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zhifa (3)
  • >> zhifa (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zhifa - compute the UDU factorization of a Hermitian  matrix
         A.   It  is typical to follow a call to xHIFA with a call to
         xHISL to solve Ax = b or to  xHIDI  to  compute  the  deter-
         minant, inverse, and inertia of A.
    
    SYNOPSIS
         SUBROUTINE ZHIFA (ZA, LDA, N, IPIVOT, INFO)
    
         SUBROUTINE CHIFA (CA, LDA, N, IPIVOT, INFO)
    
    
    
         #include <sunperf.h>
    
         void zhifa(doublecomplex *za, int lda, int n,  int  *ipivot,
                   int *info) ;
    
         void chifa(complex *ca, int lda, int  n,  int  *ipivot,  int
                   *info) ;
    
    ARGUMENTS
         xA        On entry, the upper triangle of the matrix A.   On
                   exit,  a  UDU  factorization of the matrix A.  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 matrix A.  N >= 0.
    
         IPIVOT    On exit, a vector of pivot indices.
    
         INFO      On exit:
                   INFO = 0  Subroutine completed normally.
                   INFO * 0  Returns a value k if the kth pivot block
                   is  singular  to indicate that xHISL or xHIDI will
                   divide by zero if called.
    
    SAMPLE PROGRAM
               PROGRAM TEST
               IMPLICIT NONE
         C
               INTEGER    LDA, N
               PARAMETER (N = 3)
               PARAMETER (LDA = 3)
         C
               COMPLEX    A(LDA,N), B(N)
               INTEGER    ICOL, INFO, IPIVOT(N), IROW
         C
               EXTERNAL   CHIFA, CHISL
               INTRINSIC  CONJG
    
         C
         C     Initialize the array A to store the matrix A shown below.
         C     Initialize the array B to store the vector b shown below.
         C
         C          1    1+2i  1+2i         95-180i
         C     A = 1+2i   6   -2+6i    b = 545-118i
         C         1+2i -2+6i   11         865+ 62i
         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) /
               DATA B / (95.0,-180.0), (545.0,-118.0), (865.0,62.0) /
         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
               PRINT 1030
               PRINT 1040, B
               CALL CHIFA (A, LDA, N, IPIVOT, INFO)
               IF (INFO .EQ. 0) THEN
                 CALL CHISL (A, LDA, N, IPIVOT, B)
                 PRINT 1050
                 PRINT 1040, B
               ELSE
                 PRINT 1060
               END IF
         C
          1000 FORMAT (1X, 'A in full form:')
          1010 FORMAT (4(: 3X, '(', F4.1, ',', F4.1, ')'))
          1020 FORMAT (/1X, 'A in Hermitian form:  (* in unused elements)')
          1030 FORMAT (/1X, 'b:')
          1040 FORMAT (3X, '(', F6.1, ',', F6.1, ')')
          1050 FORMAT (/1X, 'A**(-1) * b:')
          1060 FORMAT (1X, 'A is singular to working precision.')
         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)
    
          b:
            (  95.0,-180.0)
            ( 545.0,-118.0)
            ( 865.0,  62.0)
    
          A**(-1) * b:
            (   5.0,   0.0)
            (  26.0,   0.0)
            (  64.0,   0.0)
    
    
    
    


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