CHPCO(3F)							     CHPCO(3F)

NAME    [Toc]    [Back]

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

     if	 RCOND	is not needed, CHPFA is	slightly faster.  To solve  A*X	= B ,
     follow CHPCO by CHPSL.  To	compute	 INVERSE(A)*C ,	follow CHPCO by	CHPSL.
     To	compute	 INVERSE(A) , follow CHPCO by CHPDI.  To compute
     DETERMINANT(A) , follow CHPCO by CHPDI.  To compute  INERTIA(A), follow
     CHPCO by CHPDI.

SYNOPSYS    [Toc]    [Back]

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

DESCRIPTION    [Toc]    [Back]

     On	Entry

     AP	COMPLEX	(N*(N+1)/2)
	the packed form	of a Hermitian 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*CTRANS(U)
	where  U  is a product of permutation and unit
	upper triangular matrices , CTRANS(U) is the
	conjugate 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



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CHPCO(3F)							     CHPCO(3F)



	NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .  Packed Storage The	following
     program segment will pack the upper triangle of a Hermitian 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 CHPFA BLAS CAXPY,CDOTC,CSSCAL,SCASUM Fortran
     ABS,AIMAG,AMAX1,CMPLX,CONJG,IABS,REAL


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