?hesv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?hesv

Computes the solution to the system of linear equations with a Hermitian matrix A and multiple right-hand sides.

Syntax

lapack_int LAPACKE_chesv (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_zhesv (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 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^H or A = L*D*L^H, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian 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 and how `A` is factored: If `uplo = 'U'`, the array `a` stores the upper triangular part of the matrix `A`, and `A` is factored as `UDU^H`. If `uplo = 'L'`, the array `a` stores the lower triangular part of the matrix `A`, and `A` is factored as `LDL^H`.
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)), `bb`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 Hermitian 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 `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 as computed by ?hetrf.

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 ?hetrf.

If ipiv[i-1] = k > 0, then d_ii 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, 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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Developer Reference for Intel® oneAPI Math Kernel Library for C

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