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csytrf(3P)		    Sun Performance Library		    csytrf(3P)

NAME
       csytrf  -  compute  the	factorization  of a complex symmetric matrix A
       using the Bunch-Kaufman diagonal pivoting method

SYNOPSIS
       SUBROUTINE CSYTRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

       CHARACTER * 1 UPLO
       COMPLEX A(LDA,*), WORK(*)
       INTEGER N, LDA, LDWORK, INFO
       INTEGER IPIVOT(*)

       SUBROUTINE CSYTRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

       CHARACTER * 1 UPLO
       COMPLEX A(LDA,*), WORK(*)
       INTEGER*8 N, LDA, LDWORK, INFO
       INTEGER*8 IPIVOT(*)

   F95 INTERFACE
       SUBROUTINE SYTRF(UPLO, [N], A, [LDA], IPIVOT, [WORK], [LDWORK], [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER :: N, LDA, LDWORK, INFO
       INTEGER, DIMENSION(:) :: IPIVOT

       SUBROUTINE SYTRF_64(UPLO, [N], A, [LDA], IPIVOT, [WORK], [LDWORK],
	      [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER(8) :: N, LDA, LDWORK, INFO
       INTEGER(8), DIMENSION(:) :: IPIVOT

   C INTERFACE
       #include <sunperf.h>

       void csytrf(char uplo, int n, complex *a, int  lda,  int	 *ipivot,  int
		 *info);

       void  csytrf_64(char  uplo, long n, complex *a, long lda, long *ipivot,
		 long *info);

PURPOSE
       csytrf computes the factorization of a complex symmetric matrix A using
       the Bunch-Kaufman diagonal pivoting method.  The form of the factoriza‐
       tion is

	  A = U*D*U**T	or  A = L*D*L**T

       where U (or L) is a product of permutation and unit upper (lower)  tri‐
       angular	matrices,  and	D  is  symmetric  and block diagonal with with
       1-by-1 and 2-by-2 diagonal blocks.

       This is the blocked version of the algorithm, calling Level 3 BLAS.

ARGUMENTS
       UPLO (input)
		 = 'U':	 Upper triangle of A is stored;
		 = 'L':	 Lower triangle of A is stored.

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

       A (input/output)
		 On entry, the symmetric matrix A.  If UPLO = 'U', the leading
		 N-by-N upper triangular part of A contains the upper triangu‐
		 lar 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, the block diagonal matrix D and the multipliers used
		 to obtain the factor U or L (see below for further details).

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

       IPIVOT (output)
		 Details of the interchanges and the block structure of D.  If
		 IPIVOT(k) > 0, then rows and columns  k  and  IPIVOT(k)  were
		 interchanged  and D(k,k) is a 1-by-1 diagonal block.  If UPLO
		 = 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and  columns
		 k-1  and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a
		 2-by-2 diagonal  block.   If  UPLO  =	'L'  and  IPIVOT(k)  =
		 IPIVOT(k+1)  <	 0,  then  rows and columns k+1 and -IPIVOT(k)
		 were interchanged and D(k:k+1,k:k+1)  is  a  2-by-2  diagonal
		 block.

       WORK (workspace)
		 On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.

       LDWORK (input)
		 The length of WORK.  LDWORK >=1.  For best performance LDWORK
		 >= N*NB, where NB is the block size returned by ILAENV.

		 If LDWORK = -1, then a workspace query is assumed;  the  rou‐
		 tine  only  calculates	 the  optimal  size of the WORK array,
		 returns this value as the first entry of the WORK array,  and
		 no error message related to LDWORK is issued by XERBLA.

       INFO (output)
		 = 0:  successful exit
		 < 0:  if INFO = -i, the i-th argument had an illegal value
		 > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
		 has been completed,  but  the	block  diagonal	 matrix	 D  is
		 exactly  singular,  and  division by zero will occur if it is
		 used to solve a system of equations.

FURTHER DETAILS
       If UPLO = 'U', then A = U*D*U', where
	  U = P(n)*U(n)* ... *P(k)U(k)* ...,
       i.e., U is a product of terms P(k)*U(k), where k decreases from n to  1
       in  steps  of  1 or 2, and D is a block diagonal matrix with 1-by-1 and
       2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix  as  defined
       by  IPIVOT(k), and U(k) is a unit upper triangular matrix, such that if
       the diagonal block D(k) is of order s (s = 1 or 2), then

		  (   I	   v	0   )	k-s
	  U(k) =  (   0	   I	0   )	s
		  (   0	   0	I   )	n-k
		     k-s   s   n-k

       If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).  If s  =
       2,  the	upper  triangle	 of  D(k) overwrites A(k-1,k-1), A(k-1,k), and
       A(k,k), and v overwrites A(1:k-2,k-1:k).

       If UPLO = 'L', then A = L*D*L', where
	  L = P(1)*L(1)* ... *P(k)*L(k)* ...,
       i.e., L is a product of terms P(k)*L(k), where k increases from 1 to  n
       in  steps  of  1 or 2, and D is a block diagonal matrix with 1-by-1 and
       2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix  as  defined
       by  IPIVOT(k), and L(k) is a unit lower triangular matrix, such that if
       the diagonal block D(k) is of order s (s = 1 or 2), then

		  (   I	   0	 0   )	k-1
	  L(k) =  (   0	   I	 0   )	s
		  (   0	   v	 I   )	n-k-s+1
		     k-1   s  n-k-s+1

       If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).  If s  =
       2,  the	lower  triangle	 of  D(k)  overwrites  A(k,k),	A(k+1,k),  and
       A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

				  6 Mar 2009			    csytrf(3P)
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