?sytrs2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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?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 = UDU^T`
if `uplo='L'`,	`A = LDL^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` = `UDU^T`. If `uplo = 'L'`, the array `a` stores the lower triangular factor `L` of the factorization `A` = `LDL^T`.
n	The order of matrix `A`; `n`≥ 0.
nrhs	The number of right-hand sides; nrhs≥ 0.
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 ?sytrf.
b	The array `b` contains the right-hand side matrix `B`. The size of `b` is at least max(1, ldbnrhs) for column major layout and max(1, ldbn) for row major layout.
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.
ipiv	Array of size `n`. The ipiv array contains details of the interchanges and the block structure of `D` as determined by ?sytrf.

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.

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

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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

See Also