Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

?sytrs_rook

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

Syntax

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

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

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

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

call sytrs_rook( 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 A = U*D*UT or A = L*D*LT computed by ?sytrf_rook.

Input Parameters

uplo

CHARACTER*1. 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

INTEGER. The order of matrix A; n 0.

nrhs

INTEGER. The number of right-hand sides; nrhs 0.

ipiv

INTEGER. Array, size at least max(1, n). The ipiv array, as returned by ?sytrf_rook.

a, b

REAL for ssytrs_rook

DOUBLE PRECISION for dsytrs_rook

COMPLEX for csytrs_rook

DOUBLE COMPLEX for zsytrs_rook.

Arrays: a(lda,n), b(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

INTEGER. The leading dimension of a; lda max(1, n).

ldb

INTEGER. The leading dimension of b; ldb max(1, 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 sytrs_rook 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

Must be 'U' or 'L'. The default value is 'U'.

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.