eiko 0.8.0

Eiko: the GPU-accelerated Eikonal equation solver

Eiko

Eiko is a GPU-accelerated Eikonal equation solver, enabling fast computation of the shortest time-of-flight through an arbitrary 2D or 3D medium.

A few reasons to use Eiko:

1. Eiko is fast - up to 10x faster than comparable libraries.
2. Eiko is differentiable, allowing it to be used with PyTorch or JAX.
3. Eiko supports advection, allowing it to compute apodizations through a lens.

Installation

Requirements

Because Eiko compiles custom CUDA kernels during installation, your system must have the following:

• OS: Linux or Windows
• Hardware: NVIDIA GPU
• Compiler:
  • A C++ compiler (e.g., GCC for Linux, MSVC for Windows)
  • The CUDA Toolkit (provides nvcc)

Installing for MATLAB

Run setup.m to install Eiko for MATLAB.

Installing for Python

Run

pip install eiko

You now have Eiko installed and ready for use.

See also the Eiko Python installation guide.

Quick Start

An example of how to use Eiko is shown below.
See EXAMPLES for many more examples.

MATLAB example

% 1. Setup grid parameters.
N = 101;            % Number of grid points (NxN grid)
dx = 0.001;         % Grid spacing in meters (1 mm, for example)
c = 1540;           % Speed of sound in m/s (uniform medium)

% 2. Create the slowness map (1/velocity).
f = ones(N, N, 'single', 'gpuArray') / c;

% 3. Initialize the time-of-flight field.
u_init = inf(N, N, 'single', 'gpuArray'); % Unknown points set to infinity.

% Set a point source at the center of the grid to time = 0.
center_idx = ceil(N/2);
u_init(center_idx, center_idx) = 0;

% 4. Compute the numerical solution using eiko.
u_numerical = eiko(u_init, f, dx);

% 5. Visualize the result.
% Create physical coordinate axes in millimeters using dx
axis_mm = ((1:N) - center_idx) * dx * 1000;

% Set up plot.
figure;
imagesc(axis_mm, axis_mm, u_numerical * 1e6);
axis image;

% Format axes and text size.
title('Time-of-Flight Field', 'FontSize', 14, 'FontWeight', 'bold');
xlabel('x (mm)', 'FontSize', 12, 'FontWeight', 'bold');
ylabel('y (mm)', 'FontSize', 12, 'FontWeight', 'bold');

% Format colorbar.
cb = colorbar;
cb.Label.String = 'Time (\mus)';
cb.Label.FontSize = 12;

For 3D inputs, call eiko3d.

Python example

from eiko import eiko

# 1. Setup device and grid parameters.
device = torch.device("cuda")
N = 101
dx = 0.001  # Grid spacing in meters (1 mm)
c = 1540.0  # Speed of sound in m/s (uniform medium)

# 2. Create the slowness map (1/velocity) on the device.
f = torch.full((N, N), 1.0 / c, dtype=torch.float32, device=device)

# 3. Initialize the time-of-flight field.
# Unknown points are set to infinity
u_init = torch.full((N, N), float('inf'), dtype=torch.float32, device=device)

# Set a point source at the center of the grid to time = 0.
center_idx = N // 2
u_init[center_idx, center_idx] = 0.0

# 4. Compute the numerical solution.
u_numerical = eiko(u_init, f, dx=dx)

For 3D inputs, use from eiko import eiko3d.

The result should look something like this:

Project Layout

The files are as follows:

Eiko/
├── examples/       # Example scripts (tomography, lens design, etc.).
│   ├── matlab/     #   MATLAB example scripts 
│   └── python/     #   Python example scripts
├── matlab/         # MATLAB Eiko library
├── python/         # Python Eiko library
├── src/            # Core CUDA C++ Eiko implementation and interface
├── pyproject.toml  # Python package configuration (for pip install)
├── setup.m         # MATLAB compilation and setup script
├── THEORY.md       # Mathematical background and Eikonal algorithm details
└── README.md       # This file

To learn more about how Eiko works, see THEORY.

Citing

You can cite Eiko as

@misc{eiko2026,
  author = {Pr{\ae}sius, Sebastian},
  title = {Eiko: the GPU-accelerated Eikonal equation solver},
  year = {2026},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/sebftw/Eiko}}
}