% Q19DEMO script displays graphs like those of pg 25 in Demmel.
%         
% Requires: logdq.m
% 
% Usage:    >> Q19demo
% 
close all
% 
% Get a logarithmically distributed array of evaluation points.
% 
r = logspace(-16,0,511);
x = [fliplr(-r) r];        % symmetric about 0
y = log(1+x) ./ x;         % Naive (unstable method)
z = logdq(x);              % Stable method
%
subplot(2,2,1)             % Upper left corner
plot(x,y), grid
title('y = log(1+x) / x')
%
subplot(2,2,2)             % Upper right corner
plot(x,z), grid
title('y = log(1+x) / [(1+x) - 1]')
% 
% Next, zoom in near 0
% 
r = logspace(-17,-15,257);
x = [fliplr(-r) r];
y = log(1+x) ./ x;         % Naive (unstable method)
z = logdq(x);              % Stable method
%
u = 2*x/eps;               % Measure x in units of eps/2
subplot(2,2,3)             % Bottom left corner
plot(u,y), grid
axis([-10 10 -1 3])
xlabel('\times Macheps')
title('y = log(1+x) / x')
%
subplot(2,2,4)             % Bottom right corner
plot(u,z), grid
axis([-10 10 -1 3])
xlabel('\times Macheps')
title('y = log(1+x) / [(1+x) - 1]')