Parfor sliced variable error

Dear Matlab,

I have an issue with sliced variable declaration in Matlab.

The below code works perfectly fine

Block - 1
x=zeros(2,2,10);

 for i = 1:10

    x(:,:,i)= [i,3*i;5*i,7*i];

 end

 parfor i = 1:10

    x(:,:,i)= [i,2*i;4*i,6*i];

 end
 disp(x)

In my main code, original for loop implementation works as expected

 Block - 2
 %Pre initialising par for loop variables

 modes_points=zeros(max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

 %convert mat 2 cell
 modes_points = mat2cell(modes_points,max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

 for k = 1: n

    %Pre initialising par for loop variables
    mode=zeros(max_iter,length(data_sort(1,:)));

    if(k*Range <= length(data_sort(1,:)))

        %performing first iteration

        mode = FindMode(data_sort,1+(k-1)*Range,R,max_iter);

        modes_points(: ,:,1+(k-1)*Range) = zeros([size(mode)]);

However, if I implement the above with parfor loop, I get an error.

 Block-3
 %Pre initialising par for loop variables

 modes_points=zeros(max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

 %convert mat 2 cell
 modes_points = mat2cell(modes_points,max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

 parfor k = 1: n

    %Pre initialising par for loop variables
    mode=zeros(max_iter,length(data_sort(1,:)));

    if(k*Range <= length(data_sort(1,:)))

        %performing first iteration

        mode = FindMode(data_sort,1+(k-1)*Range,R,max_iter);

        modes_points(: ,:,1+(k-1)*Range) = zeros([size(mode)]);

Output of check code:

L 111 (C 1-6): The PARFOR loop cannot run due to the way variable 'modes_points' is used.

L 125 (C 9-20): Valid indices for 'modes_points' are restricted in PARFOR loops.

But, this code in parfor works

 Block-4
 %Pre initialising par for loop variables

 modes_points=zeros(max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

 %convert mat 2 cell
 modes_points = mat2cell(modes_points,max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

 parfor k = 1: n

    %Pre initialising par for loop variables
    mode=zeros(max_iter,length(data_sort(1,:)));

    if(k*Range <= length(data_sort(1,:)))

        %performing first iteration

        mode = FindMode(data_sort,1+(k-1)*Range,R,max_iter);
        modes_points = cat(3,modes_points,mode);

Runtime performance of block-2(for loop) & block-4(parfor loop with cat) is same.

Please clarify why Block-3 is causing parfor error, although it is similar to Block-1 in terms of sliced variables.

Answer 1

[Walter Roberson]

In Block 4, MATLAB can tell that modes_points is a reduction variable and handles that specially.

In Block 3, with

   parfor k = 1: n

     modes_points(: ,:,1+(k-1)*Range) = zeros([size(mode)]);

then MATLAB might not be able to prove that 1+(k-1)*Range will definitely be unique or contained within

   modes_points=zeros(max_iter,length(data_sort(1,:)),length(data_sort(:,1)));

I would suggest,

 modes_points = zeros(max_iter, length(data_sort(1,:)), Range, n);

and in the loop,

       modes_points(: ,:, 1, k) = zeros([size(mode)]);

as it is clear that 1+(k-1)*Range is emulating a Range by n matrix.

[Shawn Fernandes]

Dear Walter Roberson,

The variable 'Range' is a constant, and equals length(data)/n.

In the expression 1+(k-1)*Range, only k=1,2, 3,4....n changes for the parfor loops, remaining all values remain constant.

Variable mode is a 2d matrix. mode_points is a 3D matrix. mode_points is an array of mode, which are 2D matrices.