fastprox

Exact proximal operators and projections with derivatives. A C++17 core behind a plain-C API, with Python bindings.

• Exact. Direct algorithms (Condat's 1D TV and simplex projection, the taut string, pool-adjacent-violators) instead of iterative solvers.
• Differentiable. Jacobian-vector and vector-Jacobian products in the input, the step and the operator's parameters, for bilevel learning and implicit differentiation.
• Batched. Applied along any axis of a float32 or float64 array, with rows processed in parallel by OpenMP and results bit-identical for any number of threads.
• Permissive. MIT licensed; every kernel is written from the papers.

Install

pip install --pre fastprox     # 0.1.0rc1, a release candidate

Wheels are abi3 for CPython 3.12 and later on Linux (x86_64, aarch64), macOS (arm64 from 14.0, x86_64 from 15.0) and Windows (amd64), with the OpenMP runtime bundled.

Use

import numpy as np
import fastprox as fp

x = np.random.default_rng(0).normal(size=(64, 1000))

z = fp.tv1d(x, gamma=0.5)                 # 1D total variation along the last axis
p = fp.project_simplex(x, radius=1.0)     # each row onto the simplex
s = fp.soft_threshold(x, lam=0.1)

# Operators with derivatives
op = fp.TV1D(weights=0.8)
z, ctx = op.prox(x, 0.5, keep=True)
dz = op.jvp(ctx, dx=np.ones_like(x))      # Jacobian-vector product
gx, grads = op.vjp(ctx, g=x)              # vector-Jacobian product
print(grads.gamma, grads.weights)         # gradients in the step and the weights

Operators (0.1)

Soft thresholding (weighted), elastic net, Huber, group ℓ2, box, nonnegative orthant, ℓ2 ball, simplex, weighted ℓ1 ball, ℓ∞ norm, isotonic regression, and 1D total variation with per-edge weights. Each one has a conjugate prox through the Moreau identity.

Documentation

• API reference (C and Python)
• Benchmarks against proxTV and Condat's C code
• Design specification
• Roadmap and changelog

C library

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build && cmake --install build --prefix /usr/local

Then find_package(fastprox) and link fastprox::fastprox, or use pkg-config --cflags --libs fastprox. The header is include/fastprox.h.

License

MIT