could not broadcast input array from shape (3,1) into shape (3,)-CodePudding

I have the following python code for QR factorization. At line of Q[:,i] = u / norm , I get the error mentioned in the title. Can anyone help, please?

Q is has the shape (3,3),
u is expected to has the shape (3,1)
norm is a scalar

The error message is:

could not broadcast input array from shape (3,1) into shape (3,)

The expected output is the matrix Q with the shape (3,3).

import numpy as np

def QRfactorization(A):
    # getting the size of the matrix
    N = len(A)

    # preallocating Q 
    Q = np.zeros((N, N))
    
    for i in range(N):
        u =  A[:,i]
        for j in range(i):
            # calculating the projection
            h = np.vdot(u,Q[:,j])
            u = u - h*Q[:,j]
        norm = np.linalg.norm(u) 
        Q[:,i] = u / norm
    #getting R matrix  
    R = Q.T*A
    return Q , R

def main():
    # input is an square matrix A
    A = np.matrix([[1,2,3],[4,5,6],[1,2,3]])
    Q = QRfactorization(A)
    print(Q)

main()

CodePudding user response：

The use of numpy.matrix is discouraged, and using numpy.array also fixes this issue:

def main():
    # input is an square matrix A
    A = np.array([[1,2,3],[4,5,6],[1,2,3]])
    Q = QRfactorization(A)
    print(Q)

CodePudding user response：

You can avoid writing your own and do this directly with numpy.linalg.qr

https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html

def main():
    # input is an square matrix A
    A = np.matrix([[1,2,3],[4,5,6],[1,2,3]])
    q, r = np.linalg.qr(A)
    print(q)
    print(r)

BEWARE, you are not calculating the R-portion completely/correctly if it matters to your result, as it should be an upper-triangular matrix

results with @Nils Werner's .array() change to your method
(results are combined into a single array)

(array([[ 0.23570226,  0.66666667, -0.23570226],
       [ 0.94280904, -0.33333333, -0.94280904],
       [ 0.23570226,  0.66666667, -0.23570226]]), array([[ 0.23570226,  1.88561808,  0.70710678],
       [ 2.66666667, -1.66666667,  4.        ],
       [-0.23570226, -1.88561808, -0.70710678]]))

results from naive np.linalg.qr (same for "complete" and "reduced" modes)

[[-2.35702260e-01  6.66666667e-01 -7.07106781e-01]
 [-9.42809042e-01 -3.33333333e-01  2.22044605e-16]
 [-2.35702260e-01  6.66666667e-01  7.07106781e-01]]
[[-4.24264069 -5.65685425 -7.07106781]
 [ 0.          1.          2.        ]
 [ 0.          0.          0.        ]]