?sytrs2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?sytrs2

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

Syntax

call ssytrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )

call dsytrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )

call csytrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )

call zsytrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )

call sytrs2( a,b,ipiv[,uplo][,info] )

Include Files

mkl.fi, lapack.f90

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

uplo	CHARACTER1. 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` = `LD*L^T`.
n	INTEGER. The order of matrix `A`; `n`≥ 0.
nrhs	INTEGER. The number of right-hand sides; nrhs≥ 0.
a, b	REAL for ssytrs2 DOUBLE PRECISION for dsytrs2 COMPLEX for csytrs2 DOUBLE COMPLEX for zsytrs2 Arrays: `a(lda,)`, `b(ldb,)`. The array `a` contains the block diagonal matrix `D` and the multipliers used to obtain the factor `U` or `L` as computed by ?sytrf. The array `b` contains the right-hand side matrix `B`. The second dimension of `a` must be at least `max(1,n)`, and the second dimension of `b` at least `max(1,nrhs)`.
lda	INTEGER. The leading dimension of `a`; `lda≥ max(1, n)`.
ldb	INTEGER. The leading dimension of `b`; `ldb≥ max(1, n)`.
ipiv	INTEGER. Array of size `n`. The ipiv array contains details of the interchanges and the block structure of `D` as determined by ?sytrf.
work	REAL for ssytrs2 DOUBLE PRECISION for dsytrs2 COMPLEX for csytrs2 DOUBLE COMPLEX for zsytrs2 Workspace array, size `n`.

Output Parameters

Overwritten by the solution matrix X.

info

INTEGER. If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine sytrs2 interface are as follows:

a	Holds the matrix `A` of size (`n`, `n`).
b	Holds the matrix `B` of size (`n`, `nrhs`).
ipiv	Holds the vector of length `n`.
uplo	Indicates how the input matrix `A` has been factored. Must be 'U' or 'L'.

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

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?sytrs2

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