Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/22/2024
Public

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?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*UT or A = L*D*LT computed by ?sytrf_rook.

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*UT.

If uplo = 'L', the factorization is of the form A = L*D*LT.

n

The order of matrix A; n 0.

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.

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 (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) for column major layout and ldbnrhs) 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.

Application Notes

The total number of floating-point operations for one right-hand side vector is approximately 2n2 for real flavors or 8n2 for complex flavors.