clahef.f man page

clahef.f

Synopsis

Functions/Subroutines

subroutine clahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Function/Subroutine Documentation

subroutine clahef (character UPLO, integer N, integer NB, integer KB, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldw, * ) W, integer LDW, integer INFO)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).  

Purpose:

 CLAHEF computes a partial factorization of a complex Hermitian
 matrix A using the Bunch-Kaufman diagonal pivoting method. The
 partial factorization has the form:

 A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
       ( 0  U22 ) (  0   D  ) ( U12**H U22**H )

 A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
       ( L21  I ) (  0  A22 ) (  0      I     )

 where the order of D is at most NB. The actual order is returned in
 the argument KB, and is either NB or NB-1, or N if N <= NB.
 Note that U**H denotes the conjugate transpose of U.

 CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code
 (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
 A22 (if UPLO = 'L').
Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NB

          NB is INTEGER
          The maximum number of columns of the matrix A that should be
          factored.  NB should be at least 2 to allow for 2-by-2 pivot
          blocks.

KB

          KB is INTEGER
          The number of columns of A that were actually factored.
          KB is either NB-1 or NB, or N if N <= NB.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
          n-by-n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n-by-n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.
          On exit, A contains details of the partial factorization.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D.

          If UPLO = 'U':
             Only the last KB elements of IPIV are set.

             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
             interchanged and D(k,k) is a 1-by-1 diagonal block.

             If IPIV(k) = IPIV(k-1) < 0, then rows and columns
             k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
             is a 2-by-2 diagonal block.

          If UPLO = 'L':
             Only the first KB elements of IPIV are set.

             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
             interchanged and D(k,k) is a 1-by-1 diagonal block.

             If IPIV(k) = IPIV(k+1) < 0, then rows and columns
             k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1)
             is a 2-by-2 diagonal block.

W

          W is COMPLEX array, dimension (LDW,NB)

LDW

          LDW is INTEGER
          The leading dimension of the array W.  LDW >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
               has been completed, but the block diagonal matrix D is
               exactly singular.
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2013

Contributors:

  November 2013,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

Definition at line 179 of file clahef.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page clahef(3) is an alias of clahef.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK