[racket] math/matrix

Or ... you could take a look at

https://github.com/plt/racket/blob/master/pkgs/math-pkgs/math-lib/math/private/matrix/matrix-gauss-elim.rkt

at see if something can be improved.

/Jens Axel


2014-05-11 21:30 GMT+02:00 Jens Axel Søgaard <jensaxel at soegaard.net>:
> 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



-- 
--
Jens Axel Søgaard