lagrange interpolation, .m
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buxZED
on 16 Mar 2011
Answered: MUHAMMAD IQRAM HAFIZ
on 21 May 2024
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
on 24 Apr 2018
Edited: Hardipsinh Jadeja
on 24 Apr 2018
If size of pointx and pointy is same size then why not print the statement
Accepted Answer
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
on 15 Oct 2020
The code is included in https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/interp.pdf
Note: the File Exchange has some more advanced polyinterp functions.
More Answers (5)
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 Fig
on 16 Mar 2011
Ah, but I wasn't talking about harm, just polite behavior. The author should have been contacted first, that's all.
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.
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
4 Comments
Walter Roberson
on 19 Apr 2022
See https://www.mathworks.com/matlabcentral/fileexchange/?term=tag:%22digitize%22 for a number of File Exchange contributions that try to extract data from images of graphs.
John
on 31 Jul 2023
Edited: Walter Roberson
on 10 Oct 2023
function Y = Lagrange_371(x,y,X)
n = length(x) - 1;
Y = 0;
for i = 0:n
prod = 1;
for j = 0:n
if i ~= j
prod = prod.*(X - x(j+1))./(x(i+1) - x(j+1));
end
end
Y = Y + prod*y(i+1);
end
end
1 Comment
MUHAMMAD IQRAM HAFIZ
on 21 May 2024
function P = lagrange_interpolation_3point(x1, y1, x2, y2, x3, y3, x)
% Compute the Lagrange basis polynomials
L1 = ((x - x2) .* (x - x3)) / ((x1 - x2) * (x1 - x3));
L2 = ((x - x1) .* (x - x3)) / ((x2 - x1) * (x2 - x3));
L3 = ((x - x1) .* (x - x2)) / ((x3 - x1) * (x3 - x2));
% Compute the Lagrange polynomial
P = y1 * L1 + y2 * L2 + y3 * L3;
end
% Given points
x0 = 0; y0 = 0;
x1 = 2; y1 = 10;
x2 = 4; y2 = 20;
x3 = 8; y3 = 100;
% Point at which to evaluate the polynomial
x = 4.5;
% Calculate the interpolation polynomial at x = 4.5
P = lagrange_interpolation_3point(x1, y1, x2, y2, x3, y3, x);
% Display the result
fprintf('The interpolated value at x = %.1f is P = %.2f\n', x, P);
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