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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
Unescape Escape View File

@ -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
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@ -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' %

117
wafo/integrate.py
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@ -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
@ -49,8 +50,8 @@ def clencurt(fun, a, b, n0=5, trace=False, args=()):
-------
>>> 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))
>>> 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
--------

176
wafo/polynomial.py
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@ -1,7 +1,7 @@
"""
Extended functions to operate on polynomials
"""
# -------------------------------------------------------------------------
# ------------------------------------------------------------------------
# Name: polynomial
# Purpose: Functions to operate on polynomials.
#
@ -15,21 +15,17 @@
# Created: 30.12.2008
# Copyright: (c) pab 2008
# Licence: LGPL
# -------------------------------------------------------------------------
# ------------------------------------------------------------------------
# !/usr/bin/env python
from __future__ import absolute_import
import warnings # @UnusedImport
from numpy.polynomial import polyutils as pu
from .plotbackend import plotbackend as plt
import numpy as np
from numpy import (zeros, asarray, newaxis, arange,
logical_or, any, pi, cos, round, diff, all, exp,
where, extract, linalg, sign, concatenate, floor,
linspace, sum, meshgrid)
from numpy import (newaxis, arange, pi)
from scipy.fftpack import dct, idct as _idct
from numpy.lib.polynomial import * # @UnusedWildImport
from scipy.misc.common import pade # @UnresolvedImport
from scipy.misc import pade # @UnresolvedImport
__all__ = np.lib.polynomial.__all__
__all__ = __all__ + ['pade', 'padefit', 'polyreloc', 'polyrescl', 'polytrim',
'poly2hstr', 'poly2str', 'polyshift', 'polyishift',
@ -91,9 +87,8 @@ def polyint(p, m=1, k=None):
>>> np.polyder(P, 2)(0)
0.0
>>> P = np.polyint(p, 3, k=[6, 5, 3])
>>> P.coefficients.tolist()
[0.016666666666666666, 0.041666666666666664, 0.16666666666666666, 3.0,
5.0, 3.0]
>>> P
poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ])
Note that 3 = 6 / 2!, and that the constants are given in the order of
integrations. Constant of the highest-order polynomial term comes first:
@ -110,7 +105,7 @@ def polyint(p, m=1, k=None):
if m < 0:
raise ValueError("Order of integral must be positive (see polyder)")
if k is None:
k = zeros(m, float)
k = np.zeros(m, float)
k = np.atleast_1d(k)
if len(k) == 1 and m > 1:
k = k[0] * np.ones(m, float)
@ -118,7 +113,7 @@ def polyint(p, m=1, k=None):
raise ValueError(
"k must be a scalar or a rank-1 array of length 1 or >m.")
truepoly = isinstance(p, poly1d)
p = asarray(p)
p = np.asarray(p)
if m == 0:
if truepoly:
return poly1d(p)
@ -195,7 +190,7 @@ def polyder(p, m=1):
if m < 0:
raise ValueError("Order of derivative must be positive (see polyint)")
truepoly = isinstance(p, poly1d)
p = asarray(p)
p = np.asarray(p)
if m == 0:
if truepoly:
return poly1d(p)
@ -271,12 +266,12 @@ def polydeg(x, y):
# required to take AIC noise into account and to ensure that this minimum
# is a (likely) global minimum.
while nit < 3:
while nit < 6:
p = orthofit(x, y, n)
ys = orthoval(p, x)
# -- Akaike's Information Criterion
aic = (2 * (n + 1) * (1 + (n + 2) / (N - n - 2)) +
N * (np.log(2 * pi * sum((ys - y) ** 2) / N) + 1))
N * (np.log(2 * pi * np.sum((ys - y) ** 2) / N) + 1))
if aic >= AIC:
nit += 1
@ -444,10 +439,10 @@ def orthofit(x, y, n):
PL[1] = x - p[1, 1]
for i in range(2, n + 1):
p[1, i] = np.dot(x, PL[i - 1] ** 2) / sum(PL[i - 1] ** 2)
p[2, i] = np.dot(x, PL[i - 2] * PL[i - 1]) / sum(PL[i - 2] ** 2)
p[1, i] = np.dot(x, PL[i - 1] ** 2) / np.sum(PL[i - 1] ** 2)
p[2, i] = np.dot(x, PL[i - 2] * PL[i - 1]) / np.sum(PL[i - 2] ** 2)
PL[i] = (x - p[1, i]) * PL[i - 1] - p[2, i] * PL[i - 2]
p[0, :] = np.dot(PL, y) / sum(PL ** 2, axis=1)
p[0, :] = np.dot(PL, y) / np.sum(PL ** 2, axis=1)
return p
# ys = np.dot(p[0, :], PL) # smoothed y
@ -594,11 +589,11 @@ def polytrim(p):
else:
r = np.atleast_1d(p).copy()
# Remove leading zeros
is_not_lead_zeros = logical_or.accumulate(r != 0, axis=0)
is_not_lead_zeros = np.logical_or.accumulate(r != 0, axis=0)
if r.ndim == 1:
r = r[is_not_lead_zeros]
else:
is_not_lead_zeros = any(is_not_lead_zeros, axis=1)
is_not_lead_zeros = np.any(is_not_lead_zeros, axis=1)
r = r[is_not_lead_zeros, :]
return r
@ -952,8 +947,8 @@ def cheb2poly(ck, a=-1, b=1):
n = len(ck)
b_Nmi = zeros(1)
b_Nmip1 = zeros(1)
b_Nmi = np.zeros(1)
b_Nmip1 = np.zeros(1)
y = np.r_[2 / (b - a), -(a + b) / (b - a)]
y2 = 2. * y
@ -1003,7 +998,7 @@ def chebextr(n):
http://en.wikipedia.org/wiki/Chebyshev_nodes
http://en.wikipedia.org/wiki/Chebyshev_polynomials
"""
return - cos((pi * arange(n + 1)) / n)
return - np.cos((pi * arange(n + 1)) / n)
def chebroot(n, kind=1):
@ -1043,7 +1038,7 @@ def chebroot(n, kind=1):
"""
if kind not in (1, 2):
raise ValueError('kind must be 1 or 2')
return - cos(pi * (arange(n) + 0.5 * kind) / (n + kind - 1))
return - np.cos(pi * (arange(n) + 0.5 * kind) / (n + kind - 1))
def chebpoly(n, x=None, kind=1):
@ -1094,11 +1089,11 @@ def chebpoly(n, x=None, kind=1):
if n == 0:
p = np.ones(1)
else:
p = round(pow(2, n - 2 + kind) * poly(chebroot(n, kind=kind)))
p = np.round(pow(2, n - 2 + kind) * poly(chebroot(n, kind=kind)))
p[1::2] = 0
return p
else: # Evaluate polynomial in chebychev form
ck = zeros(n + 1)
ck = np.zeros(n + 1)
ck[0] = 1.
return _chebval(np.atleast_1d(x), ck, kind=kind)
@ -1137,12 +1132,12 @@ def chebfit(fun, n=10, a=-1, b=1, trace=False):
>>> a = 0; b = 2
>>> ck = chebfit(np.exp,7,a,b);
>>> x = np.linspace(0,4);
>>> h=plt.plot(x, np.exp(x), 'r', x, chebval(x,ck,a,b), 'g.')
>>> x1 = chebroot(9)*(b-a)/2+(b+a)/2
>>> ck1 = chebfit(np.exp(x1))
>>> h = plt.plot(x,np.exp(x), 'r', x, chebval(x,ck1,a,b),'g.')
>>> plt.close()
h=plt.plot(x, np.exp(x), 'r', x, chebval(x,ck,a,b), 'g.')
h = plt.plot(x,np.exp(x), 'r', x, chebval(x,ck1,a,b),'g.')
plt.close()
See also
--------
@ -1283,7 +1278,7 @@ def idct(x, n=None):
Examples
--------
>>> import numpy as np
>>> x = np.arange(5)
>>> x = np.arange(5)*1.0
>>> np.abs(x-idct(dct(x)))<1e-14
array([ True, True, True, True, True], dtype=bool)
>>> np.abs(x-dct(idct(x)))<1e-14
@ -1320,7 +1315,7 @@ def _chebval(x, ck, kind=1):
http://mathworld.wolfram.com/ClenshawRecurrenceFormula.html
"""
n = len(ck)
b_Nmi = zeros(x.shape) # b_(N-i)
b_Nmi = np.zeros(x.shape) # b_(N-i)
b_Nmip1 = b_Nmi.copy() # b_(N-i+1)
x2 = 2 * x
# Clenshaw reccurence
@ -1363,15 +1358,19 @@ def chebval(x, ck, a=-1, b=1, kind=1, fill=None):
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-1,1)
>>> ck = np.zeros(5); ck[-1]=1
>>> h = plt.plot(x,chebval(x,ck),x,chebpoly(4,x),'.')
>>> plt.close()
>>> y = chebval(x,ck)
h = plt.plot(x, y, x, chebpoly(4,x),'.')
plt.close()
Fit exponential function:
>>> import matplotlib.pyplot as plt
>>> ck = chebfit(np.exp,7,0,2)
>>> x = np.linspace(0,4);
>>> h=plt.plot(x,chebval(x,ck,0,2),'g',x,np.exp(x))
>>> plt.close()
>>> y2 = chebval(x,ck,0,2)
h=plt.plot(x, y2, 'g', x, np.exp(x))
plt.close()
See also
--------
@ -1383,14 +1382,14 @@ def chebval(x, ck, a=-1, b=1, kind=1, fill=None):
http://mathworld.wolfram.com/ClenshawRecurrenceFormula.html
"""
y = map_from_interval(atleast_1d(x), a, b)
y = map_from_interval(np.atleast_1d(x), a, b)
if fill is None:
f = _chebval(y, ck, kind=kind)
else:
cond = (abs(y) <= 1)
f = where(cond, 0, fill)
if any(cond):
yk = extract(cond, y)
f = np.where(cond, 0, fill)
if np.any(cond):
yk = np.extract(cond, y)
f[cond] = _chebval(yk, ck, kind=kind)
return f
@ -1418,9 +1417,11 @@ def chebder(ck, a=-1, b=1):
>>> import matplotlib.pyplot as plt
>>> ck = chebfit(np.exp,7,0,2)
>>> x = np.linspace(0,4)
>>> ck2 = chebder(ck,0,2);
>>> h = plt.plot(x,chebval(x,ck,0,2),'g',x,np.exp(x),'r')
>>> plt.close()
>>> ck2 = chebder(ck,0,2)
>>> y = chebval(x,ck2,0,2)
h = plt.plot(x, y, 'g', x, np.exp(x), 'r')
plt.close()
See also
--------
@ -1438,7 +1439,7 @@ def chebder(ck, a=-1, b=1):
"""
n = len(ck) - 1
cder = zeros(n, dtype=asarray(ck).dtype)
cder = np.zeros(n, dtype=np.asarray(ck).dtype)
cder[0] = 2 * n * ck[0]
cder[1] = 2 * (n - 1) * ck[1]
for j in range(2, n):
@ -1470,8 +1471,10 @@ def chebint(ck, a=-1, b=1):
>>> ck = chebfit(np.exp,7,0,2)
>>> x = np.linspace(0,4)
>>> ck2 = chebint(ck,0,2);
>>> h=plt.plot(x,chebval(x,ck,0,2),'g',x,np.exp(x),'r.')
>>> plt.close()
>>> y =chebval(x,ck2,0,2)
h=plt.plot(x,y,'g',x,np.exp(x),'r.')
plt.close()
See also
--------
@ -1500,14 +1503,14 @@ def chebint(ck, a=-1, b=1):
n = len(ck)
cint = zeros(n)
cint = np.zeros(n)
con = 0.25 * (b - a)
dif1 = diff(ck[-1::-2])
dif1 = np.diff(ck[-1::-2])
ix1 = np.r_[1:n - 1:2]
cint[ix1] = -(con * dif1) / ix1
if n > 3:
dif2 = diff(ck[-2::-2])
dif2 = np.diff(ck[-2::-2])
ix2 = np.r_[2:n - 1:2]
cint[ix2] = -(con * dif2) / ix2
cint = cint[::-1]
@ -1530,7 +1533,7 @@ class Cheb1d(object):
for key in ck.__dict__.keys():
self.__dict__[key] = ck.__dict__[key]
return
cki = trim_zeros(atleast_1d(ck), 'b')
cki = trim_zeros(np.atleast_1d(ck), 'b')
if len(cki.shape) > 1:
raise ValueError("Polynomial must be 1d only.")
self.__dict__['coeffs'] = cki
@ -1544,9 +1547,9 @@ class Cheb1d(object):
def __array__(self, t=None):
if t:
return asarray(self.coeffs, t)
return np.asarray(self.coeffs, t)
else:
return asarray(self.coeffs)
return np.asarray(self.coeffs)
def __repr__(self):
vals = repr(self.coeffs)
@ -1590,11 +1593,11 @@ class Cheb1d(object):
def __eq__(self, other):
other = Cheb1d(other)
return (all(self.coeffs == other.coeffs) and (self.a == other.a) and
return (np.all(self.coeffs == other.coeffs) and (self.a == other.a) and
(self.b == other.b) and (self.kind == other.kind))
def __ne__(self, other):
return any(self.coeffs != other.coeffs) or (self.a != other.a) or (
return np.any(self.coeffs != other.coeffs) or (self.a != other.a) or (
self.b != other.b) or (self.kind != other.kind)
def __setattr__(self, key, val):
@ -1631,8 +1634,8 @@ class Cheb1d(object):
if key < 0:
raise ValueError("Does not support negative powers.")
if key > self.order:
zr = zeros(key - self.order, self.coeffs.dtype)
self.__dict__['coeffs'] = concatenate((self.coeffs, zr))
zr = np.zeros(key - self.order, self.coeffs.dtype)
self.__dict__['coeffs'] = np.concatenate((self.coeffs, zr))
self.__dict__['order'] = key
self.__dict__['coeffs'][key] = val
return
@ -1714,9 +1717,9 @@ def padefit(c, m=None):
poly1d([ 0.00277778, 0.03333333, 0.2 , 0.66666667, 1. ])
poly1d([ 0.03333333, -0.33333333, 1. ])
>>> x = np.linspace(0,4);
>>> h = plt.plot(x,c(x),x,p(x)/q(x),'g-', x,np.exp(x),'r.')
>>> plt.close()
x = np.linspace(0,4)
h = plt.plot(x,c(x),x,p(x)/q(x),'g-', x,np.exp(x),'r.')
plt.close()
See also
--------
@ -1724,16 +1727,16 @@ def padefit(c, m=None):
"""
if not m:
m = int(floor((len(c) - 1) * 0.5))
c = asarray(c)
m = int(np.floor((len(c) - 1) * 0.5))
c = np.asarray(c)
return pade(c[::-1], m)
def test_pade():
cof = array(([1.0, 1.0, 1.0 / 2, 1. / 6, 1. / 24]))
cof = np.array(([1.0, 1.0, 1.0 / 2, 1. / 6, 1. / 24]))
p, q = pade(cof, 2)
t = arange(0, 2, 0.1)
assert(all(abs(p(t) / q(t) - exp(t)) < 0.3))
assert(np.all(abs(p(t) / q(t) - np.exp(t)) < 0.3))
def padefitlsq(fun, m, k, a=-1, b=1, trace=False, x=None, end_points=True):
@ -1781,9 +1784,9 @@ def padefitlsq(fun, m, k, a=-1, b=1, trace=False, x=None, end_points=True):
poly1d([ 0.01443847, 0.128842 , 0.55284547, 0.99999962])
poly1d([-0.0049658 , 0.07610473, -0.44716929, 1. ])
>>> x = np.linspace(0,4)
>>> h = plt.plot(x, polyval(c1,x)/polyval(c2,x),'g')
>>> h = plt.plot(x, np.exp(x), 'r')
x = np.linspace(0,4)
h = plt.plot(x, polyval(c1,x)/polyval(c2,x),'g')
h = plt.plot(x, np.exp(x), 'r')
See also
--------
@ -1822,9 +1825,8 @@ def padefitlsq(fun, m, k, a=-1, b=1, trace=False, x=None, end_points=True):
fs = fun
n = len(fs)
if n < npt:
warnings.warn(
'Check the result! ' +
'Number of function values should be at least: %d' % npt)
warnings.warn('Check the result! Number of function values ' +
'should be at least: %d' % npt)
if trace:
plt.plot(x, fs, '+')
@ -1833,11 +1835,11 @@ def padefitlsq(fun, m, k, a=-1, b=1, trace=False, x=None, end_points=True):
ee = np.ones((npt))
mad = 0
u = zeros((npt, ncof))
u = np.zeros((npt, ncof))
for ix in range(MAXIT):
# Set up design matrix for least squares fit.
pow1 = wt
bb = pow1 * (fs + abs(mad) * sign(ee))
bb = pow1 * (fs + abs(mad) * np.sign(ee))
for jx in range(m + 1):
u[:, jx] = pow1
@ -1848,8 +1850,8 @@ def padefitlsq(fun, m, k, a=-1, b=1, trace=False, x=None, end_points=True):
pow1 = pow1 * x
u[:, jx] = pow1
[u1, w, v] = linalg.svd(u, full_matrices=False)
cof = where(w == 0, 0.0, np.dot(bb, u1) / w)
[u1, w, v] = np.linalg.svd(u, full_matrices=False)
cof = np.where(w == 0, 0.0, np.dot(bb, u1) / w)
cof = np.dot(cof, v)
# Tabulate the deviations and revise the weights
@ -1873,10 +1875,10 @@ def padefitlsq(fun, m, k, a=-1, b=1, trace=False, x=None, end_points=True):
def main():
exp = np.exp
[c1, c2] = padefitlsq(exp, 3, 3, 0, 2)
x = linspace(0, 4)
x = np.linspace(0, 4)
plt.plot(x, polyval(c1, x) / polyval(c2, x), 'g')
plt.plot(x, exp(x), 'r')
@ -1887,15 +1889,10 @@ def main():
_pr = polyreloc(p, 2)
_pd = polyder(p)
_st = poly2str(p)
c = poly1d(
1. /
sp.gamma(
np.r_[
6 +
1:0:-
1])) # polynomial coeff exponential function
# polynomial coeff exponential function:
c = poly1d(1. / sp.gamma(np.r_[6 + 1:0:-1]))
[p, q] = padefit(c)
x = linspace(0, 4)
x = np.linspace(0, 4)
plt.plot(x, c(x), x, p(x) / q(x), 'g-', x, exp(x), 'r.')
plt.close()
x = arange(4)
@ -1906,7 +1903,7 @@ def main():
b = 2
ck = chebfit(exp, 6, a, b)
_t = chebval(0, ck, a, b)
x = linspace(0, 2, 6)
x = np.linspace(0, 2, 6)
plt.plot(x, exp(x), 'r', x, chebval(x, ck, a, b), 'g.')
# x1 = chebroot(9).'*(b-a)/2+(b+a)/2 ;
# ck1 =chebfit([x1 exp(x1)],9,a,b);
@ -1932,7 +1929,7 @@ def test_polydeg():
n = polydeg(x, y)
# n = 2
p = orthofit(x, y, n)
xi = linspace(x.min(), x.max())
xi = np.linspace(x.min(), x.max())
ys0 = orthoval(p, x)
ys = orthoval(p, xi)
@ -1947,7 +1944,8 @@ def test_polydeg():
def test_docstrings():
import doctest
print('Testing docstrings in %s' % __file__)
doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)
options = doctest.NORMALIZE_WHITESPACE | doctest.ELLIPSIS
doctest.testmod(optionflags=options, verbose=False)
def chebvandernd(deg, *xi):
@ -2280,7 +2278,7 @@ def test_chebfit2d():
n = 3
xorder, yorder = n-1, n-1
x = chebroot(n=n, kind=1)
xgrid, ygrid = meshgrid(x, x)
xgrid, ygrid = np.meshgrid(x, x)
def f(x, y):
return np.exp(-x**2-6*y**2)
@ -2314,6 +2312,6 @@ if __name__ == '__main__':
if False: # True: #
main()
else:
test_chebfit2d()
# test_docstrings()
# test_chebfit2d()
test_docstrings()
# test_polydeg()

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