Question: Vectorization of Symbolic Functions

Maple provides efficient vectorization and automatic parallelization for many common operators. For example

x -> 2*~x*~cos~(x*~x)

But in my application it is common to want to create rather long vectorized operators starting from some complicated symbolic computations. Doing conversions by hand from symbolic expressions to element-wise operations is laborious and error prone.

As a very simple example consider that it is possible to obtain (almost) the same result as above by writing the following as a vectorized operation


But there are at least two problems with this. First of all it is not nearly as efficient as the first operator and second, perhaps not unrelated, is that the datatype returned when applying this operator to a Vector/rtable of hardware floats (e.g. datatype=float[8]) becomes something  more general.

My question is how can I convert a complicated symbolic expression into an efficient numeric element-wise vector operation?

I have tried several different approaches but so far without success. In the case above for example it seemed natural to expect that the following derivative


would produce a vectorized result, but this is not the case. In another attempt I was unable to see how to perform substitions into an expression, e.g. like this

unapply(subs(`*`=`*`~, cos=cos~, diff(sin(x),x)), x)

I would be glad to receive suggestions and/or references to relevant documentation. 


Please Wait...