slogdet

CholeskyFactor.slogdet()[source]

Compute the sign and (natural) log-determinant of the matrix from its Cholesky factorization.

Returns:

  • sign (int) – The sign of the determinant of the matrix A that was factorized. This is always 1 for a positive definite matrix.

  • logdet (float) – The natural logarithm of the absolute value of the determinant of the matrix A that was factorized.

See also

logdet, det, numpy.linalg.slogdet, numpy.linalg.det, scipy.linalg.det

Notes

This function computes the sign and log-determinant of the matrix A from its Cholesky factorization. If the factorization is in \(LL^T\) form, the determinant is computed as:

\[\log \det(A) = 2 \sum_i \log L_{ii}.\]

If the factorization is in \(LDL^{\top}\) form, the determinant is computed as:

\[\log \det(A) = \sum_i \log D_{ii}.\]

Added in version 0.2.