Search Results for "algebra" - Page 2
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Showing 338 open source projects for "algebra"
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SciPy
SciPy library main repository
This is the main repository for the SciPy library, one of the core packages that make up the SciPy stack. SciPy is an open source software used in the fields of mathematics, science, and engineering, with modules for statistics, optimization, integration, linear algebra, signal and image processing, and many more. The SciPy library contains many of the user-friendly and efficient numerical routines, including those for numerical integration, interpolation, and optimization. SciPy is built to work with NumPy, a software that provides convenient and fast N-dimensional array manipulation. Both SciPy and NumPy run on all popular operating systems, are fast and easy to install, and are powerful yet easy to use. ... -
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The Operator Splitting QP Solver
The Operator Splitting QP Solver
OSQP uses a specialized ADMM-based first-order method with custom sparse linear algebra routines that exploit structure in problem data. The algorithm is absolutely division-free after the setup and it requires no assumptions on problem data (the problem only needs to be convex). It just works. OSQP has an easy interface to generate customized embeddable C code with no memory manager required. OSQP supports many interfaces including C/C++, Fortran, Matlab, Python, R, Julia, Rust. -
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Deep Learning Is Nothing
Deep learning concepts in an approachable style
Deep-Learning-Is-Nothing presents deep learning concepts in an approachable, from-scratch style that demystifies the stack behind modern models. It typically begins with linear algebra, calculus, and optimization refreshers before moving to perceptrons, multilayer networks, and gradient-based training. Implementations favor small, readable examples—often NumPy first—to show how forward and backward passes work without depending solely on high-level frameworks. Once the fundamentals are clear, the material extends to CNNs, RNNs, and attention mechanisms, explaining why each architecture suits particular tasks. ... -
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CGAL
The Computational Geometry Algorithms Library
CGAL or the Computational Geometry Algorithms Library is a C++ library that gives you easy access to a myriad of efficient and reliable geometric algorithms. These algorithms are useful in a wide range of applications, including computer aided design, robotics, molecular biology, medical imaging, geographic information systems and more. CGAL features a great range of data structures and algorithms, including Voronoi diagrams, cell complexes and polyhedra, triangulations, arrangements of... -
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TensorFlow
TensorFlow is an open source library for machine learning
Originally developed by Google for internal use, TensorFlow is an open source platform for machine learning. Available across all common operating systems (desktop, server and mobile), TensorFlow provides stable APIs for Python and C as well as APIs that are not guaranteed to be backwards compatible or are 3rd party for a variety of other languages. The platform can be easily deployed on multiple CPUs, GPUs and Google's proprietary chip, the tensor processing unit (TPU). TensorFlow... -
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TensorZero
TensorZero is an open-source stack for industrial-grade LLM apps
tensorzero is a lightweight C++ library designed for tensor operations and numerical computing. It offers a minimal and readable implementation of core tensor functionality, making it ideal for educational purposes, lightweight applications, or those wanting to understand how tensor libraries work under the hood. With no external dependencies, tensorzero is easy to integrate into C++ projects needing basic multi-dimensional array support. -
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Tulip.jl
Interior-point solver in pure Julia
...It implements the homogeneous primal-dual interior-point algorithm with multiple centrality corrections and therefore handles unbounded and infeasible problems. Tulip’s main feature is that its algorithmic framework is disentangled from linear algebra implementations. This allows to seamless integration of specialized routines for structured problems. -
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Surrogates.jl
Surrogate modeling and optimization for scientific machine learning
...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 evaluations of f. -
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mlpack
mlpack: a scalable C++ machine learning library
...In addition to its powerful C++ interface, mlpack also provides command-line programs, Python bindings, Julia bindings, Go bindings and R bindings. Written in C++ and built on the Armadillo linear algebra library, the ensmallen numerical optimization library, and parts of Boost. Aims to provide fast, extensible implementations of cutting-edge machine learning algorithms. mlpack uses CMake as a build system and allows several flexible build configuration options. You can consult any of the CMake tutorials for further documentation, but this tutorial should be enough to get mlpack built and installed. -
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Hypercomplex Algebra Toolkit (HAT)
A Matlab code toolkit for arbitrary hypercomplex algebras
A flexible toolkit using Matlab's object-oriented features to provide user-configurable support for multiple hypercomplex algebras, essentially by defining the multiplication table. Using a two-level hierarchy of classes, a large body of code is made universal across algebras (for example, the code for multiplication, and addition). Matlab itself implements array indexing, colon notation etc. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
ModelingToolkit.jl is a modeling language for high-performance symbolic-numeric computation in scientific computing and scientific machine learning. It then mixes ideas from symbolic computational algebra systems with causal and acausal equation-based modeling frameworks to give an extendable and parallel modeling system. It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as index reduction of differential-algebraic equations, make it possible to solve equations that are impossible to solve with a purely numeric-based technique. ... -
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doobie
Functional JDBC layer for Scala
doobie is a pure functional JDBC layer for Scala and Cats. It is not an ORM, nor is it a relational algebra; it simply provides a functional way to construct programs (and higher-level libraries) that use JDBC. For common use cases doobie provides a minimal but expressive high-level API. doobie is a Typelevel project. This means we embrace pure, typeful, functional programming, and provide a safe and friendly environment for teaching, learning, and contributing as described in the Scala Code of Conduct. ... -
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ArrayFire
ArrayFire, a general purpose GPU library
ArrayFire is a general-purpose tensor library that simplifies the process of software development for the parallel architectures found in CPUs, GPUs, and other hardware acceleration devices. The library serves users in every technical computing market. Data structures in ArrayFire are smartly managed to avoid costly memory transfers and to take advantage of each performance feature provided by the underlying hardware. The community of ArrayFire developers invites you to build with us if... -
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ITensors.jl
A Julia library for efficient tensor computations and tensor network
ITensors.jl is a high-performance Julia library for tensor network calculations, primarily used in quantum physics and computational science. It enables efficient manipulation of large, structured tensors with named indices and provides an intuitive interface for implementing algorithms like DMRG (Density Matrix Renormalization Group), TEBD (Time-Evolving Block Decimation), and more. ITensors.jl leverages Julia’s multiple dispatch and performance features to simplify the development of... -
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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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CUTLASS
CUDA Templates for Linear Algebra Subroutines
CUTLASS is a collection of CUDA C++ template abstractions for implementing high-performance matrix-multiplication (GEMM) and related computations at all levels and scales within CUDA. It incorporates strategies for hierarchical decomposition and data movement similar to those used to implement cuBLAS and cuDNN. CUTLASS decomposes these "moving parts" into reusable, modular software components abstracted by C++ template classes. These thread-wide, warp-wide, block-wide, and device-wide... -
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SuperPrompt
Experimental prompt framework exploring reasoning structures in AI
...These sections act as a kind of meta-instruction system intended to influence how an AI model approaches problem solving and conceptual exploration. SuperPrompt also incorporates ideas from mathematics, recursion, abstract algebra, and theoretical reasoning to encourage models to perform multi-step conceptual synthesis rather than simple direct responses. -
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NeuroMatch Academy (NMA)
NMA Computational Neuroscience course
...The pre-reqs refresher days are asynchronous, so you can go through the material on your own time. You will learn how to code in Python from scratch using a simple neural model, the leaky integrate-and-fire model, as a motivation. Then, you will cover linear algebra, calculus and probability & statistics. The topics covered on these days were carefully chosen based on what you need for the comp neuro course. -
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SymbolicUtils.jl
Symbolic expressions, rewriting and simplification
...It lets you create, rewrite and simplify symbolic expressions, and generate Julia code from them. SymbolicUtils.jl provides various utilities for symbolic computing. SymbolicUtils.jl is what one would use to build a Computer Algebra System (CAS). If you're looking for a complete CAS, similar to SymPy or Mathematica, see Symbolics.jl. If you want to build a crazy CAS for your weird Octonian algebras, you've come to the right place. Symbols in SymbolicUtils carry type information. Operations on them propagate this information. A rule-based rewriting language can be used to find subexpressions that satisfy arbitrary conditions and apply arbitrary transformations on the matches. ... -
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Kornia
Open Source Differentiable Computer Vision Library
Kornia is a differentiable computer vision library for PyTorch. It consists of a set of routines and differentiable modules to solve generic computer vision problems. At its core, the package uses PyTorch as its main backend both for efficiency and to take advantage of the reverse-mode auto-differentiation to define and compute the gradient of complex functions. Inspired by existing packages, this library is composed by a subset of packages containing operators that can be inserted within... -
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Gonum
Set of numeric libraries for the Go programming language
...Gonum is a set of packages designed to make writing numerical and scientific algorithms productive, performant, and scalable. Gonum contains libraries for matrices and linear algebra; statistics, probability distributions, and sampling; tools for function differentiation, integration, and optimization; network creation and analysis; and more. We encourage you to get started with Go and Gonum if you are tired of sluggish performance, and fighting C and vectorization, and also if you are struggling with managing programs as they grow larger. ... -
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Quantum++
Modern C++ quantum computing library
Quantum++ is a modern C++ general-purpose quantum computing library, composed solely of template header files. Quantum++ is written in standard C++17 and has very low external dependencies, using only the Eigen 3 linear algebra header-only template library and, if available, the OpenMP multiprocessing library. Quantum++ is not restricted to qubit systems or specific quantum information processing tasks, being capable of simulating arbitrary quantum processes. The main design factors taken in consideration were ease of use, high portability, and high performance. ... -
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Smile
Statistical machine intelligence and learning engine
Smile is a fast and comprehensive machine learning engine. With advanced data structures and algorithms, Smile delivers the state-of-art performance. Compared to this third-party benchmark, Smile outperforms R, Python, Spark, H2O, xgboost significantly. Smile is a couple of times faster than the closest competitor. The memory usage is also very efficient. If we can train advanced machine learning models on a PC, why buy a cluster? Write applications quickly in Java, Scala, or any JVM... -
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GluCat: Clifford algebra templates
Calculation with Clifford algebras: C++ library and Python module
GluCat is a generic library of C++ templates that implement universal Clifford algebras over the field of real numbers. The PyClical extension module for Python gives users an easy Python scripting interface for calculations in Clifford algebras. The name PyClical is an homage to Pertti Lounesto's CLICAL. -
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Maxima -- GPL CAS based on DOE-MACSYMA
Computer Algebra System written in Common Lisp
Maxima is a computer algebra system comparable to commercial systems like Mathematica and Maple. It emphasizes symbolic mathematical computation: algebra, trigonometry, calculus, and much more. For example, Maxima solves x^2-r*x-s^2-r*s=0, giving the symbolic results [x=r+s, x=-s]. It can also calculate with exact integers and fractions, native floating-point, and high-precision big floats.