Open-source alternatives to Lapack

This project is a numerical computing library designed for scientific and engineering mathematical operations. It functions as a comprehensive linear algebra framework, a statistical analysis library, and a toolkit for mathematical optimization and numerical integration. The library is distinguished by its provider-based native acceleration, which allows managed code to be swapped for platform-native binary libraries to increase the performance of computationally intensive routines. It also supports a hybrid approach to matrix storage, implementing separate strategies for dense and sparse mat

OpenBLAS is a high-performance implementation of the Basic Linear Algebra Subprograms standard designed for numerical computing and matrix operations. It serves as a hardware-accelerated numerical library and optimized math kernel library, providing a computational engine for large-scale matrix multiplication and vector operations. The library distinguishes itself through the use of hand-tuned assembly kernels and SIMD instruction mapping, such as AVX and SVE, to maximize floating-point performance on specific CPU architectures. It features a multi-threaded framework that manages parallel exe

Gonum is a numerical computing library for the Go programming language, providing a collection of packages for scientific computing, linear algebra, statistics, and optimization. It functions as a framework for performing complex numerical computations and solving systems of linear equations. The project includes a dedicated graph analysis framework for modeling network graphs and solving connectivity and pathfinding problems. It also provides a statistical analysis toolkit for computing descriptive and inferential statistics and estimating mixture entropy. The library's capability surface c

Surge is a Swift library for high-performance numerical analysis, linear algebra, digital signal processing, and accelerated image manipulation. It utilizes the Accelerate framework to provide hardware-accelerated tools for matrix mathematics and signal processing. The library provides specialized capabilities for digital signal processing, including convolution, signal similarity analysis through cross-correlation, and domain transformations using fast Fourier transforms. It also includes a suite of tools for the rapid transformation and analysis of pixel buffers and image data. Beyond sign

OpenBLAS is a high-performance library for basic linear algebra subprograms that provides optimized matrix and vector operations. It serves as a multi-architecture math backend and numerical computing framework designed to execute complex mathematical calculations and high-speed numerical analysis. The library functions as an optimized CPU math library that detects hardware at runtime to apply the most efficient operation kernels for the specific processor. It supports multiple CPU targets through a combination of optimized assembly and C implementations. The project covers high-performance

This project is a collection of foundational machine learning algorithms and data science tools implemented in Python. It focuses on building the logic of these tools using basic programming primitives rather than relying on specialized libraries. The implementation covers several core domains, including a linear algebra library for matrix and vector operations, a statistical analysis toolkit for probability and hypothesis testing, and a framework for map-reduce distributed processing. It also includes implementations for natural language processing, graph theory for network analysis, and var

libigl is a C++ geometry processing library used for analyzing and manipulating 3D triangle and tetrahedral meshes. It functions as a numerical linear algebra suite and a mesh manipulation framework, integrating a geometric deformation engine to implement rigid and polyharmonic transformations. The project is distinguished by its header-only library design and its implementation of specialized deformation techniques, including rigid-as-possible and polyharmonic shape deformation. It also provides a visualization tool for rendering surfaces and scalar fields with interactive scene controls and

nalgebra is a linear algebra library for Rust that provides matrix and vector operations with support for both compile-time and runtime dimensions. It functions as a numerical analysis library and a sparse matrix library, offering a mathematical framework capable of running in embedded environments and WebAssembly without requiring the Rust standard library. The project distinguishes itself as a geometric transformation library, utilizing homogeneous coordinates, quaternions, and isometries to handle 3D rotations, translations, and projections. It implements a variety of matrix decompositions

SciPy is a scientific computing library for Python that provides a comprehensive collection of mathematical algorithms and numerical tools for research and engineering. It functions as a high-performance numerical analysis framework, bridging high-level Python code with compiled C and Fortran routines to execute complex computations at hardware speeds. The library is built upon array-based data structures that utilize strided memory layouts to enable efficient data manipulation and slicing. By employing vectorized operation dispatch and linking to optimized hardware-specific linear algebra li

This project is a community-driven standard library for the Fortran programming language, providing a comprehensive collection of algorithms, data structures, and system utilities. It is designed to extend the language's native capabilities, offering a unified toolkit for scientific computing, numerical analysis, and general-purpose programming. The library distinguishes itself through a modular architecture that utilizes generic interface dispatch and compile-time specialization to ensure high performance across various data types. It provides standardized abstractions for external numerical

Math.js is a comprehensive JavaScript library for scientific, complex, and arbitrary precision calculations. It functions as a symbolic computation engine, a linear algebra toolkit, a statistical analysis library, and a unit conversion system. The project distinguishes itself by providing a symbolic engine capable of parsing, simplifying, and manipulating mathematical expressions algebraically without requiring immediate numerical evaluation. It includes a framework for defining and converting physical quantities with units of measure and automatic prefix support. The library covers a broad

This project is a collection of reference implementations for algorithms, mathematics, cryptography, compression, and machine learning written in C#. It serves as an educational library providing standard implementations of sorting, searching, and graph theory algorithms. The repository covers a wide range of computational domains, including combinatorial optimization for constraint satisfaction and scheduling, as well as symmetric and classical cryptographic ciphers. It also provides reference code for lossless data compression techniques and fundamental machine learning primitives such as r

ArrayFire is a hardware-agnostic compute framework and JIT-compiled tensor engine designed for high-performance numerical computing. It serves as a GPU numerical computing library and parallel signal processing toolkit that abstracts hardware backends, allowing the same codebase to execute across various GPU architectures and CPUs. The project distinguishes itself through a JIT engine that uses expression compilation to fuse operations and minimize memory overhead. It employs a deferred execution graph to optimize computation chains and provides interoperability primitives to share data and e

NumPy is a foundational library for scientific computing in Python, providing a comprehensive framework for managing and manipulating large-scale numerical information. It centers on high-performance multidimensional array objects that serve as the primary data structure for complex mathematical operations and data analysis workflows. The library distinguishes itself through specialized mechanisms for handling multidimensional data, including advanced indexing, slicing, and broadcasting techniques that allow for efficient operations across arrays of varying shapes. It utilizes strided metadat

DifferentialEquations.jl is a comprehensive numerical library designed for solving ordinary, stochastic, delay, and algebraic differential equations. It functions as a high-performance solver suite that integrates scientific machine learning, probabilistic programming, and automated differentiation into a unified framework. By leveraging multiple dispatch and symbolic-numeric integration, the library provides a flexible environment for complex mathematical modeling and simulation. The project distinguishes itself through its ability to bridge traditional numerical analysis with modern machine

NumCpp is a C++ framework and numerical computing library that provides a toolkit for multi-dimensional array management and mathematical routines. It functions as a C++ implementation of the NumPy ecosystem, offering a scientific computing framework for managing tensors and performing complex algebraic equations. The project enables high-performance array manipulation within a C++ environment without relying on a Python runtime. It distinguishes itself by providing a NumPy-like interface for executing linear algebra, managing multi-dimensional data structures, and performing numerical proces

This project is a set of exercise solutions and implementation guides for visual simultaneous localization and mapping. It provides a collection of worked code examples and mathematical solutions designed to translate theoretical localization and mapping concepts into practical implementations. The repository serves as a technical companion for academic study, featuring worked answers to SLAM exercises and a system for tracking typographical and technical corrections to maintain the accuracy of the associated written work. The codebase covers spatial mathematics and robotics geometry, includ

This project is a comprehensive educational curriculum designed to teach Python programming through the lens of data science and financial analysis. It provides a structured guide for learning how to process complex numerical information, build data models, and perform scientific computing tasks using standard industry libraries. The materials focus on practical applications, enabling users to develop skills in financial data analysis and interactive exploration. By working through these resources, learners gain experience in executing high-performance mathematical operations, transforming ra

This project is a structured learning curriculum and technical reference for mastering deep learning with TensorFlow. It provides a comprehensive guide for building, training, and deploying neural networks, combining theoretical fundamentals with practical implementation examples. The repository distinguishes itself by covering the end-to-end machine learning workflow, from low-level tensor mathematics and linear algebra to the creation of complex model architectures. It includes specific guidance on developing data pipelines for diverse data types, such as images, text, and time-series seque

This is an arbitrary-precision decimal library and fixed-point math implementation used to eliminate floating-point rounding errors. It provides tools for high-precision arithmetic, a numerical analysis toolkit, and a database decimal mapper to ensure numerical accuracy in financial and scientific calculations. The library includes specialized serialization tools to transform high-precision numbers into SQL database types, JSON, and XML formats without losing precision. It also implements a variety of rounding strategies, including banker and cash rounding, and provides mechanisms for decimal

This project is a comprehensive technical reference and programming cheatsheet for the Python language. It serves as a curated catalog of language features, syntax patterns, and standard library functions designed to help developers identify and apply correct coding patterns. The documentation covers a broad range of functional areas, including language fundamentals such as object-oriented structuring, functional logic, and list comprehensions. It also provides guidance on utilizing the standard library for data analysis, file management, networking, and concurrent execution. The reference e

This repository is a comprehensive collection of instructional guides and practical examples for Python development, focusing on machine learning, data science, and web scraping. It provides implementations for neural networks, reinforcement learning algorithms, and deep learning architectures using PyTorch, alongside detailed manuals for scientific computing and data visualization. The project distinguishes itself by offering specialized tutorials on concurrent programming to optimize CPU performance and guides for setting up Linux development environments. It covers the implementation of ad

This project is a collection of linear algebra educational notebooks and study resources. It serves as a mathematics study resource providing structured notes and explanations for learning core algebraic concepts. The material is authored as interactive math tutorials and LaTeX mathematical courseware, combining theoretical explanations with executable mathematical examples. Content is delivered through markdown-based study resources and converted into static site mathematics notes for serverless web access. The curriculum covers a range of mathematical theory, including matrix elimination,

This repository is a Chinese translation of The Art of Linear Algebra, a visual educational resource that makes abstract linear algebra concepts concrete through clear graphical diagrams. Its core approach replaces symbolic derivations with intuitive illustrations of vector and matrix operations, matrix factorizations, and eigenvalue properties, helping learners see how matrices work from multiple perspectives. The guide distinguishes itself by teaching matrix factorizations—such as LU, QR, eigenvalue decomposition, and singular value decomposition—through a family of decomposition techniqu

Magnum is a C++ middleware suite for cross-platform graphics development and real-time data visualization. It provides a hardware-agnostic rendering layer that translates graphics commands into platform-specific calls, ensuring consistent behavior across different GPU drivers and APIs such as Vulkan. The project focuses on decoupling application logic from underlying hardware through abstract graphics and system utilities. It features a plugin-based resource importer for 3D assets and audio, a hierarchical scene graph for spatial transformations, and a high-performance signal-based event syst

xtensor is a C++ multidimensional array library for numerical computing that provides N-dimensional containers with an interface mirroring the NumPy API. It utilizes a lazy evaluation expression engine to defer numerical computations until assignment, which minimizes memory allocations and intermediate copies. The library features a foreign memory array adaptor that allows it to wrap external buffers, such as NumPy arrays, to perform numerical operations in-place without duplicating data. It further optimizes performance through lazy broadcasting and a system that manages the lifetime of temp

This repository serves as a comprehensive research platform and toolkit for advancing machine learning, quantum computing, and large-scale scientific data analysis. It provides foundational frameworks for developing complex algorithmic systems, offering the necessary infrastructure for distributed training, computational graph execution, and high-performance model development. The project distinguishes itself by integrating specialized research domains with robust, privacy-preserving methodologies. It supports diverse scientific discovery through tools for quantum simulation, physics-informed