Endia is a general-purpose scientific computing library, featuring:

• Automatic differentiation: Compute derivatives of arbitrary order.
• Complex numbers: Use Endia for advanced scientific applications.
• Dual API: Choose between a PyTorch-like imperative or a JAX-like functional interface.
• JIT Compilation: Leverage MAX to speed up training and inference.

⚠️ Warning: Endia is currently in an early development stage and not yet ready for production use. The API is subject to change without notice. Stay tuned for more exciting features to come (e.g. GPU support).

1. Install Mojo 24.5 🔥

2. Add the Endia Package (at the top level of your project):

   curl -o "endia.📦" https://raw.githubusercontent.com/endia-org/Endia/main/endia.mojopkg

   But what about all the other internal dependencies? - Good news, there are none. The core of Endia is built purely on top of Mojo and MAX!

In this guide, we'll demonstrate how to compute the value, gradient, and the Hessian (i.e. the second-order derivative) of a simple function. First by using Endia's Pytorch-like API and then by using a more Jax-like functional API. In both examples, we initially define a function foo that takes an array and returns the sum of the squares of its elements.

When using Endia's imperative (PyTorch-like) interface, we compute the gradient of a function by calling the backward method on the function's output. This imperative style requires explicit management of the computational graph, including setting requires_grad=True for the input arrays (i.e. leaf nodes) and using create_graph=True in the backward method when computing higher-order derivatives.

from endia import Tensor, sum, arange
import endia.autograd.functional as F


# Define the function
def foo(x: Tensor) -> Tensor:
    return sum(x ** 2)

def main():
    # Initialize variable - requires_grad=True needed!
    x = arange(1.0, 4.0, requires_grad=True) # [1.0, 2.0, 3.0]

    # Compute result, first and second order derivatives
    y = foo(x)
    y.backward(create_graph=True)            
    dy_dx = x.grad()
    d2y_dx2 = F.grad(outs=sum(dy_dx), inputs=x)[0]

    # Print results
    print(y)        # 14.0
    print(dy_dx)    # [2.0, 4.0, 6.0]
    print(d2y_dx2)  # [2.0, 2.0, 2.0]

When using Endia's functional (JAX-like) interface, the computational graph is handled implicitly. By calling the grad or jacobian function on foo, we create a Callable which computes the full Jacobian matrix. This Callable can be passed to the grad or jacobian function again to compute higher-order derivatives.

from endia import grad, jacobian
from endia.numpy import sum, arange, ndarray


def foo(x: ndarray) -> ndarray:
    return sum(x**2)


def main():
    # create Callables for the first and second order derivatives
    foo_jac = grad(foo)
    foo_hes = jacobian(foo_jac)

    x = arange(1.0, 4.0)       # [1.0, 2.0, 3.0]

    print(foo(x))              # 14.0
    print(foo_jac(x)[ndarray]) # [2.0, 4.0, 6.0]
    print(foo_hes(x)[ndarray]) # [[2.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]

And there is so much more! Endia can handle complex valued functions, can perform both forward and reverse-mode automatic differentiation, it even has a builtin JIT compiler to make things go brrr. Explore the full list of features in the documentation.

"Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less." - Marie Curie

Guided by this core belief, we embarked on a challenging journey to build something from first principles — a framework that is both powerful 🚀 and transparent 📐. Endia is crafted to be more than just a tool; it's a window into the algorithms you work with, stripping away layers of abstraction to reveal the underlying logic 🧠. In contrast to other popular Scientific Computing libraries which are built on piles of decades-old legacy Fortran and C++ code (like NumPy, for example), Endia is built on top of a uniquely minimalistic stack:

Contributions to Endia are welcome! If you'd like to contribute, please follow the contribution guidelines in the CONTRIBUTING.md file in the repository.

If you use Endia in your research or project, please cite it as follows:

@software{Fehrenbach_Endia_2024,
  author = {Fehrenbach, Tillmann},
  license = {Apache-2.0 with LLVM Exceptions},
  doi = {10.5281/zenodo.12810766},
  month = {09},
  title = {{Endia}},
  url = {https://github.com/endia-org/Endia},
  version = {24.5.0},
  year = {2024}
}

Endia is licensed under the Apache-2.0 license with LLVM Exeptions.