Numerical Analysis Packages

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.

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

RootedTrees.jl34A collection of functionality around rooted trees to generate order conditions for RungeKutta methods in Julia for differential equations and scientific machine learning (SciML)

BifurcationKit.jl240A Julia package to perform Bifurcation Analysis

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

GaussianFilters.jl36Julia Package for discretetime linear Gaussian parametric filtering systems, namely KF, EKF, UKF, GMPHD

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.

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

LibCEED.jl148CEED Library: Code for Efficient Extensible Discretizations

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

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

Indicators.jl205Financial market technical analysis & indicators in Julia

Gridap.jl539Gridbased approximation of partial differential equations in Julia

Interpolations.jl444Fast, continuous interpolation of discrete datasets in Julia

SciMLBase.jl90The Base interface of the SciML ecosystem

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

AMD.jl16Approximate Minimum Degree Ordering in Julia

MultiFloats.jl51Fast extendedprecision floatingpoint arithmetic for Julia

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

Dualization.jl83Automatic dualization feature for MathOptInterface.jl

LowRankApprox.jl88Fast lowrank matrix approximation in Julia

Arpack.jl60Julia Wrappers for the arpackng Fortran library

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

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

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

SummationByPartsOperators.jl46A 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.jl40A fully `Distributions.jl`compliant copula package

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

PartialLeastSquaresRegressor.jl34Implementation of a Partial Least Squares Regressor

ApproximateGPs.jl34Approximations for Gaussian processes: sparse variational inducing point approximations, Laplace approximation, ...

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

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.

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)

AdvancedVI.jl46Implementation of variational Bayes inference algorithms

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

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

Expokit.jl22Julia implementation of EXPOKIT routines

FastGaussQuadrature.jl262Julia package for Gaussian quadrature

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