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NAME
     dpbfa - compute a  Cholesky  factorization  of  a  symmetric
     positive definite matrix A in banded storage.  It is typical
     to follow a call to xPBFA with a call to xPBSL to solve Ax =
     b or to xPBDI to compute the determinant of A.

SYNOPSIS
     SUBROUTINE DPBFA (DA, LDA, N, NDIAG, INFO)

     SUBROUTINE SPBFA (SA, LDA, N, NDIAG, INFO)

     SUBROUTINE ZPBFA (ZA, LDA, N, NDIAG, INFO)

     SUBROUTINE CPBFA (CA, LDA, N, NDIAG, INFO)



     #include <sunperf.h>

     void dpbfa(double *abd, int lda, int n, int m, int *info) ;

     void spbfa(float *abd, int lda, int n, int m, int *info) ;

     void zpbfa(doublecomplex *abd, int lda, int n,  int  m,  int
               *info) ;

     void cpbfa(complex *abd, int lda, int n, int m, int *info) ;

ARGUMENTS
     xA        On entry, the upper triangle of the matrix A.   On
               exit, a Cholesky factorization of the matrix A.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= NDIAG + 1.

     N         Order of the matrix A.  N >= 0.

     NDIAG     Number of diagonals.  N-1 >= NDIAG >= 0 but if N =
               0 then NDIAG = 0.

     INFO      On exit:
               INFO = 0  Subroutine completed normally.
               INFO * 0  Returns a value  of  k  if  the  leading
               minor of order k is not positive definite.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           LDA, N, NDIAG
           PARAMETER        (N = 4)
           PARAMETER        (NDIAG = 1)
           PARAMETER        (LDA = NDIAG + 1)
     C
           DOUBLE PRECISION  A(LDA,N), B(N)
           INTEGER           ICOL, INFO, IROW
     C
           EXTERNAL          DPBFA, DPBSL
     C
     C     Initialize the array A to store in banded storage mode
     C     the matrix A shown below.  Initialize the array B to
     C     store the vector B shown below.
     C
     C          2  -1   0   0        60
     C     A = -1   2  -1   0    b = 60
     C          0  -1   2  -1        60
     C          0   0  -1   2        60
     C
           DATA A / 8D8, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0 /
           DATA B / 4*6.0D1 /
     C
           PRINT 1000
           PRINT 1010, A(2,1), A(1,2)
           PRINT 1010, A(3,1), A(2,2), A(1,3)
           PRINT 1020,         A(3,2), A(2,3), A(1,4)
           PRINT 1030,                 A(3,3), A(2,4)
           PRINT 1040
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)
           PRINT 1050
           PRINT 1060, B
           CALL DPBFA (A, LDA, N, NDIAG, INFO)
           IF (INFO .EQ. 0) THEN
             CALL DPBSL (A, LDA, N, NDIAG, B)
             PRINT 1070
             PRINT 1060, B
           ELSE
             PRINT 1080
           END IF
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(3X, F5.1))
      1020 FORMAT (8X, 3(3X, F5.1))
      1030 FORMAT (16X, 3(3X, F5.1))
      1040 FORMAT (/1X, 'A in banded form:  (* in unused entries)')
      1050 FORMAT (/1X, 'b:')
      1060 FORMAT (3X, F5.1)
      1070 FORMAT (/1X, 'A**(-1) * b:')
      1080 FORMAT (/1X, 'A is not positive definite.')
     C
           END

SAMPLE OUTPUT
      A in full form:
          2.0    -1.0

         -1.0     2.0    -1.0
                 -1.0     2.0    -1.0
                         -1.0     2.0

      A in banded form:  (* in unused entries)
        *****    -1.0    -1.0    -1.0
          2.0     2.0     2.0     2.0

      b:
         60.0
         60.0
         60.0
         60.0

      A**(-1) * b:
        120.0
        180.0
        180.0
        120.0

Партнёры:

Хостинг: