Open-source alternatives to Numeric

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

MathUtilities is a collection of specialized toolkits providing engines for geometry, computer vision, mathematics, physics simulation, and signal processing. It functions as a comprehensive mathematics and physics library focused on linear algebra, numerical optimization, and geometric calculations for technical applications. The project distinguishes itself through a physics simulation toolkit and a 3D geometry engine. These provide capabilities for Verlet integration, iterative inverse kinematics solvers, distance field rendering via volumetric raymarching, and mesh geometry deformation. I

LAPACK is a comprehensive library of Fortran routines designed for high-performance numerical analysis and linear algebra. It serves as a foundational scientific computing framework, providing standardized procedures for solving systems of linear equations, eigenvalue problems, and least squares approximations. The library distinguishes itself through a hierarchical routine abstraction that organizes mathematical operations into distinct levels of complexity. It utilizes block-partitioned matrix algorithms and a column-major memory layout to optimize data locality and hardware efficiency. By

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

numbers.js is a comprehensive mathematics library for JavaScript that provides a collection of advanced functions for scientific computing and data analysis. It is designed to handle complex mathematical operations through a modular architecture, offering tools for calculus, statistics, linear algebra, and prime number analysis. The library distinguishes itself by providing explicit control over numerical precision, allowing users to define error thresholds and manage decimal accuracy to mitigate rounding discrepancies. This focus on precision is paired with a suite of computational tools tha

Smile is a comprehensive JVM machine learning library and statistical computing toolkit. It provides a suite of algorithms for classification, regression, and clustering, implemented natively for Java, Scala, and Kotlin. The project also functions as a deep learning framework, a natural language processing library, and an inference engine for large language models. The library distinguishes itself through GPU acceleration via LibTorch bindings and support for the ONNX model interchange format. It includes specialized capabilities for large language model inference, featuring Byte-Pair Encodin

Optim.jl is a numerical optimization library for the Julia programming language, providing a comprehensive framework for minimizing or maximizing univariate and multivariate functions. It offers a suite of tools for solving both constrained and unconstrained mathematical problems, utilizing a variety of gradient-based, derivative-free, and stochastic search methods. The library distinguishes itself through a modular architecture that leverages language-level multiple dispatch to automatically select efficient solvers based on input data types and objective function properties. It supports com

This project is an educational platform and research toolkit designed to teach deep learning through a combination of mathematical theory, visual diagrams, and executable code. It provides a comprehensive environment for building, training, and evaluating neural networks, grounding complex concepts in interactive computational notebooks that allow for hands-on experimentation. The framework distinguishes itself by interleaving theoretical foundations—including linear algebra, calculus, and probability—with practical implementations across multiple industry-standard libraries. It supports flex

This project is a high-performance numerical computing library designed for large-scale scientific and machine learning workloads. It functions as an automatic differentiation framework and a just-in-time compilation engine, transforming high-level Python code into optimized machine instructions. By enforcing pure functional programming patterns and immutable array semantics, the library ensures that mathematical functions remain compatible with automated graph transformations and symbolic differentiation. The platform distinguishes itself through its distributed array computing capabilities,

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

This project is a deep learning implementation library and neural network theory repository. It translates mathematical derivations from textbooks and literature into functional Python code to demonstrate how deep learning algorithms work. The codebase focuses on low-level algorithm implementation by using numerical libraries instead of high-level deep learning frameworks. This approach maps theoretical mathematical proofs to executable functions to verify principles and expose the underlying arithmetic and data flow of neural networks. The project covers the implementation of deep learning

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

This project is a machine learning educational curriculum and learning platform delivered through interactive Jupyter Notebooks. It serves as a comprehensive guide for mastering the Python data science toolkit, providing structured tutorials for numerical computing, tabular data manipulation, and statistical visualization. The curriculum includes specific implementation guides for Scikit-Learn and a practical course on TensorFlow for constructing, training, and deploying neural networks and computer vision models. It covers the end-to-end process of building predictive models, from initial pr

This project is an interactive data science environment that combines code execution, rich media visualization, and narrative documentation into a persistent, browser-based platform. It serves as a comprehensive educational resource for scientific computing, providing a framework for iterative data analysis and machine learning prototyping. The environment is distinguished by its focus on high-performance numerical computing, utilizing vectorized array operations and memory-mapped data structures to handle large-scale computations efficiently. It features a unified estimator interface that st

Numba is a just-in-time compiler that translates high-level Python functions into optimized machine code at runtime. By leveraging the LLVM compiler infrastructure, it provides a framework for accelerating numerical data processing and mathematical computations, enabling performance levels comparable to statically compiled languages. The project distinguishes itself through its ability to perform type-inference-based specialization, which generates machine instructions tailored to the specific data types used during execution. It employs a lazy compilation pipeline that defers translation unt

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

Deeplearnjs is a JavaScript deep learning framework and automatic differentiation engine designed for building and training artificial intelligence models within a web browser environment. It functions as a machine learning library that leverages WebGL to provide hardware acceleration for neural networks. The project serves as a high-performance linear algebra library, using the GPU to execute operations on multi-dimensional arrays. This enables the implementation of deep learning models and the execution of client-side machine learning inference. The framework covers the complete automatic

ndarray is a multidimensional array library for Rust that serves as a linear algebra framework and scientific computing tool. It provides the core infrastructure for creating and manipulating n-dimensional arrays, functioning as both a parallel array processor and a toolkit for numerical data analysis. The library distinguishes itself by providing efficient slicing and memory views, allowing for data sharing without copying. It leverages optimized backend math libraries for high-speed matrix multiplication and distributes heavy mathematical iterations across multiple CPU threads to accelerate

This project is a deep learning educational resource consisting of PyTorch model implementations and code examples. It provides functional Python scripts and notebooks for building, training, and optimizing neural networks using tensor-based computation. The repository includes implementations for designing custom network layers and loss functions, as well as examples of transfer learning workflows that load pretrained model weights to accelerate development. The codebase covers a broad range of deep learning capabilities, including neural network training, custom model component design, and

Umbrella is a comprehensive ecosystem of TypeScript-based libraries and a mono-repository designed for UI rendering, mathematical frameworks, WebAssembly bridging, and functional data processing. It provides a suite of tools for managing reactive data streams, binary serialization, and specialized memory management. The project includes a reactive component model for generating HTML, SVG, and Canvas elements from nested data structures, as well as a system for integrating JavaScript and WebAssembly through generated bindings. It features a mathematical framework for linear algebra, tensor ope

Flashlight is a C++ machine learning library and deep learning framework designed for building and training neural networks. It functions as a tensor manipulation library and an automatic differentiation engine that tracks operations to calculate gradients via backpropagation for model optimization. The project is distinguished by its role as a distributed training framework, utilizing all-reduce gradient synchronization and distributed environments to scale machine learning workloads across multiple nodes and devices. It features a backend-agnostic memory interface and RAII-based management

This project is a mathematics programming pattern library and translation guide designed to map academic mathematical symbols and formulas into programmable logic. It serves as a reference for converting complex notations into software implementations. The resource provides mapping guides for translating calculus, linear algebra, and set theory into iterative loops, functional code, and boolean expressions. It includes specific patterns for implementing piecewise functions, matrix operations, and standard mathematical operators using conditional logic and built-in language functions. The lib

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

This project is an educational resource and a collection of instructional materials for performing data manipulation and statistical analysis using Python. It provides a comprehensive set of guides and code examples for using the Pandas, NumPy, and Matplotlib libraries to analyze structured data. The resource includes a dedicated guide for reshaping, cleaning, and aggregating tabular data and time series via Pandas, alongside a reference for high-performance vectorized operations and linear algebra using NumPy. It also features tutorials for creating publication-quality charts, distribution p

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

This project is a reference collection of statistical learning algorithms built from scratch using NumPy for linear algebra and matrix operations. It serves as an educational resource for studying the mathematical foundations and inner workings of machine learning models through manual implementations. The codebase provides hand-coded implementations of both supervised and unsupervised learning. This includes classification and regression models such as support vector machines, decision trees, and Naive Bayes, as well as data clustering and pattern discovery methods like k-means and hierarchi

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