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This project aims to integrate Kazushige Goto’s highly optimized matrix multiplication algorithms into the [xtensor](https://github.com/xtensor-stack/xtensor/) framework, leveraging the [xsimd](https://github.com/xtensor-stack/xsimd/) library for SIMD acceleration.
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##### Background
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The GOTO algorithms, formalized by Kazushige Goto and Robert van de Geijn in their landmark paper "Anatomy of High-Performance Matrix Multiplication", are the algorithmic foundations underlying high-performance libraries such as GotoBLAS and OpenBLAS. The algorithms achieve near-peak CPU throughput through a principled exploitation of the memory hierarchy.
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xtensor library is a popular C++ library for numerical analysis with a focus on multi-dimensional arrays and broadcasting, inspired by NumPy. xtensor leverages SIMD acceleration through the xsimd library and offers language bindings for Python, Julia and R.
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By integrating Goto's algorithms into xtensor and using xsimd for SIMD optimizations, we can provide users with faster matrix operations, especially for large-scale computations.
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##### Objectives
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- Study and understand Kazushige Goto's matrix multiplication algorithms.
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- Implement these algorithms in C++ using xsimd for SIMD acceleration. This implementation could be done in a way that is not tied to the xtensor codebase for better reusability.
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- Integrate the implementation into the xtensor framework.
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- Benchmark the performance against existing xtensor matrix operations and other libraries like Eigen and BLAS.
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- Document the implementation and provide examples for users.
title: "Implementing Kazushige Goto Algorithms for Matrix Operations in xtensor",
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pageName: "MatrixOperationsInXtensor",
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shortDescription: "This project aims to integrate Kazushige Goto’s highly optimized matrix multiplication algorithms into the [xtensor](https://github.com/xtensor-stack/xtensor/) framework, leveraging the [xsimd](https://github.com/xtensor-stack/xsimd/) library for SIMD acceleration.",
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