Question

Consider the function f(x) 1 25x which is used to test various interpolation methods. For the remainder of this problem consider only the interval [-1, 1] The x-values for the knots (or base-points) of the interpolation algorithm are located at x--1,-0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75 1. (a) Create a "single" figure in Matlab that contains 6 subplots (2x3) and is labelled as figure (777), i.e the figure number is 777. Plot in each subplot the function f(x) using 1001 sample points (in black, linewidth 2, for all six subplots). Use a for loop to accomplish this task. (b) Add to each subplot the base points/knots that are used for the interpolation (plot red dots only, no lines, Markersize 25, for all six subplots). Use a for loop to accomplish this task. (a) add to subplot 1 the plot of an 4th order polynomial (1001 sample points, blue, Linewidth 6) with polyfit. (b) add to subplot 2 the plot of an 8th order polynomial (1001 sample points, blue, Linewidth 6) with polyfit. (c) add to subplot 3 the plot of a piece-wise interpolation polynomial using the method linear' and 1001 sample points (see interp1) (d) add to subplot 4 the plot of a piece-wise interpolation polynomial using the method 'nearest' and 1001 sample points (see interp1) (e) add to subplot 5 the plot of a piece-wise interpolation polynomial using the method 'spline' and 1001 sample points (see interp1) (f) add to subplot 6 the plot of a piece-wise interpolation polynomial using the method 'makima' and 1001 sample points (see interp1). If you do not have the Makima method on your Matlab version, please leave a simple comment in your code that contains the actual version of your Matlab Software

Answer 1

script file to plot figure using matlab

figPlotUsingMtlb.m

% base points/knots used
xData=-1:0.25:1;
yData=1./(1+25*xData.^2);

% 1001 sample points
xVal=-1:0.002:1;
fx=1./(1+25*xVal.^2);
for i=1:6
subplot(2,3,i), plot(xVal,fx,'-k','Linewidth',2); hold on
subplot(2,3,i), plot(xData,yData,'.r','Markersize',25);
end

% using ployfit 4th order
P=polyfit(xData,yData,4);
y_polyfit4=P(1)*xVal.^4+P(2)*xVal.^3+P(3)*xVal.^2+P(4)*xVal+P(5);
subplot(2,3,1),plot(xVal,y_polyfit4,'-b','Linewidth',6); hold on

% using ployfit 8th order
P=polyfit(xData,yData,8);
y_polyfit8=P(1)*xVal.^8+P(2)*xVal.^7+P(3)*xVal.^6+P(4)*xVal.^5+...
P(5)*xVal.^4+P(6)*xVal.^3+P(7)*xVal.^2+P(8)*xVal+P(9);
subplot(2,3,2),plot(xVal,y_polyfit8,'-b','Linewidth',6); hold on

% linear interpolation using interp1 linear
x1=xData';
y1=yData';
xq=xVal';
y_linear = interp1(x1,y1,xq,'linear');
subplot(2,3,3),plot(xVal,y_linear,'-b','Linewidth',6); hold on

% interpolation using interp1 nearest
y_nearest = interp1(x1,y1,xq,'nearest');
subplot(2,3,4),plot(xVal,y_nearest,'-b','Linewidth',6); hold on

% interpolation using interp1 spline
y_spline = interp1(x1,y1,xq,'spline');
subplot(2,3,5),plot(xVal,y_spline,'-b','Linewidth',6);

% interpolation using interp1 makima
% Version of Matlab is : MATLAB R2015a

shg
subplot(2,3,1)
title('First Subplot')
subplot(2,3,2)
title('Second Subplot')
subplot(2,3,3)
title('Third Subplot')
subplot(2,3,4)
title('Fourth Subplot')
subplot(2,3,5)
title('Fifth Subplot')
subplot(2,3,6)
title('sixth Subplot')

% will work if have MATLAB R2018a and latest versions of matlab
sgtitle('Figure(777)')

code end here

image of ploted figure

Second s Second Subplot Third Subplot 1st Subplot 0.5 0.5 0 0.5 -2 1 -1 1 -1 Fourth Subplot Fifth Subplot sixth Subplot 0.5 0.5 0.5 0