Search Results for "equations"
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Showing 39 open source projects for "equations"
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projectM
Cross-platform Music Visualization Library
Cross-platform Music Visualization Library. Open-source and Milkdrop-compatible. Experience psychedelic and mesmerizing visuals by transforming music into equations that render a limitless array of user-contributed visualizations. projectM is an open-source project that reimplements the esteemed Winamp Milkdrop by Geiss in a more modern, cross-platform reusable library. Its purpose in life is to read an audio input and to produce mesmerizing visuals, detecting tempo, and rendering advanced equations into a limitless array of user-contributed visualizations. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
...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. ModelingToolkit.jl is a symbolic-numeric modeling package. Thus it combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. -
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MathPHP
Powerful modern math library for PHP
Math PHP is a library that brings advanced mathematical functions and data analysis capabilities to PHP applications. It covers a wide range of topics, including linear algebra, calculus, statistics, probability, and numerical analysis. Math PHP is designed for developers and data scientists who require precise and efficient mathematical computations in PHP, making it suitable for scientific computing and data processing. -
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CasADi
CasADi is a symbolic framework for numeric optimization
...These expression graphs, encapsulated in Function objects, can be evaluated in a virtual machine or exported to stand-alone C code. Initial value problems in ordinary or differential-algebraic equations (ODE/DAE) can be calculated using explicit or implicit Runge-Kutta methods or interfaces to IDAS/CVODES from the SUNDIALS suite. Derivatives are calculated using sensitivity equations, up to arbitrary order. -
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DeepXDE
A library for scientific machine learning & physics-informed learning
...DeepXDE includes the following algorithms. Physics-informed neural network (PINN). Solving different problems. Solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [SIAM Rev.] Solving forward/inverse integro-differential equations (IDEs) [SIAM Rev.] fPINN: solving forward/inverse fractional PDEs (fPDEs) [SIAM J. Sci. Comput.] NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [J. Comput. Phys.] PINN with hard constraints (hPINN): solving inverse design/topology optimization [SIAM J. ... -
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SymPy
A computer algebra system written in pure Python
SymPy is an open source Python library for symbolic mathematics. Its goal is to become a full-featured computer algebra system (CAS) while maintaining the simplicity of its code. Written entirely in Python, SymPy is easy to use, comprehensible and easily extensible. It’s also very lightweight as it solely depends on mpmath, a pure Python library for arbitrary floating point arithmetic. SymPy has participated in every Google Summer of Code since 2007 and because of this has continuously... -
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LaTeX Examples
Examples for the usage of LaTeX
...It acts as a playground for learning LaTeX syntax, macros, formatting tricks, and document structuring practices. Files include sample articles, reports, book chapters, presentations (using Beamer), tables, mathematical typesetting examples (equations, aligned systems, integrals, matrices), custom macros, and styling. The project is useful both for beginners who want to see working LaTeX samples and for more advanced users seeking snippets for specific formatting needs (e.g., customizing headers, floats, customizing theorem environments). Because examples are self-contained and well-commented, users can copy, adapt, or test them without needing a large TeX toolchain. -
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Clapeyron
Framework for the development and use of fluid-thermodynamic models
Welcome to Clapeyron! This module provides both a large library of thermodynamic models and a framework for one to easily implement their own models. Clapeyron provides a framework for the development and use of fluid-thermodynamic models, including SAFT, cubic, activity, multi-parameter, and COSMO-SAC. -
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RAG Anything
RAG-Anything: All-in-One RAG Framework
RAG-Anything is an open-source unified framework that extends the Retrieval-Augmented Generation (RAG) paradigm to fully multimodal document and knowledge retrieval, enabling systems to ingest, parse, represent, and query rich content that includes text, images, tables, formulas, and other structured or visual elements. Traditional RAG systems are typically limited to text and cannot effectively work across heterogeneous document layouts, but RAG-Anything addresses this by modeling... -
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HYPRE
Parallel solvers for sparse linear systems featuring multigrid methods
Livermore’s HYPRE library of linear solvers makes possible larger, more detailed simulations by solving problems faster than traditional methods at large scales. It offers a comprehensive suite of scalable solvers for large-scale scientific simulation, featuring parallel multigrid methods for both structured and unstructured grid problems. The HYPRE library is highly portable and supports a number of languages. Work on HYPRE began in the late 1990s. It has since been used by research... -
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latexify
A library to generate LaTeX expression from Python code
...It parses Python functions and expressions into an abstract syntax tree (AST), applies symbolic rewrites for common mathematical constructs, and then emits LaTeX that compiles cleanly in standard environments. Typical use cases include turning analytical utilities—like probability mass functions, activation formulas, or recurrence relations—into equations suitable for papers, notebooks, and slide decks. The tool aims to preserve semantics such as exponentiation, summations, products, piecewise definitions, and function application while hiding Pythonic scaffolding. Users can control rendering details for names and operators so the output conforms to a project’s notation style. Because it works directly from Python source, it enables a tight authoring loop. -
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RLax
Library of JAX-based building blocks for reinforcement learning agents
...It supports both on-policy and off-policy learning, as well as value-based, policy-based, and model-based approaches. RLax is fully JIT-compilable with JAX, enabling high-performance execution across CPU, GPU, and TPU backends. The library implements tools for Bellman equations, return distributions, general value functions, and policy optimization in both continuous and discrete action spaces. It integrates seamlessly with DeepMind’s Haiku (for neural network definition) and Optax (for optimization), making it a key component in modular RL pipelines. -
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re-frame
A ClojureScript framework for building user interfaces
...It is used by both small startups and companies with over 500 developers, and it has delivered into production applications which are 40K lines of code and beyond. ClojureScript is a Lisp. Alan Kay once described Lisp as "Maxwell's equations of software". Paul Graham described how Lisp was a competitive advantage for his startup. When we use Lisp, we get to leverage 50 years of foliated excellence from the very best minds available. And then there's also a thriving ClojureScript community which delivers modern ideas and best-in-class tooling. Although re-frame leverages React (via Reagent), it only needs React to be the V in MVC, and no more. -
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Jazzy
Soulful docs for Swift & Objective-C
jazzy is a command-line utility that generates documentation for Swift or Objective-C. Instead of parsing your source files, jazzy hooks into Clang and SourceKit to use the AST representation of your code and its comments for more accurate results. The output matches the look and feel of Apple’s official reference documentation, post WWDC 2014. Jazzy can also generate documentation from compiled Swift modules using their symbol graph instead of source code. You need development tools to... -
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LMath library
Math library for Free Pascal and Lazarus.
...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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Continuation Core and Toolboxes (COCO)
Toolboxes for parameter continuation and bifurcation analysis.
Development platform and toolboxes for parameter continuation, e.g., bifurcation analysis of dynamical systems and constrained design optimization. This material is based upon work partially supported by the National Science Foundation under Grant No. 1016467 and the Danish research council (FTP) under the project number 0602-00753B. Any opinions, findings, and conclusions or recommendations expressed on this site are those of the authors and do not necessarily reflect the views of the... -
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DAE Tools Project
Object-oriented equation-based modelling and optimisation software
DAE Tools is a cross-platform equation-based object-oriented modelling, simulation and optimisation software. It is not a modelling language nor a collection of numerical libraries but rather a higher level structure – an architectural design of interdependent software components providing an API for: - Model development/specification - Activities on developed models, such as simulation, optimisation, sensitivity analysis and parameter estimation - Processing of the results, such as... -
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gophernotes
The Go kernel for Jupyter notebooks and nteract
gophernotes is a Go kernel for Jupyter notebooks and nteract. It lets you use Go interactively in a browser-based notebook or desktop app. Use gophernotes to create and share documents that contain live Go code, equations, visualizations and explanatory text. These notebooks, with the live Go code, can then be shared with others via email, Dropbox, GitHub and the Jupyter Notebook Viewer. Go forth and do data science, or anything else interesting, with Go notebooks! This project utilizes a Go interpreter called gomacro under the hood to evaluate Go code interactively. ... -
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Machine Learning Cheat Sheet
Classical equations and diagrams in machine learning
This repository is a visually rich and well-organized “cheat sheet” summarizing core machine learning concepts, algorithms, formulas, and best practices. It includes summaries of supervised and unsupervised learning methods, model evaluation metrics (accuracy, precision, recall, ROC/AUC), overfitting/underfitting, regularization (L1/L2), cross-validation, feature engineering techniques, and perhaps tips for hyperparameter tuning. Each section is presented concisely, often with diagrams,... -
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AdaAutoDiff
C++ Templates and Ada Package for Automatic Differentiation
Operators are overloaded so that a normal looking function definition provides access to not only evaluations of itself, but to evaluations of any of its analytic derivatives. Automatic differentiation means the user does not need to define the analytic expressions for all the various partial derivatives. It also means that those complex expressions are essentially calculated at compile time, and merely evaluated at runtime. First order derivatives only, forward... -
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CFD Python
Sequence of Jupyter notebooks featuring the 12 Steps to Navier-Stokes
CFD Python, a.k.a. the 12 steps to Navier-Stokes, is a practical module for learning the foundations of Computational Fluid Dynamics (CFD) by coding solutions to the basic partial differential equations that describe the physics of fluid flow. The module was part of a course taught by Prof. Lorena Barba between 2009 and 2013 in the Mechanical Engineering department at Boston University (Prof. Barba since moved to George Washington University). The module assumes only basic programming knowledge (in any language) and some background in partial differential equations and fluid mechanics. ... -
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CoRoPa stands for Computational Rough Paths. The aim of CoRoPa is to provide a software framework for various ideas related to Rough Path Theory, including rough differential equations and the digital description of serial data streams.
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Fast Matrix for Java
General purpose matrix utilities for Java in Parallel Computing
Fast Matrix for Java (fm4j) is a general-purpose matrix utility library for computing with dense matrices. fm4j encapsulated different underlying implementations and select the optimal one in run-time depending on the size of the input matrix. Moreover, fm4j employs Java (Tm) Concurrency to take advantage of the computation power of multi-cor processors. -
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Interdependent Java frameworks: AMath (abstract numbers support); AFuzzy (fuzzy numbers and methods); AMathSys (flexible solvers of linear and nonlinear algebraic and differential equations); ADSM (multi-criteria ranking and grading of alternatives).
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...Given some polyline, a finer segmented polyline is generated. The smoothed line may hit the original points or its length may be equal to the original length. Linear equations solvers are also provided.
