function [] = prob_13_11_c()
% 
% Written by:
% -- 
% John L. Weatherwax                2006-09-05
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 

v_l = [ 1   1 ]; 
v_r = [ 0.1 4 ]; 

q = linspace( 0.01, 2, 100 ); 

figure; hold on; 

% plot the state v_l:
%
hsvl = plot( v_l(1), v_l(2), 'b.', 'MarkerSize', 15 ); 

% plot one-integral/Hugoniot curves through v_l:
%
qu_prod = v_l(1)*v_l(2);
u1 = qu_prod ./ q;
hvlc = plot( q, u1, '-b' ); 

% plot the state v_r:
%
hsvr = plot( v_r(1), v_r(2), 'r.', 'MarkerSize', 15 );

% plot two-integal/Hugoniot curves through v_r:
%
u2 = repmat(v_r(2),1,length(q)); 
hvrc = plot( q, u2, '-r' ); 

% Plot the middle state (intersection of the two wave curves):
%
q_star = v_l(1)*v_l(2)/v_r(2);
u_star = v_r(2);
hvs = plot( q_star, u_star, 'k.', 'MarkerSize', 15 );

% Add some labels:
%
axis( [ 0 2 0 10 ] ); 
xlabel( 'q' ); ylabel( 'u' ); grid on; 
legend( [ hsvl hvlc hsvr hvrc hvs ], { ...
    '(q_l,v_l)', 'wave curve through v_l', ...
    '(q_r,v_r)', 'wave curve through v_r', ...
    '(q_*,v_*): Riemann intersection point' } ); 
saveas( gcf, 'prob_13_11_pt_c_pp.eps', 'psc2' );


% Draw the x-t diagram:
% 
figure; hold on; 
line( [ 0; v_r(2)*1 ], [ 0 ; 1 ] ); 
line( [ 0; 0 ], [ 0 ; 1 ] ); 
text( -.5, .5, '(q_l,u_l)' ); 
text(  .5, .5, '(q_*,u_r)' ); 
text( 1.5, .2, '(q_r,u_r)' ); 
text( 1.6, .5, '\lambda^2 = u_r' );
axis( [ -1 2 0 1 ] ); 
xlabel( 'x' ); ylabel( 't' ); %grid on; 
saveas( gcf, 'prob_13_11_pt_c_xt.eps', 'psc2' );