polynomial interpolation with lagrange form!!!

I implemented a function of lagrange form and i want to use it to interpolate the function f(x) = sin(4x) for some datapoints!! i wrote the script for that but it always gives me error !!! can anyone help me with that !!!

this is my code

xval = 0:10;

pval = xval.^2;

xx = linspace(0,10);

yy = lagrange1(xx,xval,pval);

plot(xval,pval,'o',xx,yy,'.')

[Torsten]

Since we don't see lagrange1, we can't reproduce the error.

[Anas Gharsa]

this is my lagrange1

function [Pval,Lval] = lagrange1(x,xval,f)

n = length(x); ntab=length(xval);

if nargout ==2 % in this case also the tabulation of the basis Lagrange polynomials is desired

Lval=ones(n,ntab);

for i=1:n

for j=[1:i-1,i+1:n]

Lval(i,:) = Lval(i,:).*(xval-x(j))/(x(i)-x(j));

end

end

f = f(:);

Pval = Lval'*f;

Pval=Pval'; % row vector in output

else % in this case only the tabulation of the interpolating polynomial is desired

Pval = zeros(1,ntab);

for i=1:n

Lval = ones(1,ntab);

for j=[1:i-1,i+1:n]

Lval = Lval.*(xval-x(j))/(x(i)-x(j));

end

Pval = Pval + Lval*f(i);

end

end

end

[Torsten]

And the error message ?

[Anas Gharsa]

Answer 1

[Alagu Sankar Esakkiappan]

Hello!

I see that you're trying to interpolate a polynomial but running into errors. I checked your code along with your function lagrange1 from your comments. It seems that you are running into an indexing error in the function lagrange1 on the line "Pval = Pval + Lval*f(i)". From what I observed using Breakpoint, you are trying to access f(12) when infact f only contains 11 elements to begin with.

Here are the Workspace values before the exact occurence of error:

If you try to evaluate the expression "Pval = Pval + Lval*f(i)" at this point ( based on values from above image ), you access f(12), thereby running into the error. I suggest for easier debugging, Try creating a Breakpoint on the line where error is caused in MATLAB. It'll give a more comprehensive view of the Codeflow and to narrow down exact occurence of error.

[Anas Gharsa]

okay i will try that!! thank you so for the reply