clear all
xN = [-2:.01:2];
n = [4 8 16 32]
for i=1:length(n)
    xCheb{i} = -cos((2*[1:n(i)]-1)*pi/2/n(i));
    xUnif{i} = -1+2*[1:n(i)]/(n(i)+1);
end
f1 = inline('abs(x)','x');
f2 = inline('sign(x)','x');

for i=1:length(n)
    coefCheb1{i} = polyfit(xCheb{i},f1(xCheb{i}),n(i)-1);
    coefUnif1{i} = polyfit(xUnif{i},f1(xUnif{i}),n(i)-1);
    coefCheb2{i} = polyfit(xCheb{i},f2(xCheb{i}),n(i)-1);
    coefUnif2{i} = polyfit(xUnif{i},f2(xUnif{i}),n(i)-1);
end

for i=1:length(n)
    YC1(i,:) = polyval(coefCheb1{i},xN);
    YU1(i,:) = polyval(coefUnif1{i},xN);
    YC2(i,:) = polyval(coefCheb2{i},xN);
    YU2(i,:) = polyval(coefUnif2{i},xN);
end

figure(1);clf
for i=1:length(n)
    subplot(4,4,i)
    plot(xN,f1(xN),xN,YU1(i,:));
    axis([-1.2 1.2 -.1 1.5]);
    title(['n = ' num2str(n(i))]);
    if i==1;ylabel('Unif');end
end

for i=1:length(n)
    subplot(4,4,i+4)
    plot(xN,f1(xN),xN,YC1(i,:));
    axis([-1.2 1.2 -.1 1.5]);
    if i==1;ylabel('Cheb');end
end

for i=1:length(n)
    subplot(4,4,i+8)
    plot(xN,f2(xN),xN,YU2(i,:));
    axis([-1.2 1.2 -1.5 1.5]);
    if i==1;ylabel('Unif');end
end

for i=1:length(n)
    subplot(4,4,i+12)
    plot(xN,f2(xN),xN,YC2(i,:));
    axis([-1.2 1.2 -1.5 1.5]);
    if i==1;ylabel('Cheb');end
end

print -dtiff hw3.tiff