CSPCO man page on IRIX

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CSPCO(3F)							     CSPCO(3F)

NAME
     CSPCO   - CSPCO factors a complex symmetric matrix stored in packed form
     by elimination with symmetric pivoting and estimates the condition of the
     matrix.

     If	 RCOND	is not needed, CSPFA is slightly faster.  To solve  A*X = B ,
     follow CSPCO by CSPSL.  To compute	 INVERSE(A)*C , follow CSPCO by CSPSL.
     To compute	 INVERSE(A) , follow CSPCO by CSPDI.  To compute
     DETERMINANT(A) , follow CSPCO by CSPDI.

SYNOPSYS
      SUBROUTINE CSPCO(AP,N,KPVT,RCOND,Z)

DESCRIPTION
     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.

     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.

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

									Page 1

CSPCO(3F)							     CSPCO(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 CSPFA BLAS CAXPY,CDOTU,CSSCAL,SCASUM Fortran
     ABS,AIMAG,AMAX1,CMPLX,IABS,REAL

									Page 2

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