Search Results for "numerical integration"
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Showing 51 open source projects for "numerical integration"
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QuadGK.jl
adaptive 1d numerical Gauss–Kronrod integration in Julia
This package provides support for one-dimensional numerical integration in Julia using adaptive Gauss-Kronrod quadrature. The code was originally part of Base Julia. It supports the integration of arbitrary numeric types, including arbitrary-precision (BigFloat), and even the integration of arbitrary normed vector spaces. The package provides three basic functions: quadgk, gauss, and kronrod. quadgk performs the integration, gauss computes Gaussian quadrature points and weights for integrating over the interval [a, b], and kronrod computes Kronrod points, weights, and embedded Gaussian quadrature weights for integrating over [-1, 1]. -
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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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SymbolicNumericIntegration.jl
SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals
SymbolicNumericIntegration.jl is a hybrid symbolic/numerical integration package that works on the Julia Symbolics expressions. -
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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. ... -
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Integrals.jl
A common interface for quadrature and numerical integration
Integrals.jl is an instantiation of the SciML common IntegralProblem interface for the common numerical integration packages of Julia, including both those based upon quadrature as well as Monte-Carlo approaches. By using Integrals.jl, you get a single predictable interface where many of the arguments are standardized throughout the various integrator libraries. This can be useful for benchmarking or for library implementations since libraries that internally use a quadrature can easily accept an integration method as an argument. -
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HCubature.jl
Pure-Julia multidimensional h-adaptive integration
...You can integrate real, complex, and matrix-valued integrands, for example. Note that HCubature assumes that your function f(x) can be computed at arbitrary points in the integration domain. (This is the ideal way to do numerical integration.) If you instead have f(x) precomputed at a fixed set of points, such as a Cartesian grid, you will need to use some other method (e.g. Trapz.jl for a multidimensional trapezoidal rule). -
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Diffrax
Numerical differential equation solvers in JAX
Diffrax is a numerical differential equation solving library built for the JAX ecosystem, with a strong focus on composability, differentiability, and high-performance scientific computing. The project provides tools for solving ordinary differential equations, stochastic differential equations, controlled differential equations, and related systems in a way that fits naturally into modern machine learning and differentiable programming workflows. Because it is written to work closely with... -
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Elastiknn
Elasticsearch plugin for nearest neighbor search
Elasticsearch plugin for nearest neighbor search. Store vectors and run similarity searches using exact and approximate algorithms. Methods like word2vec and convolutional neural nets can convert many data modalities (text, images, users, items, etc.) into numerical vectors, such that pairwise distance computations on the vectors correspond to semantic similarity of the original data. Elasticsearch is a ubiquitous search solution, but its support for vectors is limited. This plugin fills the... -
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Shumai
Fast Differentiable Tensor Library in JavaScript & TypeScript with Bun
Shumai is an experimental differentiable tensor library for TypeScript and JavaScript, developed by Facebook Research. It provides a high-performance framework for numerical computing and machine learning within modern JavaScript runtimes. Built on Bun and Flashlight, with ArrayFire as its numerical backend, Shumai brings GPU-accelerated tensor operations, automatic differentiation, and scientific computing tools directly to JavaScript developers. It allows seamless integration of machine learning, deep learning, and custom differentiable programs into web-based or server-side environments without relying on Python frameworks. ... -
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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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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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VisPy
Main repository for Vispy
Vispy is an open-source, high-performance interactive visualization library in Python, designed for creating scientific visualizations and interactive plots. It leverages the power of modern Graphics Processing Units (GPUs) through OpenGL to render large datasets efficiently. Vispy supports a wide range of visualization types, including 2D plots, 3D visualizations, volume rendering, and more, making it suitable for scientific research, data analysis, and educational purposes. -
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CUDA Python
Performance meets Productivity
CUDA Python is a unified Python interface for accessing and working with the NVIDIA CUDA platform, enabling developers to build GPU-accelerated applications entirely in Python. It acts as a metapackage composed of multiple submodules that provide both high-level and low-level access to CUDA functionality, including runtime APIs, driver APIs, and JIT compilation tools. The project is designed to simplify GPU programming by offering Pythonic abstractions while still exposing the full power of... -
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Taichi
Productive, portable, and performant GPU programming in Python
Taichi is an open-source, embedded DSL within Python designed for high-performance numerical and physical simulations. It uses JIT compilation (via LLVM and its runtime TiRT) to offload compute-heavy code to CPUs, GPUs, mobile devices, and embedded systems. With built-in support for sparse data structures (SNode), automatic differentiation, AOT deployment, and compatibility with CUDA, Vulkan, Metal, and OpenGL ES, it empowers disciplines like simulation, graphics, AI, and robotics -
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Axon
Nx-powered Neural Networks
...Axon provides abstractions that enable easy integration while maintaining a level of separation between each component. You should be able to use any of the APIs without dependencies on others. By decoupling the APIs, Axon gives you full control over each aspect of creating and training a neural network. At the lowest-level, Axon consists of a number of modules with functional implementations of common methods in deep learning. -
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CubeCL
Multi-platform high-performance compute language extension for Rust
CubeCL is a low-level compute language and compiler framework designed to simplify and optimize GPU programming for high-performance workloads, particularly in machine learning and numerical computing. It provides an abstraction layer that allows developers to write portable, hardware-efficient compute kernels without directly dealing with complex GPU APIs such as CUDA or OpenCL. CubeCL focuses on delivering predictable performance and composability by exposing explicit control over memory... -
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bitsandbytes
Accessible large language models via k-bit quantization for PyTorch
bitsandbytes is an open-source library designed to make training and inference of large neural networks more efficient by dramatically reducing memory usage. Built primarily for the PyTorch ecosystem, the library introduces advanced quantization techniques that allow models to operate using reduced numerical precision while maintaining high accuracy. These optimizations enable large language models and other deep learning architectures to run on hardware with limited memory resources,... -
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Mathematics Dataset
This dataset code generates mathematical question and answer pairs
The Mathematics Dataset, developed by Google DeepMind, is a synthetic dataset designed to evaluate and train machine learning models on mathematical reasoning and symbolic manipulation. It generates question-and-answer pairs across a wide range of mathematical topics typically found in school-level curricula, testing a model’s ability to reason about algebra, arithmetic, calculus, probability, and more. Each question is programmatically generated with structured templates to ensure clear... -
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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 an attached error to quantify the confidence about its accuracy. ... -
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Gonum
Set of numeric libraries for the Go programming language
Gonum is a set of numeric libraries for the Go programming language. It contains libraries for matrices, statistics, optimization, and more. 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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FlashMLA
FlashMLA: Efficient Multi-head Latent Attention Kernels
FlashMLA is a high-performance decoding kernel library designed especially for Multi-Head Latent Attention (MLA) workloads, targeting NVIDIA Hopper GPU architectures. It provides optimized kernels for MLA decoding, including support for variable-length sequences, helping reduce latency and increase throughput in model inference systems using that attention style. The library supports both BF16 and FP16 data types, and includes a paged KV cache implementation with a block size of 64 to... -
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DragonianVoice
C++ inference library for multiple SVC/TTS
DragonianVoice is a C++ inference library that unifies multiple speech synthesis, voice conversion, and singing voice synthesis models under a single, high-performance ONNX-based framework. It focuses on being a reusable native library rather than a full UI product, with bindings for C, C++, and C# so it can be embedded into other applications or engines. The project supports a wide range of model families: TTS models such as Tacotron2, VITS, EmotionalVITS, BERTVits2, GPT-SoVITS, SVC systems... -
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2D-Physics
2D physics simulation with circle collision detection using C++.
...Supports drag-and-drop manipulation, adjustable time scale, and velocity visualization. Built on a custom cPhysics library implementing Newtonian mechanics with proper numerical integration. Uses C++23, CMake, GLFW, GLEW, and ImGui. Objects can be fixed or movable, enabling orbital mechanics demonstrations and charged particle experiments. Includes preset charge values, field direction controls, and vertical sync options. Suitable for educational purposes and physics experimentation. -
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LMath library
Math library for Free Pascal and Lazarus.
LMath, based on DMath, is a mathematical library for FreePascal (FPC) and Lazarus. It is entirely written in Pascal and does not depend on external libraries. LMath provides routines and demo programs for numerical analysis, including mathematical functions, probabilities, matrices, optimization, linear and nonlinear equations, integration, Fast Fourier Transform, random numbers, curve fitting, statistics and graphics. It is organized s set of lazarus packages which makes it easily extensible and helps to include only really needed features in your project. -
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DPM-Solver
Fast ODE Solver for Diffusion Probabilistic Model Sampling
...Diffusion models are powerful generative systems capable of producing high-quality images and other data, but traditional sampling methods often require hundreds or thousands of computational steps. The project introduces a specialized numerical solver designed to approximate the diffusion process using a small number of high-order integration steps. By reformulating the sampling problem as the solution of a diffusion-related ordinary differential equation, the solver can produce high-quality samples much more efficiently. This approach significantly reduces the computational cost required to generate images while maintaining strong generation quality.
