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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)

Партнёры:

Хостинг: