Combine two different matrices to create one new matrix of all matrix combinations

2012 5 11
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1 个投票

Hi, I have the following matrices
WT_energy_supply(:,:,M) and PV_power_output(:,:,K)
which are 365 x 24 matrices and M = 3 and K = 10. Therefore there are 30 possible combinations of WY_energy_supply and PV_power_output. I am looking to create a set of matrices (in the form (:,:,Z)) that add corresponding elements in each matrix to form this new set (again 365x24 with 30 different matrices) Does anyone have any idea where to start coding this?
Thank you

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Sean de Wolski
Sean de Wolski 2012-5-11

2 个投票

Nice brain teaser!
%Sample data:
A = ones(4,4,5);
B = bsxfun(@times,ones(4,4,3),cat(3,1,2,3));
%Nice to know:
sz = size(B);
%Engine:
C = reshape(bsxfun(@plus,A, reshape(B,sz(1),sz(2),1,sz(3))),sz(1),sz(2),[]);

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Andrew Alkiviades
Andrew Alkiviades 2012-5-11
thanks for the reply Sean, but I am now a bit confused.
The bsxfun you suggest uses @times, I guess this should be @plus since I want to add the corresponding elements of each matrix.
Also, about the C = reshape(bsxfun code you have suggested, will this give me a matrix C of 365x24 elements with 30 of these matrices that each represent a combination?
If you could please explain this code a little bit further since I don't really understand how you have developed it.
Glad I could provide a nice brain teaser!
Thank you
Sean de Wolski
Sean de Wolski 2012-5-11
yes, 365x24x30.
The first bsxfun() (the one with times) is just to create sample data that is easy to check the results with. B will be a 4x4x3 matrix where the first slice(B(:,:,1)) is all ones, the second all twos etc. This way, then I add it to A, I can check quickly that it did what I want. (It did). If you inspect each variable (A,B,C) it will be obvious what I did.
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
Thanks Sean
so the above code will provide a 365x24x30 matrix
How can I access each matrix individually, say I want to view or write an excel spreadsheet of each one?
Thank you
Sean de Wolski
Sean de Wolski 2012-5-11
It is the C matrix in my example. it will be a (m x n x p*k) matrix where in your case m is 365, n is 23 p is 10 and k is 3.
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
ok both matrices are 365x24, its the number of matrices that are different.
so if I replace A and B in your example with WT_energy_supply and PV_power_output which I have in the initial question above it should work?
Sean de Wolski
Sean de Wolski 2012-5-11
I though you said they were 365x24x10 and 365x24x3?
Look at my example and see what it is doing. This will confirm or deny my algorithm.
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
they are 365x24x10 and 365x24x3 where the 10 and 3 represent 10 and 3 different manufacturers respectively. I want the sum of the PV and WT at each element in the 365x24 matrix to create a third matrix of 365x24. The third matrix however must be all the combinations of 10 and 3 and therefore a 365x24x30 matrix.
does this make things clearer?
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
nice, thanks Sean.
Therefore, to modify your code above I need the following
A = PV_power_output(:,:,K)
B = WT_energy_supply(:,:,M)
sz = size(WT_energy_supply(:,:,M));
C = reshape(bsxfun(@plus,A,reshape(B,sz(1),sz(2),1,sz(3))),sz(1),sz(2),[]);
and the just access say the fifth combination of the C matrices via C(:,:,5)
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
having tried this i get the "Index exceeds matrix dimensions" error
on the line of code where "C" is.
I'm quite confused now since i was expecting a 365x24x30 matrix! any thoughts?
Sean de Wolski
Sean de Wolski 2012-5-11
No.
A = PV_power_output;
B = WT_energy_supply;
This is the only change!!!
Now the engine stays the same
sz = size(B); %needs to know the size of the whole thing, not one slice
C = reshape(...)
I think you are being confused by the 3d indexing.
We want to do the whole operation at once, thus the individual slice extracton (i.e Matrix(:,:,page)) is going to throw off the calculation. Instead we want to pass this block, (think of it like a rubik's cube) into the engine. We then take two rubik's cubes and add the second rubik's cube to each slice (as if you were to cur off 9 cubes) of the first rubik's cube. Hope this helps.
Andrei Bobrov
Andrei Bobrov 2012-5-11
Hi Sean! In one row:
C = reshape(bsxfun(@plus,A, permute(B,[1 2 4 3])),size(A).*[1 1 size(B,3)])
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
andrei, thanks, what is the permute(B,[1 2 4 3... based on?
Andrew Alkiviades
Andrew Alkiviades 2012-5-12
@Sean
Still a bit confused on how to code "C" to take the form
C(:,:,Z) = ...

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更多回答（2 个）

Andrei Bobrov
Andrei Bobrov 2012-5-11

1 个投票

eg:
M = 3;
K = 10;
WT_energy_supply = randi(10,10,4,M);
PV_power_output = randi([10 50],10,4,K);
%solution
ij = fullfact([M K]);
out = WT_energy_supply(:,:,ij(:,1)) + PV_power_output(:,:,ij(:,2)) ;

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Sean de Wolski
Sean de Wolski 2012-5-11
+1 for fullfact().
It's like a simple way to do the [xx yy zz ww] = meshgrid(blah)
[xx(:) yy(:)...
Learn something new everyday!
Awesome-o!
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
thanks guys
If i have understood correctly, you have given me two possible solutions to my question.
which do you recommend I use :P
Sean de Wolski
Sean de Wolski 2012-5-11
really, you shoudl decide based on:
-importance of speed.
-importance of being able to understand what's going on.
-whichever side of a coin flips up (or rand > 0.5)
Andrew Alkiviades
Andrew Alkiviades 2012-5-11
having tried this code i get the following error "Array dimensions must match for binary array op."
Do I need to define M and K as 3 and 10 since I have them previously in the code for working out WT_energy_supply and PV_power_output?
This may be a stupid question but why can't I just add WT_energy_supply(:,:,M) to PV_power_output(:,:,K) since this is really what I am trying to do?
Thank you
Sean de Wolski
Sean de Wolski 2012-5-11
That's what bsxfun does for you!
think about it, how can you add two things that are different sizes?

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owr
owr 2012-5-11

0 个投票

To generate all combinations of K and M, check out the file exchange function "allcomb": href=""<http://www.mathworks.com/matlabcentral/fileexchange/10064</a>>
Ive been using it for years, works with more than 2 parameters as well.

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