Created
December 30, 2017 17:27
-
-
Save drewdaemon/4e8e5da96043fe93e70425da05f8a49f to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| def qr_gram_schmidt(A): | |
| """Compute the reduced QR decomposition of A via Modified Gram-Schmidt. | |
| Parameters: | |
| A ((m,n) ndarray): A matrix of rank n. | |
| Returns: | |
| Q ((m,n) ndarray): An orthonormal matrix. | |
| R ((n,n) ndarray): An upper triangular matrix. | |
| """ | |
| m, n = A.shape | |
| Q = A.copy() | |
| R = np.zeros((n, n)) | |
| for i in range(n): | |
| R[i, i] = la.norm(Q[:, i]) | |
| Q[:, i] = Q[:, i]/R[i, i] | |
| for j in range(i + 1, n): | |
| R[i, j] = Q[:, j] @ Q[:, i] | |
| Q[:, j] = Q[:, j] - R[i, j] * Q[:,i] | |
| return Q, R |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
When A =
array([[ 0., 1., 2., 3.],
[ 4., 5., 6., 7.],
[ 8., 9., 10., 11.],
[ 12., 13., 14., 15.]])
Scipy's output:
array([[ 0. , -0.83666003, 0.53970407, 0.09337836],
[-0.26726124, -0.47809144, -0.78920555, 0.27776718],
[-0.53452248, -0.11952286, -0.04070111, -0.83566944],
[-0.80178373, 0.23904572, 0.29020259, 0.4645239 ]]),
My output:
array([[ 0. , 0.83666003, 0. , 0.86999932],
[ 0.26726124, 0.47809144, -0.33333333, 0.41083301],
[ 0.53452248, 0.11952286, -0.66666667, 0.06041662],
[ 0.80178373, -0.23904572, -0.66666667, -0.26583313]]),