naginterfaces.library.matop.real_​symm_​posdef_​inv_​noref

naginterfaces.library.matop.real_symm_posdef_inv_noref(a)[source]

real_symm_posdef_inv_noref calculates the approximate inverse of a real symmetric positive definite matrix, using a Cholesky factorization.

For full information please refer to the NAG Library document for f01ad

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/f01/f01adf.html

Parameters
afloat, array-like, shape

The upper triangle of the positive definite symmetric matrix . The elements of the array below the diagonal need not be set.

Returns
afloat, ndarray, shape

The lower triangle of the inverse matrix is stored in the elements of the array below the diagonal, in rows to ; is stored in for . The upper triangle of the original matrix is unchanged.

Raises
NagValueError
(errno )

The matrix is not positive definite, possibly due to rounding errors.

(errno )

On entry, .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

To compute the inverse of a real symmetric positive definite matrix , real_symm_posdef_inv_noref first computes a Cholesky factorization of as , where is lower triangular. It then computes and finally forms as the product .

References

Wilkinson, J H and Reinsch, C, 1971, Handbook for Automatic Computation II, Linear Algebra, Springer–Verlag