38 lines
788 B
Matlab
38 lines
788 B
Matlab
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syms x y;
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f = (1 - x)^2 + 100 * (y - x^2)^2;
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[x, xs, gs] = newton(f, [0;0], 50000, 1e-6);
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display(x);
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display(xs);
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display(gs);
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plot(xs(1, :), xs(2, :), '-o');
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function y = at(f, xk)
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syms x y;
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y = double(subs(f, [x, y], [xk(1), xk(2)]));
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end
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function [xk, xs, gs] = newton(f, x0, max_itr, tol)
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syms x y;
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xk = x0;
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gf = gradient(f);
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hf = hessian(f, [x, y]);
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tnorm = norm(at(gf, xk), 2);
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xs = zeros(size(x0, 1), max_itr + 1);
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xs(:, 1) = x0;
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gs = zeros(1, max_itr + 1);
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gs(1) = tnorm;
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k = 1;
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while tnorm > tol && k <= max_itr + 1
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xk = xk - (at(hf, xk) \ at(gf, xk));
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tnorm = norm(at(gf, xk), 2);
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k = k + 1;
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xs(:, k) = xk;
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gs(k) = tnorm;
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end
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xs = xs(:, 1:k);
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gs = gs(:, 1:k);
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end |