Test  Status  Code Input and Output 

1  Pass 
%%% first test: fit to a constant
x = [1,2,3,4]';
y = rand(4,1);
f{1} = @(x) ones(size(x));
aref=mean(y);
assert(norm(fit_coefficients(f,x,y)aref)<1e6)

2  Pass 
%%% second test: fit to a straight line (linear regression)
x = [1,2,3,4,5]' + randn(5,1);
y = [1,2,3,4,5]' + randn(5,1);
f{1} = @(x) ones(size(x));
f{2} = @(x) x;
aref(2) = sum((xmean(x)).*(ymean(y)))/sum((xmean(x)).^2);
aref(1) = mean(y)aref(2)*mean(x);
assert(norm(fit_coefficients(f,x,y)aref')<1e6)

3  Pass 
%%% third test: polynomial fit
x = [1:15]' + randn(15,1);
y = 10+0.2*x0.5*x.^2+0.4*x.^3+0.001*log(abs(x)) + 0.2*randn(15,1);
f{1} = @(x) ones(size(x));
f{2} = @(x) x;
f{3} = @(x) x.^2;
f{4} = @(x) x.^3;
aref = fliplr(polyfit(x,y,3));
assert(norm(fit_coefficients(f,x,y)aref')<1e6)

4  Pass 
%%% fourth test: nonpolynomial fit (yes, we are that crazy)
x = [0:0.1:2*pi]';
y = 0.123 + 0.456*sin(x).*exp(0.1*x);
f{1} = @(x) ones(size(x));
f{2} = @(x) sin(x).*exp(0.1*x);
aref=[0.123 0.456]';
assert(norm(fit_coefficients(f,x,y)aref)<1e6)
