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!
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
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