Numerical Analysis Packages

Gridap.jl539Gridbased approximation of partial differential equations in Julia

Interpolations.jl444Fast, continuous interpolation of discrete datasets in Julia

ChainRules.jl358Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs

LinearMaps.jl282A 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.

FastGaussQuadrature.jl262Julia package for Gaussian quadrature

SciMLSensitivity.jl248A 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.

BifurcationKit.jl240A Julia package to perform Bifurcation Analysis

FiniteDifferences.jl237High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

FDM.jl237High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

FastTransforms.jl228:rocket: Julia package for orthogonal polynomial transforms :snowboarder:

QuadGK.jl210Adaptive 1d numerical Gauss–Kronrod integration in Julia

Indicators.jl205Financial market technical analysis & indicators in Julia

FiniteDiff.jl202Fast nonallocating calculations of gradients, Jacobians, and Hessians with sparsity support

SparseDiffTools.jl201Fast jacobian computation through sparsity exploitation and matrix coloring

LinearSolve.jl178LinearSolve.jl: HighPerformance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

LibCEED.jl148CEED Library: Code for Efficient Extensible Discretizations

HCubature.jl135PureJulia multidimensional hadaptive integration

IntervalRootFinding.jl116Find all roots of a function in a guaranteed way with Julia

NonlinearSolve.jl112Highperformance and differentiationenabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and NewtonKrylov support.

PolyChaos.jl109A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

RollingFunctions.jl90Roll a window over data; apply a function over the window.

SciMLBase.jl90The Base interface of the SciML ecosystem

LowRankApprox.jl88Fast lowrank matrix approximation in Julia

FEniCS.jl84A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

SIAMFANLEquations.jl84This is a Julia package for a book project.

Dualization.jl83Automatic dualization feature for MathOptInterface.jl

StateSpaceRoutines.jl80Package implementing common statespace routines.

RandomMatrices.jl76Random matrices package for Julia

QuasiMonteCarlo.jl75Lightweight 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)

Sobol.jl70Generation of Sobol lowdiscrepancy sequence (LDS) for the Julia language

SolveDSGE.jl67A Julia package to solve, simulate, and analyze nonlinear DSGE models.

KNITRO.jl61Julia interface to the Artelys Knitro solver

IntervalConstraintProgramming.jl60Calculate rigorously the feasible region for a set of realvalued inequalities with Julia

FundamentalsNumericalComputation.jl60Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.

Arpack.jl60Julia Wrappers for the arpackng Fortran library

SciMLExpectations.jl59Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

NumericalIntegration.jl55Basic numerical integration routines for presampled data.

InplaceOps.jl54Convenient macros for inplace matrix operations in Julia

MultiFloats.jl51Fast extendedprecision floatingpoint arithmetic for Julia

ForwardDiff2.jl51
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