An old question on Singular Value Decomposition lead me to ask this question: How could I truncate a 2-Dimensional array, to a number of columns dictated by a certain tolerance?
Specifically, please consider the following code snippet, which defines an accepted tolerance of 1e-4 and applies Singular Value Decomposition to a matrix 'A'.
#Python
tol=1e-4
U,Sa,V=np.linalg.svd(A)
S=np.diag(Sa)
The resulting singular value diagonal matrix 'S' holds non-negative singular values in decreasing order of magnitude.
What I want to obtain is a truncated 'S' matrix, in a way that the columns of the matrix holding singular values lower than 1e-4 would be removed. Then, apply this truncation to the matrix 'U'.
Is there a simple way of doing this? I have been looking around, and found some solutions to the problem for Matlab, but didn't find anything similar for Python. For Matlab, the code would look something like:
%Matlab
tol=1e-4
mask=any(Sigma>=tol,2);
sigRB=Sigma(:,mask);
mask2=any(U>=tol,2);
B=U(:,mask);
Thanks in advance. I hope my post was not too messy to understand.
I am not sure if I understand you correctly. If my solution is not what you ask for, please consider adding an example to your question.
The following code drops all columns from array s that consist only of values smaller than tol.
s = np.array([
[1, 0, 0, 0, 0, 0],
[0, .9, 0, 0, 0, 0],
[0, 0, .5, 0, 0, 0],
[0, 0, 0, .4, 0, 0],
[0, 0, 0, 0, .3, 0],
[0, 0, 0, 0, 0, .2]
])
print(s)
tol = .4
ind = np.argwhere(s.max(axis=1) < tol)
s = np.delete(s, ind, 1)
print(s)
Output:
[[1. 0. 0. 0. 0. 0. ]
[0. 0.9 0. 0. 0. 0. ]
[0. 0. 0.5 0. 0. 0. ]
[0. 0. 0. 0.4 0. 0. ]
[0. 0. 0. 0. 0.3 0. ]
[0. 0. 0. 0. 0. 0.2]]
[[1. 0. 0. 0. ]
[0. 0.9 0. 0. ]
[0. 0. 0.5 0. ]
[0. 0. 0. 0.4]
[0. 0. 0. 0. ]
[0. 0. 0. 0. ]]
I am applying max to axis 1 and then using np.argwhere to get the indices of the columns where the max value is smaller than tol.
Edit: In order to truncate the columns of matrix 'U', so it coincides in size with the reduced matrix 'S', the following code works:
k = len(S[0])
Ured = U[:,0:k]
Uredsize = np.shape(Ured) # To check it has worked
print(Uredsize)