Trouble in rewriting the for loop as a parfor loop

I want to reduce unnecessary calculations in the loop, and this is the sample code for "for" loop which reduce the number of calculations from 200 to 120 :

R_num = 20;
C_numhalf = 10;
row = 1:C_numhalf;
Ray = R_num/C_numhalf*2;
row_flip = flip(row);
a = zeros(R_num,C_numhalf);
for ii = 1:R_num
    col = [row(1:ceil(ii/Ray)) flip(row_flip((1:ceil(ii/Ray))))];
    for jj = col % 1:C_numhalf
        a(ii,jj) = 1;
    end
end
disp(a)

The problem is how to rewrite the "for" loop into "parfor" loop, the following code does not work properly and this is the help link:

https://www.mathworks.com/help/releases/R2020b/parallel-computing/sliced-variable.html#mw_7aa25a15-0a6a-4226-970f-f76c13ce95fc

R_num = 20;
C_numhalf = 10;
row = 1:C_numhalf;
Ray = R_num/C_numhalf*2;
row_flip = flip(row);
a = zeros(R_num,C_numhalf);
parfor ii = 1:R_num
    col = [row(1:ceil(ii/Ray)) flip(row_flip((1:ceil(ii/Ray))))];
    for jj = col
        a(ii,jj) = 1;
    end
end
disp(a)

I have poor knowledge of parallel computing and failed to find a solution to the problem. Any suggestions are helpful!

By the way, there is an error in the help link:

Answer 1

[Raymond Norris]

This might work, but two clarifying points

• These aren't the same

        for jj = col % 1:C_numhalf

In your example code, col might be the vector [1 10], which when used as the range in a for loop is not the same as

1:10. I'm assuming you want the vector [1 x] and not the vector 1:x.

• Depending on how you initialize a, what I'm showing may or may not work (unless you really do want to work with the vector 1:x and not [1 x]). If it's with zeros, you don't need to call zeros again in unit_of_work (just because of the way scalar expansion works). If it's any other helper function (e.g. nan), then you'll need to preallocate it with the same helper function (e.g. tempa = nan(1,C_numhalf)). If a is assigned some other way, for example a = myfcn(R_num,C_numhalf), what I'm suggesting most likely won't work. Based on your response, we might be able to write it differently.

function chenguang

R_num = 20;
C_numhalf = 10;
row = 1:C_numhalf;
Ray = R_num/C_numhalf*2;
row_flip = flip(row);
a = zeros(R_num,C_numhalf);

parfor ii = 1:R_num
  a(ii,:) = unit_of_work(row,ii,Ray,row_flip,C_numhalf);
end
disp(a)

function tempa = unit_of_work(row,ii,Ray,row_flip,C_numhalf)

col = [row(1:ceil(ii/Ray)) flip(row_flip((1:ceil(ii/Ray))))];
tempa = zeros(1,C_numhalf);
for jj = col
  tempa(1,jj) = 1;
end

[Chenguang Yan]

• I want the vector [1 x] and not the vector 1:x, when ii == 1.
• I preallocate a with a = sym(zeros(R_num,C_numhalf)) actually. Calculating the element of matrix a involves symbolic computation, which is why I hope to use parfor to speed up the calculation.

Following the method you provided, I placed the inner for loop in the local function in my own code, and the outer parfor loop seems to work normally. Thank you very much for your answers.