/usr/lib/python2.7/dist-packages/pywt/multilevel.py is in python-pywt 0.3.0-1build1.
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# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
# See COPYING for license details.
"""
Multilevel 1D and 2D Discrete Wavelet Transform
and Inverse Discrete Wavelet Transform.
"""
from __future__ import division, print_function, absolute_import
__all__ = ['wavedec', 'waverec', 'wavedec2', 'waverec2']
import numpy as np
from ._pywt import Wavelet
from ._pywt import dwt, idwt, dwt_max_level
from .multidim import dwt2, idwt2
def wavedec(data, wavelet, mode='sym', level=None):
"""
Multilevel 1D Discrete Wavelet Transform of data.
Parameters
----------
data: array_like
Input data
wavelet : Wavelet object or name string
Wavelet to use
mode : str, optional
Signal extension mode, see MODES (default: 'sym')
level : int, optional
Decomposition level. If level is None (default) then it will be
calculated using `dwt_max_level` function.
Returns
-------
[cA_n, cD_n, cD_n-1, ..., cD2, cD1] : list
Ordered list of coefficients arrays
where `n` denotes the level of decomposition. The first element
(`cA_n`) of the result is approximation coefficients array and the
following elements (`cD_n` - `cD_1`) are details coefficients arrays.
Examples
--------
>>> from pywt import multilevel
>>> coeffs = multilevel.wavedec([1,2,3,4,5,6,7,8], 'db1', level=2)
>>> cA2, cD2, cD1 = coeffs
>>> cD1
array([-0.70710678, -0.70710678, -0.70710678, -0.70710678])
>>> cD2
array([-2., -2.])
>>> cA2
array([ 5., 13.])
"""
if not isinstance(wavelet, Wavelet):
wavelet = Wavelet(wavelet)
if level is None:
level = dwt_max_level(len(data), wavelet.dec_len)
elif level < 0:
raise ValueError(
"Level value of %d is too low . Minimum level is 0." % level)
coeffs_list = []
a = data
for i in range(level):
a, d = dwt(a, wavelet, mode)
coeffs_list.append(d)
coeffs_list.append(a)
coeffs_list.reverse()
return coeffs_list
def waverec(coeffs, wavelet, mode='sym'):
"""
Multilevel 1D Inverse Discrete Wavelet Transform.
Parameters
----------
coeffs : array_like
Coefficients list [cAn, cDn, cDn-1, ..., cD2, cD1]
wavelet : Wavelet object or name string
Wavelet to use
mode : str, optional
Signal extension mode, see MODES (default: 'sym')
Examples
--------
>>> from pywt import multilevel
>>> coeffs = multilevel.wavedec([1,2,3,4,5,6,7,8], 'db2', level=2)
>>> multilevel.waverec(coeffs, 'db2')
array([ 1., 2., 3., 4., 5., 6., 7., 8.])
"""
if not isinstance(coeffs, (list, tuple)):
raise ValueError("Expected sequence of coefficient arrays.")
if len(coeffs) < 2:
raise ValueError(
"Coefficient list too short (minimum 2 arrays required).")
a, ds = coeffs[0], coeffs[1:]
for d in ds:
a = idwt(a, d, wavelet, mode, 1)
return a
def wavedec2(data, wavelet, mode='sym', level=None):
"""
Multilevel 2D Discrete Wavelet Transform.
Parameters
----------
data : ndarray
2D input data
wavelet : Wavelet object or name string
Wavelet to use
mode : str, optional
Signal extension mode, see MODES (default: 'sym')
level : int, optional
Decomposition level. If level is None (default) then it will be
calculated using `dwt_max_level` function.
Returns
-------
[cAn, (cHn, cVn, cDn), ... (cH1, cV1, cD1)] : list
Coefficients list
Examples
--------
>>> from pywt import multilevel
>>> coeffs = multilevel.wavedec2(np.ones((4,4)), 'db1')
>>> # Levels:
>>> len(coeffs)-1
2
>>> multilevel.waverec2(coeffs, 'db1')
array([[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.]])
"""
data = np.asarray(data, np.float64)
if data.ndim != 2:
raise ValueError("Expected 2D input data.")
if not isinstance(wavelet, Wavelet):
wavelet = Wavelet(wavelet)
if level is None:
size = min(data.shape)
level = dwt_max_level(size, wavelet.dec_len)
elif level < 0:
raise ValueError(
"Level value of %d is too low . Minimum level is 0." % level)
coeffs_list = []
a = data
for i in range(level):
a, ds = dwt2(a, wavelet, mode)
coeffs_list.append(ds)
coeffs_list.append(a)
coeffs_list.reverse()
return coeffs_list
def waverec2(coeffs, wavelet, mode='sym'):
"""
Multilevel 2D Inverse Discrete Wavelet Transform.
coeffs : array_like
Coefficients list [cAn, (cHn, cVn, cDn), ... (cH1, cV1, cD1)]
wavelet : Wavelet object or name string
Wavelet to use
mode : str, optional
Signal extension mode, see MODES (default: 'sym')
Returns
-------
2D array of reconstructed data.
Examples
--------
>>> from pywt import multilevel
>>> coeffs = multilevel.wavedec2(np.ones((4,4)), 'db1')
>>> # Levels:
>>> len(coeffs)-1
2
>>> multilevel.waverec2(coeffs, 'db1')
array([[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.]])
"""
if not isinstance(coeffs, (list, tuple)):
raise ValueError("Expected sequence of coefficient arrays.")
if len(coeffs) < 2:
raise ValueError(
"Coefficient list too short (minimum 2 arrays required).")
a, ds = coeffs[0], coeffs[1:]
for d in ds:
a = idwt2((a, d), wavelet, mode)
return a
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