SSPFA(3F)							     SSPFA(3F)

NAME    [Toc]    [Back]

     SSPFA   - SSPFA factors a real symmetric matrix stored in packed form by
     elimination with symmetric	pivoting.

     To	solve  A*X = B , follow	SSPFA by SSPSL.	 To compute  INVERSE(A)*C ,
     follow SSPFA by SSPSL.  To	compute	 DETERMINANT(A)	, follow SSPFA by
     SSPDI.  To	compute	 INERTIA(A) , follow SSPFA by SSPDI.  To compute
     INVERSE(A)	, follow SSPFA by SSPDI.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE SSPFA(AP,N,KPVT,INFO)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     AP	REAL (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 .  Output

     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.

     KPVT 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 SSPSL	or SSPDI 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
     SAXPY,SSWAP,ISAMAX	Fortran	ABS,AMAX1,SQRT


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