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 <edu50...@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 <jensa...@soegaard.net>: > >> 2014-05-11 6:09 GMT+02:00 Eduardo Costa <edu50...@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 ____________________ Racket Users list: http://lists.racket-lang.org/users
