Searching partial columns and returning maximum as output

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clasyf

CLASYF(l)								 )								 CLASYF(l)

NAME

       CLASYF - compute 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 fac-
       torization 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 factorization.

       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 singu-
	       lar.

LAPACK version 3.0						   15 June 2000 							 CLASYF(l)

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