Double interpolation in Matlab

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Emmanuelle 2012-9-11

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https://ww2.mathworks.cn/matlabcentral/answers/47858-double-interpolation-in-matlab

Hi,

I want to ask you somehting about interpolation in Matlab. I want to know if it's possible to do two different interpolations in the same line. I mean, for example, at the beginning do a linear interpolation and at the middle, approximately, do another kind of interpolation, like spline.

The main problem is that I've done a linear interpolation and it's perfect at the beginning but after some point, I think it would be better another type. If this is possible, how can I code where I want to change it?

Thanks a lot in advance and greetings,

Emma

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Answer 1

ajith 2012-9-11

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https://ww2.mathworks.cn/matlabcentral/answers/47858-double-interpolation-in-matlab#answer_58450

在 MATLAB Online 中打开

% Tschebyscheff and Equi-interval method for interpolation program % Function f(x)=1/(25*x^2)

clear all; %xe equi-interval %xc tschebyscheff x=-1:0.01:1; N=length(x); num = [5 9 13];

for i=1:3 xe = -1:2/(num(i)-1):1; for k=1:num(i) fe(k) = 1 / ( 1 + 25 * xe(k) * xe(k) ); % equi-interval function xc(k) = cos((2*(k-1)+1)*pi/(2*num(i))); % tschebyscheff point fc(k) = 1 / ( 1 + 25 * xc(k) * xc(k) ); % tschebyscheff function end for n=1:N

        f(n) = 1 / ( 1 + 25 * x(n) * x(n) ) ;
        pe(i,n)=0.0;
        pc(i,n)=0.0;
        for jj=1:num(i)
            l1(jj)=1.0;
            l2(jj)=1.0;
            % Lagrange interpolation
            for ii=1:num(i)
                if ii ~= jj
                    l1(jj) = ( l1(jj) * ( x(n) - xe(ii) ) ) / ( xe(jj) - xe(ii) );
                    l2(jj) = ( l2(jj) * ( x(n) - xc(ii) ) ) / ( xc(jj) - xc(ii) );
                end
            end
            pe(i,n) = pe(i,n) + fe(jj) * l1(jj);
            pc(i,n) = pc(i,n) + fc(jj) * l2(jj);
        end
        if i ==1 
            pe4(n) = pe(1,n);
            pc4(n) = pc(1,n);
        elseif i==2
            pe8(n) = pe(2,n);
            pc8(n) = pc(2,n);
        else 
            pe12(n) = pe(3,n);
            pc12(n) = pc(3,n);
        end
    end 
end

% graph plot figure(1); plot(x,f,x,pe4,x,pe8,x,pe12); legend('F(x)','P4(x)','P8(x)','P12(x)'); AXIS([-1 1 -3.7 1.5]) xlabel('x'); ylabel('Function F(x) and Pn(x)'); title(['interpolated graph by equi-interval method F(x) ‚Æ Pn(x)']);

figure(2); plot(x,f,x,pc4,x,pc8,x,pc12); legend('F(x)','P4(x)','P8(x)','P12(x)'); AXIS([-1 1 -0.2 1.1]) xlabel('x'); ylabel('Function F(x) and Pn(x)'); title(['interpolated graph by tschebyscheff point F(x) ‚Æ Pn(x)']);

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Walter Roberson 2012-9-11

http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

Emmanuelle 2012-9-12

Hi dinesh,

Thanks for your reply. I receive the following error: "Illegal use of reserved keyword "else"". I've changed some 'if' and 'else' but it doesn't work.

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