On Mar 8, 2011, at 2:05 PM, [email protected] wrote:
In fact, for realistic parameter sets, computing the gradients (with
some automatic differentiation data type) consumes about 90% of the
total runtime of my program. Evaluating the function without
differentiation (data type double) is quite cheap.
Peter, this probably means that your automatic differentiation program
is poor for this kind of problem.
There is a theorem that you can always compute the gradient of f(x)
(any function from R^n to R) with about as many additional operations
as are required to compute f(x) **once**. The technique for doing so
is called an "adjoint method", or "reverse accumulation".
So you want an AD program that advertises "reverse mode"
differentiation or something similar.
In contrast, AD programs that use "forward mode" or "forward
accumulation" differentiation are poor for differentiating multi-
variate functions (R^n to R), since they have cost that grows
proportional to n. (Forward accumulation is good for differentiating
functions from R to R^m.)
Steven
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