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28 lines
1.6 KiB
Matlab
28 lines
1.6 KiB
Matlab
function [ P01, P12, P2 ] = LagrangePolynomialSymbolic(x_list, f)
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syms x;
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format long;
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warning('off','OctSymPy:sym:rationalapprox');
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%Evaluate P0,1
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%P01 = (((x - x_list(2))/(x_list(1) - x_list(2))) * double(subs(f, x_list(1)))) + (((x - x_list(1))/(x_list(2) - x_list(1))) * double(subs(f, x_list(2))))
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P01x = (double(subs(f, x_list(1)))/(x_list(1) - x_list(2))) + (double(subs(f, x_list(2)))/(x_list(2) - x_list(1)));
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P01c = ((double(subs(f, x_list(1)))/(x_list(1) - x_list(2))) * -x_list(2)) + ((double(subs(f, x_list(2)))/(x_list(2) - x_list(1))) * -x_list(1));
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disp(['P01 = ' num2str(P01x, '%9.9g') 'x + ' num2str(P01c, '%9.9g')])
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P01 = (P01x * x) + P01c;
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%Evaluate P1,2
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%P12 = (((x - x_list(3))/(x_list(2) - x_list(3))) * double(subs(f, x_list(2)))) + (((x - x_list(2))/(x_list(3) - x_list(2))) * double(subs(f, x_list(3))))
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P12x = (double(subs(f, x_list(2)))/(x_list(2) - x_list(3))) + (double(subs(f, x_list(3)))/(x_list(3) - x_list(2)));
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P12c = ((double(subs(f, x_list(2)))/(x_list(2) - x_list(3))) * -x_list(3)) + ((double(subs(f, x_list(3)))/(x_list(3) - x_list(2))) * -x_list(2));
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disp(['P12 = ' num2str(P12x, '%9.9g') 'x + ' num2str(P12c, '%9.9g')])
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P12 = (P12x * x) + P12c;
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%Evaluate P2
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%P2 = (P2x * x) + P2c;
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P2x2 = (P01x - P12x) / (x_list(1) - x_list(3));
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P2x = ((P01c) + (P01x * -x_list(3)) - ((P12x * -x_list(1)) + (P12c))) / (x_list(1) - x_list(3));
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P2c = ((P01c * -x_list(3)) - (P12c * -x_list(1))) / (x_list(1) - x_list(3));
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disp(['P02 = ' num2str(P2x2, '%9.9g') 'x^2 + ' num2str(P2x, '%9.9g') 'x + ' num2str(P2c, '%9.9g')])
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P2 = (P2x2 * x^2) + (P2x * x) + P2c;
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end
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