A Julia Basket of Hand-Picked Krylov Methods

Julia solvers for systems of nonlinear equations and mixed complementarity problems

Efficient implementation of struct arrays in Julia

Reusable array functionality for Julia's various GPU backends.

JSON parsing and printing

MacroTools provides a library of tools for working with Julia code and expressions.

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Lazy arrays and linear algebra in Julia

Polynomial manipulations in Julia

A Julia package for defining and working with linear maps, also known as linear transformations or linear operators acting on vectors. The only requirement for a LinearMap is that it can act on a vector (by multiplication) efficiently.

An interface for tables in Julia

An alternative interface for dictionaries in Julia, for improved productivity and performance

Julia bindings to the FFTW library for fast Fourier transforms

Adaptive 1d numerical Gauss–Kronrod integration in Julia

Types and utility functions for summarizing Markov chain Monte Carlo simulations

A Julia interface to the NLopt nonlinear-optimization library

AD-backend agnostic system defining custom forward and reverse mode rules. This is the light weight core to allow you to define rules for your functions in your packages, without depending on any particular AD system.

Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

The cheapest threads you can find!

Fast jacobian computation through sparsity exploitation and matrix coloring

Mathematical functions related to statistics.

Robust, modular and efficient implementation of advanced Hamiltonian Monte Carlo algorithms

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

A combinatorics library for Julia

Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

Convenient input and display of LaTeX equation strings for the Julia language

Color manipulation utilities for Julia

Reduce time-to-first-execution of Julia code

Neural Network primitives with multiple backends

Performant arrays where each dimension can have a named axis with values

Abstract julia interfaces for working with trees

Implementation of normalising flows and constrained random variable transformations

Lazy code loading for Julia

Fortran-like arrays with arbitrary, zero or negative starting indices.

BlockArrays for Julia

Colorschemes, colormaps, gradients, and palettes