?sytrs_rook

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?sytrs_rook

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

Syntax

lapack_int LAPACKE_ssytrs_rook(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_dsytrs_rook(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_csytrs_rook(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_zsytrs_rook(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 \(A = U*D*U^{T}\) or \(A = L*D*L^{T}\) computed by ?sytrf_rook (Computes the bounded Bunch-Kaufman factorization of a symmetric matrix.) .

Input Parameters

matrix_layout

Specifies whether matrix storage layout for array b 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 factorization is of the form \(A = U*D*U^{T}\) .

If uplo = 'L' , the factorization is of the form \(A = L*D*L^{T}\) .

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.

ipiv

Array, size at least max(1, n) . The ipiv array, as returned by ?sytrf_rook (Computes the bounded Bunch-Kaufman factorization of a symmetric matrix.) .

a , b

Arrays: a, size (lda*n) , b size (ldb*nrhs) .

The array a contains the block diagonal matrix D and the multipliers used to obtain U or L as computed by ?sytrf_rook (Computes the bounded Bunch-Kaufman factorization of a symmetric matrix.) (see uplo ).

The array b contains the matrix B whose columns are the right-hand sides for the system of equations.

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 .

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 , the i -th parameter 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.

Application Notes

The total number of floating-point operations for one right-hand side vector is approximately \(2n^{2}\) for real flavors or \(8n^{2}\) for complex flavors.

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?sytrs_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes