A Fast Walsh–Hadamard Transform (FWHT) implementation in PyTorch.
Install this library using pip:
pip install hadamard-transform
For the Basic normalized fast Walsh–Hadamard transform, use:
import torch
from hadamard_transform import hadamard_transform
x = torch.rand(2 ** 10, dtype=torch.float64)
y = hadamard_transform(x)
assert torch.allclose(
hadamard_transform(y),
x
)Since the transform is not numerically-stable, it is recommended to use float64 when possible.
The input is either a vector or a batch of vectors where the first dimension is the batch dimension. Each vector's length is expected to be a power of 2!
This package also includes a pad_to_power_of_2 util, which appends zeros up to the next power of 2 if needed.
In some common cases, we use the randomized Hadamard transform, which randomly flips the axes:
import torch
from hadamard_transform import randomized_hadamard_transform, inverse_randomized_hadamard_transform
prng = torch.Generator(device='cpu')
x = torch.rand(2 ** 10, dtype=torch.float64)
seed = prng.seed()
y = randomized_hadamard_transform(x, prng),
assert torch.allclose(
inverse_randomized_hadamard_transform(y, prng.manual_seed(seed)),
x)This package also includes hadamard_transform_, randomized_hadamard_transform_, and inverse_randomized_hadamard_transform_. These are in-place implementations of the previous methods. They can be useful when approaching memory limits.
To contribute to this library, first checkout the code. Then create a new virtual environment:
cd hadamard-transform
python -m venv venv
source venv/bin/activate
Now install the dependencies and test dependencies:
pip install -e ".[test]"
To run the tests:
pytest