SLATEC Routines --- DSIDI ---

*DECK DSIDI
      SUBROUTINE DSIDI (A, LDA, N, KPVT, DET, INERT, WORK, JOB)
C***BEGIN PROLOGUE  DSIDI
C***PURPOSE  Compute the determinant, inertia and inverse of a real
C            symmetric matrix using the factors from DSIFA.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2B1A, D3B1A
C***TYPE      DOUBLE PRECISION (SSIDI-S, DSIDI-D, CHIDI-C, CSIDI-C)
C***KEYWORDS  DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX,
C             SYMMETRIC
C***AUTHOR  Bunch, J., (UCSD)
C***DESCRIPTION
C
C     DSIDI computes the determinant, inertia and inverse
C     of a double precision symmetric matrix using the factors from
C     DSIFA.
C
C     On Entry
C
C        A       DOUBLE PRECISION(LDA,N)
C                the output from DSIFA.
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        KPVT    INTEGER(N)
C                the pivot vector from DSIFA.
C
C        WORK    DOUBLE PRECISION(N)
C                work vector.  Contents destroyed.
C
C        JOB     INTEGER
C                JOB has the decimal expansion  ABC  where
C                   if  C .NE. 0, the inverse is computed,
C                   if  B .NE. 0, the determinant is computed,
C                   if  A .NE. 0, the inertia is computed.
C
C                For example, JOB = 111  gives all three.
C
C     On Return
C
C        Variables not requested by JOB are not used.
C
C        A      contains the upper triangle of the inverse of
C               the original matrix.  The strict lower triangle
C               is never referenced.
C
C        DET    DOUBLE PRECISION(2)
C               determinant of original matrix.
C               DETERMINANT = DET(1) * 10.0**DET(2)
C               with 1.0 .LE. ABS(DET(1)) .LT. 10.0
C               or DET(1) = 0.0.
C
C        INERT  INTEGER(3)
C               the inertia of the original matrix.
C               INERT(1)  =  number of positive eigenvalues.
C               INERT(2)  =  number of negative eigenvalues.
C               INERT(3)  =  number of zero eigenvalues.
C
C     Error Condition
C
C        A division by zero may occur if the inverse is requested
C        and  DSICO  has set RCOND .EQ. 0.0
C        or  DSIFA  has set  INFO .NE. 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, DCOPY, DDOT, DSWAP
C***REVISION HISTORY  (YYMMDD)
C   780814  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891107  Modified routine equivalence list.  (WRB)
C   891107  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  DSIDI