clasyf man page on Scientific

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CLASYF(1)		 LAPACK routine (version 3.2)		     CLASYF(1)

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

SYNOPSIS
       SUBROUTINE CLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KB, LDA, LDW, N, NB

	   INTEGER	  IPIV( * )

	   COMPLEX	  A( LDA, * ), W( LDW, * )

PURPOSE
       CLASYF computes a partial factorization of a complex symmetric matrix A
       using  the  Bunch-Kaufman diagonal pivoting method. The partial factor‐
       ization has the form:
       A  =  ( I  U12 ) ( A11  0  ) (  I    0	)  if UPLO = 'U', or:
	     ( 0  U22 ) (  0   D  ) ( U12' U22' )
       A  =  ( L11  0 ) ( D    0  ) ( L11' L21' )  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'
       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').

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

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

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

       A       (input/output) 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 factor‐
	       ization.

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

       IPIV    (output) 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       (workspace) COMPLEX array, dimension (LDW,NB)

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

       INFO    (output) 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.

 LAPACK routine (version 3.2)	 November 2008			     CLASYF(1)
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