Error when using distributive property

Hello!

The function below compares the output of two functions which run the same calculation. However, in one function the calculation's multiplications are distributed. It should output a matrix of 1s. However, it doesn't!

What's up with that?

function errorTest()

      compute(1:100) == distributed(1:100)

      function out = compute(a)
          out = 10.1 * (a - 1);
      end

      function out = distributed(a)
          out = 10.1 * a - 10.1;
      end
  end

Thanks!

Answer 1

[Oleg Komarov]

The propagation of floating approximations is different:

idx = abs(compute(1:100) - distributed(1:100)) > 2*eps
nnz(idx)

How many values over 2eps?

[D G]

function out = errorTest()

out = zeros(100, 2);

out(:, 1) = (compute(1:100) == distributed(1:100));

out(:, 2) = ((compute(1:100) - distributed(1:100)) > (2 * eps));

function out = compute(a)

out = 10.1 .* (a - 1);

end

function out = distributed(a)

out = 10.1 .* a - 10.1;

end

end

There is the updated code. It produces quite a few values over 2eps. There are even some over 500eps.

[Oleg Komarov]

Well, 500*eps = 1.11022302462516e-013; if you need precision to that point then it becomes an issue.

[D G]

I guess I had that backwards. If you remove the 2*, a lot of the answers are still different.

[Oleg Komarov]

Cannot really help you more than that, I don't have experience with distributed server.