CSPFA(3F)							     CSPFA(3F)

NAME    [Toc]    [Back]

     CSPFA   - CSPFA factors a complex symmetric matrix	stored in packed form
     by	elimination with symmetric pivoting.

     To	solve  A*X = B , follow	CSPFA by CSPSL.	 To compute  INVERSE(A)*C ,
     follow CSPFA by CSPSL.  To	compute	 DETERMINANT(A)	, follow CSPFA by
     CSPDI.  To	compute	 INVERSE(A) , follow CSPFA by CSPDI.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE CSPFA(AP,N,KPVT,INFO)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     AP	COMPLEX	(N*(N+1)/2)
	the packed form	of a symmetric matrix  A .  The
	columns	of the upper triangle are stored sequentially
	in a one-dimensional array of length  N*(N+1)/2	.
	See comments below for details.

     N INTEGER
	the order of the matrix	 A .  On Return

     AP	a block	diagonal matrix	and the	multipliers which
	were used to obtain it stored in packed	form.
	The factorization can be written  A = U*D*TRANS(U)
	where  U  is a product of permutation and unit
	upper triangular matrices , TRANS(U) is	the
	transpose of  U	, and  D  is block diagonal
	with 1 by 1 and	2 by 2 blocks.	KVPT	INTEGER(N)
	an integer vector of pivot indices.

     INFO INTEGER
	= 0  normal value.
	= K  if	the K-th pivot block is	singular.  This	is
	not an error condition for this	subroutine,
	but it does indicate that CSPSL	or CSPDI may
	divide by zero if called.  Packed Storage The following	program
     segment will pack the upper triangle of a symmetric matrix.
	K = 0
	DO 20 J	= 1, N
	DO 10 I	= 1, J
	K = K +	1
	AP(K)  = A(I,J)
	10    CONTINUE
	20 CONTINUE LINPACK.  This version dated 08/14/78 .  James Bunch,
     Univ. Calif. San Diego, Argonne Nat. Lab.	Subroutines and	Functions BLAS
     CAXPY,CSWAP,ICAMAX	Fortran	ABS,AIMAG,AMAX1,REAL,SQRT


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