MATLAB: Attempted to access y(15); index must be a positive integer or logical.

index must be a positive integer or logical.

Here is my code:
clear;
for t=0:0.01:4;
i=t*100+1;
if t<2
y(i)=3.5*exp(-t/2)*cos(2*pi*t);
T(i)=t;
else
y(i)=3.5*exp(-1)*cos(6*pi*t);
T(i)=t;
end
plot(T, y,'g','linewidth',2)
end
As you can see, I want to plot the piecewise function. To store y and t as vectors, I created an index i . But when i equals 15, it reports 'Attempted to access y(15); index must be a positive integer or logical.' But when t=0.14, i=15 and it makes sense, I think.So how can it be wrong? Please help me with the problem. Thanks!

Best Answer

If you do a high accuracy check on what you think is an i-value of 15, you will find that it is off from the exact integer 15 by 1 bit or so at its least significant end. That is caused by the fact that since your computer is using binary numbers, it cannot represent 0.01 exactly, and multiplying this number by an integral multiple of 100, which you are doing, does not always yield an integer. Welcome to the world of binary numbers!
Instead of your "for t=0:0.01:4; i = t*100+1;" you should write:
 for i = 1:401
   t = (i-1)/100; % <-- or else t = linspace(0,4,401) or t = 0:0.01:4
   etc.
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