Performing an Operation on a Matrix Using Complex Numbers

I have a matrix with the operation perfomed as:

a = rand(10,10);
a_x = @(x) sum((x-a)./(x+a),'all');
aa = arrayfun(a_x,a);

I want the operation for each pair to be performed in complex format. For example for one pair of the matrix ( a(1) & a(2) ) points, it will be like:

complex(a(1),-a(2)) / complex(a(1),a(2)); %% a(1) - a(2)i / a(1) + a(2)i

Which will give me:

ans =

  -0.0313 - 0.9995i

I want this operation (sum of all the relations for each point) to be performed for all the matrix components (may original matrix is 81*81).

[Walter Roberson]

To confirm, you want

complex(a(I,J),-a(K,L)) / complex(a(I,J),a(K,L));

for all I, J, and K, L? Including or excluding K,L = I,J ?

So you want (81 x 81) x (81 x 81) size output ?

[MarshallSc]

Yessir, including K,L = I,J, since I need the sum for each point, they need to be included.

This will give me a (81 x 81) in complex form for the aa (summing every relation for each point, same as):

a_x = @(x) sum((x-a)./(x+a),'all');

The difference is the subtraction in the nominator and summation in the denominator will be like:

a_x = @(x) sum ((x - ai)./(x + ai), 'all'): % obviously this is not correct, just wanted to show what I mean

Answer 1

[Matt J]

sz=size(a);

C=(a(:)-1i*a(:).');

result=reshape(C./conj(C) , [sz,sz]);

[MarshallSc]

Thanks a lot Matt. Do you know how I can sum the values of every relation for each point?

[Matt J]

Does that mean summing over one of the dimensions of your 4D array?

[MarshallSc]

The "result" should be transformed into a 10 x 10 complex double that each summation for each component is written in this way:

a(1) = a(1) - a(1)i / a(1) + a(1)i     +     a(1) - a(2)i / a(1) + a(2)i  + ...
    a(1) - a(3)i / a(1) + a(3)i   + . . .  +   a(1) - a(n)i / a(1) + a(n)i

a(2) = a(2) - a(1)i / a(2) + a(1)i     +     a(2) - a(2)i / a(2) + a(2)i  + ...
    a(2) - a(3)i / a(2) + a(3)i   + . . .  +   a(2) - a(n)i / a(2) + a(n)i
.
.
.

a(n) = a(n) - a(1)i / a(n) + a(1)i     +     a(n) - a(2)i / a(n) + a(2)i  + ...
    a(n) - a(3)i / a(n) + a(3)i   + . . .  +   a(n) - a(n)i / a(n) + a(n)i

[Matt J]

That would just be,

sum(result,[3,4])

Answer 2

[Matt J]

sz=size(a);

C=2*atan(a(:),a(:).');

result=reshape( exp(1j*C),  [sz,sz]);