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NAME
     dspsl - solve the linear system  Ax  =  b  for  a  symmetric
     matrix  A  in packed storage, which has been UDU-factored by
     xSPCO or xSPFA, and vectors b and x.

SYNOPSIS
     SUBROUTINE DSPSL (DA, N, IPIVOT, DB)

     SUBROUTINE SSPSL (SA, N, IPIVOT, SB)

     SUBROUTINE ZSPSL (ZA, N, IPIVOT, ZB)

     SUBROUTINE CSPSL (CA, N, IPIVOT, CB)



     #include <sunperf.h>

     void dspsl(double *dap, int n, int *kpvt, double *b) ;

     void sspsl(float *sap, int n, int *kpvt, float *b) ;

     void zspsl(doublecomplex *zap, int n, int *kpvt,  doublecom-
               plex *b) ;

     void cspsl(complex *cap, int n, int *kpvt, complex *b) ;

ARGUMENTS
     xA        UDU factorization of the matrix A, as computed  by
               xSPCO or xSPFA.

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

     IPIVOT    Pivot vector as computed by xSPCO or xSPFA.

     xB        On entry, the right-hand side vector b.  On  exit,
               the solution vector x.

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        15
     C     A = 0  2  0    b = 12
     C         4  0  1        15
     C
           DATA A / 1.0D0, 0.0D0, 2.0D0, 4.0D0, 0.0D0, 1.0D0 /
           DATA B / 1.5D1, 1.2D1, 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:
        15.0
        12.0
        15.0

      A**(-1) * b:
         3.0
         6.0
         3.0

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