?sytrs_rook

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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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*U^T or A = L*D*L^T 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` = `UDU^T`. If `uplo = 'L'`, the factorization is of the form `A` = `LDL^T`.
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 (ldan)`, `b size (ldbnrhs)`. 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 `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.

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.

Parent topic: Solving Systems of Linear Equations: LAPACK Computational Routines

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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

Application Notes

See Also