40 lines
1.3 KiB
Matlab
40 lines
1.3 KiB
Matlab
function [p, ps, mses] = gradientdescent(t, x, func, p0, epsilon, threshold)
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% Gradient descent for leas squares fit.
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%
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% Arguments: t, vector of time points.
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% x, vector of the corresponding measured data values.
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% p0, vector with initial parameter values.
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% func, function to be fit to the data.
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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 estimates of the parameter values.
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% ps: 2D vector with all the parameter values 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(size(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, meansquarederror(t, x, func, p)];
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gradient = msegradient(t, x, func, 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 = meansquarederror(t, x, func, p)
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mse = mean((x - func(t, p)).^2);
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end
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function gradmse = msegradient(t, x, func, p)
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gradmse = zeros(size(p));
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h = 1e-7; % stepsize for derivative
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ph = eye(length(p))*h; % ... for each parameter
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mse = meansquarederror(t, x, func, p);
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for i = 1:length(p) % for each coordinate ...
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msepi = meansquarederror(t, x, func, p(:) + ph(:,i));
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gradmse(i) = (msepi - mse)/h;
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end
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end
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