Cody

Problem 258. linear least squares fitting

Solution 576704

Submitted on 8 Feb 2015 by bkzcnldw
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Test Suite

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)<1e-6)

lsqr converged at iteration 1 to a solution with relative residual 0.47.

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((x-mean(x)).*(y-mean(y)))/sum((x-mean(x)).^2); aref(1) = mean(y)-aref(2)*mean(x); assert(norm(fit_coefficients(f,x,y)-aref')<1e-6)

lsqr converged at iteration 2 to a solution with relative residual 0.091.

3   Pass
%%% third test: polynomial fit x = [1:15]' + randn(15,1); y = -10+0.2*x-0.5*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')<1e-6)

lsqr converged at iteration 5 to a solution with relative residual 0.00037.

4   Pass
%%% fourth test: non-polynomial 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)<1e-6)

lsqr converged at iteration 2 to a solution with relative residual 1.4e-16.