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PDFIO is a native Julia implementation for reading PDF files. It's a 100% Julia implementation of the PDF specification. Other than a few well-established algorithms like flate decode (zlib library) or cryptographic operations (OpenSSL library) almost all of the APIs are written in native Julia. PDF files are in existence for over three decades. Implementations of the PDF writers are not always to the specification or they may even vary significantly from vendor to vendor.

Optimization.jl provides the easiest way to create an optimization problem and solve it. It enables rapid prototyping and experimentation with minimal syntax overhead by providing a uniform interface to >25 optimization libraries, hence 100+ optimization solvers encompassing almost all classes of optimization algorithms such as global, mixed-integer, non-convex, second-order local, constrained, etc. It allows you to choose an Automatic Differentiation (AD) backend by simply passing an argument to indicate the package to use and automatically generates the efficient derivatives of the objective and constraints while giving you the flexibility to switch between different AD engines as per your problem. ...

Flux is an elegant approach to machine learning. 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.

Package JuliaCall is an R interface to Julia, which is a high-level, high-performance dynamic programming language for numerical computing. Below is an image for Mandelbrot set. JuliaCall brings more than 100 times speedup of the calculation.