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spoco (3)
  • >> spoco (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         spoco -  compute  a  Cholesky  factorization  and  condition
         number  of  a  symmetric positive definite matrix A.  If the
         condition number is not needed then xPOFA is  slightly  fas-
         ter.  It is typical to follow a call to xPOCO with a call to
         xPOSL to solve Ax = b or to xPODI to compute the determinant
         and inverse of A.
    
    SYNOPSIS
         SUBROUTINE DPOCO (DA, LDA, N, DRCOND, DWORK, INFO)
    
         SUBROUTINE SPOCO (SA, LDA, N, SRCOND, SWORK, INFO)
    
         SUBROUTINE ZPOCO (ZA, LDA, N, DRCOND, ZWORK, INFO)
    
         SUBROUTINE CPOCO (CA, LDA, N, SRCOND, CWORK, INFO)
    
    
    
         #include <sunperf.h>
    
         void dpoco(double *da, int lda, int n, double  *drcond,  int
                   *info) ;
    
         void spoco(float *sa, int lda, int  n,  float  *srcond,  int
                   *info) ;
    
         void  zpoco(doublecomplex  *za,  int  lda,  int  n,   double
                   *drcond, int *info) ;
    
         void cpoco(complex *ca, int lda, int n, float  *srcond,  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.
    
         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
               PARAMETER        (N = 4)
               PARAMETER        (LDA = N)
         C
               DOUBLE PRECISION  A(LDA,N), B(N), RCOND, WORK(N)
               INTEGER           ICOL, INFO, IROW
         C
               EXTERNAL          DPOCO, DPOSL
         C
         C     Initialize the array A to store in symmetric storage mode
         C     the matrix A shown below.  Initialize the array B to store
         C     the vector B shown below.
         C
         C          2  -1   0   0        40
         C     A = -1   2  -1   0    b = 30
         C          0  -1   2  -1        20
         C          0   0  -1   2        10
         C
               DATA A / 2.0D0, 3*8D8, -1.0D0, 2.0D0, 2*8D8, 0.0D0, -1.0D0,
              $         2.0D0, -1.0D0, 0.0D0, 0.0D0, -1.0D0, 2.0D0 /
               DATA B / 4.0D0, 3.0D0, 2.0D0, 1.0D0 /
         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 DPOCO (A, LDA, N, RCOND, WORK, INFO)
               IF (INFO .EQ. 0) THEN
                 IF ((RCOND + 1.0D0) .EQ. 1.0D0) THEN
                   PRINT 1070
                 END IF
                 CALL DPOSL (A, LDA, N, B)
                 PRINT 1050
                 PRINT 1040, B
                 PRINT 1060, RCOND
               ELSE
                 PRINT 1080
               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, 'b:')
          1040 FORMAT (3X, F7.3)
          1050 FORMAT (/1X, 'A**(-1) * b:')
          1060 FORMAT (/1X, 'Reciprocal condition number of A:', F5.1)
          1070 FORMAT (1X, 'A may be singular to working precision.')
          1080 FORMAT (1X, 'A is not positive definite.')
         C
               END
    
    SAMPLE OUTPUT
          A in full form:
              2.000    -1.000     0.000     0.000
             -1.000     2.000    -1.000     0.000
              0.000    -1.000     2.000    -1.000
              0.000     0.000    -1.000     2.000
    
          A in symmetric form:  (* in unused entries)
              2.000    -1.000     0.000     0.000
            *******     2.000    -1.000     0.000
            *******   *******     2.000    -1.000
            *******   *******    -1.000     2.000
    
          b:
              4.000
              3.000
              2.000
              1.000
    
          A**(-1) * b:
              6.000
              8.000
              7.000
              4.000
    
          Reciprocal condition number of A:  0.1
    
    
    
    


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