Powerful convenience for Julia visualizations and data analysis

Forward Mode Automatic Differentiation for Julia

Statically sized arrays for Julia

Macro(s) for vectorizing loops.

Progress meter for long-running computations

Julia implementation of Data structures

Formatted output of timed sections in Julia

HTTP for Julia

A benchmarking framework for the Julia language

Physical quantities with arbitrary units

Basic statistics for Julia

Convert julia objects to LaTeX equations, arrays or other environments.

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Fast, continuous interpolation of discrete datasets in Julia

An optimized graphs package for the Julia programming language

Julia bindings for the Enzyme automatic differentiator

Types with default field values, keyword constructors and (un-)pack macros

Julia functional programming infrastructures and metaprogramming facilities

Iterative algorithms for solving linear systems, eigensystems, and singular value problems

Plotting for Julia based on GR, a framework for visualisation applications

Special mathematical functions in Julia

Root finding functions for Julia

A Julia Basket of Hand-Picked Krylov Methods

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

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

Julia package for Gaussian quadrature

Julia bindings to the FFTW library for fast Fourier transforms

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.

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.

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

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