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StatsBase.jl
Basic statistics for Julia
StatsBase.jl is a Julia package that provides basic support for statistics. Particularly, it implements a variety of statistics-related functions, such as scalar statistics, high-order moment computation, counting, ranking, covariances, sampling, and empirical density estimation. -
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BenchmarkTools.jl
A benchmarking framework for the Julia language
BenchmarkTools makes performance tracking of Julia code easy by supplying a framework for writing and running groups of benchmarks as well as comparing benchmark results. This package is used to write and run the benchmarks found in BaseBenchmarks.jl. The CI infrastructure for automated performance testing of the Julia language is not in this package but can be found in Nanosoldier.jl. Our story begins with two packages, "Benchmarks" and "BenchmarkTrackers". The Benchmarks package... -
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Calculus.jl
Calculus functions in Julia
The Calculus package provides tools for working with the basic calculus operations of differentiation and integration. You can use the Calculus package to produce approximate derivatives by several forms of finite differencing or to produce exact derivatives using symbolic differentiation. You can also compute definite integrals by different numerical methods. -
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Trixi.jl
Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs
Trixi.jl is a numerical simulation framework for hyperbolic conservation laws written in Julia. A key objective for the framework is to be useful to both scientists and students. Therefore, next to having an extensible design with a fast implementation, Trixi.jl is focused on being easy to use for new or inexperienced users, including the installation and postprocessing procedures. -
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Surrogates.jl
Surrogate modeling and optimization for scientific machine learning
A surrogate model is an approximation method that mimics the behavior of a computationally expensive simulation. In more mathematical terms: suppose we are attempting to optimize a function f(p), but each calculation of f is very expensive. It may be the case we need to solve a PDE for each point or use advanced numerical linear algebra machinery, which is usually costly. The idea is then to develop a surrogate model g which approximates f by training on previous data collected from... -
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FiniteDifferences.jl
High accuracy derivatives, estimated via numerical finite differences
FiniteDifferences.jl estimates derivatives with finite differences. See also the Python package FDM. FiniteDiff.jl and FiniteDifferences.jl are similar libraries: both calculate approximate derivatives numerically. You should definitely use one or the other, rather than the legacy Calculus.jl finite differencing, or reimplementing it yourself. At some point in the future, they might merge, or one might depend on the other. -
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AppleAccelerate.jl
Julia interface to the macOS Accelerate framework
Julia interface to the macOS Accelerate framework. This provides a Julia interface to some of the macOS Accelerate frameworks. At the moment, this package provides access to Accelerate BLAS and LAPACK using the libblastrampoline framework, an interface to the array-oriented functions, which provide a vectorized form for many common mathematical functions. The performance is significantly better than using standard libm functions in some cases, though there does appear to be some reduced... -
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CBinding.jl
Automatic C interfacing for Julia
Use CBinding.jl to automatically create C library bindings with Julia at runtime. In order to support the fully automatic conversion and avoid name collisions, the names of C types or functions are mangled a bit to work in Julia. Therefore everything generated by CBinding.jl can be accessed with the c"..." string macro to indicate that it lives in C-land. As an example, the function func above is available in Julia as c"func". -
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ReverseDiff
Reverse Mode Automatic Differentiation for Julia
ReverseDiff is a fast and compile-able tape-based reverse mode automatic differentiation (AD) that implements methods to take gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really). While performance can vary depending on the functions you evaluate, the algorithms implemented by ReverseDiff generally outperform non-AD algorithms in both speed and accuracy. -
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The PyPlot module for Julia
Plotting for Julia based on matplotlib.pyplot
This module provides a Julia interface to the Matplotlib plotting library from Python, and specifically to the matplotlib.pyplot module. PyPlot uses the Julia PyCall package to call Matplotlib directly from Julia with little or no overhead (arrays are passed without making a copy). (See also PythonPlot.jl for a version of PyPlot.jl using the alternative PythonCall.jl package.) This package takes advantage of Julia's multimedia I/O API to display plots in any Julia graphical backend,... -
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FEniCS.jl
A scientific machine learning (SciML) wrapper for the FEniCS
...Interfaces have been provided for the main functions and their attributes, and instructions to add further ones can be found here. A high-level API for usage with DifferentialEquations. An example can be seen in solving the heat equation with high-order adaptive time-stepping. Various gists/jupyter notebooks have been created to provide a brief overview of the overall functionality and of any differences between the pythonic FEniCS and the Julian wrapper. DifferentialEquations.jl ecosystem. Paraview can also be used to visualize various results just like in FEniCS. -
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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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Optimization.jl
Mathematical Optimization in Julia
...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 argument to indicate the package to use and automatically generates the efficient derivatives of the objective and constraints while giving you the flexibility to switch between different AD engines as per your problem. ... -
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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 for reverse-mode automatic differentiation, but ForwardDiff may still be a good choice if x is not too large, as it is much simpler. ... -
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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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WhereTraits.jl
Traits for julia: dispatch on whatever you want using where syntax
Welcome to WhereTraits.jl. This package exports one powerful macro @traits with which you can extend Julia's where syntax in order to support traits definitions. In addition, WhereTraits comes with a standardized way how to resolve ambiguities among traits, by defining an order among the traits with @traits_order. Under the hood @traits uses normal function dispatch to achieve the speed and flexibility, however, julia function dispatch can lead to ambiguities. -
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ProxSDP.jl
Semidefinite programming optimization solver
ProxSDP is an open-source semidefinite programming (SDP) solver based on the paper "Exploiting Low-Rank Structure in Semidefinite Programming by Approximate Operator Splitting". The main advantage of ProxSDP over other state-of-the-art solvers is the ability to exploit the low-rank structure inherent to several SDP problems. -
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DiffEqOperators.jl
Linear operators for discretizations of differential equations
DiffEqOperators.jl is a package for finite difference discretization of partial differential equations. It allows building lazy operators for high order non-uniform finite differences in an arbitrary number of dimensions, including vector calculus operators. For the operators, both centered and upwind operators are provided, for domains of any dimension, arbitrarily spaced grids, and for any order of accuracy. The cases of 1, 2, and 3 dimensions with an evenly spaced grid are optimized with a convolution routine from NNlib.jl. ... -
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Semagrams.jl
A graphical editor for graph-like structures
...Legacy version built with typescript is in the legacy branch, and will not receive updates; new version with scala is now in the main branch. The core of Semagrams is just a library; in order to make it do things, one needs to create an "app" that uses it. Currently, the only app that is being developed is a Petri net editor, though this will soon change. In order to run the Petri net editor standalone, install Mill and npm, and then in one terminal in scala/ run mill --watch apps.petri.fullLinkJS and in another terminal in scala/ run npm run dev. ...
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