[ новости /+++ | форум | теги | ]

NAME
     schdc - compute the Cholesky decomposition  of  a  symmetric
     positive definite matrix A.

SYNOPSIS
     SUBROUTINE DCHDC (DA, LDA, N, DWORK, IPIVOT, JOB, INFO)

     SUBROUTINE SCHDC (SA, LDA, N, SWORK, IPIVOT, JOB, INFO)

     SUBROUTINE ZCHDC (ZA, LDA, N, ZWORK, IPIVOT, JOB, INFO)

     SUBROUTINE CCHDC (CA, LDA, N, CWORK, IPIVOT, JOB, INFO)



     #include <sunperf.h>

     void dchdc(double *da, int lda, int p, int *jpivot, int job,
               int *info) ;

     void schdc(float *sa, int lda, int p, int *jpivot, int  job,
               int *info) ;

     void zchdc(doublecomplex *za, int lda, int p, int *jpvt, int
               job, int *info) ;

     void cchdc(complex *ca, int lda, int  p,  int  *jpivot,  int
               job, int *info) ;

ARGUMENTS
     xA        On entry, the upper triangle of A.  On  exit,  the
               upper triangle of the Cholesky factor, as permuted
               by pivoting if pivoting was selected.  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.

     xWORK     Scratch array with a dimension of N.

     IPIVOT    If JOB selected no pivoting  then  IPIVOT  is  not
               referenced.   On  entry, if JOB selected pivoting,
               IPIVOT  contains   integers   representing   array
               indices  that  control the selection of pivot ele-
               ments from the diagonal of A according to the sys-
               tem below:
               IPIVOT(k) > 0  A(k,k) is an initial element.
               IPIVOT(k) = 0  A(k,k) is a free element.
               IPIVOT(k) < 0  A(k,k) is a final element.
               Before the decomposition  is  computed,  symmetric
               row  and column interchanges are used to move ini-
               tial elements to the beginning of A and final ele-
               ments  to  the  end of A.  During the computation,
               symmetric row and column interchanges are used  to
               move  the  largest remaining free diagonal element
               into the pivot position.  On exit, IPIVOT(k)  con-
               tains  the index of the diagonal element of A that
               was moved into the kth position.

     JOB       Determines how decomposition is done:
                      0  without pivoting
                      not 0   with pivoting

     INFO      On exit:  Returns the index of the  last  positive
               diagonal element of the Cholesky factor.  The sub-
               routine was successful if INFO = N.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           LDA, N, NOPIV
           PARAMETER        (N = 4)
           PARAMETER        (LDA = N)
           PARAMETER        (NOPIV = 0)
     C
           DOUBLE PRECISION  A(LDA,N), WORK(N)
           INTEGER           I, INFO, IPIVOT(N), J, JOB
     C
           EXTERNAL          DCHDC
     C
     C         4  3  2  1
     C     A = 3  4  3  2
     C         2  3  4  3
     C         1  2  3  4
     C
           DATA A / 4.0D0, 3*8D8, 3.0D0, 4.0D0, 2*8D8, 2.0D0, 3.0D0, 4.0D0,
          $         8D8, 1.0D0, 2.0D0, 3.0D0, 4.0D0 /
     C
           PRINT 1000
           DO 100, I = 1, N
             PRINT 1010, (A(J,I), J = 1, I), (A(I,J), J = I + 1, N)
       100 CONTINUE
           PRINT 1020
           PRINT 1010, ((A(I,J), J = 1, N), I = 1, N)
           JOB = NOPIV
           CALL DCHDC (A, LDA, N, WORK, IPIVOT, JOB, INFO)
           IF (INFO .EQ. N) THEN
             PRINT 1030
             PRINT 1010, A(1,1), A(1,2), A(1,3), A(1,4)
             PRINT 1040,         A(2,2), A(2,3), A(2,4)
             PRINT 1050,                 A(3,3), A(3,4)
             PRINT 1060,                         A(4,4)
           ELSE
             PRINT 1070
           END IF
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(3X, F7.3))
      1020 FORMAT (/1X, 'A in symmetric form:  (* in unused entries)')
      1030 FORMAT (/1X, 'Upper Cholesky factor:')
      1040 FORMAT (10X, 3(3X, F7.3))
      1050 FORMAT (20X, 2(3X, F7.3))
      1060 FORMAT (30X, 1(3X, F7.3))
      1070 FORMAT (/1X, 'A is not positive definite.')
     C
           END

SAMPLE OUTPUT
      A in full form:
          4.000     3.000     2.000     1.000
          3.000     4.000     3.000     2.000
          2.000     3.000     4.000     3.000
          1.000     2.000     3.000     4.000

      A in symmetric form:  (* in unused entries)
          4.000     3.000     2.000     1.000
        *******     4.000     3.000     2.000
        *******   *******     4.000     3.000
        *******   *******   *******     4.000

      Upper Cholesky factor:
          2.000     1.500     1.000     0.500
                    1.323     1.134     0.945
                              1.309     1.091
                                        1.291

Партнёры:

Хостинг: