SUBROUTINE DCHDC(A,LDA,P,WORK,JPVT,JOB,INFO)
C***BEGIN PROLOGUE  DCHDC
C***DATE WRITTEN   790319   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2B1B
C***KEYWORDS  CHOLESKY DECOMPOSITION,DOUBLE PRECISION,LINEAR ALGEBRA,
C             LINPACK,MATRIX,POSITIVE DEFINITE
C***AUTHOR  DONGARRA, J., (ANL)
C           STEWART, G. W., (U. OF MARYLAND)
C***PURPOSE  Computes the Cholesky decomposition of a POSITIVE DEFINITE
C            matrix.  A pivoting option allows the user to estimate the
C            condition of a positive definite matrix or determine the
C            rank of a POSITIVE SEMIDEFINITE matrix.
C***DESCRIPTION
C
C     DCHDC computes the Cholesky decomposition of a positive definite
C     matrix.  A pivoting option allows the user to estimate the
C     condition of a positive definite matrix or determine the rank
C     of a positive semidefinite matrix.
C
C     On Entry
C
C         A      DOUBLE PRECISION(LDA,P).
C                A contains the matrix whose decomposition is to
C                be computed.  Only the upper half of A need be stored.
C                The lower part of the array A is not referenced.
C
C         LDA    INTEGER.
C                LDA is the leading dimension of the array A.
C
C         P      INTEGER.
C                P is the order of the matrix.
C
C         WORK   DOUBLE PRECISION.
C                WORK is a work array.
C
C         JPVT   INTEGER(P).
C                JPVT contains integers that control the selection
C                of the pivot elements, if pivoting has been requested.
C                Each diagonal element A(K,K)
C                is placed in one of three classes according to the
C                value of JPVT(K).
C
C                   If JPVT(K) .GT. 0, then X(K) is an initial
C                                      element.
C
C                   If JPVT(K) .EQ. 0, then X(K) is a free element.
C
C                   If JPVT(K) .LT. 0, then X(K) is a final element.
C
C                Before the decomposition is computed, initial elements
C                are moved by symmetric row and column interchanges to
C                the beginning of the array A and final
C                elements to the end.  Both initial and final elements
C                are frozen in place during the computation and only
C                free elements are moved.  At the K-th stage of the
C                reduction, if A(K,K) is occupied by a free element
C                it is interchanged with the largest free element
C                A(L,L) with L .GE. K.  JPVT is not referenced if
C                JOB .EQ. 0.
C
C        JOB     INTEGER.
C                JOB is an integer that initiates column pivoting.
C                If JOB .EQ. 0, no pivoting is done.
C                If JOB .NE. 0, pivoting is done.
C
C     On Return
C
C         A      A contains in its upper half the Cholesky factor
C                of the matrix A as it has been permuted by pivoting.
C
C         JPVT   JPVT(J) contains the index of the diagonal element
C                of a that was moved into the J-th position,
C                provided pivoting was requested.
C
C         INFO   contains the index of the last positive diagonal
C                element of the Cholesky factor.
C
C     For positive definite matrices INFO = P is the normal return.
C     For pivoting with positive semidefinite matrices INFO will
C     in general be less than P.  However, INFO may be greater than
C     the rank of A, since rounding error can cause an otherwise zero
C     element to be positive.  Indefinite systems will always cause
C     INFO to be less than P.
C
C     LINPACK.  This version dated 03/19/79 .
C     J.Dongarra J. and Stewart G. W., Argonne National Laboratory and
C     University of Maryland.
C
C
C     BLAS DAXPY,DSWAP
C     Fortran DSQRT
C***REFERENCES  DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C                 *LINPACK USERS  GUIDE*, SIAM, 1979.
C***ROUTINES CALLED  DAXPY,DSWAP
C***END PROLOGUE  DCHDC