MATLAB: Problem with piece-wise function with logical indexing.

MATLABpiece-wise

I created the following piece-wise fuction using logical indexing. 
%Piece-wise function
F = @(coef,t) ((t < 0).*...
                     0 + ...
               (t >= 0 & t < 1200).*...
                    (1/coef(1) + t./coef(2) + 1/(coef(3))*(1-exp(-t))) + ...
               (t >= 1200).*...
                    (1200/coef(2) + 1/(coef(3))*(1-exp(-t)) - 1/(coef(3))*(1-exp(-(t-1200)))));
coef0 = [200, 200000, 100];
% Test that function is valid for wide range of t.
x = linespace(-10, 1300, 1310);
plot(x,F(coef0,x))
I must be missing somethign in the syntax. The function is invalid when t<~500. The rest of the graph looks correct. When I poke around, it seems that the very last part of the fuction:
exp(-(t-1200))
is being evaluated outside of it's defined region (t >= 1200). And when t< ~500, it blows up and goes to inf.

Best Answer

But I don't understand WHY matlab is evaluating this bit of the fuction when it's outside the specified range (t>=1200).
That expression:
exp(-(t-1200))
is evaluated for all t. It does not matter what it's multiplied by, even if it's (t >= 1200), it's still evaluated for all t, since that's what is in that particular expression.
As you have noticed it's going to generate -Inf for some t. Now your (t >= 1200) is going to generate 0 for the same values, and when you multiply 0 by +/-Inf you get NaN.
One possible workaround is to make sure that the input to exp is 0 for invalid t, so you could replace that particular expression by
exp(-(t-1200) .* (t >= 1200))
As long as you ensure that no term is +/-Inf then the mulitplication by (t >= 1200) will ensure the result is 0 outside the desired range.
Note that strictly speaking, there's no logical indexing here. You're using logical vectors, but are not indexing anything.
Also note, that your first part of the expression,
(t < 0).* 0 + ...
is a bit pointless. It's always going to result in a vector of 0. And adding 0 to something does not have much effect on that something.
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