Trying to compute SVD in Python to find the most significant elements of a spectrum and created a matrix just containing the most significant parts.
In python I have:
u,s,v = linalg.svd(Pxx, full_matrices=True)
This gives 3 matrices back; where "s" contains the magnitudes that corresponds to u, v.
In order to construct a new matrix, containing all of the significant parts of the signal, I need to capture the highest values in "s" and match them with the columns in "u" and "v" and the resulting matrix should give me the most significant part of the data.
The problem is I don't know how I would do this in Python, for example, how do I find the highest numbers in "s" and select the columns in "u" and "v" in order to create a new matrix?
(I'm new to Python and numpy) so any help would be greatly appreciated
Edit:
import wave, struct, numpy as np, matplotlib.mlab as mlab, pylab as pl
from scipy import linalg, mat, dot;
def wavToArr(wavefile):
w = wave.open(wavefile,"rb")
p = w.getparams()
s = w.readframes(p[3])
w.close()
sd = np.fromstring(s, np.int16)
return sd,p
def wavToSpec(wavefile,log=False,norm=False):
wavArr,wavParams = wavToArr(wavefile)
print wavParams
return mlab.specgram(wavArr, NFFT=256,Fs=wavParams[2],detrend=mlab.detrend_mean,window=mlab.window_hanning,noverlap=128,sides='onesided',scale_by_freq=True)
wavArr,wavParams = wavToArr("wavBat1.wav")
Pxx, freqs, bins = wavToSpec("wavBat1.wav")
Pxx += 0.0001
U, s, Vh = linalg.svd(Pxx, full_matrices=True)
assert np.allclose(Pxx, np.dot(U, np.dot(np.diag(s), Vh)))
s[2:] = 0
new_a = np.dot(U, np.dot(np.diag(s), Vh))
print(new_a)
The SVD can be calculated by calling the svd() function. The function takes a matrix and returns the U, Sigma and V^T elements. The Sigma diagonal matrix is returned as a vector of singular values. The V matrix is returned in a transposed form, e.g. V.T.
The Singular Value Decomposition (SVD) of a matrix is a factorization of that matrix into three matrices. It has some interesting algebraic properties and conveys important geometrical and theoretical insights about linear transformations. It also has some important applications in data science.
The process of Singular Value Decomposition (SVD) involves breaking down a matrix A into the form . This computation allows us to retain the important singular values that the image requires while also releasing the values that are not as necessary in retaining the quality of the image.
linalg.svd
returns s
in descending order. So to select the n
highest numbers in s
, you'd simply form
s[:n]
If you set the smaller values of s
to zero,
s[n:] = 0
then matrix multiplication would take care of "selecting" the appropriate columns of U and V.
For example,
import numpy as np
LA = np.linalg
a = np.array([[1, 3, 4], [5, 6, 9], [1, 2, 3], [7, 6, 8]])
print(a)
# [[1 3 4]
# [5 6 9]
# [1 2 3]
# [7 6 8]]
U, s, Vh = LA.svd(a, full_matrices=False)
assert np.allclose(a, np.dot(U, np.dot(np.diag(s), Vh)))
s[2:] = 0
new_a = np.dot(U, np.dot(np.diag(s), Vh))
print(new_a)
# [[ 1.02206755 2.77276308 4.14651336]
# [ 4.9803474 6.20236935 8.86952026]
# [ 0.99786077 2.02202837 2.98579698]
# [ 7.01104783 5.88623677 8.07335002]]
Given the data here,
import numpy as np
import scipy.linalg as SL
import matplotlib.pyplot as plt
Pxx = np.genfromtxt('mBtasJLD.txt')
U, s, Vh = SL.svd(Pxx, full_matrices=False)
assert np.allclose(Pxx, np.dot(U, np.dot(np.diag(s), Vh)))
s[2:] = 0
new_a = np.dot(U, np.dot(np.diag(s), Vh))
print(new_a)
plt.plot(new_a)
plt.show()
produces
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