Matrix dimension does not agree when using .*

Our code is calculating Taylor polynomials. We are sure that the problem is about P1 because program is plotting PO and f(x). We would really appreciate if anyone can solve our problem.

clc 
clear all
close all

h = 0.01;       % step size
X = -pi/8:h:7*pi/8;    % domain
f=@(X)  cot(X);      % range

a=5*pi/8

Z1=@(X) diff(cot(X)) %first derivative
Z2=@(X) diff(cot(X),2) ; %second derivative
Z3=@(X) diff(cot(X),3) ; %third derivative

P0=@(X) f(a)*ones(size(X))
P1=@(X) f(a) + Z1(a).*(X-a);
P2=@(X) P1 + Z2(a) ./ factorial(2).*((X-a).^2);
P3=@(X) P2 + Z3(a) ./ factorial(3).*((X-a).^3);

xlim([0.1 3]) 
ylim([-2.5 2.5])

hold on
plot(X,f(X),'k','Linewidth',2)
plot(X,P0(X),'r','Linewidth',2)
plot(X,P1(X),'g-.','Linewidth',2)
plot(X,P2(X),'b--','Linewidth',2)
plot(X,P3(X),'m:','Linewidth',2)

The error we received:

Error using .*

Matrix dimensions must agree.

Error in Untitled>@(X)f(a)+Z1(a).*(X-a)

Error in Untitled (line 26)

plot(X,P1(X),'g-.','Linewidth',2)

Answer 1

[Kelly Kearney]

When you calculate

Y = diff(X,n)

where X is a vector, Y will have length length(X)-n. So you need to adjust X accordingly when plotting, e.g.

plot(X,f(X),'k','Linewidth',2)
plot(X,P0(X),'r','Linewidth',2)
plot(X(1:end-1),P1(X),'g-.','Linewidth',2)
plot(X(1:end-2),P2(X),'b--','Linewidth',2)
plot(X(1:end-3),P3(X),'m:','Linewidth',2)