Computing SVD in python

Question

Hello everyone i am trying to compute the SVD of a matrix with numpy but i get wrong result.

I have this matrix

X = [[ 0  0  8]
    [ 0 23 25]
    [ 0  0  0]]

I am going through this code:

U, D, VT = np.linalg.svd(X, full_matrices=False)
X_remake = (U @ np.diag(D ) @ VT)

But the result that i get is this which is obviously wrong:

X_remake = ([[0.00000000e+00, 1.13509861e-15, 8.00000000e+00],
            [0.00000000e+00, 2.30000000e+01, 2.50000000e+01],
            [0.00000000e+00, 0.00000000e+00, 0.00000000e+00]])

Have you calculated the difference between the original and the resulting matrix (element-wise)? — mkrieger1, May 30 '21 at 08:27
Does this answer your question? [Is floating point math broken?](https://stackoverflow.com/questions/588004/is-floating-point-math-broken) — mkrieger1, May 30 '21 at 08:30
I calculated the difference between the original and the resulting matrix but the result is still wrong. So if is this my problem what i have to do ? — Lefteris Kyprianou, May 30 '21 at 08:35
But you do realize that all elements in the resulting matrix are equal to the original matrix except the middle one in the first row, and for it the difference is extremely close to zero? — mkrieger1, May 30 '21 at 08:48
No the non zero elements have big difference from zero (like 4 ), but i can't understand why, it is working with (2x2) matrix but if the matrix shape is greater than 3 x 3 it is not working. — Lefteris Kyprianou, May 30 '21 at 08:52
if you `np.round()` your result, you will see, that there is nothing wrong with the result. As mentioned by mkrieger21, it's just floating point math. — Drey, May 30 '21 at 08:56
I have already seen that, but I think that you are misinterpreting what you are seeing in the result. You think that `2.30000000e+01` is wrong because it should be `23`, don't you? — mkrieger1, May 30 '21 at 08:57
What is `X_occur`? I thought we were talking about the difference between `X` and `X_remake` so far. — mkrieger1, May 30 '21 at 08:59
Okkk, now i understood what you mean, i fixed it. Thank you very much ! — Lefteris Kyprianou, May 30 '21 at 09:09

abbass biniaz · Answer 1 · 2023-01-28T17:44:33.800

0

You can use the below snippet code to rebuild the input array as follow:

X = [[ 0 , 0 , 8]   , [ 0,23, 25]  ,  [ 0,  0,  0]]
U, D, VT = np.linalg.svd(X, full_matrices=False)

D=np.diag(D)    
X_remake=np.dot(U, np.dot(D, VT))    
print(X_remake)

# array([[0.00000000e+00, 1.19457349e-15, 8.00000000e+00],
#        [0.00000000e+00, 2.30000000e+01, 2.50000000e+01],
#        [0.00000000e+00, 0.00000000e+00, 0.00000000e+00]])

edited Jan 28 '23 at 17:44

answered Jan 25 '23 at 19:59

abbass biniaz

3
3

Users find it difficult to understand code only answers with no explanation. Please add some description explaining what is does and how it solves the problem or add comments in the source code at appropriate places. – Azhar Khan Jan 27 '23 at 05:17

Computing SVD in python

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