SLATEC Routines --- DPODI ---

*DECK DPODI
      SUBROUTINE DPODI (A, LDA, N, DET, JOB)
C***BEGIN PROLOGUE  DPODI
C***PURPOSE  Compute the determinant and inverse of a certain real
C            symmetric positive definite matrix using the factors
C            computed by DPOCO, DPOFA or DQRDC.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2B1B, D3B1B
C***TYPE      DOUBLE PRECISION (SPODI-S, DPODI-D, CPODI-C)
C***KEYWORDS  DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX,
C             POSITIVE DEFINITE
C***AUTHOR  Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C     DPODI computes the determinant and inverse of a certain
C     double precision symmetric positive definite matrix (see below)
C     using the factors computed by DPOCO, DPOFA or DQRDC.
C
C     On Entry
C
C        A       DOUBLE PRECISION(LDA, N)
C                the output  A  from DPOCO or DPOFA
C                or the output  X  from DQRDC.
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        JOB     INTEGER
C                = 11   both determinant and inverse.
C                = 01   inverse only.
C                = 10   determinant only.
C
C     On Return
C
C        A       If DPOCO or DPOFA was used to factor  A , then
C                DPODI produces the upper half of INVERSE(A) .
C                If DQRDC was used to decompose  X , then
C                DPODI produces the upper half of inverse(TRANS(X)*X)
C                where TRANS(X) is the transpose.
C                Elements of  A  below the diagonal are unchanged.
C                If the units digit of JOB is zero,  A  is unchanged.
C
C        DET     DOUBLE PRECISION(2)
C                determinant of  A  or of  TRANS(X)*X  if requested.
C                Otherwise not referenced.
C                Determinant = DET(1) * 10.0**DET(2)
C                with  1.0 .LE. DET(1) .LT. 10.0
C                or  DET(1) .EQ. 0.0 .
C
C     Error Condition
C
C        A division by zero will occur if the input factor contains
C        a zero on the diagonal and the inverse is requested.
C        It will not occur if the subroutines are called correctly
C        and if DPOCO or DPOFA has set INFO .EQ. 0 .
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  DAXPY, DSCAL
C***REVISION HISTORY  (YYMMDD)
C   780814  DATE WRITTEN
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  DPODI