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HCubature.jl
Pure-Julia multidimensional h-adaptive integration
The HCubature module is a pure-Julia implementation of multidimensional "h-adaptive" integration. then hcubature(f, a, b) computes the integral, adaptively subdividing the integration volume into smaller and smaller pieces until convergence is achieved to the desired tolerance (specified by optional rtol and atol keyword arguments. Because hcubature is written purely in Julia, the integrand f(x) can return any vector-like object (technically, any type supporting +, -, * real, and norm: a... -
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ImplicitGlobalGrid.jl
Distributed parallelization of stencil-based GPU and CPU applications
ImplicitGlobalGrid is an outcome of a collaboration of the Swiss National Supercomputing Centre, ETH Zurich (Dr. Samuel Omlin) with Stanford University (Dr. Ludovic Räss) and the Swiss Geocomputing Centre (Prof. Yuri Podladchikov). It renders the distributed parallelization of stencil-based GPU and CPU applications on a regular staggered grid almost trivial and enables close to ideal weak scaling of real-world applications on thousands of GPUs [1, 2, 3]. ImplicitGlobalGrid relies on the... -
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Rotations.jl
Julia implementations for different rotation parameterizations
3D rotations made easy in Julia. This package implements various 3D rotation parameterizations and defines conversions between them. At their heart, each rotation parameterization is a 3×3 unitary (orthogonal) matrix (based on the StaticArrays.jl package), and acts to rotate a 3-vector about the origin through matrix-vector multiplication. While the RotMatrix type is a dense representation of a 3×3 matrix, we also have sparse (or computed, rather) representations such as quaternions,... -
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Wavelets.jl
A Julia package for fast discrete wavelet transforms and utilities
A Julia package for fast wavelet transforms (1-D, 2-D, 3-D, by filtering or lifting). The package includes discrete wavelet transforms, column-wise discrete wavelet transforms, and wavelet packet transforms. 1st generation wavelets using filter banks (periodic and orthogonal). Filters are included for the following types: Haar, Daubechies, Coiflet, Symmlet, Battle-Lemarie, Beylkin, Vaidyanathan. 2nd generation wavelets by lifting (periodic and general type including orthogonal and... -
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FFTW.jl
Julia bindings to the FFTW library for fast Fourier transforms
This package provides Julia bindings to the FFTW library for fast Fourier transforms (FFTs), as well as functionality useful for signal processing. These functions were formerly a part of Base Julia. Users with a build of Julia based on Intel's Math Kernel Library (MKL) can use MKL for FFTs by setting a preference in their top-level project by either using the FFTW.set_provider!() method, or by directly setting the preference using Preferences.jl. Note that this choice will be recorded for... -
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Roots.jl
Root finding functions for Julia
This package contains simple routines for finding roots, or zeros, of scalar functions of a single real variable using floating-point math. The find_zero function provides the primary interface. The basic call is find_zero(f, x0, [M], [p]; kws...) where, typically, f is a function, x0 a starting point or bracketing interval, M is used to adjust the default algorithms used, and p can be used to pass in parameters. Bisection-like algorithms. For functions where a bracketing interval is known... -
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HDF5.jl
Save and load data in the HDF5 file format from Julia
HDF5 stands for Hierarchical Data Format v5 and is closely modeled on file systems. In HDF5, a "group" is analogous to a directory, a "dataset" is like a file. HDF5 also uses "attributes" to associate metadata with a particular group or dataset. HDF5 uses ASCII names for these different objects, and objects can be accessed by Unix-like pathnames, e.g., "/sample1/tempsensor/firsttrial" for a top-level group "sample1", a subgroup "tempsensor", and a dataset "firsttrial". For simple types... -
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Convex.jl
A Julia package for disciplined convex programming
Convex.jl is a Julia package for Disciplined Convex Programming (DCP). Convex.jl makes it easy to describe optimization problems in a natural, mathematical syntax, and to solve those problems using a variety of different (commercial and open-source) solvers. Convex.jl works by transforming the problem—which possibly has nonsmooth, nonlinear constructions like the nuclear norm, the log determinant, and so forth—into a linear optimization problem subject to conic constraints. This... -
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Luxor
Simple drawings using vector graphics; Cairo "for tourists!"
Luxor is a Julia package for drawing simple static 2D vector graphics. It provides basic drawing functions and utilities for working with shapes, polygons, clipping masks, PNG and SVG images, turtle graphics, and simple animations. The focus of Luxor is on simplicity and ease of use: it should be easier to use than plain Cairo.jl, with shorter names, fewer underscores, default contexts, and simplified functions. For more complex and sophisticated graphics in 2D and 3D, Makie.jl is the best... -
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Optimization.jl
Mathematical Optimization in Julia
Optimization.jl provides the easiest way to create an optimization problem and solve it. It enables rapid prototyping and experimentation with minimal syntax overhead by providing a uniform interface to >25 optimization libraries, hence 100+ optimization solvers encompassing almost all classes of optimization algorithms such as global, mixed-integer, non-convex, second-order local, constrained, etc. It allows you to choose an Automatic Differentiation (AD) backend by simply passing an... -
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Gridap.jl
Grid-based approximation of partial differential equations in Julia
Gridap provides a set of tools for the grid-based approximation of partial differential equations (PDEs) written in the Julia programming language. The library currently supports linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element (FE) discretizations, on structured and unstructured meshes of simplices and n-cubes. It also provides methods for time integration. Gridap is extensible and modular. One can... -
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ForwardDiff.jl
Forward Mode Automatic Differentiation for Julia
ForwardDiff implements methods to take derivatives, gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really) using forward mode automatic differentiation (AD). While performance can vary depending on the functions you evaluate, the algorithms implemented by ForwardDiff generally outperform non-AD algorithms (such as finite-differencing) in both speed and accuracy. Functions like f which map a vector to a scalar are the best case... -
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ProbabilisticCircuits.jl
Probabilistic Circuits from the Juice library
This module provides a Julia implementation of Probabilistic Circuits (PCs), tools to learn structure and parameters of PCs from data, and tools to do tractable exact inference with them. Probabilistic Circuits provides a unifying framework for several family of tractable probabilistic models. PCs are represented as computational graphs that define a joint probability distribution as recursive mixtures (sum units) and factorizations (product units) of simpler distributions (input units).... -
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WordCloud.jl
Word cloud generator in julia
Word cloud (tag cloud or wordle) is a novelty visual representation of text data. The importance of each word is shown with its font size, position, or color. WordCloud.jl is the perfect tool for generating word clouds, offering several advantages. You have control over every aspect of generating a word cloud. You can customize the shape, color, angle, position, distribution, density, and spacing to align with your preferences and artistic style. This visualization solution guarantees... -
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NonlinearSolve.jl
High-performance and differentiation-enabled nonlinear solvers
Fast implementations of root-finding algorithms in Julia that satisfy the SciML common interface. For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation that contains the unreleased features. NonlinearSolve.jl is a unified interface for the nonlinear solving packages of Julia. The package includes its own high-performance nonlinear solvers which include the ability to swap out to fast direct and iterative... -
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LossFunctions.jl
Julia package of loss functions for machine learning
This package represents a community effort to centralize the definition and implementation of loss functions in Julia. As such, it is a part of the JuliaML ecosystem. The sole purpose of this package is to provide an efficient and extensible implementation of various loss functions used throughout Machine Learning (ML). It is thus intended to serve as a special purpose back-end for other ML libraries that require losses to accomplish their tasks. To that end we provide a considerable amount... -
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NeuralOperators.jl
DeepONets, Neural Operators, Physics-Informed Neural Ops in Julia
Neural operator is a novel deep learning architecture. It learns an operator, which is a mapping between infinite-dimensional function spaces. It can be used to resolve partial differential equations (PDE). Instead of solving by finite element method, a PDE problem can be resolved by training a neural network to learn an operator mapping from infinite-dimensional space (u, t) to infinite-dimensional space f(u, t). Neural operator learns a continuous function between two continuous function... -
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Reduce.jl
Symbolic parser for Julia language term rewriting using REDUCE algebra
REDUCE is a portable general-purpose computer algebra system. It is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations (as illustrated in the screenshot below) but also provides a full programming language, with a syntax similar to other modern programming languages. REDUCE supports alternative user interfaces... -
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PowerSimulations.jl
Julia for optimization simulation and modeling of PowerSystems
PowerSimulations.jl is a Julia package for power system modeling and simulation of Power Systems operations. Provide a flexible modeling framework that can accommodate problems of different complexity and at different time scales. Streamline the construction of large-scale optimization problems to avoid repetition of work when adding/modifying model details. Exploit Julia's capabilities to improve computational performance of large-scale power system quasi-static simulations. The flexible... -
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ParallelStencil.jl
Package for writing high-level code for parallel stencil computations
ParallelStencil empowers domain scientists to write architecture-agnostic high-level code for parallel high-performance stencil computations on GPUs and CPUs. Performance similar to CUDA C / HIP can be achieved, which is typically a large improvement over the performance reached when using only CUDA.jl or AMDGPU.jl GPU Array programming. For example, a 2-D shallow ice solver presented at JuliaCon 2020 [1] achieved a nearly 20 times better performance than a corresponding GPU Array... -
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CxxWrap
Package to make C++ libraries available in Julia
This package aims to provide a Boost. Python-like wrapping for C++ types and functions to Julia. The idea is to write the code for the Julia wrapper in C++, and then use a one-liner on the Julia side to make the wrapped C++ library available there. The mechanism behind this package is that functions and types are registered in C++ code that is compiled into a dynamic library. This dynamic library is then loaded into Julia, where the Julia part of this package uses the data provided through a... -
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Measurements.jl
Error propagation calculator and library for physical measurements
Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration. Physical measures are typically reported with an error, a quantification of the uncertainty of the accuracy of the measurement. Whenever you perform mathematical operations involving these quantities you have also to propagate the uncertainty, so that the resulting number will also have... -
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ReinforcementLearning.jl
A reinforcement learning package for Julia
A collection of tools for doing reinforcement learning research in Julia. Provide elaborately designed components and interfaces to help users implement new algorithms. Make it easy for new users to run benchmark experiments, compare different algorithms, and evaluate and diagnose agents. Facilitate reproducibility from traditional tabular methods to modern deep reinforcement learning algorithms. Make it easy for new users to run benchmark experiments, compare different algorithms, and... -
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CUDA.jl
CUDA programming in Julia
High-performance GPU programming in a high-level language. JuliaGPU is a GitHub organization created to unify the many packages for programming GPUs in Julia. With its high-level syntax and flexible compiler, Julia is well-positioned to productively program hardware accelerators like GPUs without sacrificing performance. The latest development version of CUDA.jl requires Julia 1.8 or higher. If you are using an older version of Julia, you need to use a previous version of CUDA.jl. This will... -
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FileTrees.jl
Parallel file processing made easy
Easy everyday parallelism with a file tree abstraction. Read a directory structure as a Julia data structure, (lazy-)load the files, apply map and reduce operations on the data while not exceeding available memory if possible. Make up a file tree in memory, create some data to go with each file (in parallel), write the tree to disk (in parallel). FileTrees is a set of tools to lazy-load, process and save file trees. Built-in parallelism allows you to max out all threads and processes that...
