lagrange interpolation, .m
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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
댓글 수: 2
Hardipsinh Jadeja
2018년 4월 24일
편집: Hardipsinh Jadeja
2018년 4월 24일
If size of pointx and pointy is same size then why not print the statement
채택된 답변
Matt Tearle
2011년 3월 16일
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.
댓글 수: 7
Walter Roberson
2020년 10월 15일
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.
추가 답변 (5개)
Matt Fig
2011년 3월 16일
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?
댓글 수: 3
Matt Fig
2011년 3월 16일
Ah, but I wasn't talking about harm, just polite behavior. The author should have been contacted first, that's all.
Matt Tearle
2011년 3월 16일
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
2021년 1월 30일
%% 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
댓글 수: 4
Walter Roberson
2022년 4월 19일
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
2023년 7월 31일
편집: Walter Roberson
2023년 10월 10일
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
댓글 수: 1
MUHAMMAD IQRAM HAFIZ
2024년 5월 21일
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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