matrixmultiplyaccumulate

Matrix multiply accumulate, often abbreviated MMA or MAC, is a fundamental operation in linear algebra and high-performance computing. It combines a matrix product with an accumulation step into an existing matrix.

Formally, given A ∈ R^{m×k}, B ∈ R^{k×n}, and C ∈ R^{m×n}, with scalars α and β, the operation computes C := αAB + βC. The dimensions require k to match on the inner product, and the result is an m×n matrix. If α = 1 and β = 0, it reduces to the standard C := AB.

Hardware and software implementations rely on multiply-accumulate units or fused multiply-add (FMA) to perform a product and an add in a single instruction. Performance depends on data locality, so algorithms use tiling or blocking to reuse A, B, and C in caches and registers. SIMD and GPU GEMM kernels are specialized to exploit this pattern.

In software, matrixmultiplyaccumulate is the core operation behind the GEMM routine in BLAS and many linear algebra libraries. It often provides alpha and beta parameters and works with various data types and memory layouts.

Applications span neural networks, scientific computing, graphics, and large-scale data analysis, where efficient repeated matrix products with accumulation update results are essential.

Related concepts include general matrix multiply (GEMM), multiply-accumulate (MAC) units, fused multiply-add (FMA), and the BLAS standard.