?sysv_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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Date 3/22/2024

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?sysv_rook

Computes the solution to the system of linear equations with a real or complex symmetric coefficient matrix A and multiple right-hand sides.

Syntax

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

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

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

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

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

Include Files

mkl.fi, lapack.f90

Description

The routine solves for X the real or complex system of linear equations A*X = B, where A is an n-by-n symmetric matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.

The diagonal pivoting method is used to factor A as A = U*D*U^T or A = L*D*L^T, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

The ?sysv_rook routine is called to compute the factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.

The factored form of A is then used to solve the system of equations A*X = B.

Input Parameters

uplo	CHARACTER*1. Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of `A` is stored: If `uplo = 'U'`, the upper triangle of `A` is stored. If `uplo = 'L'`, the lower triangle of `A` is stored.
n	INTEGER. The order of matrix `A`; `n`≥ 0.
nrhs	INTEGER. The number of right-hand sides; the number of columns in `B; nrhs≥ 0`.
a, b, work	REAL for ssysv_rook DOUBLE PRECISION for dsysv_rook COMPLEX for csysv_rook DOUBLE COMPLEX for zsysv_rook. Arrays: `a`(size `lda` by ), `b`(size `ldb` by ), `work(*)`. The array `a` contains the upper or the lower triangular part of the symmetric matrix `A` (see `uplo`). The second dimension of `a` must be at least `max(1, n)`. The array `b` contains the matrix `B` whose columns are the right-hand sides for the systems of equations. The second dimension of `b` must be at least `max(1,nrhs)`. `work` is a workspace array, dimension at least `max(1,lwork)`.
lda	INTEGER. The leading dimension of `a`; `lda≥ max(1, n)`.
ldb	INTEGER. The leading dimension of `b`; `ldb≥ max(1, n)`.
lwork	INTEGER. The size of the `work` array; `lwork`≥ 1. If `lwork = -1`, then a workspace query is assumed; the routine only calculates the optimal size of the `work` array, returns this value as the first entry of the `work` array, and no error message related to `lwork` is issued by xerbla. See Application Notes below for details and for the suggested value of `lwork`.

Output Parameters

a	If `info = 0`, `a` is overwritten by the block-diagonal matrix `D` and the multipliers used to obtain the factor `U` (or `L`) from the factorization of `A` as computed by sytrf_rook.
b	If `info = 0`, `b` is overwritten by the solution matrix `X`.
ipiv	INTEGER. Array, size at least `max(1, n)`. Contains details of the interchanges and the block structure of `D`, as determined by sytrf_rook. If `ipiv(k) > 0`, then rows and columns `k` and `ipiv`(`k`) were interchanged and `D`_{k, k} is a 1-by-1 diagonal block. If `uplo = 'U'` and `ipiv(k) < 0` and `ipiv(k - 1) < 0`, then rows and columns `k` and -`ipiv`(`k`) were interchanged, rows and columns `k` - 1 and -`ipiv`(`k` - 1) were interchanged, and `D_{k-1:k, k-1:k}` is a 2-by-2 diagonal block. If `uplo = 'L'` and `ipiv(k) < 0` and `ipiv(k + 1) < 0`, then rows and columns `k` and `-ipiv`(`k`) were interchanged, rows and columns `k` + 1 and `-ipiv`(`k` + 1) were interchanged, and `D_{k:k+1, k:k+1}` is a 2-by-2 diagonal block.
`work(1)`	If `info` = 0, on exit `work(1)` contains the minimum value of `lwork` required for optimum performance. Use this `lwork` for subsequent runs.
info	INTEGER. If `info = 0`, the execution is successful. If `info = -i`, the `i`-th parameter had an illegal value. If `info = i`, `d_ii` is 0. The factorization has been completed, but `D` is exactly singular, so the solution could not be computed.

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 sysv_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'.

Parent topic: LAPACK Linear Equation Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sysv_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters

LAPACK 95 Interface Notes

See Also