# chpco.f

          SUBROUTINE CHPCO (AP, N, KPVT, RCOND, Z)
    C***BEGIN PROLOGUE  CHPCO
    C***PURPOSE  Factor a complex Hermitian matrix stored in packed form by
    C            elimination with symmetric pivoting and estimate the
    C            condition number of the matrix.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2D1A
    C***TYPE      COMPLEX (SSPCO-S, DSPCO-D, CHPCO-C, CSPCO-C)
    C***KEYWORDS  CONDITION NUMBER, HERMITIAN, LINEAR ALGEBRA, LINPACK,
    C             MATRIX FACTORIZATION, PACKED
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     CHPCO factors a complex Hermitian matrix stored in packed
    C     form by elimination with symmetric pivoting and estimates
    C     the condition of the matrix.
    C
    C     if  RCOND  is not needed, CHPFA is slightly faster.
    C     To solve  A*X = B , follow CHPCO by CHPSL.
    C     To compute  INVERSE(A)*C , follow CHPCO by CHPSL.
    C     To compute  INVERSE(A) , follow CHPCO by CHPDI.
    C     To compute  DETERMINANT(A) , follow CHPCO by CHPDI.
    C     To compute  INERTIA(A), follow CHPCO by CHPDI.
    C
    C     On Entry
    C
    C        AP      COMPLEX (N*(N+1)/2)
    C                the packed form of a Hermitian matrix  A .  The
    C                columns of the upper triangle are stored sequentially
    C                in a one-dimensional array of length  N*(N+1)/2 .
    C                See comments below for details.
    C
    C        N       INTEGER
    C                the order of the matrix  A .
    C
    C     Output
    C
    C        AP      a block diagonal matrix and the multipliers which
    C                were used to obtain it stored in packed form.
    C                The factorization can be written  A = U*D*CTRANS(U)
    C                where  U  is a product of permutation and unit
    C                upper triangular matrices , CTRANS(U) is the
    C                conjugate transpose of  U , and  D  is block diagonal
    C                with 1 by 1 and 2 by 2 blocks.
    C
    C        KVPT    INTEGER(N)
    C                an integer vector of pivot indices.
    C
    C        RCOND   REAL
    C                an estimate of the reciprocal condition of  A .
    C                For the system  A*X = B , relative perturbations
    C                in  A  and  B  of size  EPSILON  may cause
    C                relative perturbations in  X  of size  EPSILON/RCOND .
    C                If  RCOND  is so small that the logical expression
    C                           1.0 + RCOND .EQ. 1.0
    C                is true, then  A  may be singular to working
    C                precision.  In particular,  RCOND  is zero  if
    C                exact singularity is detected or the estimate
    C                underflows.
    C
    C        Z       COMPLEX(N)
    C                a work vector whose contents are usually unimportant.
    C                If  A  is close to a singular matrix, then  Z  is
    C                an approximate null vector in the sense that
    C                NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
    C
    C     Packed Storage
    C
    C          The following program segment will pack the upper
    C          triangle of a Hermitian matrix.
    C
    C                K = 0
    C                DO 20 J = 1, N
    C                   DO 10 I = 1, J
    C                      K = K + 1
    C                      AP(K) = A(I,J)
    C             10    CONTINUE
    C             20 CONTINUE
    C
    C***REFERENCES  J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
    C                 Stewart, LINPACK Users' Guide, SIAM, 1979.
    C***ROUTINES CALLED  CAXPY, CDOTC, CHPFA, CSSCAL, SCASUM
    C***REVISION HISTORY  (YYMMDD)
    C   780814  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890831  Modified array declarations.  (WRB)
    C   891107  Modified routine equivalence list.  (WRB)
    C   891107  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900326  Removed duplicate information from DESCRIPTION section.
    C           (WRB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  CHPCO