function [ fx, fp ] = testzero ( x )

%TESTZERO evaluates one of several scalar nonlinear test functions.
%
%  Form:
%
%    function [ fx, fp ] = testzero ( x )
%
%  Discussion:
%
%    To make use of this function while running MATLAB, you must issue 
%    the command
%      global IPROB
%    and then set IPROB to a value between 1 and 8 to select a 
%    particular problem.
%
%  Example:
%
%    global IPROB = 1
%
%    [ fx, fp ] = testzero ( x )
%
%  Modified:
%
%    15 November 1999
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    As discussed above, the global parameter IPROB must be set to
%    a value between 1 and 8 to choose a function.
%
%    Input, X is the point at which the function should be evaluated;
%
%    Output, FX is the value of the selected function at X.
%    Output, FP is the derivative of the function at X.
%
global IPROB

if IPROB == 1
  fx = sin ( x ) - 0.5 * x;
  fp = cos ( x ) - 0.5;
elseif IPROB == 2
  fx = 2.0 * x - exp ( - x );
  fp = 2.0 + exp ( - x );
elseif IPROB == 3
  fx = x * exp ( - x );
  fp = exp ( - x ) * ( 1.0 - x );
elseif IPROB == 4
  fx = exp ( x ) - 1.0 / ( 10.0 * x )^2;
  fp = exp ( x ) + 2.0 / ( 100.0 * x^3 );
elseif IPROB == 5
  fx = ( x + 3.0 ) * ( x - 1.0 )^2;
  fp = ( 3.0 * x + 5.0 ) * ( x - 1.0 );
elseif IPROB == 6
  fx = exp ( x ) - 2.0 - 1.0 / ( 10.0 * x )^2 + 2.0 / ( 100.0 * x )^3;
  fp = exp ( x ) + 2.0 / ( 100.0 * x^3 ) - 6.0 / ( 1000000.0 * x^4 );
elseif IPROB == 7
  fx = x^3;
  fp = 3.0 * x^2;
elseif IPROB == 8
  fx = cos ( x ) - x;
  fp = - sin ( x ) - 1.0;
else
  error ( 'TESTZERO - Fatal error; Value of IPROB was out of range.' )
end