Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 12/16/2022
Public

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?sysv

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 (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 (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 (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 (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 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 array b contains the matrix B whose columns are the right-hand sides for the systems of equations.

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 as computed by ?sytrf.

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, as determined by ?sytrf.

If ipiv[i-1] = k >0, then dii is a 1-by-1 diagonal block, and the i-th row and column of A was interchanged with the k-th row and column.

If uplo = 'U' and ipiv[i] = ipiv[i-1] = -m < 0, then D has a 2-by-2 block in rows/columns i and i+1, and (i)-th row and column of A was interchanged with the m-th row and column.

If uplo = 'L'and ipiv[i] = ipiv[i-1] = -m < 0, then D has a 2-by-2 block in rows/columns i and i+1, and (i+1)-th row and column of A was interchanged with the m-th row and column.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i 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.