clasyf()

subroutine clasyf	(	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 )

CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

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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

[in]	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 !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	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. !>
[out]	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. !>
[in,out]	A	!> 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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	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. !>
[out]	W	!> W is COMPLEX array, dimension (LDW,NB) !>
[in]	LDW	!> LDW is INTEGER !> The leading dimension of the array W. LDW >= max(1,N). !>
[out]	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.

Contributors:

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