CCHDC(3F)							     CCHDC(3F)

NAME    [Toc]    [Back]

     CCHDC   - CCHDC computes the Cholesky decomposition of a positive
     definite matrix.  A pivoting option allows	the user to estimate the
     condition of a positive definite matrix or	determine the rank of a
     positive semidefinite matrix.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE CCHDC(A,LDA,P,WORK,JPVT,JOB,INFO)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     A COMPLEX(LDA,P).
	A contains the matrix whose decomposition is to
	be computed.  Only the upper half of A need be stored.
	The lower part of The array A is not referenced.

     LDA INTEGER.
	LDA is the leading dimension of	the array A.

     P INTEGER.
	P is the order of the matrix.

     WORK COMPLEX.
	WORK is	a work array.

     JPVT INTEGER(P).
	JPVT contains integers that control the	selection
	of the pivot elements, if pivoting has been requested.
	Each diagonal element A(K,K)
	is placed in one of three classes according to the
	value of JPVT(K)).
	If JPVT(K)) .GT. 0, then X(K) is an initial
	element.
	If JPVT(K)) .EQ. 0, then X(K) is a free	element.
	If JPVT(K)) .LT. 0, then X(K) is a final element.
	Before the decomposition is computed, initial elements
	are moved by symmetric row and column interchanges to
	the beginning of the array A and final
	elements to the	end.  Both initial and final elements
	are frozen in place during the computation and only
	free elements are moved.  At the K-th stage of the
	reduction, if A(K,K) is	occupied by a free element
	it is interchanged with	the largest free element
	A(L,L) with L .GE. K.  JPVT is not referenced if
	JOB .EQ. 0.

     JOB INTEGER.
	JOB is an integer that initiates column	pivoting.
	IF JOB .EQ. 0, no pivoting is done.
	IF JOB .NE. 0, pivoting	is done.  On Return



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CCHDC(3F)							     CCHDC(3F)



     A A contains in its upper half the	Cholesky factor
	of the matrix A	as it has been permuted	by pivoting.

     JPVT JPVT(J) contains the index of	the diagonal element
	of A that was moved into the J-th position,
	provided pivoting was requested.

     INFO contains the index of	the last positive diagonal
	element	of the Cholesky	factor.	 For positive definite matrices	INFO =
     P is the normal return.  For pivoting with	positive semidefinite matrices
     INFO will in general be less than P.  However, INFO may be	greater	than
     the rank of A, since rounding error can cause an otherwise	zero element
     to	be positive.  Indefinite systems will always cause

     INFO to be	less than P. LINPACK.  This version dated 03/19/79 .

     J University of Maryland.	BLAS CAXPY,CSWAP Fortran SQRT,REAL,CONJG


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