JAX bindings to FINUFFT

This package provides a JAX interface to the Flatiron Institute Non-uniform Fast Fourier Transform (FINUFFT) library. Take a look at the FINUFFT docs for all the necessary definitions, conventions, and more information about the algorithms and their implementation. This package uses a low-level interface to directly expose the FINUFFT library to JAX's XLA backend, as well as implementing differentiation rules for the transforms.

Included features

This library includes CPU and GPU (CUDA) support. GPU support is implemented through the cuFINUFFT interface of the FINUFFT library.

Type 1, 2, and 3 transforms are supported in 1, 2, and 3 dimensions on the CPU and GPU. All of these functions support forward, reverse, and higher-order differentiation, as well as batching using vmap.

The FINUFFT plan interface is not directly exposed, although within a given jax-finufft call, plans are reused where possible, and transforms sharing the same non-uniform points are stacked/vectorized. All of the tuning options one can set in the plan interface are available through the opts argument of the jax-finufft API (see Advanced Usage).

Installation

The easiest way to install jax-finufft is from a pre-compiled binary on PyPI or conda-forge. Only CPU binaries currently are available on PyPI, while conda-forge has both CPU and GPU binaries. If you want GPU support without using conda, you can install jax-finufft from source as detailed below. This is also useful when you want to build finufft optimized for your hardware.

Install binary from PyPI

To install a binary wheel from PyPI using uv, run the following command in a venv:

uv pip install jax-finufft

To install with pip instead of uv, simply drop uv from that command.

Install binary from conda-forge

To install a CPU build using mamba (or conda), run:

mamba install -c conda-forge jax-finufft

To install a GPU-enabled build, run:

mamba install -c conda-forge 'jax-finufft=*=cuda*'

Make note of the installed package version, like conda-forge/linux-64::jax-finufft-1.1.0-cuda129py312h8ad7275_1. The cuda129 substring indicates the package was built for CUDA 12.9. Your NVIDIA driver will need to support this version of CUDA. Only one CUDA build per major CUDA version is provided at present.

Install from source

Dependencies

Unsurprisingly, a key dependency is JAX, which can be installed following the directions in the JAX documentation. If you're going to want to run on a GPU, make sure that you install the appropriate JAX build.

The non-Python dependencies that you'll need are:

• FFTW,
• OpenMP (for CPU, optional),
• CUDA (for GPU, optional. We build against CUDA 12 and 13; 11.8 may work, too.)

Below we provide some example workflows for installing the required dependencies:

mamba create -n jax-finufft -c conda-forge python jax fftw cxx-compiler
mamba activate jax-finufft

mamba create -n gpu-jax-finufft -c conda-forge python fftw cxx-compiler jax 'jaxlib=*=*cuda*'
mamba activate gpu-jax-finufft
mamba install cuda libcufft-static -c nvidia
export CMAKE_PREFIX_PATH=$CONDA_PREFIX:$CMAKE_PREFIX_PATH

ml modules/2.4 \
   gcc \
   python \
   uv \
   fftw \
   cuda/12.8 \
   cudnn/9

export CMAKE_ARGS="$CMAKE_ARGS -DCMAKE_CUDA_ARCHITECTURES=80;90;120 -DJAX_FINUFFT_USE_CUDA=ON"

Other ways of installing JAX are given on the JAX website; the "local CUDA" install methods are preferred for jax-finufft as this ensures the CUDA extensions are compiled with the same Toolkit version as the CUDA runtime. However, in theory, this is not required as long as both JAX and jax-finufft use CUDA with the same major version.

Note that jax is both a build-time and run-time dependency of jax-finufft. If the build-time version of jax is different from the run-time version, you may encounter issues. Most users will not need to worry about this, but if you do, consider installing jax-finufft without build isolation to enforce consistency.

Notes on CUDA versions

While jax-finufft may build with a wide range of CUDA versions, the resulting binaries may not be compatible with JAX (resulting in odd runtime errors, like failed cuDNN or cuBLAS initialization). For the greatest chance of success, we recommend building with the same version as JAX was built with. To discover that, one can look at the requirements in JAX's build directory (be sure to select the git tag for your version of JAX). Similarly, when installing from PyPI, we encourage using jax[cuda12-local] or ``jax[cuda13-local]` so JAX and jax-finufft use the same CUDA libraries. jax-finufft has optional dependencies of the same name for convenience.

Depending on how challenging the installation is, users might want to run jax-finufft in a container. The .devcontainer directory is a good starting point for this.

Configuring the build

There are several important CMake variables that control aspects of the jax-finufft and (cu)finufft builds. These include:

• JAX_FINUFFT_USE_CUDA [disabled by default]: build with GPU support
• CMAKE_CUDA_ARCHITECTURES [default native]: the target GPU architecture. native means the GPU arch of the build system.
• FINUFFT_ARCH_FLAGS [default -march=native]: the target CPU architecture. The default is the native CPU arch of the build system.

Each of these can be set as -Ccmake.define.NAME=VALUE arguments to pip install or uv pip install. For example, to build with GPU support from the repo root, run:

uv pip install -Ccmake.define.JAX_FINUFFT_USE_CUDA=ON .

Use multiple -C arguments to set multiple variables. The -C argument will work with any of the source installation methods (e.g. PyPI source dist, GitHub, pip install, uv pip install, uv sync, etc).

Build options can also be set with the CMAKE_ARGS environment variable. For example:

export CMAKE_ARGS="$CMAKE_ARGS -DJAX_FINUFFT_USE_CUDA=ON"

GPU build configuration

Building with GPU support requires passing JAX_FINUFFT_USE_CUDA=ON to CMake. See Configuring the build.

By default, jax-finufft will build for the GPU of the build machine. If you need to target a different compute capability, such as 8.0 for Ampere, set CMAKE_CUDA_ARCHITECTURES as a CMake define:

uv pip install -Ccmake.define.JAX_FINUFFT_USE_CUDA=ON -Ccmake.define.CMAKE_CUDA_ARCHITECTURES=80 .

CMAKE_CUDA_ARCHITECTURES also takes a semicolon-separated list.

To detect the arch for a specific GPU, one can run:

$ nvidia-smi --query-gpu=compute_cap --format=csv,noheader
8.0

The values are also listed on the NVIDIA website.

In some cases, you may also need the following at runtime:

export LD_LIBRARY_PATH="$CUDA_HOME/extras/CUPTI/lib64:$LD_LIBRARY_PATH"

If CUDA_HOME isn't set, you'll need to replace it with the path to your CUDA installation in the above line, often something like /usr/local/cuda.

Install source from PyPI

The source code for all released versions of jax-finufft are available on PyPI, and this can be installed using:

uv pip install jax-finufft --no-binary jax-finufft

Install source from GitHub

Alternatively, you can check out the source repository from GitHub:

git clone --recurse-submodules https://github.com/flatironinstitute/jax-finufft
cd jax-finufft

After cloning the repository, you can install the local copy using the uv "project interface":

uv sync

or using the pip interface:

uv pip install -e .

where the -e flag optionally runs an "editable" install.

As yet another alternative, the latest development version from GitHub can be installed directly (i.e. without cloning first) with

uv pip install git+https://github.com/flatironinstitute/jax-finufft.git

Usage

This library provides three high-level functions (and these should be all that you generally need to interact with): nufft1, nufft2, and nufft3 (for the three "types" of transforms). If you're already familiar with the Python interface to FINUFFT, please note that the function signatures here are different!

For example, here's how you can do a 1-dimensional type 1 transform:

import numpy as np

from jax_finufft import nufft1

M = 100000
N = 200000

rng = np.random.default_rng(123)
x = 2 * np.pi * rng.random(M)
c = rng.standard_normal(M) + 1j * rng.standard_normal(M)
f = nufft1(N, c, x, eps=1e-6, iflag=1)

Noting that the eps and iflag are optional, and that (for good reason, we promise!) the order of the positional arguments is reversed from the finufft Python package.

The syntax for a 2-, or 3-dimensional transform is:

f = nufft1((Nx, Ny), c, x, y)  # 2D
f = nufft1((Nx, Ny, Nz), c, x, y, z)  # 3D

The syntax for a type 2 transform is (also allowing optional iflag and eps parameters):

c = nufft2(f, x)  # 1D
c = nufft2(f, x, y)  # 2D
c = nufft2(f, x, y, z)  # 3D

The syntax for a type 3 transform with "source points" x, y, z and "target points" s, t, u is:

f = nufft3(c, x, s)  # 1D
f = nufft3(c, x, y, s, t)  # 2D
f = nufft3(c, x, y, z, s, t, u)  # 3D

All of these functions support batching using vmap, and forward and reverse mode differentiation.

Stacked Transforms and Broadcasting

A "stacked", or "vectorized", finufft transform is one where the same non-uniform points are reused for multiple sets of source strengths. In the JAX interface, this is achieved by broadcasting. In the following example, only one finufft plan is created and one setpts call made, with a stack of 32 source strengths:

import numpy as np

from jax_finufft import nufft1

M = 100000
N = 200000
S = 32

rng = np.random.default_rng(123)
x = 2 * np.pi * rng.random(M)
c = rng.standard_normal((S, M)) + 1j * rng.standard_normal((S, M))
f = nufft1(N, c, x)

To verify that a stacked transform is being used, see Inspecting the finufft calls.

Note that the broadcasting occurs because an implicit axis of length 1 is inserted in the second-to-last dimension of x. Currently, this is the only style of broadcasting that is supported when the strengths and points have unequal numbers of non-core dimensions. For other styles of broadcasting, insert axes of length 1 into the inputs. Any broadcast axes (even non-consecutive ones) are grouped and stacked in the transform.

Matched, but not broadcast, axes will be executed as separate transforms, each with their own setpts calls (but a single shared plan). In the following example (which continues from the previous), 1 plan is created and 4 setpts and 4 execute calls are made, each executing a stack of 32 transforms:

P = 4

x = 2 * np.pi * rng.random((P, 1, M))
c = rng.standard_normal((P, S, M)) + 1j * rng.standard_normal((P, S, M))
f = nufft1(N, c, x)

Selecting a platform

If you compiled jax-finufft with GPU support, you can force it to use a particular backend by setting the environment variable JAX_PLATFORMS=cpu or JAX_PLATFORMS=cuda.

Advanced usage

Options

The tuning parameters for the library can be set using the opts parameter to nufft1, nufft2, and nufft3. For example, to explicitly set the CPU up-sampling factor that FINUFFT should use, you can update the example from above as follows:

from jax_finufft import options

opts = options.Opts(upsampfac=2.0)
nufft1(N, c, x, opts=opts)

The corresponding option for the GPU is gpu_upsampfac. In fact, all options for the GPU are prefixed with gpu_, with the exception of modeord.

One complication here is that the vector-Jacobian product for a NUFFT requires evaluating a NUFFT of a different type. This means that you might want to separately tune the options for the forward and backward pass. This can be achieved using the options.NestedOpts interface. For example, to use a different up-sampling factor for the forward and backward passes, the code from above becomes:

import jax

opts = options.NestedOpts(
  forward=options.Opts(upsampfac=2.0),
  backward=options.Opts(upsampfac=1.25),
)
jax.grad(lambda args: nufft1(N, *args, opts=opts).real.sum())((c, x))

or, in this case equivalently:

opts = options.NestedOpts(
  type1=options.Opts(upsampfac=2.0),
  type2=options.Opts(upsampfac=1.25),
)

For descriptions of the options, see these pages in the FINUFFT docs:

• CPU: https://finufft.readthedocs.io/en/latest/opts.html
• GPU: https://finufft.readthedocs.io/en/latest/c_gpu.html#options-for-gpu-code

Inspecting the finufft calls

When evaluating a single NUFFT, it's fairly obvious that jax-finufft will execute one finufft transform under the hood. However, when evaluating a stacked NUFFT, or taking the gradients of a NUFFT, the sequence of calls may be less obvious. One way to inspect exactly what finufft calls are being made is to enable finufft's debug output by passing opts=Opts(debug=True) or opts=Opts(gpu_debug=True).

For example, taking the Stacked Transforms example and enabling debug output, we see the following:

>>> f = nufft1(N, c, x, eps=1e-6, iflag=1, opts=Opts(debug=True))
[FINUFFT_PLAN_T] new plan: FINUFFT version 2.4.1 .................
[FINUFFT_PLAN_T] 1d1: (ms,mt,mu)=(200000,1,1) (nf1,nf2,nf3)=(400000,1,1)
               ntrans=32 nthr=16 batchSize=16  spread_thread=2
[FINUFFT_PLAN_T] kernel fser (ns=7):            0.000765 s
[FINUFFT_PLAN_T] fwBatch 0.05GB alloc:          0.00703 s
[FINUFFT_PLAN_T] FFT plan (mode 64, nthr=16):   0.00892 s
[setpts] sort (didSort=1):              0.00327 s
[execute] start ntrans=32 (2 batches, bsize=16)...
[execute] done. tot spread:             0.0236 s
               tot FFT:                         0.0164 s
               tot deconvolve:                  0.00191 s

Evidently, we are creating a single plan with 32 transforms, and finufft has chosen to batch them into two sets of 16. setpts is only called once, as is execute, as we would expect for a stacked transform.

Notes on the Implementation of the Gradients

The NUFFT gradients are implemented as Jacobian-vector products (JVP, i.e. forward-mode autodiff), with associated transpose rules that implement the vector-Jacobian product (VJP, reverse mode). These are found in ops.py, in the jvp and transpose functions.

The JVP of a D-dimensional type 1 or 2 NUFFT requires D transforms of the same type in D dimensions (considering just the gradients with respect to the non-uniform locations). Each transform is weighted by the frequencies (as a overall scaling for type 1, and at the Fourier strength level for type 2). These transforms are fully stacked, and finufft plans are reused where possible.

Furthermore, the JAX jvp evaluates the function in addition to its JVP, so 1 more transform is necessary. This transform is not stacked with the JVP transforms. Likewise, 1 more is needed when the gradient with respect to the source or Fourier strengths is requested. However, this transform is stacked with the JVP.

In reverse mode, the VJP of a type 1 NUFFT requires type 2 transforms, and type 2 requires type 1. In either case, the function evaluation returned under JAX's vjp still requires an NUFFT of the original type (which cannot be stacked with the VJP transforms, as they are of a different type).

For type 3, the JVP requires 2*D type 3 transforms of dimension D to evaluate the gradients with respect to both the source and target locations. The strengths of each transform are weighted by the source or target locations. The source and target transforms are stacked separately. As with type 1 and 2, the strengths gradient transform is stacked with the source locations and the function evaluation transform is not stacked.

The VJP of a type 3 NUFFT also uses type 3 NUFFTs, but with the source and target points swapped.

In all of the above, whenever a user requests stacked transforms via broadcasting, this does not introduce new plans or finufft calls—the stacks simply get deeper. New sets of non-uniform points necessarily introduce new setpts and new executions, but not new plans.

To see all of the stacking behavior in action, take a look at Inspecting the finufft calls.

Similar libraries

• finufft: The "official" Python bindings to FINUFFT. A good choice if you're not already using JAX and if you don't need to differentiate through your transform.
• A list of other finufft binding libraries (e.g. for Julia, TensorFlow, PyTorch) is maintained at https://finufft.readthedocs.io/en/latest/users.html#other-wrappers-to-cu-finufft

License & attribution

This package, developed by Dan Foreman-Mackey is licensed under the Apache License, Version 2.0, with the following copyright:

Copyright 2021-2026 The Simons Foundation, Inc.

If you use this software, please cite the primary references listed on the FINUFFT docs.