Numerical Analysis Packages
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SparseDiffTools.jl201Fast jacobian computation through sparsity exploitation and matrix coloring
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LinearSolve.jl178LinearSolve.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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QuadGK.jl210Adaptive 1d numerical Gauss–Kronrod integration in Julia
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RootedTrees.jl34A 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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BifurcationKit.jl240A Julia package to perform Bifurcation Analysis
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FundamentalsNumericalComputation.jl60Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.
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GaussianFilters.jl36Julia Package for discrete-time linear Gaussian parametric filtering systems, namely KF, EKF, UKF, GM-PHD
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SciMLSensitivity.jl248A 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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NonlinearSolve.jl112High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
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LibCEED.jl148CEED Library: Code for Efficient Extensible Discretizations
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Sobol.jl70Generation of Sobol low-discrepancy sequence (LDS) for the Julia language
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FiniteDiff.jl202Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support
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Indicators.jl205Financial market technical analysis & indicators in Julia
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Gridap.jl539Grid-based approximation of partial differential equations in Julia
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Interpolations.jl444Fast, continuous interpolation of discrete datasets in Julia
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SciMLBase.jl90The Base interface of the SciML ecosystem
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FastTransforms.jl228:rocket: Julia package for orthogonal polynomial transforms :snowboarder:
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AMD.jl16Approximate Minimum Degree Ordering in Julia
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MultiFloats.jl51Fast extended-precision floating-point arithmetic for Julia
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RollingFunctions.jl90Roll a window over data; apply a function over the window.
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Dualization.jl83Automatic dualization feature for MathOptInterface.jl
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LowRankApprox.jl88Fast low-rank matrix approximation in Julia
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Arpack.jl60Julia Wrappers for the arpack-ng Fortran library
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ChainRules.jl358Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs
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FDM.jl237High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)
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FiniteDifferences.jl237High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)
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SummationByPartsOperators.jl46A 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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Copulas.jl40A fully `Distributions.jl`-compliant copula package
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IntervalConstraintProgramming.jl60Calculate rigorously the feasible region for a set of real-valued inequalities with Julia
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PartialLeastSquaresRegressor.jl34Implementation of a Partial Least Squares Regressor
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ApproximateGPs.jl34Approximations for Gaussian processes: sparse variational inducing point approximations, Laplace approximation, ...
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SIAMFANLEquations.jl84This is a Julia package for a book project.
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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.
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QuasiMonteCarlo.jl75Lightweight 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.jl46Implementation of variational Bayes inference algorithms
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FEniCS.jl84A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language
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PolyChaos.jl109A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.
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Expokit.jl22Julia implementation of EXPOKIT routines
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FastGaussQuadrature.jl262Julia package for Gaussian quadrature
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SolveDSGE.jl67A Julia package to solve, simulate, and analyze nonlinear DSGE models.
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