# dppco.f

          SUBROUTINE DPPCO (AP, N, RCOND, Z, INFO)
    C***BEGIN PROLOGUE  DPPCO
    C***PURPOSE  Factor a symmetric positive definite matrix stored in
    C            packed form and estimate the condition number of the
    C            matrix.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2B1B
    C***TYPE      DOUBLE PRECISION (SPPCO-S, DPPCO-D, CPPCO-C)
    C***KEYWORDS  CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
    C             MATRIX FACTORIZATION, PACKED, POSITIVE DEFINITE
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     DPPCO factors a double precision symmetric positive definite
    C     matrix stored in packed form
    C     and estimates the condition of the matrix.
    C
    C     If  RCOND  is not needed, DPPFA is slightly faster.
    C     To solve  A*X = B , follow DPPCO by DPPSL.
    C     To compute  INVERSE(A)*C , follow DPPCO by DPPSL.
    C     To compute  DETERMINANT(A) , follow DPPCO by DPPDI.
    C     To compute  INVERSE(A) , follow DPPCO by DPPDI.
    C
    C     On Entry
    C
    C        AP      DOUBLE PRECISION (N*(N+1)/2)
    C                the packed form of a symmetric 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     On Return
    C
    C        AP      an upper triangular matrix  R , stored in packed
    C                form, so that  A = TRANS(R)*R .
    C                If  INFO .NE. 0 , the factorization is not complete.
    C
    C        RCOND   DOUBLE PRECISION
    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       DOUBLE PRECISION(N)
    C                a work vector whose contents are usually unimportant.
    C                If  A  is singular to working precision, 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     Packed Storage
    C
    C          The following program segment will pack the upper
    C          triangle of a symmetric 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  DASUM, DAXPY, DDOT, DPPFA, DSCAL
    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  DPPCO