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homework2.m
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homework2.m
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%% ----- Homework 2 ----- %%
clc;
clear;
close all;
R = 2;
I = [2 4 8 16 32 64];
time1 = zeros(length(I),1);
time2 = zeros(length(I),1);
time3 = zeros(length(I),1);
for ii = 1:length(I)
for mc = 1:250
A = randn(I(ii),I(ii)) + 1j*randn(I(ii),I(ii));
B = randn(I(ii),I(ii)) + 1j*randn(I(ii),I(ii));
tic;
pinv(tensor.mtx_prod_kr(A,B));
aux = toc;
time1(ii,1) = time1(ii,1) + aux;
tic;
(tensor.mtx_prod_kr(A,B).'*tensor.mtx_prod_kr(A,B))...
\(tensor.mtx_prod_kr(A,B).');
aux = toc;
time2(ii,1) = time2(ii,1) + aux;
tic;
tensor.mtx_prod_had((A.'*A),(B.'*B))\(tensor.mtx_prod_kr(A,B).');
aux = toc;
time3(ii,1) = time3(ii,1) + aux;
end
end
time1 = time1/250;
time2 = time2/250;
time3 = time3/250;
figure
txt = ['1st Method'];
plot(I,time1,'-d','color', [0.3010 0.7450 0.9330], "linewidth", 2,...
"markersize", 8, "DisplayName", txt);
hold on;
txt = ['2nd Method'];
plot(I,time2,'-d','color', [0.8500 0.3250 0.0980], "linewidth", 2,...
"markersize", 8, "DisplayName", txt);
hold on;
txt = ['3rd Method'];
plot(I,time3,'-d','color', [0.4660 0.6740 0.1880], "linewidth", 2,...
"markersize", 8, "DisplayName", txt);
hold off;
title(['Khatri-Rao product performance considering 2 columns'])
xlabel('Number of rows')
ylabel('Time (s)')
legend_copy = legend("location", "northwest");
set(legend_copy,'Interpreter','tex','location','northwest',"fontsize", 12)
grid on;
saveas(gcf,'hw2a1.png')
R = 4;
I = [2 4 8 16 32 64];
time1 = zeros(length(I),1);
time2 = zeros(length(I),1);
time3 = zeros(length(I),1);
for ii = 1:length(I)
for mc = 1:250
A = randn(I(ii),I(ii)) + 1j*randn(I(ii),I(ii));
B = randn(I(ii),I(ii)) + 1j*randn(I(ii),I(ii));
tic;
pinv(tensor.mtx_prod_kr(A,B));
aux = toc;
time1(ii,1) = time1(ii,1) + aux;
tic;
(tensor.mtx_prod_kr(A,B).'*tensor.mtx_prod_kr(A,B))...
\(tensor.mtx_prod_kr(A,B).');
aux = toc;
time2(ii,1) = time2(ii,1) + aux;
tic;
tensor.mtx_prod_had((A.'*A),(B.'*B))\(tensor.mtx_prod_kr(A,B).');
aux = toc;
time3(ii,1) = time3(ii,1) + aux;
end
end
time1 = time1/250;
time2 = time2/250;
time3 = time3/250;
figure
txt = ['1st Method'];
plot(I,time1,'-d','color', [0.3010 0.7450 0.9330], "linewidth", 2,...
"markersize", 8, "DisplayName", txt);
hold on;
txt = ['2nd Method'];
plot(I,time2,'-d','color', [0.8500 0.3250 0.0980], "linewidth",...
2, "markersize", 8, "DisplayName", txt);
hold on;
txt = ['3rd Method'];
plot(I,time3,'-d','color', [0.4660 0.6740 0.1880], "linewidth",...
2, "markersize", 8, "DisplayName", txt);
hold off;
title(['Khatri-Rao product performance considering 4 columns'])
xlabel('Number of rows')
ylabel('Time (s)')
legend_copy = legend("location", "northwest");
set(legend_copy,'Interpreter','tex','location','northwest',"fontsize", 12)
grid on;
saveas(gcf,'hw2a2.png')
I = 4;
R = 2;
N = [2 4 6 8];
time1 = zeros(length(N),1);
time2 = zeros(length(N),1);
for nn = 1:length(N)
for mc = 1:250
tic;
for ii = 1:N(nn)
if ii == 1
A1 = randn(I,R) + 1j*randn(I,R);
continue
else
A2 = randn(I,R) + 1j*randn(I,R);
A1 = tensor.mtx_prod_kron(A1,A2);
end
end
aux = toc;
time1(nn,1) = time1(nn,1) + aux;
end
end
time1 = time1/250;
figure
txt = ['\bf ⋄^{N}_{n = 1} (A^{(n)}_{4 \times 2})'];
semilogy(N,time1,'-d','color', [0.3010 0.7450 0.9330], "linewidth", 2,...
"markersize", 8, "DisplayName", txt);
title(['Multiple Khatri-Rao products performance'])
xlabel('Number of Products')
ylabel('Time (s)')
legend_copy = legend("location", "northwest");
set(legend_copy,'Interpreter','tex','location','northwest',"fontsize", 12)
grid on;
saveas(gcf,'hw2a3.png')