# dpodi.f

          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