Stuck with simple matrix calculation, can you help?

So I have two matrixes, both 44x72, let's call them A and V. What I need to do is multiply each value in row/column "ij" by the same value in the other matrix. Then I need to sum all these values up and divide by the sum of all the values in matrix A. Here's another way to think about what I need to do:

Answer = Sum(Aij x Vij) / Sum(Aij) over all i,j grid cells

Sounds easy to do but I can't figure it out. Thanks in advance for the help!

Aaron

Answer 1

[Fangjun Jiang]

B=A.*V;
SumA=sum(sum(A));
if SumA~=0
  C=sum(sum(B))/SumA;
end

[Aaron Burdick]

Thanks so much! That worked!

[Fangjun Jiang]

I am curious to know the status of your previous question regarding importfile(). Is that a auto-generated function?

[James Tursa]

sum(A(:)) and sum(B(:)) are a bit cleaner than sum(sum(A)) and sum(sum(B))

[Fangjun Jiang]

Good point! Will keep that in mind!

[Sean de Wolski]

@James, sadly not always (or even usually) faster.

[Fangjun Jiang]

@Sean, How do we know which method is more efficient in general? I mean, it shouldn't require a test case every time. Is there any documentation guidance?

[Fangjun Jiang]

@Sean, How do we know which method is more efficient in general? I mean, it shouldn't require a test case every time. Is there any documentation guidance?

[Sean de Wolski]

No, it can't easily be documented because it's system and version dependent: yours will surely be different than mine. This happened with Matt Fig and me on a question a few months ago. I had a vectorized solution that used big matrices, he used a well designed for-loop. Mine was much faster on my system, his was faster on his.

As for the (:), here are three methods for doing the sum. On mine the sum(sum()) is the fastest followed by reshape (with the numel(), reshape is slowed to the speed of a drunk turtle with a []) and then colon comes in third. I think the newer versions have a faster colon (<humor!>).

A = magic(1000);

[t1 t2 t3] = deal(0);

for ii = 1:100

tic

B = sum(sum(A));

t1 = t1+toc;

tic

C = sum(A(:));

t2 = t2+toc;

tic

D = sum(reshape(A,numel(A),1));

t3 = t3+toc;

end

[t1 t2 t3]

When I make A have more dimensions, say 5, both reshape and colon are faster. But for 2d stuff, sum(sum is fair.

[Fangjun Jiang]

Thanks Sean for the insight!