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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

Партнёры:

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