Question

Use MATLAB or Scilab to solve the following problems 1. Create a MATLAB subroutine called Lagrange.m that receives two set data points, x and y and plots the curve by interpolating the missing points (h-X-x-1) using Lagrange interpolation form

Answer 1

1) Below code is subroutine lagrange, Save this subroutine as lagrange.m. and call the function in the main program.

explanation of the code is in the comments.

function y=lagrange(x,pointx,pointy)
%% In this function x is the points to be calculted, y is the interpolated value
%% calculate the input size
n=size(pointx,2);

%% Generate the initial values of the x
L=ones(n,size(x,2));

%% Calcaulate the missing points using legranges interpolation formule
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

%%Sorting X and Y
X=[x pointx];
Y=[y pointy];
[sortedX, sortIndex] = sort(X)
sortedY = Y(sortIndex)
%% Plot the graph
plot(pointx,pointy,'Color','red');
hold on;
plot(sortedX,sortedY,'Color','blue');
hold off;
legend('original','after Inter polation');

2) Data sets are compared using the below program

close all;
clc;
clear all;
%% Given input data points
pointX=[1,4];
pointY=[3,7];

%% Missing points
x=[2,4];

%% Interpolating using the Sub routine
y=lagrange(x,pointX,pointY);

%% Given input data points
pointX=[-1,0,3];
pointY=[5,8,-10];

%% Missing points
x=[1,2];
figure;
%% Interpolating using the Sub routine
y=lagrange(x,pointX,pointY);

%% Given input data points
pointX=[-10,4,7,12];
pointY=[-2,5,3,20];

%% Missing points
x=[-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,5,6,8,9,10,11];
figure;
%% Interpolating using the Sub routine
y=lagrange(x,pointX,pointY);

Below plots shows the data set before interpolation and after interpolation

a) Below plot is for data point (1,3) (4,7)

b) Below plot is for data point (-1,5) (0,8)(3,-10)

c) below is the plot for(-10,-2) (4,5) (7,3) (12,20)