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NAME
     zhpdi - compute the determinant, inertia, and inverse  of  a
     Hermitian  matrix  A  in packed storage, which has been UDU-
     factored by xHPCO or xHPFA.

SYNOPSIS
     SUBROUTINE ZHPDI (ZA, N, IPIVOT, DDET, INERT, ZWORK, JOB)

     SUBROUTINE CHPDI (CA, N, IPIVOT, SDET, INERT, CWORK, JOB)



     #include <sunperf.h>

     void zhpdi(doublecomplex *za, int  n,  int  *ipivot,  double
               *det, int *inert, int job) ;

     void chpdi(complex *ca, int n, int *ipivot, float *det,  int
               *inert, int job) ;

ARGUMENTS
     xA        On entry, the UDU factorization of the matrix,  as
               computed  by  xHPCO  or  xHPFA.  On exit, if the c
               digit of JOB <> 0, then A contains the upper  tri-
               angle  of  the  inverse  of the original matrix A;
               otherwise unchanged.

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

     IPIVOT    Pivot vector as computed by xHPCO or xHPFA.

     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; determines operation sub-
               routine will perform:
                    a <> 0    Compute the inertia.
                    b <> 0    Compute the determinant.
                    c <> 0    Compute the inverse.

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
           REAL       DET(2), RCOND
           COMPLEX    A(LENGTA), WORK(N)
           INTEGER    INERT(3), IPIVOT(N), JOB
     C
           EXTERNAL   CHPCO, CHPDI
     C
     C     Initialize the array A to store the matrix A shown below.
     C
     C          1    1+2i  1+2i
     C     A = 1+2i   6   -2+6i
     C         1+2i -2+6i   11
     C
           DATA A / (1.0,0.0), (1.0,-2.0), (6.0,0.0),
          $         (1.0,-2.0), (6.0,-2.0), (11.0,0.0) /
     C
           PRINT 1000
           PRINT 1010, A(1), A(2), A(4)
           PRINT 1010, CONJG(A(2)), A(3), A(5)
           PRINT 1010, CONJG(A(4)), CONJG(A(5)), A(6)
           CALL CHPCO (A, N, IPIVOT, RCOND, WORK)
           PRINT 1020, RCOND
           IF ((RCOND + 1.0) .EQ. 1.0) THEN
             PRINT 1030
           END IF
           JOB = IDOINR + IDODET + IDOINV
           CALL CHPDI (A, N, IPIVOT, DET, INERT, WORK, JOB)
           PRINT 1040, DET(1) * (10.0D0 ** DET(2))
           PRINT 1050, INERT
           PRINT 1060
           PRINT 1010, A(1), A(2), A(4)
           PRINT 1010, CONJG(A(2)), A(3), A(5)
           PRINT 1010, CONJG(A(4)), CONJG(A(5)), A(6)
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(: 3X, '(', F5.1, ',', F5.1, ')'))
      1020 FORMAT (/1X, 'Reciprocal condition number of A:', F6.3)
      1030 FORMAT (1X, 'A may be singular to working precision.')
      1040 FORMAT (/1X, 'Determinant of A: ', F6.3)
      1050 FORMAT (1X, 'Inertia of A: <', I1, ',', I1, ',', I1, '>')
      1060 FORMAT (/1X, 'A**(-1):')
     C
           END

SAMPLE OUTPUT
      A in full form:
        (  1.0,  0.0)   (  1.0, -2.0)   (  1.0, -2.0)
        (  1.0,  2.0)   (  6.0,  0.0)   (  6.0, -2.0)
        (  1.0,  2.0)   (  6.0,  2.0)   ( 11.0,  0.0)

      Reciprocal condition number of A: 0.001

      Determinant of A:  0.008
      Inertia of A: <3,0,0>

      A**(-1):
        ( 26.0,  0.0)   ( -1.0, 12.0)   ( -4.0, -2.0)
        ( -1.0,-12.0)   (  6.0,  0.0)   ( -1.0,  2.0)
        ( -4.0,  2.0)   ( -1.0, -2.0)   (  1.0,  0.0)

Партнёры:

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