function [] = prob_13_12()
% 
% Written by:
% -- 
% John L. Weatherwax                2006-09-07
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 

% The state is defined by q=(v,\phi):
% 
q_l = [ 0   1  ];
q_r = [ 1  0.5 ]; 

% Compute the shock/CD speeds:
% 
s1 = q_l(2)^2; 
s2 = q_r(2)^2 + q_r(2)*q_l(2) + q_l(2)^2; 

% Compute the middle state:
%
q_m(1) = q_r(1)*q_l(2)/q_r(2); 
q_m(2) = q_l(2); 

% Draw the x-t diagram solution to this Riemann problem (at time="time"):
% 
time=1.0; 

figure; hold on; 
line( [ 0; s1*time ], [ 0 ; time ] ); 
line( [ 0; s2*time ], [ 0 ; time ] ); 
text(   .379, .885,  ['(v_l,\phi_l)=(',num2str(q_l(1)),', ',num2str(q_l(2)),')'] ); 
text(  1.04, 0.87,   ['(v_m,\phi_m)=(',num2str(q_m(1)),', ',num2str(q_m(2)),')'] ); 
text(  1.35, 0.689,  ['(v_r,\phi_r)=(',num2str(q_r(1)),', ',num2str(q_r(2)),')'] ); 
text( .131, .385, ['s^1 = \phi_l^2=',num2str(s1)] );
text( .458, 0.151, ['s^2 = \phi_r^2 + \phi_r \phi_l + \phi_l^2=',num2str(s2)] );
%axis( [ -1 2 0 1 ] ); 
xlabel( 'x' ); ylabel( 't' ); %grid on; 
saveas( gcf, 'prob_13_12_xt.eps', 'psc2' );