Re: Compiling SingularValueDecomposition

*To*: mathgroup at smc.vnet.net*Subject*: [mg89830] Re: Compiling SingularValueDecomposition*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Sun, 22 Jun 2008 03:22:12 -0400 (EDT)*References*: <g3ihod$fc9$1@smc.vnet.net>

Frank Hu wrote: > Hi, group, > > I'm trying to speed up a piece of code that uses > SingularValueDecomposition by compiling it. But I couldn't get it to > compile. For a simple demonstration, try > > fx=Compile[{{x, _Real, 2}}, SingularValueDecomposition[x], > {{SingularValueDecomposition, _Real, 3}}] > > and fx[[4]] is > {{1, 5}, {54, Function[{x}, SingularValueDecomposition[x]], 3, 2, 0, > 3, 2, 1}, {2}} > > The "Function" there tells fx wasn't compiled successfully. Calling > fx[{{1., 2.}, {3., 4.}}] will generate the following warnings > > CompiledFunction::cfte: Compiled expression {<<1>>} should be a rank > 2 tensor of machine-size real numbers. >> > CompiledFunction::cfex: Could not complete external evaluation at > instruction 2; proceeding with uncompiled evaluation. >> > > Any suggestions? > There is no point in trying to compile SingularValueDecomposition. It is already a highly optimized function, implemented in a low level language for machine precision numbers, so it should be nearly as fast as a C version for large enough matrices. But we still have to explain why Mathematica throws that error. There is a small mistake in the pattern that you used. Try this (but remember that it does not speed things up): fx = Compile[{{x, _Real, 2}}, SingularValueDecomposition[x], {{SingularValueDecomposition[_], _Real, 3}}] The above example will work for the 2*2 test input, but keep in mind that generally SingularValueDecomposition does *not* return a rank 3 tensor (it returns a list of 3 matrices), so it will not work for other inputs. Here's a list of compilable functions: http://support.wolfram.com/mathematica/kernel/Symbols/System/Compile.html Unfortunately it was written for version 3.0, but it is still useful as a guideline for version 6.0/