?hetrs2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/22/2024

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?hetrs2

Solves a system of linear equations with a UDU- or LDL-factored Hermitian coefficient matrix.

Syntax

call chetrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )

call zhetrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )

call hetrs2( a, b, ipiv [,uplo] [,info] )

Include Files

mkl.fi, lapack.f90

Description

The routine solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization of A:

if `uplo='U'`,	`A = UDU^H`
if `uplo='L'`,	`A = LDL^H`

where

U and L are upper and lower triangular matrices with unit diagonal
D is a Hermitian block-diagonal matrix.

The factorization is computed by ?hetrf.

Input Parameters

uplo	CHARACTER1. Must be 'U' or 'L'. Indicates how the input matrix `A` has been factored: If `uplo = 'U'`, the array `a` stores the upper triangular factor `U` of the factorization `A` = `UDU^H`. If `uplo = 'L'`, the array `a` stores the lower triangular factor `L` of the factorization `A` = `LD*L^H`.
n	INTEGER. The order of matrix `A`; `n`≥ 0.
nrhs	INTEGER. The number of right-hand sides; nrhs≥ 0.
a, b	COMPLEX for chetrs2 DOUBLE COMPLEX for zhetrs2 Arrays: `a(lda,)`, `b(ldb,)`. The array `a` contains the block diagonal matrix `D` and the multipliers used to obtain the factor `U` or `L` as computed by ?hetrf. The array `b` contains the right-hand side matrix `B`. The second dimension of `a` must be at least `max(1,n)`, and the second dimension of `b` at least `max(1,nrhs)`.
lda	INTEGER. The leading dimension of `a`; `lda≥ max(1, n)`.
ldb	INTEGER. The leading dimension of `b`; `ldb≥ max(1, n)`.
ipiv	INTEGER. Array of size `n`. The ipiv array contains details of the interchanges and the block structure of `D` as determined by ?hetrf.
work	COMPLEX for chetrs2 DOUBLE COMPLEX for zhetrs2 Workspace array, size `n`.

Output Parameters

Overwritten by the solution matrix X.

info

INTEGER. If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine hetrs2 interface are as follows:

a	Holds the matrix `A` of size (`n`, `n`).
b	Holds the matrix `B` of size (`n`, `nrhs`).
ipiv	Holds the vector of length `n`.
uplo	Must be 'U' or 'L'. The default value is 'U'.

Parent topic: Solving Systems of Linear Equations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hetrs2

Syntax

Include Files

Description

Input Parameters

Output Parameters

LAPACK 95 Interface Notes

See Also