?sysv_rook

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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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

lapack_int LAPACKE_ssysv_rook (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , float * a , lapack_int lda , lapack_int * ipiv , float * b , lapack_int ldb );

lapack_int LAPACKE_dsysv_rook (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , double * a , lapack_int lda , lapack_int * ipiv , double * b , lapack_int ldb );

lapack_int LAPACKE_csysv_rook (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , lapack_complex_float * a , lapack_int lda , lapack_int * ipiv , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_zsysv_rook (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , lapack_complex_double * a , lapack_int lda , lapack_int * ipiv , lapack_complex_double * b , lapack_int ldb );

Include Files

mkl.h

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

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
uplo	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	The order of matrix `A`; `n`≥ 0.
nrhs	The number of right-hand sides; the number of columns in `B; nrhs≥ 0`.
a, b	Arrays: `a`(size max(1, ldan)), `b`of size max(1, ldbnrhs) for column major layout and max(1, ldb*n) for row major layout. 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)`.
lda	The leading dimension of `a`; `lda≥ max(1, n)`.
ldb	The leading dimension of `b`; `ldb`≥ max(1, n) for column major layout and `ldb`≥nrhs) for row major layout.

Output Parameters

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.

If info = 0, b is overwritten by the solution matrix X.

ipiv

Array, size at least max(1, n). Contains details of the interchanges and the block structure of D.

If ipiv[k - 1] > 0, then rows and columns k and ipiv[k - 1] were interchanged and D_{k, k} is a 1-by-1 diagonal block.

If uplo = 'U' and ipiv[k - 1] < 0 and ipiv[k - 2] < 0, then rows and columns k and -ipiv[k - 1] were interchanged, rows and columns k - 1 and -ipiv[k - 2] were interchanged, and D_{k-1:k, k-1:k} is a 2-by-2 diagonal block.

If uplo = 'L' and ipiv[k - 1] < 0 and ipiv[k] < 0, then rows and columns k and -ipiv[k - 1] were interchanged, rows and columns k + 1 and -ipiv[k ] were interchanged, and D_{k:k+1, k:k+1} is a 2-by-2 diagonal block.

Return Values

This function returns a value info.

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.

Parent topic: LAPACK Linear Equation Driver Routines

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?sysv_rook

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