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/