Array processing using Taylor Series and FOR Loops to approximate sin value for each element in that array.

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Humza Khan
Humza Khan on 18 Oct 2021
Commented: dpb on 19 Oct 2021
I am using x = [-3:0.5:3] as a test value
My code is giving correct sin(x) values for the negative part of this array. However, it gives 0's for when x goes to 0 or greater. The array can be of any type and dimensions.
Taylor Series:
function [y] = SINM(x)
%SINM This function takes the array x and processes the approximate sin
%value of it.
% The value of sin is approximately calculated using Taylor Series
% from the input array x.
Sum = zeros(size(x));
T = 1E-12; %defining tolerance.
y = zeros(size(x));
[i,j] = size(x);
for n = 0:30
for k = 1:i
for l = 1:j
an(k,l) = ((-1)^n).*((x(k,l).^((2*n)+1))./factorial((2*n)+1));
Sum(k,l) = Sum(k,l) + an(k,l);
if abs(an(k,l)) < T || n==30
break
elseif abs(an(k,l)) > T
disp 'More Iterations are needed to reach the specified tolerance.';
end
end
end
end
y = Sum;
end
This the code I have written so far, but I am confused as to why it gives the output of 0 when x >= 0. ^
How can i fix this code to get sin values for all values in the array?
This is the result I am getting.
%SINM(x)...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%More Iterations are needed to reach the specified tolerance...
%...
%...
%...
%ans =
% Columns 1 through 6
% -0.1411 -0.5985 -0.9093 -0.9975 -0.8415 -0.4794
% Columns 7 through 12
% 0 0 0 0 0 0
% Column 13
% 0
  6 Comments
Humza Khan
Humza Khan on 19 Oct 2021
Sorry about that! I asked my TA about it who explained the loop structure for 2-D arrays. His explanation made sense so i deleted my query the first time around. But when I started to do it again, I was stuck again so I posted it again for some external guidance.

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Accepted Answer

Matt J
Matt J on 18 Oct 2021
Edited: dpb on 18 Oct 2021
The array can be of any type and dimensions.
If so, why does your code assume it will be 2D? Can't it be 3D or 4D? In any case, consider the following modification (which will work for any dimension).
SINM(-3:0.5:3)
More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance. More Iterations are needed to reach the specified tolerance.
ans = 1×13
-0.1411 -0.5985 -0.9093 -0.9975 -0.8415 -0.4794 0 0.4794 0.8415 0.9975 0.9093 0.5985 0.1411
function [y] = SINM(x)
%SINM This function takes the array x and processes the approximate sin
%value of it.
% The value of sin is approximately calculated using Taylor Series
% from the input array x.
y = zeros(size(x));
T = 1E-12; %defining tolerance.
for i=1:numel(x)
for n = 0:30
an = ((-1)^n).*((x(i).^((2*n)+1))./factorial((2*n)+1));
y(i) = y(i)+an;
if abs(an) < T || n==30
break
elseif abs(an) > T
disp 'More Iterations are needed to reach the specified tolerance.';
end
end
end
end
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