# dspdi.f

          SUBROUTINE DSPDI (AP, N, KPVT, DET, INERT, WORK, JOB)
    C***BEGIN PROLOGUE  DSPDI
    C***PURPOSE  Compute the determinant, inertia, inverse of a real
    C            symmetric matrix stored in packed form using the factors
    C            from DSPFA.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2B1A, D3B1A
    C***TYPE      DOUBLE PRECISION (SSPDI-S, DSPDI-D, CHPDI-C, CSPDI-C)
    C***KEYWORDS  DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX,
    C             PACKED, SYMMETRIC
    C***AUTHOR  Bunch, J., (UCSD)
    C***DESCRIPTION
    C
    C     DSPDI computes the determinant, inertia and inverse
    C     of a double precision symmetric matrix using the factors from
    C     DSPFA, where the matrix is stored in packed form.
    C
    C     On Entry
    C
    C        AP      DOUBLE PRECISION (N*(N+1)/2)
    C                the output from DSPFA.
    C
    C        N       INTEGER
    C                the order of the matrix A.
    C
    C        KPVT    INTEGER(N)
    C                the pivot vector from DSPFA.
    C
    C        WORK    DOUBLE PRECISION(N)
    C                work vector.  Contents ignored.
    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        AP     contains the upper triangle of the inverse of
    C               the original matrix, stored in packed form.
    C               The columns of the upper triangle are stored
    C               sequentially in a one-dimensional array.
    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 will occur if the inverse is requested
    C        and  DSPCO  has set RCOND .EQ. 0.0
    C        or  DSPFA  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  DSPDI