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

Question

Humza Khan 2021-10-18

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1566531-array-processing-using-taylor-series-and-for-loops-to-approximate-sin-value-for-each-element-in-that

评论： dpb 2021-10-19

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

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...

%...

%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

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John D'Errico 2021-10-18

What was the purpose of asking this question multiple times?

Humza Khan 2021-10-19

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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Answer 1

Matt J 2021-10-18

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1566531-array-processing-using-taylor-series-and-for-loops-to-approximate-sin-value-for-each-element-in-that#answer_811278

编辑：dpb 2021-10-18

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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Humza Khan 2021-10-19

编辑：Humza Khan 2021-10-19

Yes, The thing was that i was not sure if I was allowed to use the numel() function for the assignment. But I got confirmation of its usage so it all makes sense to me as using numel() makes the entire process much more efficient and flexible so that it could process arrays of all dimensions.