Numerical Analysis Packages
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QuasiMonteCarlo.jl101Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)
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AdvancedVI.jl78Implementation of variational Bayes inference algorithms
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LinearSolve.jl244LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.
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SciMLBase.jl130The Base interface of the SciML ecosystem
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Indicators.jl216Financial market technical analysis & indicators in Julia
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LibCEED.jl196CEED Library: Code for Efficient Extensible Discretizations
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ChainRules.jl435Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs
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SummationByPartsOperators.jl94A Julia library of summation-by-parts (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.
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FastTransforms.jl259:rocket: Julia package for orthogonal polynomial transforms :snowboarder:
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SciMLSensitivity.jl329A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.
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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.
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MultiFloats.jl75Fast, SIMD-accelerated extended-precision arithmetic for Julia
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Gridap.jl691Grid-based approximation of partial differential equations in Julia
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NonlinearSolve.jl227High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
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Copulas.jl88A fully `Distributions.jl`-compliant copula package
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RandomMatrices.jl85Random matrices package for Julia
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BifurcationKit.jl301A Julia package to perform Bifurcation Analysis
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SparseDiffTools.jl238Fast jacobian computation through sparsity exploitation and matrix coloring
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QuadGK.jl268Adaptive 1d numerical Gauss–Kronrod integration in Julia
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FundamentalsNumericalComputation.jl97Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.
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HCubature.jl153Pure-Julia multidimensional h-adaptive integration
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Sobol.jl77Generation of Sobol low-discrepancy sequence (LDS) for the Julia language
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GridInterpolations.jl52Multidimensional grid interpolation in arbitrary dimensions
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FEniCS.jl96A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language
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Interpolations.jl523Fast, continuous interpolation of discrete datasets in Julia
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FastGaussQuadrature.jl298Julia package for Gaussian quadrature
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Arpack.jl69Julia Wrappers for the arpack-ng Fortran library
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SciMLExpectations.jl65Fast uncertainty quantification for scientific machine learning (SciML) and differential equations
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PolyChaos.jl116A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.
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KNITRO.jl77A Julia interface to the Artelys Knitro solver
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PartialLeastSquaresRegressor.jl40Implementation of a Partial Least Squares Regressor
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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.
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RollingFunctions.jl115Roll a window over data; apply a function over the window.
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RootedTrees.jl37A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)
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SolveDSGE.jl79A Julia package to solve, simulate, and analyze nonlinear DSGE models.
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FiniteDiff.jl247Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support
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FDM.jl296High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)
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FiniteDifferences.jl296High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)
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Dualization.jl95Automatic dualization feature for MathOptInterface.jl
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IntervalRootFinding.jl127Library for finding the roots of a function using interval arithmetic
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