# cpoco.f

          SUBROUTINE CPOCO (A, LDA, N, RCOND, Z, INFO)
    C***BEGIN PROLOGUE  CPOCO
    C***PURPOSE  Factor a complex Hermitian positive definite matrix
    C            and estimate the condition number of the matrix.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2D1B
    C***TYPE      COMPLEX (SPOCO-S, DPOCO-D, CPOCO-C)
    C***KEYWORDS  CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
    C             MATRIX FACTORIZATION, POSITIVE DEFINITE
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     CPOCO factors a complex Hermitian positive definite matrix
    C     and estimates the condition of the matrix.
    C
    C     If  RCOND  is not needed, CPOFA is slightly faster.
    C     To solve  A*X = B , follow CPOCO by CPOSL.
    C     To compute  INVERSE(A)*C , follow CPOCO by CPOSL.
    C     To compute  DETERMINANT(A) , follow CPOCO by CPODI.
    C     To compute  INVERSE(A) , follow CPOCO by CPODI.
    C
    C     On Entry
    C
    C        A       COMPLEX(LDA, N)
    C                the Hermitian matrix to be factored.  Only the
    C                diagonal and upper triangle are used.
    C
    C        LDA     INTEGER
    C                the leading dimension of the array  A .
    C
    C        N       INTEGER
    C                the order of the matrix  A .
    C
    C     On Return
    C
    C        A       an upper triangular matrix  R  so that  A =
    C                CTRANS(R)*R where  CTRANS(R)  is the conjugate
    C                transpose.  The strict lower triangle is unaltered.
    C                If  INFO .NE. 0 , the factorization is not complete.
    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.  If INFO .NE. 0 , RCOND is unchanged.
    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                If  INFO .NE. 0 , Z  is unchanged.
    C
    C        INFO    INTEGER
    C                = 0  for normal return.
    C                = K  signals an error condition.  The leading minor
    C                     of order  K  is not positive definite.
    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, CPOFA, 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   890831  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  CPOCO