function testEstimateExp(estimateFun, lowerBound, upperBound, numSamplePoints)
%function testEstimateExp(@estimateFun)   
% Helper function for APMA 4300 Homework Assignment #1 Call this function to
% verify your estimateExp function, it will plot the Matlab exp function
% against your estimateExp function, your absolute error at each point, and
% display your average absolute error in ulps.
% testEstimateExp(@estimateExp, lowerBound, upperBound, numSamplePoints)
% allows you to customize lowerBound, upperBound, and numSamplePoints.
%
% estimateExp       - function pointer to student estimateExp function
% lowerBound        - lower bound of linearly spaced sampling region
% upperBound        - upper bound of linearly spaced sampling region
% numSamplePoints   - number of points to sample in region
    
    DEFAULT_LOWER_BOUND = -20;
    DEFAULT_UPPER_BOUND =  20;
    DEFAULT_NUM_SAMPLE_POINTS = 20;
    
    % The below switch structure tests the MATLAB variable nargin, which is
    % set to the number of arguments the user called the current function
    % with.  Type help switch or help nargin for more information on these.
    switch nargin
     case 1
      lowerBound = DEFAULT_LOWER_BOUND;
      upperBound = DEFAULT_UPPER_BOUND;
      numSamplePoints = DEFAULT_NUM_SAMPLE_POINTS;
     case 4
     otherwise
      error(['Wrong number of arguments to function.  Type help' ...
	     ' testEstimateExp for usage']);
    end
    
    % Create an array of evenly spaced points with linspace.
    xPoints = linspace(lowerBound, upperBound, numSamplePoints);
    
    % Now at each point, calculate the estimate and the true value, and use
    % Matlab's eps function to get the numerical value of the ulp at each
    % exp(x)
    % first - check for vectorized function
    try 
       expEstimate     = estimateFun(xPoints);
       expTrue         = exp(xPoints);
       expUlp          = eps(expTrue);
    catch
       for i=1:length(xPoints)
	  expEstimate(i) = estimateFun(xPoints(i));
	  expTrue(i)     = exp(xPoints(i));
	  expUlp(i)      = eps(expTrue(i));
       end
    end
    
    % Basic plotting
    figure;  %clears figure
    subplot(2,1,1); %Sets up a 2 x 1 subplot and picks window 1
    semilogy(xPoints, expEstimate, 'b--x');  %See help semilogy for info on this monster
    hold on;        %Freezes plotting window
    semilogy(xPoints, expTrue, 'r-o');
    legend('Student estimate', 'true','Location','NorthWest'); %See help legend
    title('Estimated versus true exp(x)');
    xlabel('x');
    ylabel('y');
    grid;
    hold off;
    
    subplot(2,1,2); %Now selects window 2 of the 2 x 1 subplot
    absoluteErrorUlps = abs(expEstimate-expTrue)./expUlp;
    meanAbsoluteErrorUlps = mean(absoluteErrorUlps);
    plot(xPoints,absoluteErrorUlps, '.m-');
    hold on
    %this needs to be a vector of values to draw a line
    plot(xPoints,ones(size(xPoints))*meanAbsoluteErrorUlps, 'r-');
    legend('Absolute Error', 'Averaged Absolute Error','Location','NorthWest');
    %A complicated title string like this requires me to build it first
    %using sprintf before I pass it to title
    titleString = sprintf('Absolute Averaged Error of Student Estimate (ulps): %d', ...
		    meanAbsoluteErrorUlps);
    title(titleString);
    xlabel('x');
    ylabel('error (ulps)');
    grid;
    hold off