How can I write this exponential function in matlab?

hi, please can anyone help me write the following functions in matlab?

Answer 1

[Walter Roberson]

f = @(x) exp(-x.^2/4) .* cos(2*pi*x);
g = @(x) exp(x) .* (x <= 0) + sin(2*pi*x)./max(x,realmin) .* (x>0);

[rohail khan]

thank you so much Walter

[rohail khan]

please can you explain the meaning of : max(x,realmin) in your code

[Walter Roberson]

Suppose x is 0 exactly. Then sin(2*pi*x)/x would be 0/0 which would be NaN. The (x>0) after that would multiply the NaN by 0, but NaN times anything is NaN, so you cannot use logical computations like this to mask out a NaN result.

Instead you need to avoid the NaN result. One way of doing that is to detect that you are dividing by 0 and to substitute a different value that is not 0.

The expression max(x,realmin) is equivalent to a vectorized version of

if x <= realmin
  temp = realmin;
else
  temp = x;
end

realmin is about 1E-308 -- a very small value but not 0. So max(x,realmin) substitutes the positive value realmin for all negative and 0 values, which is enough to prevent division by 0.

Another way of coding it would have been

sin(2*pi*x)./(x + (x == 0)) .* (x>0);

x == 0 would be 0 for all non-zero x and so would not change any x that was not 0. x == 0 would be 1 for x of 0, so for the case of any non-zero value (x+(x==0)) would be the same as the value and for zero exactly it would be 1, thereby preventing division by 0.

Answer 2

[Rajulapati Naveen]

f = @(x) exp(-x.^2/4) .* cos(2*pi*x); g = @(x) exp(x) .* (x <= 0) + sin(2*pi*x)./max(x,realmin) .* (x>0);

[Walter Roberson]

What difference is there between that and what I posted https://www.mathworks.com/matlabcentral/answers/391290-how-can-i-write-this-exponential-function-in-matlab#answer_312468