Computes the Bunch-Kaufman factorization of a complex Hermitian matrix using packed storage.

Syntax

lapack_int LAPACKE_chptrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * ap , lapack_int * ipiv );

lapack_int LAPACKE_zhptrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * ap , lapack_int * ipiv );

Include Files

  • mkl.h

Description

The routine computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method:

  • if uplo='U', A = U*D*UH

  • if uplo='L', A = L*D*LH,

where A is the input matrix, U and L are products of permutation and triangular matrices with unit diagonal (upper triangular for U and lower triangular for L), and D is a Hermitian block-diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks. U and L have 2-by-2 unit diagonal blocks corresponding to the 2-by-2 blocks of D.

Note

This routine supports the Progress Routine feature. See Progress Function for details.

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 packed and how A is factored:

If uplo = 'U', the array ap stores the upper triangular part of the matrix A, and A is factored as U*D*UH.

If uplo = 'L', the array ap stores the lower triangular part of the matrix A, and A is factored as L*D*LH.

n

The order of matrix A; n 0.

ap

Array, size at least max(1, n(n+1)/2). The array ap contains the upper or the lower triangular part of the matrix A (as specified by uplo) in packed storage (see Matrix Storage Schemes).

Output Parameters

ap

The upper or lower triangle of A (as specified by uplo) is overwritten by details of the block-diagonal matrix D and the multipliers used to obtain the factor U (or L).

ipiv

Array, size at least max(1, n). Contains details of the interchanges and the block structure of D. If ipiv[i-1] = k >0, then dii is a 1-by-1 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. Division by 0 will occur if you use D for solving a system of linear equations.

Application Notes

The 2-by-2 unit diagonal blocks and the unit diagonal elements of U and L are not stored. The remaining elements of U and L are stored in the array ap, but additional row interchanges are required to recover U or L explicitly (which is seldom necessary).

If ipiv[i-1] = i for all i = 1...n, then all off-diagonal elements of U (L) are stored explicitly in the corresponding elements of the array a.

If uplo = 'U', the computed factors U and D are the exact factors of a perturbed matrix A + E, where

|E|  c(n)ε P|U||D||UT|PT

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

A similar estimate holds for the computed L and D when uplo = 'L'.

The total number of floating-point operations is approximately (4/3)n3.

After calling this routine, you can call the following routines:

?hptrs

to solve A*X = B

?hpcon

to estimate the condition number of A

?hptri

to compute the inverse of A.

Для получения подробной информации о возможностях оптимизации компилятора обратитесь к нашему Уведомлению об оптимизации.
Выберите цвет&nbsp;фиксируемой кнопки: 
Orange (only for download buttons)