/usr/share/pyshared/pywt/functions.py is in python-pywt 0.2.0-3.
This file is owned by root:root, with mode 0o644.
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# Copyright (c) 2006-2010 Filip Wasilewski <filip.wasilewski@gmail.com>
# See COPYING for license details.
# $Id: functions.py 154 2010-03-13 13:18:59Z filipw $
"""
Other wavelet related functions.
"""
__all__ = ["intwave", "centfrq", "scal2frq", "qmf", "orthfilt"]
from math import sqrt
from _pywt import Wavelet
from numerix import asarray, array, float64
from numerix import integrate
from numerix import argmax, mean
from numerix import fft
WAVELET_CLASSES = (Wavelet)
def wavelet_for_name(name):
if not isinstance(name, basestring):
raise TypeError("Wavelet name must be of string type, not %s" % type(name))
try:
wavelet = Wavelet(name)
except ValueError:
raise
#raise ValueError("Invalid wavelet name - %s." % name)
return wavelet
def intwave(wavelet, precision=8):
"""
intwave(wavelet, precision=8) -> [int_psi, x] - for orthogonal wavelets
intwave(wavelet, precision=8) -> [int_psi_d, int_psi_r, x] - for other wavelets
intwave((function_approx, x), precision=8) -> [int_function, x] - for (function approx., x grid) pair
Integrate *psi* wavelet function from -Inf to x using the rectangle
integration method.
wavelet - Wavelet to integrate (Wavelet object, wavelet name string
or (wavelet function approx., x grid) pair)
precision = 8 - Precision that will be used for wavelet function
approximation computed with the wavefun(level=precision)
Wavelet's method.
(function_approx, x) - Function to integrate on the x grid. Used instead
of Wavelet object to allow custom wavelet functions.
"""
if isinstance(wavelet, tuple):
psi, x = asarray(wavelet[0]), asarray(wavelet[1])
step = x[1] - x[0]
return integrate(psi, step), x
else:
if not isinstance(wavelet, WAVELET_CLASSES):
wavelet = wavelet_for_name(wavelet)
functions_approximations = wavelet.wavefun(precision)
if len(functions_approximations) == 2: # continuous wavelet
psi, x = functions_approximations
step = x[1] - x[0]
return integrate(psi, step), x
elif len(functions_approximations) == 3: # orthogonal wavelet
phi, psi, x = functions_approximations
step = x[1] - x[0]
return integrate(psi, step), x
else: # biorthogonal wavelet
phi_d, psi_d, phi_r, psi_r, x = functions_approximations
step = x[1] - x[0]
return integrate(psi_d, step), integrate(psi_r, step), x
def centfrq(wavelet, precision=8):
"""
centfrq(wavelet, precision=8) -> float - for orthogonal wavelets
centfrq((function_aprox, x), precision=8) -> float - for (function approx., x grid) pair
Computes the central frequency of the *psi* wavelet function.
wavelet - Wavelet (Wavelet object, wavelet name string
or (wavelet function approx., x grid) pair)
precision = 8 - Precision that will be used for wavelet function
approximation computed with the wavefun(level=precision)
Wavelet's method.
(function_approx, xgrid) - Function defined on xgrid. Used instead
of Wavelet object to allow custom wavelet functions.
"""
if isinstance(wavelet, tuple):
psi, x = asarray(wavelet[0]), asarray(wavelet[1])
else:
if not isinstance(wavelet, WAVELET_CLASSES):
wavelet = wavelet_for_name(wavelet)
functions_approximations = wavelet.wavefun(precision)
if len(functions_approximations) == 2:
psi, x = functions_approximations
else:
psi, x = functions_approximations[1], functions_approximations[-1] # (psi, x) for (phi, psi, x) and (psi_d, x) for (phi_d, psi_d, phi_r, psi_r, x)
domain = float(x[-1] - x[0])
assert domain > 0
index = argmax(abs(fft(psi)[1:]))+2
if index > len(psi)/2:
index = len(psi)-index+2
return 1.0/(domain/(index-1))
def scal2frq(wavelet, scale, delta, precision=8):
"""
scal2frq(wavelet, scale, delta, precision=8) -> float - for orthogonal wavelets
scal2frq(wavelet, scale, delta, precision=8) -> float - for (function approx., x grid) pair
wavelet
scale
delta - sampling
"""
return centfrq(wavelet, precision=precision)/(scale*delta)
def qmf(filter):
filter = array(filter)[::-1]
filter[1::2] = -filter[1::2]
return filter
def orthfilt(scaling_filter):
assert len(scaling_filter) % 2 == 0
scaling_filter = asarray(scaling_filter, dtype=float64)
rec_lo = sqrt(2) * scaling_filter / sum(scaling_filter)
dec_lo = rec_lo[::-1]
rec_hi = qmf(rec_lo)
dec_hi = rec_hi[::-1]
return (dec_lo, dec_hi, rec_lo, rec_hi)
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