DSPCO(3F)							     DSPCO(3F)

NAME    [Toc]    [Back]

     DSPCO   - DSPCO factors a double precision	symmetric matrix stored	in
     packed form by elimination	with symmetric pivoting	and estimates the
     condition of the matrix.

     IF	 RCOND	is not needed, DSPFA is	slightly faster.  To solve  A*X	= B ,
     follow DSPCO by DSPSL.  To	compute	 INVERSE(A)*C ,	follow DSPCO by	DSPSL.
     To	compute	 INVERSE(A) , follow DSPCO by DSPDI.  To compute
     DETERMINANT(A) , follow DSPCO by DSPDI.  To compute  INERTIA(A), follow
     DSPCO by DSPDI.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE DSPCO(AP,N,KPVT,RCOND,Z)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     AP	DOUBLE PRECISION (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.

     RCOND DOUBLE PRECISION
	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.

     Z DOUBLE PRECISION(N)
	a work vector whose contents are usually unimportant.



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DSPCO(3F)							     DSPCO(3F)



	If  A  is close	to a singular matrix, then  Z  is
	an approximate null vector in the sense	that
	NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .  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 .  Cleve Moler,
     University	of New Mexico, Argonne National	Lab.  Subroutines and
     Functions LINPACK DSPFA BLAS DAXPY,DDOT,DSCAL,DASUM Fortran
     DABS,DMAX1,IABS,DSIGN


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