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flt

Fast Legendre transform for NumPy and JAX

This is a minimal Python package for fast discrete Legendre transforms (DLTs). The implementation uses a recursive version of the matrix relations by Alpert & Rokhlin (1991) to compute the DLT via a discrete cosine transform (DCT).

The package can be installed using pip:

pip install flt

For more information, please see the documentation.

Current functionality covers the absolutely minimal use case. Please open an issue on GitHub if you would like to see anything added.

Array backends

The flt package supports generic array backends via single dispatch. Currently available implementations are:

  • NumPy (+SciPy)
  • JAX

Other implementations are easily added, even from third-party code, and will be picked up by the flt methods automatically.

Example

The main functionality of the flt module in contained in the pair flt.dlt and flt.idlt of discrete Legendre transforms:

>>> import jax
>>> import flt
>>> key = jax.random.key(42)
>>> x = jax.random.uniform(key, shape=(100,))
>>> a = flt.dlt(x)
>>> y = flt.idlt(a)
>>> jax.numpy.allclose(x, y)
Array(True, dtype=bool)