naginterfaces.library.matop.real_​mod_​chol_​perturbed_​a

naginterfaces.library.matop.real_mod_chol_perturbed_a(uplo, a, offdiag, ipiv)[source]

real_mod_chol_perturbed_a computes the positive definite perturbed matrix from the factors of a modified Cholesky factorization of a real symmetric matrix, .

For full information please refer to the NAG Library document for f01me

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/f01/f01mef.html

Parameters
uplostr, length 1

Indicates whether the upper or lower triangular part of was stored and how it was factorized.

The upper triangular part of was stored and we compute such that .

The lower triangular part of was stored and we compute such that .

afloat, array-like, shape

The modified Cholesky factor of , as returned by real_modified_cholesky().

offdiagfloat, array-like, shape

The array as returned by real_modified_cholesky().

ipivint, array-like, shape

The array as returned by real_modified_cholesky().

Returns
afloat, ndarray, shape

If , the upper triangular part of is returned and the elements of the array below the diagonal are not referenced.

If , the lower triangular part of is returned and the elements of the array above the diagonal are not referenced.

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: .

Notes

real_mod_chol_perturbed_a computes the positive definite perturbed matrix from the factors provided by a previous call to real_modified_cholesky(). For a symmetric, possibly indefinite matrix , real_modified_cholesky() finds the Cheng–Higham modified Cholesky factorization

when . Here is a unit lower triangular matrix, is a permutation matrix, is a symmetric block diagonal matrix (with blocks of order or ). The matrix is not explicitly formed.

If , we compute from the factorization , where is a unit upper triangular matrix.

References

Cheng, S H and Higham, N J, 1998, A modified Cholesky algorithm based on a symmetric indefinite factorization, SIAM J. Matrix Anal. Appl. (19(4)), 1097–1110