % x = cos(pi*0:n/n)
# % f = f(x)
# %
# % N+1
# % c(k) = (2/N) sum f''(n)*cos(pi*(2*k-2)*(n-1)/N), 1 <= k <= N/2+1.
# % n=1
# x = cos(pi*0:n/n)
# f = f(x)
#
# N+1
# c(k) = (2/N) sum f''(n)*cos(pi*(2*k-2)*(n-1)/N), 1 <= k <= N/2+1.
# n=1
fft = np.fft.fft
tmp = np.real(fft(f[:n, :], axis=0))
c = 2 / n * (tmp[0:n / 2 + 1, :] + np.cos(np.pi * s2) * f[n, :])
c[0, :] = c[0, :] / 2
c[n / 2, :] = c[n / 2, :] / 2
# % alternative call
# c2 = dct(f)
c = c[0:n / 2 + 1, :] / ((s2 - 1) * (s2 + 1))
Q = (af - bf) * np.sum(c, axis=0)
# Q = (a-b).*sum( c(1:n/2+1,:)./repmat((s2-1).*(s2+1),1,Na))
abserr = (bf - af) * np.abs(c[n / 2, :])
@ -238,9 +235,9 @@ def h_roots(n, method='newton'):
Example
-------
>>> import numpy as np
>>> [x,w] = h_roots(10)
>>> np.sum(x*w)
-5.2516042729766621e-19
>>> x, w = h_roots(10)
>>> np.allclose(np.sum(x*w), -5.2516042729766621e-19)
True
See also
--------
@ -451,7 +448,7 @@ def la_roots(n, alpha=0, method='newton'):
>>> import numpy as np
>>> [x,w] = h_roots(10)
>>> np.sum(x*w)
-5.2516042729766621e-19
1.3352627380516791e-17
See also
--------
@ -555,9 +552,9 @@ def p_roots(n, method='newton', a=-1, b=1):
-------
Integral of exp(x) from a = 0 to b = 3 is: exp(3)-exp(0)=
>>> import numpy as np
>>> [x,w] = p_roots(11,a=0,b=3)
>>> np.sum(np.exp(x)*w)
19.085536923187668
>>> x, w = p_roots(11, a=0, b=3)
>>> np.allclose(np.sum(np.exp(x)*w), 19.085536923187668)
True
See also
--------
@ -723,15 +720,22 @@ def qrule(n, wfun=1, alpha=0, beta=0):
Examples:
---------
>>> import numpy as np
# integral of x^2 from a = -1 to b = 1
>>> [bp,wf] = qrule(10)
>>> sum(bp**2*wf) # integral of x^2 from a = -1 to b = 1
0.66666666666666641
>>> np.allclose(sum(bp**2*wf), 0.66666666666666641)
True
# integral of exp(-x.^2)*x.^2 from a = -inf to b = inf
>>> [bp,wf] = qrule(10,2)
>>> sum(bp**2*wf) # integral of exp(-x.^2)*x.^2 from a = -inf to b = inf
0.88622692545275772
>>> np.allclose(sum(bp**2*wf), 0.88622692545275772)
True
# integral of (x+1)*(1-x)^2 from a = -1 to b = 1
>>> [bp,wf] = qrule(10,4,1,2)
>>> (bp*wf).sum() # integral of (x+1)*(1-x)^2 from a = -1 to b = 1
0.26666666666666755
>>> np.allclose((bp*wf).sum(), 0.26666666666666755)
True
See also
--------
@ -841,23 +845,24 @@ class _Gaussq(object):
---------
integration of x**2 from 0 to 2 and from 1 to 4
>>> from scitools import numpyutils as npt
>>> A = [0, 1]; B = [2,4]
>>> fun = npt.wrap2callable('x**2')
>>> [val1,err1] = gaussq(fun,A,B)
>>> val1
array([ 2.6666667, 21. ])
>>> err1
array([ 1.7763568e-15, 1.0658141e-14])
>>> import numpy as np
>>> A = [0, 1]
>>> B = [2, 4]
>>> fun = lambda x: x**2
>>> val1, err1 = gaussq(fun,A,B)
>>> np.allclose(val1, [ 2.6666667, 21. ])
True
>>> np.allclose(err1, [ 1.7763568e-15, 1.0658141e-14])
True
Integration of x^2*exp(-x) from zero to infinity:
>>> fun2 = npt.wrap2callable('1')
>>> val2, err2 = gaussq(fun2, 0, npt.inf, wfun=3, alpha=2)
>>> val3, err3 = gaussq(lambda x: x**2,0, npt.inf, wfun=3, alpha=0)
>>> val2, err2
(array([ 2.]), array([ 6.6613381e-15]))
>>> val3, err3
(array([ 2.]), array([ 1.7763568e-15]))
>>> fun2 = lambda x : np.ones(np.shape(x))
>>> val2, err2 = gaussq(fun2, 0, np.inf, wfun=3, alpha=2)
>>> val3, err3 = gaussq(lambda x: x**2,0, np.inf, wfun=3, alpha=0)
>>> np.allclose(val2, 2), err2[0] < 1e-14
(True, True)
>>> np.allclose(val3, 2), err3[0] < 1e-14
(True, True)
Integrate humps from 0 to 2 and from 1 to 4
>>> val4, err4 = gaussq(humps,A,B)
@ -1024,23 +1029,29 @@ class _Quadgr(object):
--------
>>> import numpy as np
>>> Q, err = quadgr(np.log,0,1)
>>> quadgr(np.exp,0,9999*1j*np.pi)
(-2.0000000000122662, 2.1933237448479304e-09)
>>> q, err = quadgr(np.exp,0,9999*1j*np.pi)
>>> np.allclose(q, -2.0000000000122662), err < 1.0e-08
(True, True)
>>> quadgr(lambda x: np.sqrt(4-x**2),0,2,1e-12)
(3.1415926535897811, 1.5809575870662229e-13)
>>> q, err = quadgr(lambda x: np.sqrt(4-x**2), 0, 2, abseps=1e-12)
>>> np.allclose(q, 3.1415926535897811), err < 1.0e-12
(True, True)
>>> quadgr(lambda x: x**-0.75,0,1)
(4.0000000000000266, 5.6843418860808015e-14)
>>> q, err = quadgr(lambda x: x**-0.75, 0, 1)
>>> np.allclose(q, 4), err < 1.e-13
(True, True)
>>> quadgr(lambda x: 1./np.sqrt(1-x**2),-1,1)
(3.141596056985029, 6.2146261559092864e-06)
>>> q, err = quadgr(lambda x: 1./np.sqrt(1-x**2), -1, 1)
>>> np.allclose(q, 3.141596056985029), err < 1.0e-05
(True, True)
>>> quadgr(lambda x: np.exp(-x**2),-np.inf,np.inf,1e-9) #% sqrt(pi)
(1.7724538509055152, 1.9722334876348668e-11)
>>> q, err = quadgr(lambda x: np.exp(-x**2), -np.inf, np.inf, 1e-9)
>>> np.allclose(q, np.sqrt(np.pi)), err < 1e-9
(True, True)
>>> quadgr(lambda x: np.cos(x)*np.exp(-x),0,np.inf,1e-9)
(0.50000000000000044, 7.3296813063450372e-11)
>>> q, err = quadgr(lambda x: np.cos(x)*np.exp(-x), 0, np.inf, 1e-9)
>>> np.allclose(q, 0.5), err < 1e-9
(True, True)
See also
--------

4606
wafo/polynomial.py
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