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cpbco (3)
  • >> cpbco (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         cpbco -  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
    
    
    
    


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