faster way to add certain elements ?
in [Matlab]
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From: Sean on 15 Jun 2010 15:47 "Juliette Salexa" <juliette.physicist(a)gmail.com> wrote in message <hv8i1e$3g4$1(a)fred.mathworks.com>... > Thanks Sean and Doug. > > I can't see the difference between your methods though! =( > The only difference is I had a small typo in mine. :{ snip: > A=(1:3^12)';I=rand(3^12,1); > B=zeros(length(A)/3,3)'; > >I'm multiplying each of the 3 copies by a different number - If I could get A.*I (as in the above example) without having to make 3 copies of each element of A, that would be very nice! But I can't think of a way to do that =( > If the numbers you gave in your examples are correct i.e. you A vector is 1:n this will also work - not sure if it's faster. A = (1:63)'; B = ones(63,1); % just so the results are known to be right/wrong s = length(A)/3; %length of one column if using reshape v = [s+1:s+s]'*3; %vector of sums v = kron(v,[1;1;1]); %repeated 3x so it lines up with second vector C = v.*B;
From: Doug Schwarz on 15 Jun 2010 15:59 Juliette Salexa wrote: > Thanks Sean and Doug. > > I can't see the difference between your methods though! =( > > I do appreciate that using REPMAT instead of EXPAND speeds things up by > about a factor of 3. > But, as I said in the initial post, the profiler suggests that RESHAPE > is taking up a significant percentage of the time: Then the profiler's suggestion is wrong. Reshape uses negligible time. All it does is change the array header that stores how many rows and columns there are. It doesn't move any data. It is always very fast no matter how large the argument. Always. (Did I emphasize that enough?) As Matt said, look into bsxfun. -- Doug Schwarz dmschwarz&ieee,org Make obvious changes to get real email address.
From: James Tursa on 15 Jun 2010 17:00 Doug Schwarz <see(a)sig.for.address.edu> wrote in message <sYQRn.44917$rU6.8009(a)newsfe10.iad>... > Juliette Salexa wrote: > > Thanks Sean and Doug. > > > > I can't see the difference between your methods though! =( > > > > I do appreciate that using REPMAT instead of EXPAND speeds things up by > > about a factor of 3. > > But, as I said in the initial post, the profiler suggests that RESHAPE > > is taking up a significant percentage of the time: > > Then the profiler's suggestion is wrong. Reshape uses negligible time. > All it does is change the array header that stores how many rows and > columns there are. It doesn't move any data. It is always very fast no > matter how large the argument. Always. (Did I emphasize that enough?) Except for sparse matrices, where a data copy is involved. (Not this application of course). James Tursa
From: James Tursa on 15 Jun 2010 17:12 "Matt J " <mattjacREMOVE(a)THISieee.spam> wrote in message <hv8kjc$fvi$1(a)fred.mathworks.com>... > > In any case, you can avoid using repmat by using bsxfun instead, which is more memory efficient e.g., for poster's original code: A = (1:3^12)'; I = rand(3^12,1); B = repmat(sum(reshape(A,length(A)/3,3),2),1,3).'; B = B(:).*I; it would look something like this: A = (1:3^12)'; I = rand(3^12,1); Ar = reshape(sum(reshape(A,length(A)/3,3),2),1,[]); Ir = reshape(I,3,[]); B = bsxfun(@times,Ar,Ir); B = B(:); James Tursa
From: Juliette Salexa on 16 Jun 2010 13:15
Thank you everyone, I think James Tursa's solution sped up my computation by about 1.6 hours (I have to test still) ================== Matt J: > As an FYI, you don't need to be computing lengthOfAover3. You can just do > temp=reshape(A,[],3); I think this might be slower because matlab has to calculate what the missing dimension is (when repeated 10000 times that overhead could build up) > You're ignoring the contribution of A.*I. No doubt that contributes an appreciable fraction. You're right, I retested, and the multiplication was actually taking longer than the RESHAPE. Thanks for pointing that out! > You mean you have a vector and need to multiply it by different scalars? Not quite. each element is multiplied by 3 different scalars, and those 3 scalars are different for each element. ================== Sean: > If the numbers you gave in your examples are correct i.e. you A vector is 1:n this will also work - not sure if it's faster. KRON is known to be slow (about twice as slow as EXPAND for what we're doing here), since it's written to handle very general cases, and consequently isn't optimized for simple things like replicating elements. ================== Doug: > Then the profiler's suggestion is wrong. Reshape uses negligible time. Thanks, sorry for doubting you =) It turns out that (as Matt J suggested), multiplication was taking a lot of the time, so RESHAPE was only taking about 8 seconds (a third of what I thought) ================== James: > it would look something like this: .... I think that works perfectly and significantly speeds up the calculation, Thanks! ================== Summary: replace KRON by EXPAND: 2x speedup replace EXPAND by repmat: 3x speedup (6x speedup in total) replace repmat by bsxfun: 2x speedup (12x speedup in total) And this can be done in one-line (not the fastest solution, but very compact): reshape(bsxfun(@times,reshape(sum(reshape(A,[],3),2),1,[]),reshape(I,3,[])),[],1); Thanks again Doug, Sean, Matt J and James for your fantastic help! |