Search Results for "numeric"

...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.

...A rule-based rewriting language can be used to find subexpressions that satisfy arbitrary conditions and apply arbitrary transformations on the matches. The library also contains a set of useful simplification rules for expressions of numeric symbols and numbers. These can be remixed and extended for special purposes.

...Simple syntax, so the Python code looks like Python and the Julia code looks like Julia. Intuitive and flexible conversions between Julia and Python: anything can be converted, you are in control. Fast non-copying conversion of numeric arrays in either direction: modify Python arrays (e.g. bytes, array. array, numpy.ndarray) from Julia or Julia arrays from Python. Helpful wrappers: interpret Python sequences, dictionaries, arrays, dataframes and IO streams as their Julia counterparts, and vice versa.

LazySets.jl is a Julia package for calculus with convex sets. The aim is to provide a scalable library for solving complex set-based problems, such as those encountered in differential inclusions or reachability analysis techniques in the domain of formal verification. Typically, one is confronted with a set-based recurrence with a given initial set and/or input sets, and for visualization purposes, the final result has to be obtained through an adequate projection onto low dimensions. This...

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].

TensorBoardLogger.jl is a native library for logging arbitrary data to Tensorboard, extending Julia's standard Logging framework. It can also be used to deserialize TensoBoard's .proto files. The fundamental type defined in this package is a TBLogger, which behaves like other standard loggers in Julia such as ConsoleLogger or TextLogger. You can create one by passing it the path to the folder where you want to store the data. You can also pass an optional second argument to specify the...

...It aims to be user friendly and performant, but also generic in the sense that the algorithms can be called with inputs of any (suitable) scalar types. This means that if fast numeric dynamics evaluations are required, a user can supply Float64 or Float32 inputs. However, if symbolic quantities are desired for analysis purposes, they can be obtained by calling the algorithms with e.g. SymPy.Sym inputs. If gradients are required, e.g. the ForwardDiff.Dual type, which implements forward-mode automatic differentiation, can be used.

...The project introduces AD from a foundational calculus perspective and gradually builds towards toy implementations that resemble systems like PyTorch and TensorFlow. It clarifies the differences and connections between forward mode, reverse mode, symbolic, numeric, tracing, and source transformation approaches to differentiation. Unlike production-grade AD systems that are often obscured by complex implementation details, these examples are deliberately simple and coherent to highlight the fundamental ideas. The repository is organized as a set of Julia notebooks, allowing learners to explore concepts interactively and compare different methods side by side. ...