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NAME
     dsidi - compute the determinant, inertia, and inverse  of  a
     symmetric  matrix A, which has been UDU-factored by xSICO or
     xSIFA.

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

     SUBROUTINE SSIDI (SA, LDA, N, IPIVOT,  SDET,  INERT,  SWORK,
               JOB)

     SUBROUTINE ZSIDI (ZA, LDA, N, IPIVOT, ZDET, ZWORK, JOB)

     SUBROUTINE CSIDI (CA, LDA, N, IPIVOT, CDET, CWORK, JOB)



     #include <sunperf.h>

     void dsidi(double *da, int lda, int  n,  int  *kpvt,  double
               *det, int *inert, int job) ;

     void ssidi(float *sa, int lda, int n, int *kpvt, float *det,
               int *inert, int job) ;

     void zsidi(doublecomplex *za, int lda,  int  n,  int  *kpvt,
               doublecomplex *det, int job) ;

     void csidi(complex *ca, int lda, int n, int  *kpvt,  complex
               *det, int job) ;

ARGUMENTS
     xA        On entry, the UDU factorization of the  matrix  A,
               as  computed by xSICO or xSIFA.  On exit, if the c
               digit of JOB * 0, then the  upper  triangle  of  A
               contains  the upper triangle of the inverse of the
               original matrix A if the  inverse  was  requested,
               otherwise unchanged.  The strict lower triangle of
               A is not referenced.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= max(1,N).

     N         Order of the original matrix A.  N >= 0.

     IPIVOT    Pivot vector as computed by x SICO or xSIFA.

     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
               xSICO  has  set RCOND = 0 or if xSIFA has set INFO
               >= 0.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           IDODET, IDOINR, IDOINV, LDA, N
           PARAMETER        (IDODET = 10)
           PARAMETER        (IDOINR = 100)
           PARAMETER        (IDOINV = 1)
           PARAMETER        (N = 4)
           PARAMETER        (LDA = N)
     C
           DOUBLE PRECISION  A(LDA,N), DET(2), WORK(N)
           INTEGER           ICOL, INERT(3), INFO, IPIVOT(N), IROW, JOB
     C
           EXTERNAL DSIFA, DSIDI
     C
     C     Initialize the array A to store the matrix A shown below.
     C
     C         -.5   -.5   -.5   -.5
     C     A = -.5  -1.5  -1.5  -1.5
     C         -.5  -1.5  -2.5  -2.5
     C         -.5  -1.5  -2.5  -3.5
     C
           DATA A / -5.0D-1, 3*8D8, -5.0D-1, -1.5D0, 2*8D8, -5.0D-1,
          $         -1.5D0, -2.5D0, 8D8, -5.0D-1, -1.5D0, -2.5D0, -3.5D0 /
     C
           PRINT 1000
           DO 100, IROW = 1, N
             PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),

          $              (A(IROW,ICOL), ICOL = IROW + 1, N)
       100 CONTINUE
           PRINT 1020
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
           CALL DSIFA (A, LDA, N, IPIVOT, INFO)
           IF (INFO .EQ. 0) THEN
             JOB = IDOINR + IDODET + IDOINV
             CALL DSIDI (A, LDA, N, IPIVOT, DET, INERT, WORK, JOB)
             PRINT 1030, DET(1) * (10.0D0 ** DET(2))
             PRINT 1040, INERT
             PRINT 1050
           DO 110, IROW = 1, N
             PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
          $              (A(IROW,ICOL), ICOL = IROW + 1, N)
       110 CONTINUE
           ELSE
             PRINT 1060
           END IF
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(3X, F5.1))
      1020 FORMAT (/1X, 'A in symmetric form:  (* in unused elements)')
      1030 FORMAT (/1X, 'Determinant of A: ', F6.3)
      1040 FORMAT (1X, 'Inertia of A: <', I1, ',', I1, ',', I1, '>')
      1050 FORMAT (/1X, 'A**(-1):')
      1060 FORMAT (/1X, 'A is too poorly conditioned.')
     C
           END

SAMPLE OUTPUT
      A in full form:
         -0.5    -0.5    -0.5    -0.5
         -0.5    -1.5    -1.5    -1.5
         -0.5    -1.5    -2.5    -2.5
         -0.5    -1.5    -2.5    -3.5

      A in symmetric form:  (* in unused elements)
         -0.5    -0.5    -0.5    -0.5
        *****    -1.5    -1.5    -1.5
        *****   *****    -2.5    -2.5
        *****   *****   *****    -3.5

      Determinant of A:  0.500
      Inertia of A: <0,4,0>

      A**(-1):
         -3.0     1.0     0.0     0.0
          1.0    -2.0     1.0     0.0
          0.0     1.0    -2.0     1.0
          0.0     0.0     1.0    -1.0

Партнёры:

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