Question about assigning value in a matrix.

Hi, all, again, I want to do the work quickly: I have a large matrix A, and I want to assign value in some entry in each row.

For example:
A=zeros(4);
a=[1,2;
 2,3;
 3,2;
 4,1];

I want (1,2), (2,3),(3,2), (4,1) of matrix A be 1. How shall I make it work in no more than 3 commands?

What I am doing now is using loops:

for i=1:4
A(a(i,1),a(i,2)=1;
end

However, as i is very large like 3^14, the program is very slow. So I wonder is there a way to speed the programming?

Thanks.

Answer 1

[Walter Roberson]

idx = sub2ind(size(A), [1 2 3 4], [2 3 2 1]);
A(idx) = 1;

[C Zeng]

Thanks, Walter! So sub2ind can find the index of A quickly by loops, right? I will definitely try this code. I like it!

[Sean de Wolski]

I've always found for-loops to be significantly faster than sub2ind and ind2sub. Especially as the number of indices gets large.

It's been a few years since I was timing it for my own work though...

[C Zeng]

Oh, really? I always found that MATLAB is not efficient for large loops. That is why I tried to avoid large loops.

Answer 2

[Azzi Abdelmalek]

A=zeros(4);
a=[1,2;
2,3;
3,2;
4,1];
idx= sub2ind(size(A),a(:,1),a(:,2));
A(idx)=1

[C Zeng]

Yes, Azzi! Thanks.

Answer 3

[Sean de Wolski]

I've always found for-loops to be significantly faster than sub2ind and ind2sub. Especially as the number of indices gets large.

It's been a few years since I was timing it for my own work though...

[C Zeng]

Sean, let me do a simple experiment and let u know.

[Azzi Abdelmalek]

The for loop, in this case, is almost twice faster

[Sean de Wolski]

function testFORIND2SUB

n = 1000;
idx = ceil(rand(n,2)*n); %two dimensions
[t1,t2] = deal(0);

for ii = 1:100
    A = magic(n);
    tic
        for jj = 1:n
            A(idx(jj,1),idx(jj,2)) = 0;
        end
    t1=t1+toc;
    A = magic(n);

      %With SUB2IND
      tic
      idxLinear = sub2ind([n n],idx(:,1),idx(:,2));
      A(idxLinear) = 0;    
      t2 = t2+toc;
  end
  t2./t1

So for 1000x2 I'm seeing a 60% speed up.

[Sean de Wolski]

Now this might be somewhere that MEXing this with MATLAB Coder could buy you even more speedup. I'll try that tomorrow.

[C Zeng]

Oh, I see. Yes, you may be right. Interested in more speedup!

[Sean de Wolski]

For longer idx I am seeing the sub2ind approach be faster.

[C Zeng]

Sean, yes, my test result also shows it. For 3^10 rows (I assume it is large): Using for loops takes ~565 seconds while sub2ind procedure takes ~446 seconds.

Do you think if there is room for improvement? Ideally I hope it can compute for 3^14.

[Sean de Wolski]

How many times do you have to do this? I ran it yesterday with 3^14 and it took circa 25 seconds.

[C Zeng]

2 times each, Sean. My problem is complex, M is a matrix with 3^10 rows, and around 400 columns. Here is the sample code:

for i=1:M1
    pr=(rR(i:i+M-1)-1)/10; %pr is the vector of probabilities
    prMatrix=zeros(M2);
    for j=1:M2
        prMatrix(j,j)=pr(j);
    end
    x=Y*prMatrix; % x is sample yield for each polnicy
    x=round(x);  % only consider yield as integer
    % matrix computation(faster!)
    %
    TotalCollect=sum(x,2); % total collection for each policy
    TotalCollect=TotalCollect+1;
    TempMatrix=zeros(3^M2, n);
    %{
    for j=1:3^M2 %---slow!
        TempMatrix(j,TotalCollect(j))=1;
    end
    %}

      %use sub2ind procedure
      row=(1:1:3^M2)';
      idx=sub2ind(size(TempMatrix),row,TotalCollect);
      TempMatrix(idx)=1;
      %}
      Pr=Pr+TempMatrix;

end

[Sean de Wolski]

Well a few things real quick:

prMatrix = diag(pr);

Skips the first for-loop and call to zeros()

Second, you migh twant to consider taking the outer for-loop and converting it to a parfor with the Parallel Computing Toolbox. This would allow this to work in Parallel, over a few workers and speed things up that way.

Alternatively, just run it over the weekend or overnight, at two times total and 556 seconds, that's still only 20 minutes...

[C Zeng]

Thanks, Sean!

Let me try it again. I have to run large data on server, because 3^12 is memory out here.

[C Zeng]

Sean, thanks for your advice. My program got speedup. sub2ind will be faster if the size is large.