Speed up python code for computing matrix cofactors

user_136598 0
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As part of a complex task, I need to compute matrix cofactors. I did this in a straightforward way using this nice code for computing matrix minors. Here is my code:

def matrix_cofactor(matrix):
    C = np.zeros(matrix.shape)
    nrows, ncols = C.shape
    for row in xrange(nrows):
        for col in xrange(ncols):
            minor = matrix[np.array(range(row)+range(row+1,nrows))[:,np.newaxis],
                           np.array(range(col)+range(col+1,ncols))]
            C[row, col] = (-1)**(row+col) * np.linalg.det(minor)
    return C

It turns out that this matrix cofactor code is the bottleneck, and I would like to optimize the code snippet above. Any ideas as to how to do this?

linear-algebra matrix numpy python performance
4 Answers

Instead of using the inverse and determinant, I'd suggest using the SVD

def cofactors(A):
    U,sigma,Vt = np.linalg.svd(A)
    N = len(sigma)
    g = np.tile(sigma,N)
    g[::(N+1)] = 1
    G = np.diag(-(-1)**N*np.product(np.reshape(g,(N,N)),1)) 
    return U @ G @ Vt
user_23082880 
from sympy import *
A = Matrix([[1,2,0],[0,3,0],[0,7,1]])
A.adjugate().T

And the output (which is cofactor matrix) is:

Matrix([
[ 3, 0,  0],
[-2, 1, -7],
[ 0, 0,  3]])
user_88480250
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