Make a function that recieves an N-D vector and returns its pseudo-random gradient.

[felix91gr]

• Input: N-D vector
• Output: N-D unitary, pseudorandom vector

To-Do:

• Implement function
• Add test for length (n) and size (unitary) of output vector
• Add test for expected value of output vector (0ⁿ)
• Add tests to check that the output is deterministic.

[felix91gr]

This is implemented. I must now add some sanity tests to check that it gives:

• Unitary N-D vectors (API contract)
• An expected value of 0^N (no directional bias)

[felix91gr]

All tests have been added.

All I have left to do for this issue is to make the "Unitary Gradients" test more precise. Currently I'm comparing the length of the vectors to 0 with a fixed tolerance of 0.01. This is to cover for floating-point precision errors. But there are better ways. I want to be using ulp (units of least precision), which are the standard for covering up for floating point precision errors. After adding that to that test, this issue should be more or less complete.

[felix91gr]

Update on this:

• I have a version of the unitary-gradients-test that uses native float comparison tools ✅
• The statistical test had a typo and after fixing it, it fails. That's because I modelled it wrongly. I have a draft of what it should do instead, and after applying that it should be a really good test.
• I realized there's one more property left to test, and it's the fact that the gradients are deterministic. If you call f(x) twice, the output should be the same. I have to test this holds for (a) single threaded programs and (b) multithreaded ones.

After I finish this semester I will complete this issue once and for all :3

[felix91gr]

The statistical test has proved harder than I can provide atm. I'm gonna disable it for now, and upload the other tests as they are. I'll solve it later.