subroutine dlinfs(n, x, y, beta1, beta2, lambda, kount, p, q, r,
     1                  ifault)
 
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    Package:  SLRPACK
 
    Version:  October, 1985
 
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    PURPOSE
    -------
 
    This user-callable subroutine solves the simple model,
    y = beta1 + (beta2)x, under the Chebychev norm criterion.
 
    DESCRIPTION
    -----------
 
    1.  The Y's are observed values of the dependent variable and the
        X's are the observed values of the independent variables, the
        predictor variables.
 
    2.  The general Chebychev problem is to minimize LAMBDA where
 
             LAMBDA = MAX( |Y(i) - BETA1 - X(i)*BETA2| ) , over all i,
 
        such that
 
             Y(i)-LAMBDA <= BETA1 + X(i)*BETA2 <= Y(i)+LAMBDA
 
    3.  The optimal value of (BETA1, BETA2)' will minimize the
        maximum deviation and LAMBDA will be the value of this deviation.
 
    INPUT PARAMETERS
    ----------------
 
    N      Integer scalar (unchanged on output).
           Number of observations.
 
           N must be at least 3.
 
    X      Double precision vector dimensioned at least N (unchanged
                on output).
           Observed values of the independent variable.
 
    Y      Double precision vector dimensioned at least N (unchanged
                on output).
           Observed values of the dependent variable.
 
    OUTPUT PARAMETERS
    -----------------
 
    BETA1      Double precision scalar.
               The estimated intercept term for the fitted line.
 
    BETA2      Double precision scalar.
               The estimated slope term for the fitted line.
 
    LAMBDA     Double precision scalar.
               The least maximum absolute deviation, also
               the objective function value.
 
    P          Integer scalar.
               Indicates which row of X is the p-th constraint.
 
    Q          Integer scalar.
               Indicates which row of X is the q-th constraint.
 
    R          Integer scalar.
               Indicates which row of X is the r-th constraint.
 
    KOUNT      Integer scalar.
               The number of iterations.
 
    IFAULT     Integer scalar.
               Failure indicator.
 
               = 0    normal termination
 
               = 1    the data set is too small
                      cannot compute BETA1, BETA2, LAMBDA, P, Q, R
 
               = 2    all x values are equal
                      cannot compute BETA1, BETA2, LAMBDA, P, Q, R
 
               = 3    the data are collinear, all constraints are feasible
                      cannot compute P, Q, R
 
    PRECISION
    ---------
 
    All calculations are done in double precision.
 
    LANGUAGE
    --------
 
    All code is written in standard Fortran 77.
 
    OTHER SUBROUTINES
    -----------------
 
    PORT  subroutine  R1MACH
 
    REFERENCE
    ---------
 
    Sklar, M. and R. Armstrong (1983). "A Linear Programming Algorithm
         for the Simple Model for Discrete Chebychev Curve Fitting",
         Computers and Operations Research 10, 237-248.
 
    Sklar, M. and R. Armstrong (1984). "An Algorithm for Discrete
       Chebychev Curve Fitting for the Simple Model Using A Dual
       Linear Programming Approach", Communications in Statistics:
       Simulation and Computation, 13(4), 555-569.
 
    AUTHORS
    -------
 
    Michael G. Sklar and Ronald D. Armstrong
    University of Georgia
 
    NBS CONTACT
    -----------
 
    Sally E. Howe
    Scientific Computing Division
 
    National Engineering Labratory
    301-921-3395
 
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