Sliced Variables in N Choose K Search

I am trying to generate computations for a problem of the form N Choose K. The function is computational expensive, so I would like to use parallel computing. Using a preallocated array and sliced variables, originally my code looked like this:

A = NaN(100,100);
parfor x = 1:100
    for y = x+1:100
        A(x,y) = somefunction(x,y)
    end
end

When I try to run I get the following error:

Error: When indexing the sliced variable 'A', the range of the for-loop variable 'y' must be a row vector of positive constant numbers or variables. For more information, see Parallel for Loops in MATLAB, "Nested for-Loops with Sliced Variables".

The problem is the y variable as it is not constant. To solve this issue, I changed the code to:

A = NaN(100,100);
parfor x = 1:100
    for y = 1:100
        if y > x
            A(x,y) = somefunction(x,y)
        end
    end
end

Which it now works. However, it seems to me that having to run the check y > x so many times is very inefficient.

Would there be a better way?

[Andres Morales]

"However, it seems to me that having to run the check y > x so many times is very inefficient."

Not sure if the statement above is valid. Maybe doing the y = x+1:100 is more inefficient.

[Bruno Luong]

IMO the if test cost is negligible.

Answer 1

[Edric Ellis]

This is a limitation of the parfor analysis when it comes to indexing sliced variables in a nested for loop. There is another workaround, but I suspect it is actually even less efficient than the one that you found:

somefunction = @(x,y) x+y;
A = NaN(10);
parfor x = 1:10
    tmp = A(x,:); % Extract row x
    for y = (x+1):10
        tmp(y) = somefunction(x,y);
    end
    A(x,:) = tmp;
end

Starting parallel pool (parpool) using the 'Processes' profile ...
Connected to the parallel pool (number of workers: 2).

disp(A)

   NaN     3     4     5     6     7     8     9    10    11
   NaN   NaN     5     6     7     8     9    10    11    12
   NaN   NaN   NaN     7     8     9    10    11    12    13
   NaN   NaN   NaN   NaN     9    10    11    12    13    14
   NaN   NaN   NaN   NaN   NaN    11    12    13    14    15
   NaN   NaN   NaN   NaN   NaN   NaN    13    14    15    16
   NaN   NaN   NaN   NaN   NaN   NaN   NaN    15    16    17
   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN    17    18
   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN    19
   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN