?hetrs2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?hetrs2

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

Syntax

lapack_int LAPACKE_chetrs2(int matrix_layout, char uplo, lapack_int n, lapack_int nrhs,
                           const lapack_complex_float *a, lapack_int lda,
                           const lapack_int *ipiv, lapack_complex_float *b,
                           lapack_int ldb);

lapack_int LAPACKE_zhetrs2(int matrix_layout, char uplo, lapack_int n, lapack_int nrhs,
                           const lapack_complex_double *a, lapack_int lda,
                           const lapack_int *ipiv, lapack_complex_double *b,
                           lapack_int ldb);

Include Files

mkl.h

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' ,

\(A = U*D*U^{H}\)

if uplo='L' ,

\(A = L*D*L^{H}\)

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

matrix_layout

Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

uplo

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 \(A = U*D*U^{H}\) .

If uplo = 'L' , the array a stores the lower triangular factor \(L\) of the factorization \(A = L*D*L^{H}\) .

n: Specifies the order of the matrix A . The value of n must be at least zero.

nrhs

The number of right-hand sides; nrhs ≥ 0.

a , b

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) .

a

The array a of size max(1, lda * n ) contains the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ?hetrf .

b

The array b of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout contains the right-hand side matrix B .

lda

The leading dimension of a ; lda≥ max(1, n) .

ldb

The leading dimension of b ; ldb≥ max(1, n)ldb ≥ max(1, n ) for column major layout and ldb ≥ nrhs for row major layout .

ipiv

Array of size n . The ipiv array contains details of the interchanges and the block structure of D as determined by ?hetrf .

work

Workspace array, size n .

Output Parameters

b

Overwritten by the solution matrix X .

Return Values

This function returns a value info .

If info = 0 , the execution is successful.
If info = -i , parameter i had an illegal value.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?hetrs2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes