[racket] performance problem in math/matrix

The attached patch should fix it.

Tobias


On Sun, 20 Jan 2013 15:09:42 +0100, Jens Axel Søgaard  
<jensaxel at soegaard.net> wrote:

> Hi Berthold,
>
> 2013/1/20 Berthold Bäuml <berthold.baeuml at dlr.de>:
>> I tried a little test with mildly large Flonum matrices using  
>> math/matrix in Typed
>> Racket. Two 1000x1000 dimensional matrices should be multiplied with  
>> (array-
>> strictness #t). Running this in DrRacket results in an "out of memory"  
>> error (also
>> having set the memory limit to 1GB) and running it with racket on the  
>> command
>> line makes the computer start to heavily swap.
>
>> Where is this high memory consumption coming from?
>
> I consider this a bug in matrix*.
>
> The culprit is inline-matrix-multiply in "untyped-matrix-arithmetic.rkt".
> When multiplying an mxp matrix with an pxn  matrix, it builds a
> temporary array of size n*p*m with all products needed, then
> it computes sums of these products.
>
> Replacing this algorithm with the standard O(n^3) ought to be easy.
>
> Numpy (and Mathematica, I believe) uses BLAS and LAPACK, which use
> Strassen's algorithm (or better?) for matrices this large, so there will
> still be a performance gap.
>
> If this performance gaps turns out to be too large, we must figure
> out a way to integrate BLAS and LAPACK bindings into math/matrix.
>
> For the time being, I have attached an implementation of math/matrix
> using supporting matrices over doubles (math/matrix supports
> matrices over Racket numbers). The implementation uses Racket
> bindings  to BLAS and LAPACK.   All names ought to the same,
> just replace "matrix" with "flmatrix".
>
> Your example becomes:
>
> #lang racket
> (require "flmatrix.rkt")
> (define dim 1000)
> (define big1 (build-flmatrix dim dim (lambda (i j) (random))))
> (define big2 (build-flmatrix dim dim (lambda (i j) (random))))
> (define res (time (flmatrix* big1 big2)))
>
> Note: Disable "Populate "compiled" directories (for faster loading)"
>           to run it in DrRacket. To disable: Choose the language menu.
>           Choose the menu item "Choose language". Click the button
>           "advanced". Then disable.
>
> If it is enabled, I currently get this curious error from the compiler:
>
> ../collects/compiler/cm.rkt:438:6: write: cannot marshal value that is
> embedded in compiled code
>   value: #<ctype:float>
>
> I unsure whether it is a bug in my code, or in cm.rkt.
>


-- 
---------------------------------------------------------
Tobias Hammer
DLR / Institute of Robotics and Mechatronics
Muenchner Str. 20, D-82234 Wessling
Tel.: 08153/28-1487
Mail: tobias.hammer at dlr.de
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