SLATEC Routines --- DPOCO ---

*DECK DPOCO
      SUBROUTINE DPOCO (A, LDA, N, RCOND, Z, INFO)
C***BEGIN PROLOGUE  DPOCO
C***PURPOSE  Factor a real symmetric positive definite matrix
C            and estimate the condition of the matrix.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2B1B
C***TYPE      DOUBLE PRECISION (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     DPOCO factors a double precision symmetric positive definite
C     matrix and estimates the condition of the matrix.
C
C     If  RCOND  is not needed, DPOFA is slightly faster.
C     To solve  A*X = B , follow DPOCO by DPOSL.
C     To compute  INVERSE(A)*C , follow DPOCO by DPOSL.
C     To compute  DETERMINANT(A) , follow DPOCO by DPODI.
C     To compute  INVERSE(A) , follow DPOCO by DPODI.
C
C     On Entry
C
C        A       DOUBLE PRECISION(LDA, N)
C                the symmetric 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 = TRANS(R)*R
C                where  TRANS(R)  is the transpose.
C                The strict lower triangle is unaltered.
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 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  DASUM, DAXPY, DDOT, DPOFA, 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  DPOCO