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jointD.py
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jointD.py
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# Disclaimer: This code is a python implementation of the extended Jacobi
# technique for simultaneous diagonalization in the jadeR(CM, m) function from
# https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/23ed4823-a05f-47da-99e9-4e84f74c955d/c77c8388-dd0e-4c1a-9067-edfa8989fef4/previews/iPPG_dataset_and_Matlab_package/jadeR.m/index.html
# by stash-196
# The technique is discussed in "Cardoso and Souloumiac, 1996, Jacobi Angles for Simultaneous Diagonalization"
# at https://epubs.siam.org/doi/abs/10.1137/S0895479893259546
import numpy as np
import math
verbose = 1
def jointD(Matrices):
CM = np.hstack(tuple(Matrices))
m, n = CM.shape
nbcm = int(n/m)
if 0:
## Init by diagonalizing a *single* cumulant matrix. It seems to save
## some computation time `sometimes'. Not clear if initialization is really worth
## it since Jacobi rotations are very efficient. On the other hand, it does not
## cost much...
if verbose:
print('Initialization of the diagonalization')
D, V = np.linalg.eig(CM[:, list(range(m))])
for u in range(0, m*nbcm, m):
CM[:, u:u+m] = CM[:, u:u+m] @ V
CM = V.T @ CM
else: ##The dont-try-to-be-smart init //lol
V = np.eye(m)
## Computing the initial value of the contrast
Diag = np.zeros(m)
On = 0
Range = np.array(range(m))
for im in range(nbcm):
Diag = np.diag(CM[:, Range])
On = On + np.sum(Diag * Diag)
Range += m
Off = np.sum(CM * CM) - On
seuil = 1e-7 # threshold on small angles. //Should be scaled... but idk
encore = 1
sweep = 0 # sweep number
updates = 0 # Total number of rotations
upds = 0 # Number -f rotations in a given sweep
g = np.zeros((2, nbcm))
gg = np.zeros((2, 2))
G = np.zeros((2, 2))
c = 0
s = 0
ton = 0
toff = 0
theta = 0
Gain = 0
## Joint diagonalization proper
if verbose: print('Contrast optimization by joint diagonalization\n')
while encore:
encore = 0
if verbose: print('Sweep', sweep)
sweep += 1
upds = 0
Vkeep = V
for p in range(m-1):
for q in range(p+1, m):
Ip = list(range(p, m*nbcm, m))
Iq = list(range(q, m*nbcm, m))
# Computation of Givens angle
g = np.array([CM[p, Ip] - CM[q, Iq], CM[p, Iq] + CM[q, Ip]])
# print('g = \n', g)
gg = g @ g.T
ton = gg[0, 0] - gg[1, 1]
toff = gg[0, 1] + gg[1, 0]
theta = 0.5 * math.atan2(toff, ton + np.sqrt(ton * ton + toff * toff))
Gain = (np.sqrt(ton * ton + toff * toff) - ton) / 4
if abs(theta) > seuil:
encore = 1
upds += 1
c = math.cos(theta)
s = math.sin(theta)
G = np.array([[c, -s], [s, c]])
pair = np.array([p, q]).T
V[:, pair] = V[:, pair] @ G
CM[pair, :] = G.T @ CM[pair, :]
CM[:, Ip + Iq] = np.hstack([c * CM[:, Ip] + s * CM[:, Iq], -s * CM[:, Ip] + c * CM[:, Iq]])
On = On + Gain
Off = Off - Gain
# print(' {}, {}, {}'.format(p, q, Off/On))
if verbose: print(' completed in {} rotations'.format(upds))
updates += upds
#returns a list of diagonal matrices and eigen vector matrix
return list(np.array_split(CM, nbcm, 1)), V
# % Copyright (c) 2013, Jean-Francois Cardoso
# % All rights reserved.
# %
# %
# % BSD-like license.
# % Redistribution and use in source and binary forms, with or without modification,
# % are permitted provided that the following conditions are met:
# %
# % Redistributions of source code must retain the above copyright notice,
# % this list of conditions and the following disclaimer.
# %
# % Redistributions in binary form must reproduce the above copyright notice,
# % this list of conditions and the following disclaimer in the documentation
# % and/or other materials provided with the distribution.
# %
# %
# % THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS
# % OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
# % AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER
# % OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# % DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# % DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER
# % IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
# % OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
if __name__ == "__main__":
# Checking to see if it works with Random Symmetric Commutative Matrices
# n = 5
# A = np.random.rand(n, n)
# A = (A + A.T)/2
# w, v = np.linalg.eig(A)
# B = np.random.rand(n)
# B = np.diag(B)
# B = v @ B @ v.T
# Or explicitly pick them
A = np.array([
[-0.1332, -0.5041, 0.8295, -0.7784, -0.0687],
[-0.5041, -0.8479, -1.1886, 0.0981, 0.7626],
[0.8295, -1.1886, -0.8655, -0.8128, 0.4876],
[-0.7784, 0.0981, -0.8128, 0.3335, -0.0424],
[-0.0687, 0.7626, 0.4876, -0.0424, 0.8620],
])
B = np.array([
[0.4531, 0.1442, 0.0488, -0.1342, -0.0728],
[0.1442, -0.6669, -0.6133, 0.3468, 0.2286],
[0.0488, -0.6133, -0.6185, -0.5847, 0.1302],
[-0.1342, 0.3468, -0.5847, -0.2836, -0.0181],
[-0.0728, 0.2286, 0.1302, -0.0181, -0.4216],
])
# Input list or tuple
newDs, newV = jointD((A, B))
# Test reproducibility
newA = newV @ newDs[0] @ newV.T
newB = newV @ newDs[1] @ newV.T
print(newA)
print(newB)