% 
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 
clc; 
clear; 

addpath('~/Matlab'); 

% Lets plot the exact profit value function: 
%
npts_delta = 200; 
deltas = linspace( 0, 2.0, npts_delta ); 
pf = deltas .* ( 1 - normcdf(deltas) );

figure; 
plot( deltas, pf, '-o' ); hold on; 
[dum,ind_max] = max( pf );
vline( deltas(ind_max) ) ; 
title('White Noise Threshold Design'); xlabel('Amount of Sigma away from the Mean'); ylabel('Profit Value');
if( 1 ) saveas( gcf, '../../WriteUp/Graphics/Chapter7/pure_white_noise_band_design', 'eps' ); end 


% Next lets perform the white noise simulation from the book:
%
npts = 5000; 
npts = 75; % much smaller sample size 
spread_t = randn(npts,1); 

prob_as_function_of_delta = [];
for di=1:npts_delta, 
  d = deltas(di); 
  inds_above = find(spread_t >=  d); 
  inds_below = find(spread_t <= -d); 
  count = 0.5*(length(inds_above)+length(inds_below)); % a count of the number of times we exceed the threshold in either direction 
  prob_est = count / npts; 
  prob_as_function_of_delta = [prob_as_function_of_delta,prob_est];
end

figure; 
plot( deltas, prob_as_function_of_delta, '-o' ); 
title(['Probability Estimates from Counts: ',num2str(npts),' samples']); xlabel('Amount of Sigma away from the Mean'); ylabel('Probability');
if( 1 ) saveas( gcf, '../../WriteUp/Graphics/Chapter7/prob_estimates_from_counts', 'eps' ); end 

figure; 
pf = deltas .* prob_as_function_of_delta; 
plot( deltas, pf, '-o' ); hold on; 
[dum,ind_max] = max(pf);
vline( deltas(ind_max) ); 
title(['Profitability of Thresholds: ',num2str(npts),' samples']); xlabel('Amount of Sigma away from the Mean'); ylabel('Profit Value');
if( 1 ) saveas( gcf, '../../WriteUp/Graphics/Chapter7/profitabilty_thresholds', 'eps' ); end