Re: Re: Re: Compile nested loops with depending index variables...

*To*: mathgroup at smc.vnet.net*Subject*: [mg61424] Re: [mg61338] Re: Re: Compile nested loops with depending index variables...*From*: "Christoph Lhotka" <lhotka at astro.univie.ac.at>*Date*: Wed, 19 Oct 2005 02:16:04 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

First thank you all, but the main problem is still unbsolved. My specific problem is, that I have two rectangular arrays say a and b of about 500 000 numbers (complex or real) each. I want to create a new array of the same dimension and length, where each element has to be constructed by a law depending on the position in above lists of the form: a[[i,j,k,l]]=F[a[[i,j,k,l]],b[[i,j,k,l]]] (where F means some function based on basic arithmetics) IT IS NOT NECESSARY TO RUN THROUGH ALL INDICES! SO IF i=I0, j<i, k<j, l<k for any I0=1,...,n! To save computation time I wanted to compile and didn't succeed. Using a small C++ program and MathLink will speed it up, but transferring millions of numbers from the kernel to the C program and vice versa seems to slow it down again. I think that it should be a basic feature for any compiler to understand such a basic code construct like: Do[a[[i,j,k,l]]=a[[i,j,k,l]]+b[[i,j,k,l]],{i,1,n},{j,1,i},{k,1,j},{l,1,k}], but it doesn't work. Won't you agree with me? kind regards Christoph On Sun, 16 Oct 2005 00:17:54 -0400 (EDT) albert <awnl at arcor.de> wrote: > Hi Christoph, > > this is from the HelpBrowser about Compile: > > o Nested lists given as input to a compiled function must be full arrays of > numbers. > > > the table you construct is not a "full array of numbers", since the length > of each element is different: > > In[4]:= Length /@ Table[{i,j},{i,0,n},{j,0,i}] > > Out[4]= {1, 2, 3, 4} > > and obviously Compile not only doesn't like this sort of nested lists as > input but also can't handle these anyware within the compiled code. This is > not too surprising but not explicitly documented so. So I think if you > really need to compile your code you need to change it in such a way that > it constructs a "full array", e.g. the following compiles fine: > > fc = Compile[{n}, Table[If[j <= i, {i, j}, {-1, -1}], {i, 0, n}, {j, 0, > n}]] > > you could then reconstruct the original nested list by: > > DeleteCases[fc[2], {-1, -1}, Infinity] > > It depends on your actual problem whether this is more efficient than not > compiling, and usually only trying out will give you the answer. Memory > usage is of course worse than when using the not compiled nested Table... > > This is another approach that is probably more memory efficient: > > fc = Compile[{{i, _Integer}}, Table[{i, j}, {j, 0, i}]] > ffc = Function[{n}, Table[fc[i], {i, 0, n}]] > > note that using Function instead of ffc[n_] is often slightly more > efficient > because you avoid complicated pattern matching. The drawback is that you > can't do checks about correct input that easily (like in ffc[n_Integer])... > > just try what is the most efficient way for your problem, I wouldn't > exclude > that not compiling gives you the fastest code in the end... > > hth > > albert > -- Mag. Christoph Lhotka -- University of Vienna / Institute for Astronomy mail. lhotka at astro.univie.ac.at