Select the largest two numbers with their indices

Hi,

I have the following random variable:

h=randn(4,4)+1i.*randn(4,4);

suppose that

|hi|^2=abs(h(i,1))^2+abs(h(i,2))^2+abs(h(i,3))^2+abs(h(i,4))^2

I need to select the largest two, i.e.: |hi|^2+||hj||^2 is the maximum, and the indices i and j, in the most efficient way. How?

Thanks

Answer 1

[Andrew Newell]

Here is one approach that is efficient enough:

n = 4;
h=randn(n)+1i.*randn(n);
h2 = sum(h.*conj(h),2); %sum of squares for each row
[h2sort,isort] = sort(h2,'descend');
iLargest = isort(1:2);
h2Largest = h2(iLargest);
disp(['Sum of two largest values = ',num2str(h2Largest'*h2Largest)])

(Edited in view of the discussion below.)

[Saed]

I will try this one, but does this retrieve the indices too. I mean if |h1|^2+|h4|^2 is the maximum, I need to know that i=1 and j=4, because later on, I will use them as h1=h(i=1,:) and h2=h(j=4,:), and use h1 and h2 as the best two random variable in the power sense.

Now I am doing some maintenance on my MATLAB so I have not tried the segment yet.

Thanks

[Walter Roberson]

Yes, it displays the indices.

[Walter Roberson]

I figure there is no need to do the sums. Just find the two largest h2 values. The largest sum is going to be formed by adding the largest values.

[Andrew Newell]

Oh, is that what he means by "the largest two"?

[Saed]

yes right, the largest two numbers will have the largest sum. Thanks

Answer 2

[Walter Roberson]

Does "the most efficient way" have to do with time to program the solution, best-case execution time, worst-case execution time, average execution time, memory consumption, algorithmic complexity, some other factor?

If you want the best execution time, then the solution could involve sending the numbers to an FPGA (which you would have to program) and retrieving the answer from it. On the other hand, due to the overhead of communicating with an FPGA, perhaps a Mex routine would be faster.

Is strict IEEE754 compliance required in the calculations?

You will be writing the code in Assembly Language, right?

[Saed]

What I meant in terms MATLAB syntax without involving too much loops.