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lagrange interpolation, .m

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buxZED
buxZED on 16 Mar 2011
Answered: SAM Arani on 30 Jan 2021
can anyone explain me how to use this program
function y=lagrange(x,pointx,pointy)
%
%LAGRANGE approx a point-defined function using the Lagrange polynomial interpolation
%
% LAGRANGE(X,POINTX,POINTY) approx the function definited by the points:
% P1=(POINTX(1),POINTY(1)), P2=(POINTX(2),POINTY(2)), ..., PN(POINTX(N),POINTY(N))
% and calculate it in each elements of X
%
% If POINTX and POINTY have different number of elements the function will return the NaN value
%
% function wrote by: Calzino
% 7-oct-2001
%
n=size(pointx,2);
L=ones(n,size(x,2));
if (size(pointx,2)~=size(pointy,2))
fprintf(1,'\nERROR!\nPOINTX and POINTY must have the same number of elements\n');
y=NaN;
else
for i=1:n
for j=1:n
if (i~=j)
L(i,:)=L(i,:).*(x-pointx(j))/(pointx(i)-pointx(j));
end
end
end
y=0;
for i=1:n
y=y+pointy(i)*L(i,:);
end
end
  2 Comments
Hardipsinh Jadeja
Hardipsinh Jadeja on 24 Apr 2018
If size of pointx and pointy is same size then why not print the statement

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Accepted Answer

Matt Tearle
Matt Tearle on 16 Mar 2011
pointx and pointy are two vectors of data values, x is a vector of points where you want to interpolate. For example:
x = 0:10;
y = x.^2;
xx = linspace(0,10);
yy = lagrange(xx,x,y);
plot(x,y,'o',xx,yy,'.')
As an aside, with no offense intended to Calzino, there are other options available for interpolation. Firstly, of course, interp1 is a standard MATLAB function, with options for linear, cubic spline, and PCHIP interpolation. Cleve Moler (aka The Guy Who Wrote MATLAB) also has a Lagrange interpolation function available for download.
  7 Comments
Walter Roberson
Walter Roberson on 15 Oct 2020
Note: the File Exchange has some more advanced polyinterp functions.

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More Answers (2)

Matt Fig
Matt Fig on 16 Mar 2011
This is really a question for the author of the program. I believe it is also bad etiquette to post somebody's code like that without permission.
Did you try to contact the author?
  3 Comments
Matt Tearle
Matt Tearle on 16 Mar 2011
Fair call. I guess it does open the door for people to bash the author's code in a separate location, which would be uncool.

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SAM Arani
SAM Arani on 30 Jan 2021
%% Lagrangian interpolation
clear;clc;close all;
X=[-3 -2.5 -1 0 2 3.75 4.25 7];
Y=(sqrt(1+abs(X)));
xq=min(X):0.1:max(X);
f=(sqrt(1+abs(xq)));
syms x
S=0;
for i=1:length(X)
temp=X;
A=temp(i);
temp(i)=[];
L=prod((x-temp)./(A-temp),'all');
S=(L*Y(i))+S;
L=[];
end
figure()
fplot(S,'black--',[min(X) max(X)]);
hold on
F=interp1(X,Y,xq);
plot(xq,F,"bo");
hold on
plot(xq,f,"r*");
legend("Lagrangian","interp1","f(x)",'Location','north');
xlabel(" X axis ");
ylabel(" Y axis");
title("Lagrangian interpolation VS interp1-MatlabFunction")
Above we can see an easy way to implement lagrangian interpolation which has been checked with matlab interp1() function;
From MohammadReza Arani
mohammadrezaarani@ut.ac.ir

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