Parfor and symmetric matrix

Hi,

I need to fill in a matrix. Since it is symmetrical, the two for loops look like this

for i = 1 : m
    for j = i : n
    operation on the matrix ....
    end
end
    

The other elements of the matrix are filled in by using "permute" (it is a 3D matrix).

I am now modifying the code to make it parallelizable. I tried with the parfor like this

parfor i = 1 : m
    for j = i : n
    operation on the matrix ....
    end
end
    

At running time, I get the error because matlab does not know the value of "i". I guess this is because the two "for" are not independent.

My question is:

• is there a way to fill in a symmetric matrix by exploiting the symmetry, and using the parfor? Or shall I ignore the symmetry, have the second "for" starting from 1, and getting rid of "permute" ?

Answer 1

[Matt J]

[I,J]=ndgrid(1:m,1:n);

keep=J>=I;
I=I(keep);
J=J(keep);

parfor k=1:numel(I)

    i=I(k);
    j=J(k);
    
    operation on the matrix ....
    
end

[Maria]

This is a very elegant way I would have never thought about... Thanks!

[Maria]

mmm...I just tried the code with a generic matrix, and the parfor still does not work, see code below:

m = 3;
n = 3;
[I,J]=ndgrid(1:m,1:n);
keep=J>=I;
I=I(keep);
J=J(keep);
 
H = rand(2,2);
parfor k=1:numel(I)
    i=I(k);
    j=J(k);
    
    H(i,j) = 3;
end

[Matt J]

Here's one possible fix.

temp = zeros(m,n);
H=0;
parfor k=1:numel(I)
    dH=temp;
    i=I(k);
    j=J(k);
    
    dH(i,j) = 3;
    H=H+dH;
end

[Matt J]

Another possible fix (probably better):

temp = zeros(size(I));
H=0;
parfor k=1:numel(I)
    temp(k)=3;
end

idx=sub2ind([m,n],I,J);
H(idx)=temp(:);