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Topic: Pure functions vs rule based functions inside NIntegrate
Replies: 1   Last Post: Jan 28, 2014 6:08 AM

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Yi Wang

Posts: 33
Registered: 3/30/12
Pure functions vs rule based functions inside NIntegrate
Posted: Jan 26, 2014 3:05 AM
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As I was told, only pure functions can be compiled. Also, NIntegrate or NDSolve first compiles a function before doing numerical operations. Thus, I would have expected that using pure functions in NIntegrate or NDSolve could be faster than rule based functions.

However, in tests I didn't find such a difference. For example,

f1[x_, y_] := Sin[Sin[x Sin[y]]];
AbsoluteTiming@NIntegrate[f1[x, y], {x, 0, 100}, {y, 0, 100}]


f2 = Sin[Sin[#1 Sin[#2]]] &
AbsoluteTiming@NIntegrate[f2[x, y], {x, 0, 100}, {y, 0, 100}]

takes about the same time. How can I tell if both are compiled, or neither, and why?


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