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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