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dpofa (3)
  • >> dpofa (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dpofa - compute a  Cholesky  factorization  of  a  symmetric
         positive  definite matrix A.  It is typical to follow a call
         to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to
         compute the determinant and inverse of A.
    
    SYNOPSIS
         SUBROUTINE DPOFA (DA, LDA, N, INFO)
    
         SUBROUTINE SPOFA (SA, LDA, N, INFO)
    
         SUBROUTINE ZPOFA (ZA, LDA, N, INFO)
    
         SUBROUTINE CPOFA (CA, LDA, N, INFO)
    
    
    
         #include <sunperf.h>
    
         void dpofa(double *da, int lda, int n, int *info) ;
    
         void spofa(float *sa, int lda, int n, int *info) ;
    
         void cpofa(complex *ca, int lda, int n, int *info) ;
    
         void zpofa(doublecomplex *za, int lda, int n, int *info) ;
    
    ARGUMENTS
         xA        On entry, the upper triangle of the matrix A.   On
                   exit,  a  Cholesky  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.
    
         INFO      On exit:
                   INFO = 0  Subroutine completed normally.
                   INFO > 0  Returns a value k if the  leading  minor
                   of order k is not positive definite.
    
    SAMPLE PROGRAM
               PROGRAM TEST
               IMPLICIT NONE
         C
               INTEGER           LDA, N
               PARAMETER        (N = 5)
               PARAMETER        (LDA = N)
         C
               DOUBLE PRECISION  A(LDA,N), B(N)
               INTEGER           ICOL, INFO, IROW
    
         C
               EXTERNAL          DPOFA, DPOSL
         C
         C     Initialize the array A to store in symmetric storage mode the
         C     matrix A shown below.  Initialize the array B to store the vector
         C     B shown below.
         C
         C          5  4  3  2  1        120
         C          4  5  4  3  2         60
         C     A =  3  4  5  4  3    b =  40
         C          2  3  4  5  4         60
         C          1  2  3  4  5        120
         C
               DATA A / 5.0D0, 4*8D8, 4.0D0, 5.0D0, 3*8D8, 3.0D0, 4.0D0, 5.0D0,
              $         2*8D8, 2.0D0, 3.0D0, 4.0D0, 5.0D0, 1*8D8, 1.0D0, 2.0D0,
              $         3.0D0, 4.0D0, 5.0D0 /
               DATA B / 1.2D2, 6.0D1, 4.0D1, 6.0D1, 1.2D2 /
         C
               PRINT 1000
               DO 100, IROW = 1, N
                 PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
              $              (A(IROW,ICOL), ICOL = IROW + 1, N)
           100 CONTINUE
               PRINT 1020
               PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
               PRINT 1030
               PRINT 1040, B
               CALL DPOFA (A, LDA, N, INFO)
               IF (INFO .EQ. 0) THEN
                 CALL DPOSL (A, LDA, N, B)
                 PRINT 1050
                 PRINT 1040, B
               ELSE
                 PRINT 1060
               END IF
         C
          1000 FORMAT (1X, 'A in full form:')
          1010 FORMAT (5(3X, F7.3))
          1020 FORMAT (/1X, 'A in symmetric form:  (* in unused entries)')
          1030 FORMAT (/1X, 'b:')
          1040 FORMAT (3X, F7.3)
          1050 FORMAT (/1X, 'A**(-1) * b:')
          1060 FORMAT (/1X, 'A is not positive definite.')
         C
               END
    
    SAMPLE OUTPUT
          A in full form:
              5.000     4.000     3.000     2.000     1.000
              4.000     5.000     4.000     3.000     2.000
              3.000     4.000     5.000     4.000     3.000
              2.000     3.000     4.000     5.000     4.000
              1.000     2.000     3.000     4.000     5.000
    
          A in symmetric form:  (* in unused entries)
              5.000     4.000     3.000     2.000     1.000
            *******     5.000     4.000     3.000     2.000
            *******   *******     5.000     4.000     3.000
            *******   *******   *******     5.000     4.000
            *******   *******   *******   *******     5.000
    
          b:
            120.000
             60.000
             40.000
             60.000
            120.000
    
          A**(-1) * b:
             50.000
            -20.000
            -20.000
            -20.000
             50.000
    
    
    
    


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