Run parfor loop inside a function

I am trying to parallelize my code (function dfdx presented below), but a warning message : ( The entire array or structure 'th','x' is a broadcast variable this might result in unnecessary communication overhead) appears under th(9) and x(5,i), I am confusing Why does it only under th(9) in df7dx7 and under x(5,i) in df8dx8.

the question : what is the origine of this warning, and how can I handle it.

function [Fx]=dfdx(x,th,gama,T0,a,StateDim,nCpts,dt)

Fx = zeros(StateDim,StateDim,nCpts);

   parfor i=1:nCpts

    df7dx7 = -x(7,i)^(1/a - 1)/(a*(th(9) + T0));
    df8dx1 = (gama*(1/(exp(th(5)*(th(6) - x(1,i))) + 1) - 2))/(T0*(1/(exp(th(5)*(th(6) - 1)) + 1) - 2)*(gama + 1)) + (th(5)*gama*x(1,i)*exp(th(5)*(th(6) - x(1,i))))/(T0*(1/(exp(th(5)*(th(6) - 1)) + 1) - 2)*(exp(th(5)*(th(6) - x(1,i))) + 1)^2*(gama + 1));
    df8dx5 = -(th(9)*x(8,i))/(T0*x(7,i)*(th(9) + T0)); 
    df8dx7 = (x(8,i)*(th(9)*x(5,i) + T0*x(7,i)^(1/a)))/(T0*x(7,i)^2*(th(9) + T0)) - (x(7,i)^(1/a - 1)*x(8,i))/(a*x(7,i)*(th(9) + T0));
    df8dx8 = -(th(9)*x(5,i) + T0*x(7,i)^(1/a))/(T0*x(7,i)*(th(9) + T0));

Fxi = [0 1 0 0 0 0 0 0;
           -th(2)^2 -2*th(2) 0 0 0 0 0 0;
           0 0 0 1 0 0 0 0;
           0 0 -th(4)^2 -2*th(4) 0 0 0 0;
           0 0 0 0 0 1 0 0;
           0 0 0 0 -th(8)^2 -2*th(8) 0 0;
           0 0 0 0 1/(th(9)+T0) 0 df7dx7 0;
           df8dx1 0 1/(T0*(gama+1)) 0 df8dx5 0 df8dx7 df8dx8];

       Fx(:,:,i) = eye(StateDim,StateDim) + dt*Fxi;
  end

Answer 1

[OCDER]

The warning is just stating that the vector variables (th and x) will be copied to every worker for every iteration of the for loop. This could cause a lot of read/write delays, but is sometimes unavoidable like in your case. The editor doesn't know that x and th are actually small and easy to copy around, so it'll just throw a warning instead. To hide the warning, use temporary variables.

https://www.mathworks.com/help/distcomp/broadcast-variable.html

About why only certain th and x get the warning in the editor, the editor doesn't seem to mark all warnings at once - just the (first?) ones that it knows of.

Try this out:

function [Fx]=dfdx(x,th,gama,T0,a,StateDim,nCpts,dt)
Fx = zeros(StateDim,StateDim,nCpts);
parfor i=1:nCpts
    TH = th; %Tells matlab that th is a real broadcast variable.
    X = x; %Tells matlab that x is a real broadcast variable.

      df7dx7 = -X(7,i)^(1/a - 1)/(a*(TH(9) + T0));
      df8dx1 = (gama*(1/(exp(TH(5)*(TH(6) - X(1,i))) + 1) - 2))/(T0*(1/(exp(TH(5)*(TH(6) - 1)) + 1) - 2)*(gama + 1)) + (TH(5)*gama*X(1,i)*exp(TH(5)*(TH(6) - X(1,i))))/(T0*(1/(exp(TH(5)*(TH(6) - 1)) + 1) - 2)*(exp(TH(5)*(TH(6) - X(1,i))) + 1)^2*(gama + 1));
      df8dx5 = -(TH(9)*X(8,i))/(T0*X(7,i)*(TH(9) + T0)); 
      df8dx7 = (X(8,i)*(TH(9)*X(5,i) + T0*X(7,i)^(1/a)))/(T0*X(7,i)^2*(TH(9) + T0)) - (X(7,i)^(1/a - 1)*X(8,i))/(a*X(7,i)*(TH(9) + T0));
      df8dx8 = -(TH(9)*X(5,i) + T0*X(7,i)^(1/a))/(T0*X(7,i)*(TH(9) + T0));

      Fxi = [0 1 0 0 0 0 0 0;
             -TH(2)^2 -2*TH(2) 0 0 0 0 0 0;
             0 0 0 1 0 0 0 0;
             0 0 -TH(4)^2 -2*TH(4) 0 0 0 0;
             0 0 0 0 0 1 0 0;
             0 0 0 0 -TH(8)^2 -2*TH(8) 0 0;
             0 0 0 0 1/(TH(9)+T0) 0 df7dx7 0;
             df8dx1 0 1/(T0*(gama+1)) 0 df8dx5 0 df8dx7 df8dx8];
     Fx(:,:,i) = eye(StateDim,StateDim) + dt*Fxi;
  end