High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

Library for validated numerics using interval arithmetic

Arrays with arbitrarily nested named components.

XGBoost Julia Package

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

Krylov methods for linear problems, eigenvalues, singular values and matrix functions

Calculus functions in Julia

StateSpaceModels.jl is a Julia package for time-series analysis using state-space models.

Julia bindings to the FFTW library for fast Fourier transforms

Julia interface to SymPy via PyCall

Adaptive 1d numerical Gauss–Kronrod integration in Julia

:rocket: Julia package for orthogonal polynomial transforms :snowboarder:

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.

The JuliaFEM software library is a framework that allows for the distributed processing of large Finite Element Models across clusters of computers using simple programming models. It is designed to scale up from single servers to thousands of machines, each offering local computation and storage.

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.

Symbolic parser for Julia language term rewriting using REDUCE algebra

Fast jacobian computation through sparsity exploitation and matrix coloring

Mathematical functions related to statistics.

Multi-threaded BLAS-like library that provides pure Julia matrix multiplication

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

Computational algebraic number theory

A Julia package for large-scale tensor computations, with a hint of category theory

Financial market technical analysis & indicators in Julia

Algorithms inspired by graph Laplacians: linear equation solvers, sparsification, clustering, optimization, etc.

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

Intel MKL linear algebra backend for Julia

Graph visualization for Julia.

Abstract julia interfaces for working with trees

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

CEED Library: Code for Efficient Extensible Discretizations

Graph-based molecule modeling toolkit for cheminformatics

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

BlockArrays for Julia

Julia wrappers of SymEngine