?sytrs_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?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*U^T or A = L*D*L^T computed by ?sytrf_rook.

Input Parameters

uplo	CHARACTER1. 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` = `LD*L^T`.
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

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.

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

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