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NAME
     sspco - compute the UDU factorization and  condition  number
     of a symmetric matrix A in packed storage.  If the condition
     number is not needed then xSPFA is slightly faster.   It  is
     typical  to  follow  a call to xSPCO with a call to xSPSL to
     solve Ax =  b  or  to  xSPDI  to  compute  the  determinant,
     inverse, and inertia of A.

SYNOPSIS
     SUBROUTINE DSPCO (DA, N, IPIVOT, DRCOND, DWORK)

     SUBROUTINE SSPCO (SA, N, IPIVOT, SRCOND, SWORK)

     SUBROUTINE ZSPCO (ZA, N, IPIVOT, DRCOND, ZWORK)

     SUBROUTINE CSPCO (CA, N, IPIVOT, SRCOND, CWORK)



     #include <sunperf.h>

     void dspco(double *dap, int n, int *kpvt, double *rcond) ;

     void sspco(float *sap, int n, int *kpvt, float *rcond) ;

     void zspco(doublecomplex *zap,  int  n,  int  *kpvt,  double
               *rcond) ;

     void cspco(complex *cap, int n, int *kpvt, float *rcond) ;

ARGUMENTS
     xA        On entry, the upper triangle of the matrix A.   On
               exit, a UDU factorization of the matrix A.

     N         Order of the matrix A.  N >= 0.

     IPIVOT    On exit, a vector of pivot indices.

     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.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           LENGTA, N
           PARAMETER        (N = 3)
           PARAMETER        (LENGTA = (N * N + N) / 2)
     C
           DOUBLE PRECISION  A(LENGTA), B(N), RCOND, WORK(N)
           INTEGER           IPIVOT(N)
     C
           EXTERNAL          DSPCO, DSPSL
     C
     C     Initialize the array A to store in packed symmetric format
     C     the matrix A shown below.  Initialize the array B to store
     C     the vector b shown below.
     C
     C         1  0  4        30
     C     A = 0  2  0    b =  4
     C         4  0  1        15
     C
           DATA A / 1.0D0, 0.0D0, 2.0D0, 4.0D0, 0.0D0, 1.0D0 /
           DATA B / 3.0D1, 4.0D0, 1.5D1 /
     C
           PRINT 1000
           PRINT 1010, A(1), A(2), A(4)
           PRINT 1010, A(2), A(3), A(5)
           PRINT 1010, A(4), A(5), A(6)
           PRINT 1020
           PRINT 1030, B
           CALL DSPCO (A, N, IPIVOT, RCOND, WORK)
           IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
             PRINT 1040
           END IF
           CALL DSPSL (A, N, IPIVOT, B)
           PRINT 1050
           PRINT 1030, B
     C
      1000 FORMAT (1X, 'A:')
      1010 FORMAT (3(3X, F4.1))
      1020 FORMAT (/1X, 'b:')
      1030 FORMAT (3X, F4.1)
      1040 FORMAT (1X, 'A may be singular to working precision.')
      1050 FORMAT (/1X, 'A**(-1) * b:')
     C
           END

SAMPLE OUTPUT
      A:
         1.0    0.0    4.0
         0.0    2.0    0.0
         4.0    0.0    1.0

      b:
        30.0
         4.0
        15.0

      A**(-1) * b:
         2.0
         2.0
         7.0

Партнёры:

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