I have the following code that prints/graphs out the result of a Taylor Series Approximation.
close all;
clear;
clc;
fprintf('#\tf(pi/3)\t\t\t\tfn(pi/3)\t\t\tEt\n');
% actual function
syms x;
f(x)=exp(-x)*cos(x);
h = ezplot(f);
grid on;
hold on;
set(h,'Color','b', 'LineWidth', 3);
% presets for Taylor.
a=1;
maxorder=10;
% Taylor Series
y(x)=f(a);
for n=1:maxorder
d(x) = diff(f(x),x,n);
y(x) = y(x) + d(a)*((x-a)^n)/factorial(n);
error=double(f(pi/3))-double(y(pi/3));
fprintf('%.0f\t%.14f\t%.14f\t%.14f\n',n,double(f(pi/3)),double(y(pi/3)),error);
end
h = ezplot(y);
axis([0, 4.5,-1, 1]);
set(h,'Color','r', 'LineWidth', 3);
set(gca,'FontSize', 15');
title('Taylor Series of e^{-x}cos(x)');
However, the table that gets printed out is for some reason getting truncated 4 places after the decimal point. Typing:
get(0,'format')
into the Matlab terminal tells me the formatting is set to long. I have no clue why this could be happening.
This is what the table looks like:
# f(pi/3) fn(pi/3) Et
1 0.17550000000000 0.17480000000000 0.00070000000000
2 0.17550000000000 0.17550000000000 0.00000000000000
3 0.17550000000000 0.17550000000000 0.00000000000000
4 0.17550000000000 0.17550000000000 0.00000000000000
5 0.17550000000000 0.17550000000000 0.00000000000000
6 0.17550000000000 0.17550000000000 0.00000000000000
7 0.17550000000000 0.17550000000000 0.00000000000000
8 0.17550000000000 0.17550000000000 0.00000000000000
9 0.17550000000000 0.17550000000000 0.00000000000000
10 0.17550000000000 0.17550000000000 0.00000000000000
This rounding seem to happen only with symbolic functions. It does happen when those are not used. Any idea why and how I can fix that?
I can reproduce your output setting digits(4). Set it back to 32 and everything should be okay.
The digits functions allows to set the precision of mupad variable precision arithmetic. The precision was reduced to 4 digits for some reason.