Vectorising piecewise quadratic interpolation function

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Su-Yeon Chung 2021-8-11

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https://ww2.mathworks.cn/matlabcentral/answers/896067-vectorising-piecewise-quadratic-interpolation-function

回答： darova 2021-8-20

I am struggling with the vectorisation of the following code. Could you please help me?

function v = polyinterp(x,y,u)
    n = length(x);
    v = zeros(size(u));
    for k = 1:n
        w = ones(size(u));
        for j = [1:k-1 k+1:n]
            w = (u-x(j))./(x(k)-x(j)).*w;
        end
        v = v + w*y(k);
    end
end

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darova 2021-8-11

Maybe in this case the code is more readable without vectorising

Su-Yeon Chung 2021-8-11

Thanks for your comment! Even it's a better code, I want to know what the vertorised version would be.

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Answer 1

darova 2021-8-20

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https://ww2.mathworks.cn/matlabcentral/answers/896067-vectorising-piecewise-quadratic-interpolation-function#answer_771464

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Here is the vectorized version (not tested)

xkj0 = x-x';
xkj0 = xkj0.*eye(size(xkj0)) + eye(size(xkj0)); % make diagonal elements all ones (dividing by zero)
Xkj = repmat(xkj0,[1 1 length(u)]);             % 3D matrix of differences xk-xj
U = repmat(reshape(u,1,1,[]),length(x)*[1 1]);  % 3D matrix u
X = repmat(x(:),1,length(x),3);                 % 3D matrix x
W = (U-X)./Xkj;
Y = repmat(y(:),1,length(y),3);                 % 3D matrix y
temp = prod(W.*Y,2);                            % don't know direction of multiplication (rows?columns?)
v = sum(temp,1);                                % summing rows (maybe columns)?