Coding Unit test

[edouardoyallon]

Hi,

I did a series of unit test, however (it's not upload yet coz it's on tamaris) some of them should be deeper and more complicated to ensure with have the same behaviour as with MATLAB.

[lostanlen]

Some interesting unit tests are:

• constant signal : ||S0|| should be exactly ||x||, ||S1|| and ||S2|| should be exactly zero.
• horizontal sine wave of period 2^j : ||S0|| should be exactly zero, ||S1|| should be exactly ||x||, ||S2|| should be exactly zero.
• same for vertical sine wave of period 2^j.
• The Morlet wavelet have the desired bandwidth, according to the specified cutoff, default is 3dB.
• The number of wavelets per octave is greater than the quality factor, whatever be the cutoff.
• Littlewood-Paley sum of all filterbanks is stricly below 1.

Tests of approximate equality:

• wavelets are approximately analytic : with the exception of the highest center frequency wavelet, the max amplitude at negative frequencies is below epsilon=1e-3.
• any oriented sine wave of sufficiently high period : ||S0|| should be approximately zero, ||S1|| should be approximately ||x||, ||S2|| should be approximately zero.
• Zero-padding: the scattering transform of a Dirac in the top left pixel should yield almost zero energy in the bottom right pixel.
• Point processes and random textures : S1 should be covariant with rotation for angles /theta = 2\pi * k/nOrientations, near the center of the picture.

[edouardoyallon]

I totally agree with everything you propose. I transferred the code from Tamaris I had(unit_test.lua..). Well, I begin by the low level(complex, FFT, padding..), I'll try to go in higher level when I'll be sure of the low-level ones! I'd like to do one complicated test per function we coded that does work in Lua, such that if one day one of us decide to go deeply into CUDA, it'll be simple. I guess Laurent might have many cool insights on the way to proceed! Any helps are welcome!

[edouardoyallon]

I've done something slightly different from scatnet for the padding: first, I constantly verified that pad > unpad was giving the same, this was not correctly done in both version of scatnet in 2d at least. secondly, I've ensured that the padding will have to be 2*ds and not ds. Thus, in critic sampling, it will mean that for instance 1 1 2 2 3 3 4 4 under a sampling of 2^1 will be padded such that 1 1 1 1 2 2 3 3 4 4 4 4 and the operation downsampling+padding will return 1 2 3 4 instead of 1 1 2 3. I think it worth it.(even only for symetry reasons)

[lostanlen]

You don't need to pad and unpad between layers.

[edouardoyallon]

Padding/unpadding of U has been fixed. There is a slight speed improvement with large tensors. Still working on more units tests.