?sytrs2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?sytrs2

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

Syntax

lapack_int LAPACKE_ssytrs2(int matrix_layout, char uplo, lapack_int n, lapack_int nrhs,
                           const float *a, lapack_int lda, const lapack_int *ipiv,
                           float *b, lapack_int ldb);

lapack_int LAPACKE_dsytrs2(int matrix_layout, char uplo, lapack_int n, lapack_int nrhs,
                           const double *a, lapack_int lda, const lapack_int *ipiv,
                           double *b, lapack_int ldb);

lapack_int LAPACKE_csytrs2(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_zsytrs2(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 symmetric matrix \(A\) using the factorization of \(A\) :

if uplo='U' ,

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

if uplo='L' ,

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

where

\(U\) and \(L\) are upper and lower triangular matrices with unit diagonal
\(D\) is a symmetric block-diagonal matrix.

The factorization is computed by ?sytrf .

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

If uplo = 'L' , the array a stores the lower triangular factor \(L\) of the factorization \(A = L*D*L^{T}\) .

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

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 ?sytrf .

b

The array b contains the right-hand side matrix B .

The size of b is at least max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout.

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 ?sytrf .

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

?sytrs2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes