Numerical Analysis Packages

Gridap.jl691Gridbased approximation of partial differential equations in Julia

Interpolations.jl523Fast, continuous interpolation of discrete datasets in Julia

ChainRules.jl435Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs

SciMLSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

LinearMaps.jl303A 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.

BifurcationKit.jl301A Julia package to perform Bifurcation Analysis

FastGaussQuadrature.jl298Julia package for Gaussian quadrature

FDM.jl296High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

FiniteDifferences.jl296High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

QuadGK.jl268Adaptive 1d numerical Gauss–Kronrod integration in Julia

FastTransforms.jl259:rocket: Julia package for orthogonal polynomial transforms :snowboarder:

FiniteDiff.jl247Fast nonallocating calculations of gradients, Jacobians, and Hessians with sparsity support

LinearSolve.jl244LinearSolve.jl: HighPerformance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

SparseDiffTools.jl238Fast jacobian computation through sparsity exploitation and matrix coloring

NonlinearSolve.jl227Highperformance and differentiationenabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and NewtonKrylov support.

Indicators.jl216Financial market technical analysis & indicators in Julia

LibCEED.jl196CEED Library: Code for Efficient Extensible Discretizations

HCubature.jl153PureJulia multidimensional hadaptive integration

SciMLBase.jl130The Base interface of the SciML ecosystem

IntervalRootFinding.jl127Library for finding the roots of a function using interval arithmetic

PolyChaos.jl116A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

RollingFunctions.jl115Roll a window over data; apply a function over the window.

SIAMFANLEquations.jl114This is a Julia package of nonlinear solvers. These codes are used in my book, Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia.

LowRankApprox.jl109Fast lowrank matrix approximation in Julia

QuasiMonteCarlo.jl101Lightweight and easy generation of quasiMonte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

FundamentalsNumericalComputation.jl97Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.

FEniCS.jl96A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

Dualization.jl95Automatic dualization feature for MathOptInterface.jl

SummationByPartsOperators.jl94A Julia library of summationbyparts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable semidiscretizations, paying special attention to boundary conditions.

Copulas.jl88A fully `Distributions.jl`compliant copula package

StateSpaceRoutines.jl86Package implementing common statespace routines.

RandomMatrices.jl85Random matrices package for Julia

SolveDSGE.jl79A Julia package to solve, simulate, and analyze nonlinear DSGE models.

AdvancedVI.jl78Implementation of variational Bayes inference algorithms

KNITRO.jl77A Julia interface to the Artelys Knitro solver

Sobol.jl77Generation of Sobol lowdiscrepancy sequence (LDS) for the Julia language

MultiFloats.jl75Fast, SIMDaccelerated extendedprecision arithmetic for Julia

Arpack.jl69Julia Wrappers for the arpackng Fortran library

SciMLExpectations.jl65Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

IntervalConstraintProgramming.jl63Calculate rigorously the feasible region for a set of realvalued inequalities with Julia
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