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Linnea is an experimental tool for the automatic generation of optimized code for linear algebra problems. It is developed at the High-Performance and Automatic Computing group at RWTH Aachen University.


Linnea is a prototype of a compiler/program synthesis tool that automates the translation of the mathematical description of a linear algebra problem to an efficient sequence of calls to BLAS and LAPACK kernels. The main idea of Linnea is to construct a search graph that represents a large number of programs, taking into account knowledge about linear algebra, numerical linear algebra and high-performance computing. The algebraic nature of the domain is used to reduce the size of the search graph, without reducing the size of the search space that is explored.

The input to Linnea are linear algebra expressions. As operands, matrices, vectors and scalars are supported. Operands can be annotated with properties, such as \(lower triangular\) or \(symmetric\). Supported operations are addition, multiplication, transposition and inversion. At the moment, Linnea generates Julia code using BLAS and LAPACK wrappers whenever possible.