clasyf_rook(3)

NAME

clasyf_rook.f –

SYNOPSIS

Functions/Subroutines

subroutine clasyf_rook (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman (‘rook’) diagonal pivoting method.

Function/Subroutine Documentation

subroutine clasyf_rook (characterUPLO, integerN, integerNB, integerKB, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex, dimension( ldw, * )W, integerLDW, integerINFO)

CLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman (‘rook’) diagonal pivoting method.

Purpose:


CLASYF_ROOK computes a partial factorization of a complex symmetric
        matrix A using the bounded Bunch -
    Kaufman("rook") 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 **T U22 **T)
                                                                      A = (L11 0)(D 0)(L11 * *T L21 * *T) 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.CLASYF_ROOK is an auxiliary routine called by CSYTRF_ROOK.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
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

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

          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 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 is COMPLEX array, dimension (LDA,N)
          On entry, the symmetric 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) < 0 and IPIV(k-1) < 0, then rows and
             columns k and -IPIV(k) were interchanged and rows and
             columns k-1 and -IPIV(k-1) were inerchaged,
             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) < 0 and IPIV(k+1) < 0, then rows and
             columns k and -IPIV(k) were interchanged and rows and
             columns k+1 and -IPIV(k+1) were inerchaged,
             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

          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
  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 184 of file clasyf_rook.f.

Author

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