SPPCO(3F)							     SPPCO(3F)

NAME    [Toc]    [Back]

     SPPCO   - SPPCO factors a real symmetric positive definite	matrix stored
     in	packed form and	estimates the condition	of the matrix.

     If	 RCOND	is not needed, SPPFA is	slightly faster.  To solve  A*X	= B ,
     follow SPPCO by SPPSL.  To	compute	 INVERSE(A)*C ,	follow SPPCO by	SPPSL.
     To	compute	 DETERMINANT(A)	, follow SPPCO by SPPDI.  To compute
     INVERSE(A)	, follow SPPCO by SPPDI.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE SPPCO(AP,N,RCOND,Z,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 .  On Return

     AP	an upper triangular matrix  R ,	stored in packed
	form, so that  A = TRANS(R)*R .
	If  INFO .NE. 0	, the factorization is not complete.

     RCOND REAL
	an estimate of the reciprocal condition	of  A .
	For the	system	A*X = B	, relative perturbations
	in  A  and  B  of size	EPSILON	 may cause
	relative perturbations in  X  of size  EPSILON/RCOND .
	If  RCOND  is so small that the	logical	expression
	1.0 + RCOND .EQ. 1.0
	is true, then  A  may be singular to working
	precision.  In particular,  RCOND  is zero  if
	exact singularity is detected or the estimate
	underflows.  If	INFO .NE. 0 , RCOND is unchanged.

     Z REAL(N)
	a work vector whose contents are usually unimportant.
	If  A  is singular to working precision, then  Z  is
	an approximate null vector in the sense	that
	NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
	If  INFO .NE. 0	, Z  is	unchanged.

     INFO INTEGER
	= 0  for normal	return.
	= K  signals an	error condition.  The leading minor
	of order  K  is	not positive definite.	Packed Storage The following



									Page 1






SPPCO(3F)							     SPPCO(3F)



     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 .  Cleve Moler,
     University	of New Mexico, Argonne National	Lab.  Subroutines and
     Functions LINPACK SPPFA BLAS SAXPY,SDOT,SSCAL,SASUM Fortran
     ABS,AMAX1,REAL,SIGN


									PPPPaaaaggggeeee 2222