RE: st: Why is Mata much slower than MATLAB at matrix inversion?

[Pradipto Banerjee <pradipto.banerjee@adainvestments.com>]

Patrick,

I had the same issue. I think different applications have their pros and cons. Both Stata and Matlab have their places.

Stata is great for data manipulation and data visualization, merging databases, or trying to quickly see whether a few variables are related to others, carrying out variety of regressions both across time and cross-section, i.e. primarily to build insights from a database without first building a whole set of tools around a database.

On the other hand, once all the insights are developed in Stata, Matlab is perhaps preferable to build the rest of the application because it is faster, has many use toolboxes like optimization, integrates well with the engineering & financial world (e.g. Bloomberg, lots of financial databases & APIs), programming is much easier, awesome editor and is very good as a single environment to develop a complete package.

Thanks.


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Patrick Roland
Sent: Saturday, July 21, 2012 4:29 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Why is Mata much slower than MATLAB at matrix inversion?

As a brief followup, and since StataCorp have responded, I tested
matrix multiplication too. Stata 12.0 takes fully 100 times longer to
multiply two 2000x2000 matrices than MATLAB R2011b.

This code took ~21 seconds in Mata:

mata
j = rnormal(2000,2000,0,1)
timer_on(1)
g =j*j'
timer_off(1)
timer()
end

This code took ~0.21 seconds in MATLAB:

j = randn(2000,2000);
tic;
g = j*j';
toc;

Happy to stand corrected if I've made a mistake.


On Fri, Jul 20, 2012 at 6:19 PM, Richard Herron
<richard.c.herron@gmail.com> wrote:
> Snap. Yes, your m from -runiform()- will certainly be invertible.
>
> Richard Herron
>
>
> On Fri, Jul 20, 2012 at 7:14 PM, Patrick Roland
> <patrick.rolande@gmail.com> wrote:
>> To be clear, my point was that all Mata matrix inverse functions are
>> slower than MATLAB. It does seem though that this is not true for
>> small matrices (e.g. 100x100), but the difference is easily an order
>> of magnitude when it comes to larger matrices (2000x2000).
>>
>> The fact that I compared cholinv() and a general inverse function
>> should be to Mata's favor, since cholinv should presumably be faster
>> if it exploits the special structure of the matrix.
>>
>> X'X is positive definite if X is invertible (as in my example),
>> because a'X'Xa  = (Xa)'(Xa) > 0.
>>
>> On Fri, Jul 20, 2012 at 2:48 PM, David M. Drukker <ddrukker@stata.com> wrote:
>>> Patrick Roland <patrick.rolande@gmail.com> posted that the Mata function
>>> -cholinv()- is slower than a Matlab function for large matrices.
>>>
>>> Others have discussed some issues with Patrick's example.  Despite these
>>> issues, we took Patrick's post seriously, looked at the code, and found
>>> something that could be sped up.
>>>
>>> We will release a faster version of -cholinv()- in an upcoming executable
>>> update.
>>>
>>> Note that any speed difference related to -cholinv()- is only noticeable for
>>> large matrices.  For small matrices, such as variance-covariance matrices
>>> for models with 100 or fewer parameters, the difference is much harder to
>>> find.  For example, the computation takes about .001 seconds on my machine.
>>>
>>> Best,
>>> David
>>> ddrukker@stata.com
>>>
>>>
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