39 lines
856 B
Matlab
39 lines
856 B
Matlab
function [xk, xs, gs] = Newton(f, x0, max_itr, tol, bt)
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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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fl = matlabFunction(f);
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gfl = matlabFunction(gf);
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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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pk = - (at(hf, xk) \ at(gf, xk));
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if bt
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alpha = backtracking(fl, gfl, pk, xk, 1, 0.9, 1e-4);
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else
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alpha = 1;
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end
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xk = xk + alpha * pk;
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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
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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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