Parfor function for numerical simulations

Hello ppl ,

I am learning parallel computing with matlab . I have several sequence of functions which is being called from the main function for each iteration . So each iteration is dependent upon the previous iteration for results . Now the sub functions defined within the main function has for loops which are independent and i want to apply parfor for this to speed up the calculation.

example

for i=1:iter
  %sequence of codes
  [U,V,T]=Mac(u,v,T,rho,....)
end

mac.m

% all variables below comes from the previous loop . 
for i=2:imax-1
  for j=2:jmax-1

      Up1(i,j)=U1(i,j)-(delt/delx)*(E1(i+1,j)-E1(i,j))-(delt/dely)*(F1(i,j+1)-F1(i,j));
      Up2(i,j)=U2(i,j)-(delt/delx)*(E2(i+1,j)-E2(i,j))-(delt/dely)*(F2(i,j+1)-F2(i,j));
      Up3(i,j)=U3(i,j)-(delt/delx)*(E3(i+1,j)-E3(i,j))-(delt/dely)*(F3(i,j+1)-F3(i,j));
      Up4(i,j)=U4(i,j)-(delt/delx)*(E4(i+1,j)-E4(i,j))-(delt/dely)*(F4(i,j+1)-F4(i,j));
  end
end

I dont know or cant understand in invoking parfor to this kind of code.

I was reading to some of the example files in which they have used to separate the primary and secondary variable (just for calculation) while using matrix like below

matlabpool ('open',2);      % Call to open the distributed processing
x = zeros(100,10);          % Initialize the main variable
parfor i = 1:100            % Parallel loop
   y = zeros(1,10);       % Initialize the secondary variable
   for j = 1:10           % Inner loop
       y(j) = i;
   end
   y                      % Display the inner variable (note the random execution about "i" in the command window)
   x(i,:) = y;            % Get values from loop into the main variable
end

How could i just start writing my code lines in this format. Bcz of terms like E1(i+1,j)-E1(i,j) , how would i just do the columnwise operations for the parfor ? .

Answer 1

[Edric Ellis]

You might need to extract the columns of E1 etc. before working on them. For example

    parfor colIdx = 1:numColumns
      E1Column = E1(:, colIdx);
      resultColumn = zeros(numRows, 1);
      for rowIdx = 2:numRows-1
          resultColumn(rowIdx) = E1Column(rowIdx+1) + E1Column(rowIdx);
      end
      result(:, colIdx) = resultColumn;
    end