Search Results for "notation"

Julia-based implementation of ellipsis array indexing notation. This implements the notation .. for indexing arrays. It's similar to Python, in that it means "all the columns before (or after)". Note: .. slurps dimensions greedily, meaning that the first occurrence of .. in an index expression creates as many slices as possible. Other instances of .. afterward are treated simply as slices.

This package lets you work with multi-dimensional arrays in index notation, by defining a few macros which translate this to broadcasting, permuting, and reducing operations.

ParallelStencil empowers domain scientists to write architecture-agnostic high-level code for parallel high-performance stencil computations on GPUs and CPUs. Performance similar to CUDA C / HIP can be achieved, which is typically a large improvement over the performance reached when using only CUDA.jl or AMDGPU.jl GPU Array programming. For example, a 2-D shallow ice solver presented at JuliaCon 2020 [1] achieved a nearly 20 times better performance than a corresponding GPU Array...

Tullio is a very flexible einsum macro. It understands many array operations written in index notation -- not just matrix multiplication and permutations, but also convolutions, stencils, scatter/gather, and broadcasting. Used by itself the macro writes ordinary nested loops much like Einsum.@einsum. One difference is that it can parse more expressions, and infer ranges for their indices. Another is that it will use multi-threading (via Threads.

...It's a 100% pure Julia stack and provides lightweight abstractions on top of Julia's native GPU and AD support. Flux makes the easy things easy while remaining fully hackable. Flux provides a single, intuitive way to define models, just like mathematical notation. Julia transparently compiles your code, optimizing and fusing kernels for the GPU, for the best performance. Existing Julia libraries are differentiable and can be incorporated directly into Flux models. Cutting-edge models such as Neural ODEs are first class, and Zygote enables overhead-free gradients. GPU kernels can be written directly in Julia via CUDA.jl. ...

Gridap provides a set of tools for the grid-based approximation of partial differential equations (PDEs) written in the Julia programming language. The library currently supports linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element (FE) discretizations, on structured and unstructured meshes of simplices and n-cubes. It also provides methods for time integration. Gridap is extensible and modular. One can...

This is a package for Structural Equation Modeling in development. It is written for extensibility, that is, you can easily define your own objective functions and other parts of the model. At the same time, it is (very) fast. We provide fast objective functions, gradients, and for some cases hessians as well as approximations thereof. As a user, you can easily define custom loss functions. For those, you can decide to provide analytical gradients or use finite difference approximation /...