Solves a system of linear equations with a UDUT- or LDLT-factored Hermitian coefficient matrix.

Syntax

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

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

Include Files

  • mkl.h

Description

The routine solves for X the system of linear equations A*X = B with a Hermitian matrix A, given the Bunch-Kaufman factorization of A:

if uplo='U',

A = U*D*UH

if uplo='L',

A = L*D*LH,

where U and L are upper and lower triangular matrices with unit diagonal and D is a symmetric block-diagonal matrix. The system is solved with multiple right-hand sides stored in the columns of the matrix B. You must supply to this routine the factor U (or L) and the array ipiv returned by the factorization routine ?hetrf.

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 how the input matrix A has been factored:

If uplo = 'U', the array a stores the upper triangular factor U of the factorization A = U*D*UH.

If uplo = 'L', the array a stores the lower triangular factor L of the factorization A = L*D*LH.

n

The order of matrix A; n 0.

nrhs

The number of right-hand sides; nrhs 0.

ipiv

Array, size at least max(1, n).

The ipiv array, as returned by ?hetrf.

a

The array aof size max(1, lda*n) contains the factor U or L (see uplo).

b

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

The size of b is at least max(1, ldb*nrhs) for column major layout and max(1, ldb*n) for row major layout.

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

b

Overwritten by the solution matrix X.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, parameter i had an illegal value.

Application Notes

For each right-hand side b, the computed solution is the exact solution of a perturbed system of equations (A + E)x = b, where

|E|  c(n)ε P|U||D||UH|PT or |E|  c(n)ε P|L||D||LH|PT

c(n) is a modest linear function of n, and ε is the machine precision.

If x0 is the true solution, the computed solution x satisfies this error bound:


Equation

where cond(A,x)= || |A-1||A| |x| || / ||x|| ||A-1|| ||A|| = κ(A).

Note that cond(A,x) can be much smaller than κ(A).

The total number of floating-point operations for one right-hand side vector is approximately 8n2.

To estimate the condition number κ(A), call ?hecon.

To refine the solution and estimate the error, call ?herfs.

Para obter informações mais completas sobre otimizações do compilador, consulte nosso aviso de otimização.
Selecione a cor do botão adesivo: 
Orange (only for download buttons)