[racket] math/matrix

Hi Eduardo,

The math/matrix library uses the arrays from math/array to represent matrices.

If you want to try the same representation as Bigloo, you could try Will Farr's
matrix library:

http://planet.racket-lang.org/package-source/wmfarr/simple-matrix.plt/1/1/planet-docs/simple-matrix/index.html

I am interested in hearing the results.

/Jens Axel



2014-05-11 21:18 GMT+02:00 Eduardo Costa <edu500ac at gmail.com>:
> What is bothering me is the time Racket is spending in garbage collection.
>
> ~/wrk/scm/rkt/matrix$ racket matrix.rkt
> 0.9999999999967226
> cpu time: 61416 real time: 61214 gc time: 32164
>
> If I am reading the output correctly, Racket is spending 32 seconds out of
> 61 seconds in garbage collection.
>
>  I am following Junia Magellan's computer language comparison and I cannot
> understand why Racket needs the garbage collector for doing Gaussian
> elimination. In a slow Compaq/HP machine, solving a system of 800 linear
> equations takes 17.3 seconds in Bigloo, but requires 58 seconds in Racket,
> even after removing the building of the linear system from consideration.
> Common Lisp is also much faster than Racket in processing arrays. I would
> like to point out that Racket is very fast in general. The only occasion
> that it lags badly behind Common Lisp and Bigloo is when one needs to deal
> with arrays.
>
> Basically, Junia is using Rasch method to measure certain latent traits of
> computer languages, like productivity and coaching time. In any case, she
> needs to do a lot of matrix calculations to invert the Rasch model. Since
> Bigloo works with homogeneous vectors, she wrote a few macros to access the
> elements of a matrix:
>
> (define (mkv n) (make-f64vector n))
> (define $ f64vector-ref)
> (define $! f64vector-set!)
> (define len f64vector-length)
>
> (define-syntax $$
>    (syntax-rules ()
>       (($$ m i j) (f64vector-ref (vector-ref m i) j))))
>
> (define-syntax $$!
>    (syntax-rules ()
>       (($$! matrix row column value)
>        ($! (vector-ref matrix row) column value))))
>
> I wonder whether homogeneous vectors would speed up Racket. In the same
> computer that Racket takes 80 seconds to build and invert a system of
> equations, Bigloo takes 17.3 seconds, as I told before. Common Lisp is even
> faster. However, if one subtracts the gc time from Racket's total time, the
> result comes quite close to Common Lisp or Bigloo.
>
> ~/wrk/bgl$ bigloo -Obench bigmat.scm -o big
> ~/wrk/bgl$ time ./big
> 0.9999999999965746 1.000000000000774 0.9999999999993039 0.9999999999982576
> 1.000000000007648 0.999999999996588
>
> real    0m17.423s
> user    0m17.384s
> sys    0m0.032s
> ~/wrk/bgl$
>
> Well, bigloo may perform global optimizations, but Common Lisp doesn't. When
> one is not dealing with matrices, Racket is faster than Common Lisp. I hope
> you can tell me how to rewrite the program in order to avoid garbage
> collection.
>
> By the way, you may want to know why not use Bigloo or Common Lisp to invert
> the Rasch model. The problem is that Junia and her co-workers are using
> hosting services that do not give access to the server or to the jailshell.
> Since Bigloo requires gcc based compilation, Junia discarded it right away.
> Not long ago, the hosting service stopped responding to the sbcl Common Lisp
> compiler for reasons that I cannot fathom.  Although Racket 6.0 stopped
> working too, Racket 6.0.1 is working fine. This left Junia, her co-workers
> and students with Racket as their sole option. As for myself, I am just
> curious.
>
>
> 2014-05-11 6:23 GMT-03:00 Jens Axel Søgaard <jensaxel at soegaard.net>:
>
>> 2014-05-11 6:09 GMT+02:00 Eduardo Costa <edu500ac at gmail.com>:
>> > The documentation says that one should expect typed/racket to be faster
>> > than
>> > racket. I tested the math/matrix library and it seems to be almost as
>> > slow
>> > in typed/racket as in racket.
>>
>> What was (is?) slow was a call in an untyped module A to a function
>> exported
>> from a typed module B. The functions in B must check at runtime that
>> the values coming from A are of the correct type. If the A was written
>> in Typed Racket, the types would be known at compile time.
>>
>> Here math/matrix is written in Typed Racket, so if you are writing an
>> untyped module, you will in general want to minimize the use of,say,
>> maxtrix-ref. Instead operations that works on entire matrices or
>> row/columns are preferred.
>>
>> > (: sum : Integer Integer -> Flonum)
>> > (define (sum i n)
>> >   (let loop ((j 0) (acc 0.0))
>> >     (if (>= j mx) acc
>> >         (loop (+ j 1) (+ acc (matrix-ref A i j))) )))
>> >
>> > (: b : (Matrix Flonum))
>> > (define b (build-matrix mx 1 sum))
>>
>> The matrix b contains the sums of each row in the matrix.
>> Since matrices are a subset of arrays, you can use array-axis-sum,
>> which computes sum along a given axis (i.e. a row or a column when
>> speaking of matrices).
>>
>> (define A (matrix [[0. 1. 2.]
>>                    [3. 4. 5.]
>>                    [6. 7. 8.]]))
>>
>> > (array-axis-sum A 1)
>> - : (Array Flonum)
>> (array #[3.0 12.0 21.0])
>>
>> However as Eric points out, matrix-solve is an O(n^3) algorithm,
>> so the majority of the time is spent in matrix-solve.
>>
>> Apart from finding a way to exploit the relationship between your
>> matrix A and the column vector b, I see no obvious way of
>> speeding up the code.
>>
>> Note that when you benchmark with
>>
>>    time racket matrix.rkt
>>
>> you will include startup and compilation time.
>> Therefore if you want to time the matrix code,
>> insert a literal (time ...) call.
>>
>> --
>> Jens Axel Søgaard
>
>



-- 
--
Jens Axel Søgaard