%   
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; clc; clear; 

D = 10;
G = 400;
Dstar = 0.5;
Gstar = 5;
C = 0.002;
min_deltaS = -0.05;
max_deltaS = +0.05;


% Plot deltaPi_worst as a function of lambda by griding lambda:
%
n_pts = 100; 
lambda_min = -300;
lambda_max = 0;
lambdas = linspace( lambda_min+0.1*abs(lambda_min), lambda_max, n_pts );
dPi_worst = zeros(1,n_pts);
for ii = 1:length(lambdas)
  dPi_worst(ii) = deltaPi_vs_lambda(lambdas(ii), D,G,Dstar,Gstar,C,min_deltaS,max_deltaS);
end

% Get a very coarse initial guess at the location of the maximum:
%
[mv,mi] = max(dPi_worst); lambda_initial_guess = lambdas(mi);

% Use an optimization routine to compute this value (not just a grid search):
%
min_opts = optimset('fminunc');
min_opts = optimset(min_opts, 'LargeScale', 'off' );
lambda_opt = fminunc( @(x) -deltaPi_vs_lambda(x, D,G,Dstar,Gstar,C,min_deltaS,max_deltaS), lambda_initial_guess, min_opts );


plot( lambdas, dPi_worst, '-' ); 
xlabel('lambda'); ylabel('delta Pi (worst)');
axis( [lambda_min,lambda_max, min(dPi_worst), max(dPi_worst)+10*abs(max(dPi_worst))] );

addpath('~/Matlab/');
vline(lambda_opt);
text( -150, -5, ['optimal lambda=',num2str(lambda_opt)] );

saveas( gcf, '../../WriteUp/Graphics/Chapter43/optimization_for_lambda', 'epsc' );


% Plot the unhedged and hedged dPi in both cases:
%
deltaSs = linspace( min_deltaS, max_deltaS, 500 );
dPi_UH  = deltaSs * D + 0.5 * ( deltaSs.^2 ) * G;
dPi_H   = deltaSs * ( D + lambda_opt * Dstar ) + 0.5 * ( deltaSs.^2 ) * ( G + lambda_opt * Gstar );

figure; 
h_uh = plot( deltaSs*100, dPi_UH, '-r' ); hold on; 
h_h = plot( deltaSs*100, dPi_H, '-g' ); 
xlabel('delta S (percent)'); ylabel('delta Pi');
legend( [h_uh,h_h], {'dP unhedged', 'dP hedged'}, 'location', 'northwest' );

saveas( gcf, '../../WriteUp/Graphics/Chapter43/deltaS_vs_dPi', 'epsc' );