[Haskell] Matrix multiplication

[Timothy Goddard]

On Thu, 24 Apr 2008 04:01:50 Tillmann Vogt wrote:
> Hi,
>
> I am currently experimenting with parallelizing C-programs. I have
> therefore written a matrix vector multiplication example that needs 13
> seconds to run (5 seconds with OpenMP). Because I like Haskell I did the
> same in this language, but it takes about 134 seconds. Why is it so
> slow? Does someone have an idea?
>
>
> module Main where
>
> main = do putStrLn (show (stupid_mul 100))
>          putStrLn "100 multiplications done"
>
> stupid_mul 0  = []
> stupid_mul it = (s_mul it) : stupid_mul (it-1) -- without "it" after
> s_mul only one multiplication is executed
>
> s_mul it = mul (replicate 4000 [0..3999])  (replicate 4000 2)
>
> mul :: [[Double]] -> [Double] -> [Double]
> mul [] _ = []
> mul (b:bs) c | sp==0 = sp : (mul bs c) -- always false, force evaluation
>
>                   | otherwise =  (mul bs c)
>
>  where sp = (scalar b c)
>
> scalar :: [Double] -> [Double] -> Double
> scalar _ [] = 0
> scalar [] _ = 0
> scalar (v:vs) (w:ws) = (v*w) + (skalar vs ws)
>
>
>
> and here the C-program
>
> #include <stdio.h>
> #include <stdlib.h>
> #include <time.h>
>
> #define M 4000
> #define N 4000
> #define IT 100
>
> double a[M], b[M][N], c[N];
>
> int main(int argc, char *argv[])
> {
>   double d;
>   int i, j, l;
>   time_t start,end;
>
>   printf("Initializing matrix B and vector C\n");
>   for(j=0; j<N; j++) c[j] = 2.0;
>   for(i=0; i<M; i++) for(j=0; j<N; j++) b[i][j] = j;
>
>   printf("Executing %d matrix mult. for M = %d N = %d\n",IT,M,N);
>   time (&start);
>
>   for(l=0; l<IT; l++)
>
>   #pragma  omp parallel for default(none) \
>            shared(a,b,c) private(i,j,l)
>
>   for(i=0; i<M; i++)
>   {
>      a[i] = 0.0;
>      for (j=0; j<N; j++) a[i] += b[i][j]*c[j];
>   }
>   time (&end);
>
>   d = difftime (end,start);
>   printf ("calculation time: %.2lf seconds\n", d );
>   return 0;
> }
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You haven't even told us which compilers you're using so it's pretty difficult 
to do. I can't even get your code to compile - there are typos in it so 
you've obviously altered it since compiling yourself.

While this program may be wrong, I've dashed off this attempt that takes about 
1.3 seconds on my not-too-powerful machine:

module Main
  where

import Control.Monad

rows = 4000
cols = 4000
iterations = 100

main = do
  let
    vector :: [Double]
    vector = replicate cols 2.0
    matrix :: [[Double]]
    matrix = replicate rows (map fromIntegral [0..cols-1])
    a = map (sum . (zipWith (*) vector)) matrix
  replicateM_ iterations (putStrLn (show a))

Those who understand how Haskell programs are executed will now be 
screaming "cheating!". This program when optimised by GHC (which I use) will 
only actually do the calculation once and print it 100 times. That is, after 
all, the same output you asked for. It may even be taking more shortcuts 
using identities around map and replicate but I'm not sure.

When mapping imperative languages to functional ones a little understanding of 
how it is executed goes a long way. Performance of your programs will benefit 
immensely if you know how your program will be run. I'm new to Haskell but 
have already realised that performance can be altered by orders of magnitude 
by making possible optimisations more visible to the compiler with how things 
are set out.

P.S. I would really recommend increasing use of higher level functions such as 
map. They make code much more readable and the most common also receive 
special optimisations from many compilers.

Cheers,

Tim