Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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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 = U*D*UT

if uplo='L',

A = L*D*LT

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

CHARACTER*1. 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 = U*D*UT.

If uplo = 'L', the array a stores the lower triangular factor L of the factorization A = L*D*LT.

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

b

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'.