Do not use any of MATLAB\'s built injunctions or commands. This MUST be implemen

Question

Do not use any of MATLAB's built injunctions or commands. This MUST be implemented using matrix and vector components via FOR loops in your construction. the continuous Linear interpolation spline S_1, n(x) formula for a given dataset of independent variable x_i and dependent variable y_i, where i= 1, 2, ... n it can be written as S_l, n(x) = p_1(x) = y_o x - x_1/x_0 - x_1 + y_1 x - x_0/x_1 = x_0 x Element [x_0, x_1] p_2(x) = y_1 x - x^2/x_1 + x_2 + y_2 x - x_1/x_2 - x_1 x Element [x_1, x_2] p_n(x)=y_n-x_n-1 x Element [x_n-1, x_n] Write the function for spline approximation of y using the algorithm This function must have the interface [y] = innerspring (XDATA, YDATA. x) where XDATA and YD AT A are the vectors of n data points and it should return the value of y at given x. If x is a vector, the function should return a vector y where each element of y corresponds to the element of x.

Explanation / Answer

function [y]=linearSpline(XDATA,YDATA,x)

%%% finding array size

N=size(XDATA)

%%% finding length of x vector

x_N=size(x);

for i=1:N-1

for j =1:x_N

if x(j)>=XDATA(i) && x(j)<=XDATA(i+1)

y(j)=YDATA(i)*(x(j)-XDATA(i+1))/(XDATA(i)-XDATA(i+1))+YDATA(i+1)*(x(j)-XDATA(i))/(XDATA(i+1)-XDATA(i))

end

end

end

end

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