playIt.m

% AUTHOR: Yujia Yan

toSolve= [
17,  19  ,18  ,17  ,15  ,14, 12, 11, 10,  9,  8,  19,24, 32, 6,  4, 19 ,26, 44 ,48,48, 36, 34,32,31,48, 37, 34,32, 31, 34,32,37, 40, 20,  19  ,18  ,17  ,15  ,14, 12, 11, 10,  9,  8,  19,24, 32, 6,  4, 19 ,26];
iters=[
64,  64,  64,  32,  16,  16, 16, 16, 16, 16, 16,  16,16, 16,16, 16, 16, 16, 64,32,64, 64, 64,64,64,64, 64, 64,64, 64, 64,64,64, 64, 64,  64,  64,  32,  16,  16, 16, 16, 16, 16, 16,  16,16, 16,16, 16, 16, 16];
pitchShift=[
0 ,   0,  -1,  -1,   0,   4,  2,  1,  0,  2,  4,   6, 8, 10,12, 64, 32, 24,  0,12,17, 4,   2, 1 ,0, 0, 18, 16,12, 7,  9,  9 ,9, 64,0 ,   0,  -1,  -1,   0,   4,  2,  1,  0,  2,  4,   6, 8, 10,12, 64, 32, 24,];
pluckOn=[
0,    0,   0,   0,   0,   0,  0,  0,  0,  0,  0,   0, 0,  0, 0,  0,  0 , 1,  0, 1, 1, 1,   1, 1, 1, 1, 1,   1, 1, 1,  1,  1, 1,  0, 1,    1,   1,   1,   1,   1,  1,  1,  1,  1,  1,   1, 1,  1, 1,  1,  1 , 1];
windOn=[
1,    1,   1,   1,   1,   1,  1,  1,  1,  1,  1,   1, 1,  1, 1,  1,  1,  1,  0, 1  0,   1, 0, 0, 1, 1,   1, 1, 1,  1,  1, 1, 1,  0,1,    1,   1,   1,   1,   1,  1,  1,  1,  1,  1,   1, 1,  1, 1,  1,  1,  1,];
rate=1.0
count=0;
for i= 1:length(toSolve)
	fprintf(' Now solving for the Klee-Minty Problem: %.0f \n', toSolve(i))
	pluck=pluckOn(i);
	wind=windOn(i);
	if(toSolve(i)< 30)
	[A, b, c]= KleeMinty(toSolve(i));
	BASIS= toSolve(i)+1:2*toSolve(i);
	else
	[A,b,c]=hilbertLP(toSolve(i)-30);
	BASIS= toSolve(i)-30+1:2*(toSolve(i)-30);
	end
	step=0;
	%%script provided in the lecture resource
	% The Simplex Algorithm
	% INPUT c, A, b, BASIS / c is a row vector
	% pie = marginal cost
	% d = reduced cost
	% jE = entering variable index
	% jL = leaving variable index
	% bbar = current basic solution
	% 
	INVB = inv(A(:,BASIS)); %(inverse of basis)
	bbar = INVB*b; %(the current basic solutions)
	degen = 0; %(This variable counts degenerate pivots.)
	for step =1:iters(i) %(Limit iterations to 10000.)
		toSolve(i)
		cB = c(BASIS); %Cost function associated with the basis

		pie = cB*INVB; %BTRAN: Calculate marginal cost 
		d = c-pie*A; %PRICING: Calculate reduced cost 
		[dmin,jE] = min(d); %(Find the entering variable.)
		if dmin >=-1e-10, break, end %(Stop if all reduced costs >=0.)
			y = INVB*A(:,jE); %(FTRAN: update incoming column)
			INDEX = find(y>1e-6); %(Find positive components of y.)
			if isempty(INDEX) %(if y<=0 stop, LP is unbounded)
				error('problem is unbounded')
			end

		RATIO = bbar(INDEX)./y(INDEX); %RATIO test
		[theta,t] = min(RATIO);
		if theta < 1e-10 %(If theta = 0, the pivot is degenerate.) 

			degen = degen + 1;
		end
		jL = INDEX(t); %(index of smallest ratio)
		BASIS(jL) = jE; %(UPDATE: Replace col jL with col jE.)
		INVB = inv(A(:,BASIS)); %(inverse of the basis)
		bbar = INVB*b;
		if(wind)
		playSin(0.1,freqMapping(jE+pitchShift(i)), length(d)/32*rate, 44100, jE*0.0001*3/(length(d)+0.01), jE/(length(d)+0.01) );
	end
	if(pluck)	
		playKarplusStrong(0.05,freqMapping(jE+pitchShift(i))/2,44100, length(d)/32) ;
	end
		pause(length(d)*rate/64/2)
		bbar
	end
		n = length(c);
		x= zeros(n,1);
		x(BASIS) = bbar;% Return Solution
end