42 lines
1.3 KiB
Matlab
42 lines
1.3 KiB
Matlab
function [p, ps, mses] = gradientDescentPower(x, y, p0, epsilon, threshold)
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% Gradient descent for fitting a power-law.
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%
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% Arguments: x, vector of the x-data values.
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% y, vector of the corresponding y-data values.
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% p0, vector with initial values for c and alpha.
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% epsilon: factor multiplying the gradient.
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% threshold: minimum value for gradient
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%
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% Returns: p, vector with the final parameter values.
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% ps: 2D-vector with all the parameter tuples traversed.
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% mses: vector with the corresponding mean squared errors
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p = p0;
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gradient = ones(1, length(p0)) * 1000.0;
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ps = [];
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mses = [];
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while norm(gradient) > threshold
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ps = [ps, p(:)];
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mses = [mses, meanSquaredErrorPower(x, y, p)];
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gradient = meanSquaredGradientPower(x, y, p);
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p = p - epsilon * gradient;
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end
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end
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function mse = meanSquaredErrorPower(x, y, p)
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mse = mean((y - p(1)*x.^p(2)).^2);
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end
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function gradmse = meanSquaredGradientPower(x, y, p)
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gradmse = zeros(size(p, 1), size(p, 2));
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h = 1e-5; % stepsize for derivatives
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mse = meanSquaredErrorPower(x, y, p);
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for i = 1:length(p) % for each coordinate ...
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pi = p;
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pi(i) = pi(i) + h; % displace i-th parameter
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msepi = meanSquaredErrorPower(x, y, pi);
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gradmse(i) = (msepi - mse)/h;
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end
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end
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