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Removed duplicated dea3 from integrate and misc.py import from numdifftools.extrapolate.dea3 instead

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pepified
master
Per A Brodtkorb 9 years ago
parent 990e2a5151
commit d0867b5c72
5 changed files with 17 additions and 165 deletions
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79
wafo/integrate.py
Unescape Escape View File

@ -8,6 +8,8 @@ from scipy import special as sp
from .plotbackend import plotbackend as plt
from scipy.integrate import simps, trapz
from .demos import humps
from .misc import dea3
from .dctpack import dct
# from pychebfun import Chebfun
_EPS = np.finfo(float).eps
@ -18,79 +20,6 @@ __all__ = ['dea3', 'clencurt', 'romberg',
'gaussq', 'richardson', 'quadgr', 'qdemo']
def dea3(v0, v1, v2):
'''
Extrapolate a slowly convergent sequence
Parameters
----------
v0,v1,v2 : array-like
3 values of a convergent sequence to extrapolate
Returns
-------
result : array-like
extrapolated value
abserr : array-like
absolute error estimate
Description
-----------
DEA3 attempts to extrapolate nonlinearly to a better estimate
of the sequence's limiting value, thus improving the rate of
convergence. The routine is based on the epsilon algorithm of
P. Wynn, see [1]_.
Example
-------
# integrate sin(x) from 0 to pi/2
>>> import numpy as np
>>> Ei= np.zeros(3)
>>> linfun = lambda k : np.linspace(0, np.pi/2., 2.**(k+5)+1)
>>> for k in np.arange(3):
... x = linfun(k)
... Ei[k] = np.trapz(np.sin(x),x)
>>> En, err = dea3(Ei[0],Ei[1],Ei[2])
>>> En, err
(array([ 1.]), array([ 0.0002008]))
>>> TrueErr = Ei-1.
>>> TrueErr
array([ -2.0080568e-04, -5.0199908e-05, -1.2549882e-05])
See also
--------
dea
Reference
---------
.. [1] C. Brezinski (1977)
"Acceleration de la convergence en analyse numerique",
"Lecture Notes in Math.", vol. 584,
Springer-Verlag, New York, 1977.
'''
E0, E1, E2 = np.atleast_1d(v0, v1, v2)
abs = np.abs # @ReservedAssignment
max = np.maximum # @ReservedAssignment
delta2, delta1 = E2 - E1, E1 - E0
err2, err1 = abs(delta2), abs(delta1)
tol2, tol1 = max(abs(E2), abs(E1)) * _EPS, max(abs(E1), abs(E0)) * _EPS
with warnings.catch_warnings():
warnings.simplefilter("ignore") # ignore division by zero and overflow
ss = 1.0 / delta2 - 1.0 / delta1
smalle2 = (abs(ss * E1) <= 1.0e-3).ravel()
result = 1.0 * E2
abserr = err1 + err2 + abs(E2) * _EPS * 10.0
converged = (err1 <= tol1) & (err2 <= tol2).ravel() | smalle2
k4, = (1 - converged).nonzero()
if k4.size > 0:
result[k4] = E1[k4] + 1.0 / ss[k4]
abserr[k4] = err1[k4] + err2[k4] + abs(result[k4] - E2[k4])
return result, abserr
def clencurt(fun, a, b, n0=5, trace=False, args=()):
'''
Numerical evaluation of an integral, Clenshaw-Curtis method.
@ -183,13 +112,11 @@ def clencurt(fun, a, b, n0=5, trace=False, args=()):
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, :])
# % old call
# % c = 2/n * cos(s2*s'*pi/n) * f
c[0, :] = c[0, :] / 2
c[n / 2, :] = c[n / 2, :] / 2
# % alternative call
# % c = dct(f)
# c2 = dct(f)
c = c[0:n / 2 + 1, :] / ((s2 - 1) * (s2 + 1))
Q = (af - bf) * np.sum(c, axis=0)

14
wafo/interpolate.py
Unescape Escape View File

@ -1102,10 +1102,10 @@ def test_smoothing_spline():
dy1 = pp1(x1)
y01 = pp0(x1)
# dy = y-y1
import matplotlib.pyplot as plb
import matplotlib.pyplot as plt
plb.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
plb.show('hold')
plt.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
plt.show('hold')
pass
# tck = interpolate.splrep(x, y, s=len(x))
@ -1250,10 +1250,10 @@ def test_pp():
pp(1)
pp(1.5)
dpp = pp.derivative()
import pylab as plb
x = plb.linspace(-1, 3)
plb.plot(x, pp(x), x, dpp(x), '.')
plb.show()
import matplotlib.pyplot as plt
x = np.linspace(-1, 3)
plt.plot(x, pp(x), x, dpp(x), '.')
plt.show()
def test_docstrings():

76
wafo/misc.py
Unescape Escape View File

@ -17,6 +17,7 @@ from scipy.special import gammaln
from scipy.integrate import trapz, simps
import warnings
from time import strftime, gmtime
from numdifftools.extrapolation import dea3
from .plotbackend import plotbackend
from collections import OrderedDict
try:
@ -33,7 +34,7 @@ __all__ = ['now', 'spaceline', 'narg_smallest', 'args_flat', 'is_numlike',
'parse_kwargs', 'detrendma', 'ecross', 'findcross', 'findextrema',
'findpeaks', 'findrfc', 'rfcfilter', 'findtp', 'findtc',
'findoutliers', 'common_shape', 'argsreduce', 'stirlerr',
'getshipchar',
'getshipchar', 'dea3',
'betaloge', 'gravity', 'nextpow2', 'discretize', 'polar2cart',
'cart2polar', 'meshgrid', 'ndgrid', 'trangood', 'tranproc',
'plot_histgrm', 'num2pistr', 'test_docstrings', 'lazywhere',
@ -2107,79 +2108,6 @@ def gravity(phi=45):
0.0000059 * sin(2 * phir) ** 2.)
def dea3(v0, v1, v2):
'''
Extrapolate a slowly convergent sequence
Parameters
----------
v0, v1, v2 : array-like
3 values of a convergent sequence to extrapolate
Returns
-------
result : array-like
extrapolated value
abserr : array-like
absolute error estimate
Description
-----------
DEA3 attempts to extrapolate nonlinearly to a better estimate
of the sequence's limiting value, thus improving the rate of
convergence. The routine is based on the epsilon algorithm of
P. Wynn, see [1]_.
Example
-------
# integrate sin(x) from 0 to pi/2
>>> import numpy as np
>>> import numdifftools as nd
>>> Ei= np.zeros(3)
>>> linfun = lambda k : np.linspace(0,np.pi/2.,2.**(k+5)+1)
>>> for k in np.arange(3):
... x = linfun(k)
... Ei[k] = np.trapz(np.sin(x),x)
>>> [En, err] = nd.dea3(Ei[0], Ei[1], Ei[2])
>>> truErr = Ei-1.
>>> (truErr, err, En)
(array([ -2.00805680e-04, -5.01999079e-05, -1.25498825e-05]),
array([ 0.00020081]), array([ 1.]))
See also
--------
dea
Reference
---------
.. [1] C. Brezinski (1977)
"Acceleration de la convergence en analyse numerique",
"Lecture Notes in Math.", vol. 584,
Springer-Verlag, New York, 1977.
'''
E0, E1, E2 = np.atleast_1d(v0, v1, v2)
abs = np.abs # @ReservedAssignment
max = np.maximum # @ReservedAssignment
delta2, delta1 = E2 - E1, E1 - E0
err2, err1 = abs(delta2), abs(delta1)
tol2, tol1 = max(abs(E2), abs(E1)) * _EPS, max(abs(E1), abs(E0)) * _EPS
with warnings.catch_warnings():
warnings.simplefilter("ignore") # ignore division by zero and overflow
ss = 1.0 / delta2 - 1.0 / delta1
smallE2 = (abs(ss * E1) <= 1.0e-3).ravel()
result = 1.0 * E2
abserr = err1 + err2 + abs(E2) * _EPS * 10.0
converged = (err1 <= tol1) & (err2 <= tol2).ravel() | smallE2
k4, = (1 - converged).nonzero()
if k4.size > 0:
result[k4] = E1[k4] + 1.0 / ss[k4]
abserr[k4] = err1[k4] + err2[k4] + abs(result[k4] - E2[k4])
return result, abserr
def nextpow2(x):
'''
Return next higher power of 2

11
wafo/polynomial.py
Unescape Escape View File

@ -724,7 +724,7 @@ def poly2str(p, variable='x'):
N = len(coeffs) - 1
for k in range(len(coeffs)):
for k in range(N+1):
coefstr = '%.4g' % abs(coeffs[k])
if coefstr[-4:] == '0000':
coefstr = coefstr[:-5]
@ -733,21 +733,18 @@ def poly2str(p, variable='x'):
if coefstr != '0':
newstr = '%s' % (coefstr,)
else:
if k == 0:
newstr = '0'
else:
newstr = ''
newstr = '0' if k == 0 else ''
elif power == 1:
if coefstr == '0':
newstr = ''
elif coefstr == 'b' or coefstr == '1':
elif coefstr in ['b', '1']:
newstr = var
else:
newstr = '%s*%s' % (coefstr, var)
else:
if coefstr == '0':
newstr = ''
elif coefstr == 'b' or coefstr == '1':
elif coefstr in ['b', '1']:
newstr = '%s**%d' % (var, power,)
else:
newstr = '%s*%s**%d' % (coefstr, var, power)

2
wafo/spectrum/core.py
Unescape Escape View File

@ -1811,7 +1811,7 @@ class SpecData1D(PlotData):
rind = Rind(**options)
if (Nx > 1):
# (M,m) or (M,m)v distribution wanted
if ((def_nr == 0 or def_nr == 2)):
if def_nr in [0, 2]:
asize = [Nx1, Nx1]
else:
# (M,m,TMm), (M,m,TMm)v (M,m,TMd)v or (M,M,Tdm)v

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