Matlab矩阵运算无循环

Question

I have an issue with a code performing some array operations. It is getting too slow, because I am using loops. I am trying for some time to optimize this code and to re-write it with less or without loops. Until now unsuccessfully. Can you please help me solve this:

YVal = 1:1:100000;
M_MAX = 1000;
N_MAX = 2000;
clear YTemp
tic
for M=1:1:M_MAX 
    for N = 1:1:N_MAX 
       YTemp(M,N) = sum(YVal (N+1:N+M)  ) - sum(YVal   (1:M)  );  
    end
end

For large N_MAX and M_MAX the execution time of these two loops is very high. How can I optimize this?

Thank you!

Answer 1

Assuming YVal is larger than N_MAX+M_MAX

sum1 = cumsum( YVal(1:(M_MAX+N_MAX)) ); % sum1(M) = sum(YVal(1:M))

If I'm not mistaken, then

sum( YVal( N+1:N+M ) ) = sum1( N + M ) - sum1( N )

And therefore

YTemp( M, N ) = sum1( N + M ) - sum1( N ) - sum1( M )

Using ndgrid

[M N] = ndgrid( 1:M_MAX, 1:N_MAX );
YTemp = sum1( N + M ) - sum1( N ) - sum1( M );

Have I got it right?

EDIT:
Another go without ndgrid

sum1 = cumsum( YVal( 1 : (N_MAX+M_MAX) ) );
YTemp = bsxfun( @minus, ...
            bsxfun( @minus, ...
                sum1( bsxfun( @plus, 1:N_MAX, (1:M_MAX)' ) ) , sum1 ),...
                    sum1' );

Answer 2

You should be able to speed it up a little by hoisting the invariant term out of the inner loop, eg

for M=1:1:M_MAX 
    sum2 = sum(YVal(1:M));
    for N = 1:1:N_MAX 
       YTemp(M,N) = sum(YVal(N+1:N+M)) - sum2;  
    end
end