clasyf-f(3)

clasyf.f –

Synopsis

Functions/Subroutines

subroutine clasyf (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CLASYF computes a partial factorization of a complex symmetric matrix, using the diagonal pivoting method.

Function/Subroutine Documentation

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

CLASYF computes a partial factorization of a complex symmetric matrix, using the diagonal pivoting method.

Purpose:

 CLASYF computes a partial factorization of a complex symmetric 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**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.
 Note that U**T denotes the transpose of U.
 CLASYF is an auxiliary routine called by CSYTRF. 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 UPLO = 'L', only the first KB elements 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 UPLO = 'U' and 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' and 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 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:

September 2012

Definition at line 158 of file clasyf.f.

Author

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