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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)

Партнёры:

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