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Expression Templates Library (ETL) 1.3.0

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ETL is a header only library for C++ that provides vector and matrix classes with support for Expression Templates to perform very efficient operations on them.

At this time, the library support compile-time sized matrix and vector and runtime-sized matrix and vector with all element-wise operations implemented. It also supports 1D and 2D convolution, matrix multiplication (naive algorithm and Strassen) and FFT.

You can clone this repository directly to get all ETL features. I advice using it as a submodule of your current project, but you can install it anywhere you like. There are several branches you can chose from

  • master: The main development branch
  • stable: The last stable version

You can also access by tag to a fixed version such as the tag 1.0.


The Reference Documentation is always available on the wiki. This document contains the most basic information that should be enough to get you started.

The library is header-only and does not need to be built it at all, you just have to include its header files.

Most of the headers are not meant to be included directly inside a program. Here are the header that are made to be included:

  • etl.hpp: Contains all the features of the library
  • etl_light.hpp: Contains the basic features of the library (no matrix multiplication, no convolution, no FFT)

You should always include one of these headers in your program. You should never include any other header from the library.

Data structures

Several data structures are available:

  • fast_matrix<T, Dim...>: A matrix of variadic size with elements of type T. This must be used when you know the size of the vector at compile-time. The number of dimensions can be anything. The data is stored is stored directly inside the matrix.
  • fast_dyn_matrix<T, Dim...>: Variant of fast_matrix where the data is stored on the heap.
  • dyn_matrix<T, D>: A matrix with element of type T. The size of the matrix can be set at runtime. The matrix can have D dimensions.

There also exists typedefs for vectors:

  • fast_vector<T, Rows>>
  • fast_dyn_vector<T, Rows>>
  • dyn_vector<T>

You have to keep in mind that fast_matrix directly store its values inside it, therefore, it can be very large and should rarely be stored on the stack. Moreover, that also makes it very expensive to move and copy. This is why fast_dyn_matrix may be an interesting alternative.

Element-wise operations

Classic element-wise operations can be done on vector and matrix as if it was done on scalars. Matrices and vectors can also be added,subtracted,divided, ... by scalars.

etl::dyn_vector<double> a{1.0,2.0,3.0};
etl::dyn_vector<double> b{3.0,2.0,1.0};
etl::dyn_vector<double> c;

c = 1.4 * (a + b) / b + b + a / 1.2;

All the operations are only executed once the expression is evaluated to be assigned to a data structure.

Unary operators

Several unary operators are available. Each operation is performed on every element of the vector or the matrix.

Available operators:

  • log
  • abs
  • sign
  • max/min
  • sigmoid
  • noise: Add standard normal noise to each element
  • logistic_noise: Add normal noise of mean zero and variance sigmoid(x) to each element
  • exp
  • softplus
  • bernoulli

Several transformations are also available:

  • hflip: Flip the vector or the matrix horizontally
  • vflip: Flip the vector or the matrix vertically
  • fflip: Flip the vector or the matrix horizontally and vertically. It is the equivalent of hflip(vflip(x))
  • sub: Return a sub part of the matrix. The first dimension is forced to a special value. It works with matrices of any dimension.
  • dim/row/col: Return a vector representing a sub part of a matrix (a row or a col)
  • reshape: Interpret a vector as a matrix


Several reduction functions are available:

  • sum: Return the sum of a vector or matrix
  • mean: Return the sum of a vector or matrix
  • dot: Return the dot product of two vector or matrices


The header convolution.hpp provides several convolution operations both in 1D (vector) and 2D (matrix).

The header mutiplication.hpp provides the matrix multiplication operation. mmul is the naive algorithm (ijk), which strassen_mmul implements Strassen algorithm.

It is possible to pass an expression rather than an data structure to functions. Keep in mind that expression are lazy, therefore if you pass a + b to a matrix multiplication, an addition will be run each time an element is accessed, therefore, it is not often efficient.


It is also possible to generate sequences of data and perform operations on them.

For now, two generators are available:

  • normal_generator: Generates real numbers distributed on a normal distribution
  • sequence_generator(c=0): Generates numbers in sequence from c

All sequences are considered to have infinite size, therefore, they can be used to initialize or modify any containers or expressions.


This library is completely header-only, there is no need to build it.

However, this library makes extensive use of C++17 and some features of C++20, therefore, a recent compiler is necessary to use it. This library is currently tested on the following compilers:

  • GCC 9.3.0 and greater

If compilation does not work on one of these compilers, or produces warnings, please open an issue on Github and I'll do my best to fix the issue.

The library has never been tested on Windows.

The folders include and lib/include must be included with the -I option.

There are no link-time dependencies.

If you have problems compiling this library, I'd be glad to help, but I do not guarantee that this will work on every compiler. I strongly expect it to not build under Visual Studio.


This library is distributed under the terms of the MIT license, see LICENSE file for details.