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NAME
     sspdi - compute the determinant, inertia, and inverse  of  a
     symmetric  matrix  A  in packed storage, which has been UDU-
     factored by xSPCO or xSPFA.

SYNOPSIS
     SUBROUTINE DSPDI (DA, N, IPIVOT, DDET, INERT, DWORK, JOB)

     SUBROUTINE SSPDI (SA, N, IPIVOT, SDET, INERT, SWORK, JOB)

     SUBROUTINE ZSPDI (ZA, N, IPIVOT, ZDET, ZWORK, JOB)

     SUBROUTINE CSPDI (CA, N, IPIVOT, CDET, CWORK, JOB)



     #include <sunperf.h>

     void dspdi(double *dap, int n, int *kpvt, double  *det,  int
               *inert, int job) ;

     void sspdi(float *sap, int n, int  *kpvt,  float  *det,  int
               *inert, int job) ;

     void zspdi(doublecomplex *zap, int n, int *kpvt,  doublecom-
               plex *det, int job) ;

     void cspdi(complex *cap, int n, int *kpvt, complex *det, int
               job) ;

ARGUMENTS
     xA        On entry, the UDU factorization of the  matrix  A,
               as  computed  by xSPCO or SPFA.  On exit, if the c
               digit of JOB * 0, then A contains the upper trian-
               gle  of the inverse of the original matrix A; oth-
               erwise unchanged.

     N         Order of the original matrix A.  N * 0.

     IPIVOT    Pivot vector as computed by xSPCO or xSPFA.

     xDET      On exit, if the b digit of JOB * 0, then DET  con-
               tains the determinant of the matrix A.  The deter-
               minant is stored as b * (10 ** expon) where  b  is
               stored  in  DET(1)  and expon is stored in DET(2).
               1.0 <= |DET(1)| <= 10.0  or  DET(1) = 0.0.  If the
               b digit of JOB = 0, DET is not referenced.

     INERT     On exit, if the a digit of JOB  <>  0  then  INERT
               contains an integer triplet where:
               INERT(1) = number of positive eigenvalues
               INERT(2) = number of negative eigenvalues
               INERT(3) = number of zero eigenvalues
               If the a digit of JOB = 0 then INERT is not refer-
               enced.

     xWORK     Scratch array with a dimension of N.

     JOB       Integer in the form abc for real subroutines or bc
               for  complex subroutines; determines operation the
               subroutine will perform:
                    a <> 0    Compute the inertia.
                    b <> 0    Compute the determinant.
                    c <> 0    Compute the inverse.
               Note that the inverse should not  be  computed  if
               xSPCO  has  set RCOND = 0 or if xSPFA has set INFO
               <> 0.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           IDODET, IDOINR, IDOINV, LENGTA, N
           PARAMETER        (IDODET = 10)
           PARAMETER        (IDOINR = 100)
           PARAMETER        (IDOINV = 1)
           PARAMETER        (N = 3)
           PARAMETER        (LENGTA = (N * N + N) / 2)
     C
           DOUBLE PRECISION  A(LENGTA), DET(2), RCOND, WORK(N)
           INTEGER           INERT(3), IPIVOT(N), JOB
     C
           EXTERNAL          DSPCO, DSPDI
     C
     C     Initialize the array A to store in packed symmetric format
     C     the matrix A shown below.
     C
     C         1  0  4
     C     A = 0  2  0
     C         4  0  3
     C
           DATA A / 3.0D0, 2.0D0, 2.0D0, 1.0D0, 1.0D0, 1.0D0 /
     C
           PRINT 1000
           PRINT 1010, A(1), A(2), A(4)
           PRINT 1010, A(2), A(3), A(5)
           PRINT 1010, A(4), A(5), A(6)
           CALL DSPCO (A, N, IPIVOT, RCOND, WORK)
           IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
             PRINT 1020
           END IF
           JOB = IDODET + IDOINV + IDOINR
           CALL DSPDI (A, N, IPIVOT, DET, INERT, WORK, JOB)
           PRINT 1030, DET(1) * (10.0D0 ** DET(2))
           PRINT 1040, INERT
           PRINT 1050
           PRINT 1010, A(1), A(2), A(4)
           PRINT 1010, A(2), A(3), A(5)
           PRINT 1010, A(4), A(5), A(6)
     C
      1000 FORMAT (1X, 'A:')
      1010 FORMAT (3(3X, F5.2))
      1020 FORMAT (1X, 'A may be singular to working precision.')
      1030 FORMAT (/1X, 'Determinant of A: ', F7.3)
      1040 FORMAT (1X, 'Inertia of A: <', I1, ',', I1, ',', I1, '>')
      1050 FORMAT (/1X, 'A**(-1):')
     C
           END

SAMPLE OUTPUT
      A:
         3.00    2.00    1.00
         2.00    2.00    1.00
         1.00    1.00    1.00

      Determinant of A:   1.000
      Inertia of A: <3,0,0>

      A**(-1):
         1.00   -1.00    0.00
        -1.00    2.00   -1.00
         0.00   -1.00    2.00

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