lagrange interpolation, .m

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buxZED
buxZED 2011-3-16
回答： MUHAMMAD IQRAM HAFIZ 2024-5-21
can anyone explain me how to use this program
http://www.mathworks.com/matlabcentral/fileexchange/899-lagrange-polynomial-interpolation
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 个评论
Jatin Arora
Jatin Arora 2016-8-8
How to run this code
Hardipsinh Jadeja
Hardipsinh Jadeja 2018-4-24
编辑：Hardipsinh Jadeja 2018-4-24
If size of pointx and pointy is same size then why not print the statement

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采纳的回答

Matt Tearle
Matt Tearle 2011-3-16
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 个评论
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Russell
Russell 2020-10-15
@Matt Tearle
That link is dead, I don't suppose you have an updated one?
Walter Roberson
Walter Roberson 2020-10-15
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.

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更多回答（5 个）

Matt Fig
Matt Fig 2011-3-16
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 个评论
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Matt Fig
Matt Fig 2011-3-16
Ah, but I wasn't talking about harm, just polite behavior. The author should have been contacted first, that's all.
Matt Tearle
Matt Tearle 2011-3-16
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 2021-1-30
%% 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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image-pro
image-pro 2022-4-19
yes, but how to code all this?
Walter Roberson
Walter Roberson 2022-4-19
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.

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norah
norah 2023-5-10
how can i find error bound ?
John
John 2023-7-31
编辑：Walter Roberson 2023-10-10
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 个评论
Oussama
Oussama 2023-10-10
bonsoir ,comment appliquer cette fonction sur un exemple

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MUHAMMAD IQRAM HAFIZ
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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