naginterfaces.library.lapacklin.zhpsv

naginterfaces.library.lapacklin.zhpsv(uplo, ap, b)[source]

zhpsv computes the solution to a complex system of linear equations

where is an Hermitian matrix stored in packed format and and are matrices.

For full information please refer to the NAG Library document for f07pn

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07pnf.html

Parameters
uplostr, length 1

If , the upper triangle of is stored.

If , the lower triangle of is stored.

apcomplex, array-like, shape

The Hermitian matrix , packed by columns.

bcomplex, array-like, shape

The right-hand side matrix .

Returns
apcomplex, ndarray, shape

The block diagonal matrix and the multipliers used to obtain the factor or from the factorization or as computed by zhptrf(), stored as a packed triangular matrix in the same storage format as .

ipivint, ndarray, shape

Details of the interchanges and the block structure of . More precisely,

if , is a pivot block and the th row and column of were interchanged with the th row and column;

if and , is a pivot block and the th row and column of were interchanged with the th row and column;

if and , is a pivot block and the th row and column of were interchanged with the th row and column.

bcomplex, ndarray, shape

If no exception or warning is raised, the solution matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

Element of the diagonal is exactly zero. The factorization has been completed, but the block diagonal matrix is exactly singular, so the solution could not be computed.

Notes

zhpsv uses the diagonal pivoting method to factor as if or if , where (or ) is a product of permutation and unit upper (lower) triangular matrices, is Hermitian and block diagonal with and diagonal blocks. The factored form of is then used to solve the system of equations .

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore

Higham, N J, 2002, Accuracy and Stability of Numerical Algorithms, (2nd Edition), SIAM, Philadelphia