Improving speed in construction of a matrix

Hi.

Im currently implementing a code, where part of the code constructs a matrix several million times. Currently, the construction of this matrix takes much more time, than the actual computing invovled with the matrix. Its a rather simple matrix, but takes a third of the total runtime. I want to construct it faster, but cant seem to bring the time down. Ive tried two approaches.

One implementation:

B = zeros(9,9);
B(1:3,1) = A(1,:);
B(4:6,2) = A(1,:);
B(7:9,3) = A(1,:);
B(1:3,4) = A(2,:);
B(4:6,5) = A(2,:);
B(7:9,6) = A(2,:);
B(1:3,7) = A(3,:);
B(4:6,8) = A(3,:);
B(7:9,9) = A(3,:);

And the other implementation:

Z = zeros(3,1);
B =[A(:,1) Z Z A(:,2) Z Z A(:,3) Z Z
    Z A(:,1) Z Z A(:,2) Z Z A(:,3) Z
    Z Z A(:,1) Z Z A(:,2) Z Z A(:,3)];

Both giving a inaduqate execution time. Is there a faster way to construct this type of matrix?

[Torsten]

How long is "inadequate" ?

A = rand(3,3);
B = zeros(9,9);
Z = zeros(3,1);
tic
for i = 1:100000
B(1:3,1) = A(1,:);
B(4:6,2) = A(1,:);
B(7:9,3) = A(1,:);
B(1:3,4) = A(2,:);
B(4:6,5) = A(2,:);
B(7:9,6) = A(2,:);
B(1:3,7) = A(3,:);
B(4:6,8) = A(3,:);
B(7:9,9) = A(3,:);
end
toc

Elapsed time is 0.979855 seconds.

tic
for i = 1:100000
    B =[A(:,1) Z Z A(:,2) Z Z A(:,3) Z Z
    Z A(:,1) Z Z A(:,2) Z Z A(:,3) Z
    Z Z A(:,1) Z Z A(:,2) Z Z A(:,3)];
end
toc

Elapsed time is 0.620697 seconds.

[Walter Roberson]

Z = zeros(3,1);
A1 = A(:,1); A2 = A(:,2); A3 = A(:,3);
B =[A1 Z Z A2 Z Z A3 Z Z
    Z A1 Z Z A2 Z Z A3 Z
    Z Z A1 Z Z A2 Z Z A3];

[Matt J]

Your two implementations give different results:

A=reshape(1:9,3,3)

A = 3×3

1 4 7 2 5 8 3 6 9

B = zeros(9,9);
B(1:3,1) = A(1,:);
B(4:6,2) = A(1,:);
B(7:9,3) = A(1,:);
B(1:3,4) = A(2,:);
B(4:6,5) = A(2,:);
B(7:9,6) = A(2,:);
B(1:3,7) = A(3,:);
B(4:6,8) = A(3,:);
B(7:9,9) = A(3,:)

B = 9×9

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9

Z = zeros(3,1);
B =[A(:,1) Z Z A(:,2) Z Z A(:,3) Z Z
    Z A(:,1) Z Z A(:,2) Z Z A(:,3) Z
    Z Z A(:,1) Z Z A(:,2) Z Z A(:,3)]

B = 9×9

1 0 0 4 0 0 7 0 0 2 0 0 5 0 0 8 0 0 3 0 0 6 0 0 9 0 0 0 1 0 0 4 0 0 7 0 0 2 0 0 5 0 0 8 0 0 3 0 0 6 0 0 9 0 0 0 1 0 0 4 0 0 7 0 0 2 0 0 5 0 0 8 0 0 3 0 0 6 0 0 9

[cTroels]

The function is called 1-10 million times, dependent on the problem, taking 40 seconds of 120 seconds total runtime.

[Matt J]

I think it unlikely you are going to be able to reliably optimize such an infinitessimal task in MCode. Different computers will give you different relative performance. You need to try to reorganize your computation in large vectorized batches.

[cTroels]

I was able to bring the execution time of the function down to 4s by just writing out the whole matrix explicitly. Should have done that initially i guess. But thanks for the suggestions! Appreciate the inputs.

Answer 1

[Benjamin Thompson]

Not sure where your data for A is coming from, or where the output of B is going to. if each A -> B mapping is independent try parfor if you have a multicore processor or using a gpuArray.