Construct an nn.Module based on Butterfly that exactly performs the 2D FFT. Parameters: n1: size of the FFT on the last input dimension.

Compute Fisher information matrix numerically, using per-sample gradient

Parameters: input: (..., size) if real or (..., size, 2) if complex Return: output: (..., size) if real or (.

Parameters: input: (batch, c, h, w) if real or (batch, c, h, w, 2) if complex Return: output: (batch, nstack

Parameters: input: (batch, *, in_size) Return: output: (batch, *, out_size)

Generate (a batch of) permutations for training

returns the original stream e.g. sys.stdout

Matrix corresponding to the discrete Hartley transform. https://en.wikipedia.org/wiki/Discrete_Hartley_transform

https://en.wikipedia.org/wiki/Hilbert_matrix

Construct an nn.Module based on Butterfly that exactly performs the 2D iFFT. Parameters: n1: size of the iFFT on the last input dimension

Check that each of the 4 blocks of a matrix is diagonal (in other words, that the matrix is a butterfly factor). Assumes that the matrix is sq

Checks whether "mat" is in B_k.

Naive multiplication P^T v where P is the matrix of coefficients of Legendre polynomials. Parameters: v: (batch_size, n) Return:

Converts permutation matrix to its enumeration (list) form. Args: matperm: (..., n, n) Returns: listperm: (..., n) - listperm[t,i] i

Returns the sequence of permutations to transform permutation vector v into a modular-balanced matrix, as well as the resultant modular-b

Returns a sequence of butterfly factors that, when multiplied together, create L. Assumptions: L is a modular-balanced permutation matrix. Dir

Convert config to one compatible with Ray Tune. Entry as list whose first element is "_grid" is converted to ray.tune.grid_search. "_sample" i

Converts a batch of permutations to its matricial form. Args: listperm: 2D tensor of permutations of shape [batch_size, n_objects] so that

Converts a batch of permutations to its enumeration (list) form. Args: matperm: a 3D tensor of permutations of shape = [batch_size, n_o

Samples arbitrary-shaped standard gumbel variables. Args: shape: list of integers eps: float, for numerical stability Returns: A

Performs incomplete Sinkhorn normalization to log_alpha. By a theorem by Sinkhorn and Knopp [1], a sufficiently well-behaved matrix with pos

Decompose the permutations v to get the right/right twiddle factor, and new permutations that only permute elements that are size//2 indices

Parameter: v: a permutation, stored as a vector, in left-multiplication format. (i.e., applying v to a vector x is equivalent

Convert a permutation matrix to a permutation vector. Parameters: p: a matrix storing the permutation. left: whether it's in left-

Project a vector v onto the simplex. That is, return argmin_w ||w - v||^2 where w >= 0 elementwise and sum(w) = z. Parameters: v: Tens

Initialize bias the same way as torch.nn.Linear.