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NAME
     zhidi - compute the determinant, inertia, and inverse  of  a
     Hermitian  matrix A, which has been UDU-factored by xHICO or
     xHIFA.

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

     SUBROUTINE CHIDI (CA, LDA, N, IPIVOT,  SDET,  INERT,  CWORK,
               JOB)



     #include <sunperf.h>

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

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

ARGUMENTS
     xA        On entry, the UDU factorization of the  matrix  A,
               as  computed by xHICO or xHIFA.  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 xHICO or xHIFA.

     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  the
               subroutine 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, LDA, N
           PARAMETER (IDODET = 10)
           PARAMETER (IDOINR = 100)
           PARAMETER (IDOINV = 1)
           PARAMETER (N = 3)
           PARAMETER (LDA = 3)
     C
           REAL       DET(2), RCOND
           COMPLEX    A(LDA,N), WORK(N)
           INTEGER    ICOL, INERT(3), IPIVOT(N), IROW, JOB
     C
           EXTERNAL   CHICO, CHIDI
     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), (8E8,8E8),  (8E8,8E8),
          $        (1.0,-2.0), (6.0,0.0),  (8E8,8E8),
          $        (1.0,-2.0), (6.0,-2.0), (11.0,0.0) /
     C
           PRINT 1000
           DO 100, IROW = 1, N
             PRINT 1010, (CONJG(A(ICOL,IROW)), ICOL = 1, IROW),
          $              (A(IROW,ICOL), ICOL = IROW + 1, N)
       100 CONTINUE
           PRINT 1020
           DO 110, IROW = 1, N
             PRINT 1010, (A(IROW,ICOL), ICOL = 1, N)
       110 CONTINUE
           CALL CHICO (A, LDA, N, IPIVOT, RCOND, WORK)
           PRINT 1030, RCOND
           IF ((RCOND + 1.0) .EQ. 1.0) THEN
             PRINT 1040
           END IF
           JOB = IDOINR + IDODET + IDOINV
           CALL CHIDI (A, LDA, N, IPIVOT, DET, INERT, WORK, JOB)
           PRINT 1050, DET(1) * (10.0D0 ** DET(2))
           PRINT 1060, INERT
           PRINT 1070
           DO 120, IROW = 1, N
             PRINT 1010, (CONJG(A(ICOL,IROW)), ICOL = 1, IROW),
          $              (A(IROW,ICOL), ICOL = IROW + 1, N)
       120 CONTINUE
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(: 3X, '(', F5.1, ',', F5.1, ')'))
      1020 FORMAT (/1X, 'A in Hermitian form:  (* in unused elements)')
      1030 FORMAT (/1X, 'Reciprocal condition number of A:', F6.3)
      1040 FORMAT (1X, 'A may be singular to working precision.')
      1050 FORMAT (/1X, 'Determinant of A: ', F6.3)
      1060 FORMAT (1X, 'Inertia of A: <', I1, ',', I1, ',', I1, '>')
      1070 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)

      A in Hermitian form:  (* in unused elements)
        (  1.0,  0.0)   (  1.0, -2.0)   (  1.0, -2.0)
        (*****,*****)   (  6.0,  0.0)   (  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:

Хостинг: