On 26/09/2012 19:42, Paul Carrico wrote:
Dear All,
A funny result for calculating the norm of a tensor ... for ounce a
"traditional" method (that probably uses vectorization in back stage)
is faster than the norm function ...
Paul
mode(0);
A= [ 1 2 3 ; 4 5 6; 7 8 9]
n= 1000
fori = 1 : n
for j = 1 : n
B(i,j) = i*j;
end
end
/// Scilab function/
_tic_();
_norm_(B)
t1= _toc_()
/// "traditional" method/
/// norm = sqrt(trace(A_transp * A))/
_tic_
norm_= (_trace_(B'*B))**0.5
t2= _toc_()
Hi
Yep, same result for me, the handmade computation is 4 times faster.
Maybe norm i written assuming B is a complex hypermatrix or something.
But the real improvement would be to use a "vectorized" code to generate
B, try this:
tic
n= 1000
fori = 1 : n
for j = 1 : n
B(i,j) = i*j;
end
end
toc
tic
BB=(1:n)'*(1:n);
toc
the second method is several hundred times faster than the first.
Note that the first method uses loops when matrix computations are able
to do the job, and, worst, B is not initialized.
This means that every while, scilab will notice that B is larger than
expected, and will ask for a new, larger place in memory to store B,
will copy the existing B from the old place to the new one, only to find
out later that B is actually even bigger.
I do not know how exactly this is implemented, but this can happen
basically for each new value of i, so 1000 time.
The take away message is: when having to building a matrix with a loop,
"initailize" your matrix:
tic
n= 1000
fori = 1 : n
for j = 1 : n
Bad(i,j) = i*j;
end
end
bad=toc()
tic
Good = zeros(n,n);
n= 1000
fori = 1 : n
for j = 1 : n
Good(i,j) = i*j;
end
end
good=toc()
bad/good
//(in my PC this is already 3x faster)
tic
best=(1:n)'*(1:n);
best=toc()
bad/best
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