An experimental tool for the automatic generation of optimized code for linear algebra problems.
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 requires Python 3.6 and can be installed with
pip install git+git://github.com/HPAC/linnea.git. (Depending on your setup, you may have to use
pip3 instead of
pip.) To uninstall Linnea, use
pip uninstall linnea. This also removes the commandline tool.
If you intend to contribute to Linnea, you can install it from local sources by running
pip install -e . in your local development directory.
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 (see https://julialang.org), using BLAS and LAPACK wrappers whenever possible.
Linnea can be used in two different ways.
At the moment, Linnea is primarily a Python module. An example script for how to use Linnea within Python can found in
examples/run_linnea.py. The input expressions are represented as Python objects. As an example, consider the description of a lower triangular linear system (omitting imports):
n = 1000 L = Matrix("L", (n, n)) L.set_property(properties.LOWER_TRIANGULAR) L.set_property(properties.FULL_RANK) x = Vector("x", (n, 1)) y = Vector("y", (n, 1)) input = Equations(Equal(y, Times(Inverse(L), x)))
Further examples of input problems are provided in the
Options can be set with a number of
When installing Linnea via
pip, the commandline tool
linnea is installed. As input, it takes a description of the input problem in a simple custom language. With this language, the same lower triangular system is described as:
n = 1000 Matrix L(n, n) <LowerTriangular, FullRank> ColumnVector x(n) <> ColumnVector y(n) <> y = inv(L)*x
Further examples are provided in
examples/inputX.la. Notice that the primary purpose of this input format is to make it slightly easier to try out Linnea. There are no plans to establish this as an actual language. New features will probably not be immediately available in this language, and the language may change in the future without being backward compatible.
The list of commandline options is available via
As output, Linnea generates a directory structure that contains code files, as well a file containing a description of the derivation graph, the primary datastructure used by Linnea. Which files are generated can be set as options. Likewise, the location of the output can be specified. By default, it is the current directory.
For the linear system from the previous examples, the following code will be generated:
using LinearAlgebra.BLAS using LinearAlgebra function algorithm0(ml0, ml1) # cost 1e+06 # L: ml0, full, x: ml1, full # tmp1 = (L^-1 x) trsv!('L', 'N', 'N', ml0, ml1) # tmp1: ml1, full # y = tmp1 return (ml1) end
Linnea offers a number of options which can be set through
linnea.config in Python or as commandline options for the commandline tool. Alternatively, all options can also be specified in a
linnea_config.json file (see
examples) which has to be located in the same directory where Linnea is run, or at the user's
$HOME folder. Both commandline options and
linnea.config options override what is specified in
linnea_config.json. As a fallback, reasonable default values are used.
There are the following options (those are the names used in Python, the commandline options have slightly different names. See
output_code_pathThe output of Linnea will be stored in this directory. The default is the current directory.
output_nameLinnea creates a new directory that contains all output files. This is the name of this directory. The default is
languageNot available for the commandline tool. For now, the only allowed option is
julia_data_typeThe data type used in the generated code. Either
Float64. The default is
merging_branchesWhether or not to merge branches in the derivation graph. The default is
dead_endsWhether or not to eliminate dead ends in the derivation graph early. The default is
algorithms_limitThe upper limit for the number of algorithms that are written to files. The default is
strategyThe strategy used to find algorithms. Either
exhaustive. The default is
generate_graphWhether or not to generate a
.gvfile of the derivation graph. The default is
graph_styleStyle of the derivation graph. Either
minimal. The default is
full. Only applies if
generate_graphis set to
generate_derivationWhether or not to generate a description of how the algorithms were derived. The default is
generate_codeWhether or not to generate the actual code of the algorithms. The default is
generate_experimentsWhether or not to generate code that can be used to run the algorithms. The default is
verbosityLevel of verbosity. The default is
A number of publications that discuss different aspects of Linnea can be found here.
- Henrik Barthels
- Marcin Copik
- Diego Fabregat Traver
- Julius Hohnerlein
- Manuel Krebber
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