Error when calculating singular values of a matrix

Question

I’m trying to calculate the singular values of a matrix using 2 methods. The matrix I’m using is the red channel of a sunflower image. Here’s the image if you need it.

The first method is using SVD:

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np

A = mpimg.imread('sunflower.jpeg')
R = A[:,:,0]

U, S, V = np.linalg.svd(R)
print(S)

The second is using an alternate approach to calculating singular values, where you take the square root of the eigenvalues of R.T*R.

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np

A = mpimg.imread('sunflower.jpeg')
R = A[:,:,0]

rW = np.linalg.eigvals(np.dot(R.T, R))
singvals = np.sqrt(rW)
print(singvals)

Hypothetically they should yield the same result, but that’s not what I’m getting. Any help would be appreciated!

Asked By: TheIndex

||

Source

Answer 1

When I run your code after casting R to be .astype(np.int64), and round the values to 6 decimal places, and compare the two return values as set, I get that they return the same values. I suspect that one or more of

Unexpected int overflow
Floating point rounding errors
Order of the singular values

is the source of the difference between the two…

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np

A = mpimg.imread('sunflower.jpeg')
R = A[:,:,0].astype(np.int64)

U, S, V = np.linalg.svd(R)

rW = np.linalg.eigvals(np.dot(R.T, R))
singvals = np.sqrt(rW)

set(S.round(6)) == set(singvals.round(6))
# True

Answered By: Chrysophylaxs

Error when calculating singular values of a matrix

Question:

Answers: