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NAME
     dppco -  compute  a  Cholesky  factorization  and  condition
     number  of  a symmetric positive definite matrix A in packed
     storage.  If the condition number is not needed  then  xPPFA
     is slightly faster.  It is typical to follow a call to xPPCO
     with a call to xPPSL to solve Ax = b or to xPPDI to  compute
     the determinant and inverse of A.

SYNOPSIS
     SUBROUTINE DPPCO (DA, N, DRCOND, DWORK, INFO)

     SUBROUTINE SPPCO (SA, N, SRCOND, SWORK, INFO)

     SUBROUTINE ZPPCO (ZA, N, DRCOND, ZWORK, INFO)

     SUBROUTINE CPPCO (CA, N, SRCOND, CWORK, INFO)



     #include <sunperf.h>

     void dppco(double *dap, int n, double *drcond, int *info) ;

     void sppco(float *sap, int n, float *srcond, int *info) ;

     void zppco(doublecomplex *zap, int n,  double  *drcond,  int
               *info) ;

     void cppco(complex *cap, 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.

     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           LENGTA, N
           PARAMETER        (N = 4)
           PARAMETER        (LENGTA = (N * N + N) / 2)
     C
           DOUBLE PRECISION  A(LENGTA), B(N), RCOND, WORK(N)
           INTEGER           INFO
     C
           EXTERNAL          DPPCO, DPPSL
     C
     C     Initialize the array A to store in packed symmetric storage
     C     mode the matrix A shown below.  Initialize the array B to store
     C     the matrix B shown below.
     C
     C         4  3  2  1        60
     C     A = 3  4  3  2    b = 20
     C         2  3  4  3        20
     C         1  2  3  4        60
     C
           DATA A / 4.0D0, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,
          $         1.0D0, 2.0D0, 3.0D0, 4.0D0 /
           DATA B / 6.0D1, 2.0D1, 2.0D1, 6.0D1 /
     C
           PRINT 1000
           PRINT 1010, A(1), A(2), A(4), A(7)
           PRINT 1010, A(2), A(3), A(5), A(8)
           PRINT 1010, A(4), A(5), A(6), A(9)
           PRINT 1010, A(7), A(8), A(9), A(10)
           PRINT 1020
           PRINT 1030, B
           CALL DPPCO (A, N, RCOND, WORK, INFO)
           IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
             PRINT 1040
           END IF
           CALL DPPSL (A, N, B)
           PRINT 1050, RCOND
           PRINT 1060
           PRINT 1030, B
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (5(3X, F7.3))
      1020 FORMAT (/1X, 'b:')
      1030 FORMAT (3X, F7.3)
      1040 FORMAT (1X, 'A may be singular to working precision.')
      1050 FORMAT (/1X, 'Reciprocal condition of A:', F5.2)
      1060 FORMAT (/1X, 'A**(-1) * b:')
     C
           END

SAMPLE OUTPUT
      A in full form:
          4.000     3.000     2.000     1.000
          3.000     4.000     3.000     2.000
          2.000     3.000     4.000     3.000
          1.000     2.000     3.000     4.000

      b:
         60.000
         20.000
         20.000
         60.000

      Reciprocal condition of A: 0.04

      A**(-1) * b:
         32.000
        -20.000
        -20.000
         32.000

Партнёры:

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