Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/31/2023
Public

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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*UT or A = L*D*LT, 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, lda*n)), bof size max(1, ldb*nrhs) 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 ldbnrhs) for row major layout.

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.

b

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 Dk, 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 Dk-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 Dk: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, dii is 0. The factorization has been completed, but D is exactly singular, so the solution could not be computed.