?hetrs2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Download PDF

ID 766686

Date 4/28/2026

Version

Public

?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 , mkl_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 = 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

uplo

CHARACTER*1 . 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

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) .

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

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

b

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.

Return Values

No return value, info is an Output Parameter.

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’ .

NOTE:

Select Your Language

Using Intel.com Search

Quick Links

Recent Searches

Advanced Search

Only search in

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hetrs2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes