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NAME
     dpbco -  compute  a  Cholesky  factorization  and  condition
     number  of  a symmetric positive definite matrix A in banded
     storage.  If the condition number is not needed  then  xPBFA
     is slightly faster.  It is typical to follow a call to xPBCO
     with a call to xPBSL to solve Ax = b or to xPBDI to  compute
     the determinant of A.

SYNOPSIS
     SUBROUTINE DPBCO (DA, LDA, N, NDIAG, DRCOND, DWORK, INFO)

     SUBROUTINE SPBCO (SA, LDA, N, NDIAG, SRCOND, SWORK, INFO)

     SUBROUTINE ZPBCO (ZA, LDA, N, NDIAG, DRCOND, ZWORK, INFO)

     SUBROUTINE CPBCO (CA, LDA, N, NDIAG, SRCOND, CWORK, INFO)



     #include <sunperf.h>

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

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

     void zpbco(doublecomplex *abd, int lda, int n, int m, double
               *drcond, int *info) ;

     void cpbco(complex *abd,  int  lda,  int  n,  int  m,  float
               *srcond, 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.

     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.

     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, NDIAG
           PARAMETER        (N = 4)
           PARAMETER        (NDIAG = 1)
           PARAMETER        (LDA = NDIAG + 1)
     C
           DOUBLE PRECISION  A(LDA,N), B(N), RCOND, WORK(N)
           INTEGER           ICOL, INFO, IROW
     C
           EXTERNAL          DPBCO, 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 DPBCO (A, LDA, N, NDIAG, RCOND, WORK, INFO)
           IF (INFO .EQ. 0) THEN
             IF ((RCOND + 1.0D0) .EQ. 1.0D0) THEN
               PRINT 1100
             END IF
             CALL DPBSL (A, LDA, N, NDIAG, B)
             PRINT 1070, RCOND
             PRINT 1080
             PRINT 1060, B
           ELSE
             PRINT 1090
           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, 'Reciprocal condition number of A:', F5.1)
      1080 FORMAT (/1X, 'A**(-1) * b:')
      1090 FORMAT (/1X, 'A is not positive definite.')
      1100 FORMAT (1X, 'A may be singular to working precision.')
     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

      Reciprocal condition number of A:  0.1

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

Партнёры:

Хостинг: