nest-open-source / nest-cam / v366 / eigen / 9d75fdbcd2b5a2fdab03a859ddefda95ce1217ed / . / doc / NewExpressionType.dox

namespace Eigen { | |

/** \page TopicNewExpressionType Adding a new expression type | |

<!--<span style="font-size:130%; color:red; font-weight: 900;"></span>--> | |

\warning | |

Disclaimer: this page is tailored to very advanced users who are not afraid of dealing with some %Eigen's internal aspects. | |

In most cases, a custom expression can be avoided by either using custom \ref MatrixBase::unaryExpr "unary" or \ref MatrixBase::binaryExpr "binary" functors, | |

while extremely complex matrix manipulations can be achieved by a nullary functors as described in the \ref TopicCustomizing_NullaryExpr "previous page". | |

This page describes with the help of an example how to implement a new | |

light-weight expression type in %Eigen. This consists of three parts: | |

the expression type itself, a traits class containing compile-time | |

information about the expression, and the evaluator class which is | |

used to evaluate the expression to a matrix. | |

\b TO \b DO: Write a page explaining the design, with details on | |

vectorization etc., and refer to that page here. | |

\eigenAutoToc | |

\section TopicSetting The setting | |

A circulant matrix is a matrix where each column is the same as the | |

column to the left, except that it is cyclically shifted downwards. | |

For example, here is a 4-by-4 circulant matrix: | |

\f[ \begin{bmatrix} | |

1 & 8 & 4 & 2 \\ | |

2 & 1 & 8 & 4 \\ | |

4 & 2 & 1 & 8 \\ | |

8 & 4 & 2 & 1 | |

\end{bmatrix} \f] | |

A circulant matrix is uniquely determined by its first column. We wish | |

to write a function \c makeCirculant which, given the first column, | |

returns an expression representing the circulant matrix. | |

For simplicity, we restrict the \c makeCirculant function to dense | |

matrices. It may make sense to also allow arrays, or sparse matrices, | |

but we will not do so here. We also do not want to support | |

vectorization. | |

\section TopicPreamble Getting started | |

We will present the file implementing the \c makeCirculant function | |

part by part. We start by including the appropriate header files and | |

forward declaring the expression class, which we will call | |

\c Circulant. The \c makeCirculant function will return an object of | |

this type. The class \c Circulant is in fact a class template; the | |

template argument \c ArgType refers to the type of the vector passed | |

to the \c makeCirculant function. | |

\include make_circulant.cpp.preamble | |

\section TopicTraits The traits class | |

For every expression class \c X, there should be a traits class | |

\c Traits<X> in the \c Eigen::internal namespace containing | |

information about \c X known as compile time. | |

As explained in \ref TopicSetting, we designed the \c Circulant | |

expression class to refer to dense matrices. The entries of the | |

circulant matrix have the same type as the entries of the vector | |

passed to the \c makeCirculant function. The type used to index the | |

entries is also the same. Again for simplicity, we will only return | |

column-major matrices. Finally, the circulant matrix is a square | |

matrix (number of rows equals number of columns), and the number of | |

rows equals the number of rows of the column vector passed to the | |

\c makeCirculant function. If this is a dynamic-size vector, then the | |

size of the circulant matrix is not known at compile-time. | |

This leads to the following code: | |

\include make_circulant.cpp.traits | |

\section TopicExpression The expression class | |

The next step is to define the expression class itself. In our case, | |

we want to inherit from \c MatrixBase in order to expose the interface | |

for dense matrices. In the constructor, we check that we are passed a | |

column vector (see \ref TopicAssertions) and we store the vector from | |

which we are going to build the circulant matrix in the member | |

variable \c m_arg. Finally, the expression class should compute the | |

size of the corresponding circulant matrix. As explained above, this | |

is a square matrix with as many columns as the vector used to | |

construct the matrix. | |

\b TO \b DO: What about the \c Nested typedef? It seems to be | |

necessary; is this only temporary? | |

\include make_circulant.cpp.expression | |

\section TopicEvaluator The evaluator | |

The last big fragment implements the evaluator for the \c Circulant | |

expression. The evaluator computes the entries of the circulant | |

matrix; this is done in the \c .coeff() member function. The entries | |

are computed by finding the corresponding entry of the vector from | |

which the circulant matrix is constructed. Getting this entry may | |

actually be non-trivial when the circulant matrix is constructed from | |

a vector which is given by a complicated expression, so we use the | |

evaluator which corresponds to the vector. | |

The \c CoeffReadCost constant records the cost of computing an entry | |

of the circulant matrix; we ignore the index computation and say that | |

this is the same as the cost of computing an entry of the vector from | |

which the circulant matrix is constructed. | |

In the constructor, we save the evaluator for the column vector which | |

defined the circulant matrix. We also save the size of that vector; | |

remember that we can query an expression object to find the size but | |

not the evaluator. | |

\include make_circulant.cpp.evaluator | |

\section TopicEntry The entry point | |

After all this, the \c makeCirculant function is very simple. It | |

simply creates an expression object and returns it. | |

\include make_circulant.cpp.entry | |

\section TopicMain A simple main function for testing | |

Finally, a short \c main function that shows how the \c makeCirculant | |

function can be called. | |

\include make_circulant.cpp.main | |

If all the fragments are combined, the following output is produced, | |

showing that the program works as expected: | |

\include make_circulant.out | |

*/ | |

} | |