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zhico (3)
  • >> zhico (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zhico - compute the UDU factorization and  condition  number
         of  a  Hermitian  matrix  A.  If the condition number is not
         needed then xHIFA is slightly faster.  It is typical to fol-
         low  a call to xHICO with a call to xHISL to solve Ax = b or
         to xHIDI to compute the determinant, inverse, and inertia of
         A.
    
    SYNOPSIS
         SUBROUTINE ZHICO (ZA, LDA, N, IPIVOT, DRCOND, ZWORK)
    
         SUBROUTINE CHICO (CA, LDA, N, IPIVOT, SRCOND, CWORK)
    
    
    
         #include <sunperf.h>
    
         void zhico(doublecomplex *za, int lda, int n,  int  *ipivit,
                   double *rcond) ;
    
         void chico(complex *ca, int lda, int n, int  *ipivit,  float
                   *rcond) ;
    
    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.
    
         xRCOND    On exit, an estimate of the  reciprocal  condition
                   number  of  A.  0.0 >= RCOND >= 1.0.  As the value
                   of RCOND gets smaller, operations with A  such  as
                   solving  Ax  = b may become less stable.  If RCOND
                   satisfies RCOND + 1.0 = 1.0 then A may be singular
                   to working precision.
    
         xWORK     Scratch array with a dimension of N.
    
    SAMPLE PROGRAM
               PROGRAM TEST
               IMPLICIT NONE
         C
               INTEGER    LDA, N
               PARAMETER (N = 3)
               PARAMETER (LDA = 3)
         C
               REAL       RCOND
               COMPLEX    A(LDA,N), B(N), WORK(N)
               INTEGER    ICOL, IPIVOT(N), IROW
         C
               EXTERNAL   CHICO, 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 CHICO (A, LDA, N, IPIVOT, RCOND, WORK)
               PRINT 1050, RCOND
               IF ((RCOND + 1.0) .EQ. 1.0) THEN
                 PRINT 1060
               END IF
               CALL CHISL (A, LDA, N, IPIVOT, B)
               PRINT 1070
               PRINT 1040, B
         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, 'Reciprocal condition number of A:', F6.3)
          1060 FORMAT (1X, 'A may be singular to working precision.')
          1070 FORMAT (/1X, 'A**(-1) * b:')
         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)
    
          Reciprocal condition number of A: 0.001
    
          A**(-1) * b:
            (   5.0,   0.0)
            (  26.0,   0.0)
            (  64.0,   0.0)
    
    
    
    


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