C-----------------------------------------------------------------------
C IMSL Name:  LFIDS/DLFIDS (Single/Double precision version)
C
C Purpose:    Use iterative refinement to improve the solution of a
C             real symmetric positive definite system of linear
C             equations.
C
C Usage:      CALL LFIDS (N, A, LDA, FAC, LDFAC, B, X, RES)
C
C Example 1:
C                                  Declare variables
      INTEGER    LDA, LDFAC, N
      PARAMETER  (LDA=3, LDFAC=3, N=3)
      REAL       A(LDA,LDA), B(N), COND, FAC(LDFAC,LDFAC), RES(N,3),
     &           X(N,3)
C
C                                  Set values for A and B
C
C                                  A = (  1.0  -3.0   2.0)
C                                      ( -3.0  10.0  -5.0)
C                                      (  2.0  -5.0   6.0)
C
C                                  B = (  1.0  -3.0   2.0)
C
      DATA A/1.0, -3.0, 2.0, -3.0, 10.0, -5.0, 2.0, -5.0, 6.0/
      DATA B/1.0, -3.0, 2.0/
C                                  Factor the matrix A
      CALL LFCDS (N, A, LDA, FAC, LDFAC, COND)
C                                  Print the estimated condition number
      CALL UMACH (2, NOUT)
      WRITE (NOUT,99999) COND, 1.0E0/COND
C                                  Compute the solutions
      DO 10  I=1, 3
         CALL LFIDS (N, A, LDA, FAC, LDFAC, B, X(1,I), RES(1,I))
         B(2) = B(2) + .2E0
   10 CONTINUE
C                                  Print solutions and residuals
      CALL WRRRN ('The solution vectors are', N, 3, X, N, 0)
      CALL WRRRN ('The residual vectors are', N, 3, RES, N, 0)
C
99999 FORMAT ('  COND = ',F5.3,/,'  L1 Condition number = ',F9.3)
      END
C   COND = 0.001
C   L1 Condition number =   673.839
C
C  The solution vectors are
C          1       2       3
C  1   1.000   2.600   4.200
C  2   0.000   0.400   0.800
C  3   0.000  -0.200  -0.400
C
C    The residual vectors are
C           1        2        3
C  1   0.0000   0.0000   0.0000
C  2   0.0000   0.0000   0.0000
C  3   0.0000   0.0000   0.0000