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

namespace Eigen { | |

/** \page TopicCustomizing_NullaryExpr Matrix manipulation via nullary-expressions | |

The main purpose of the class CwiseNullaryOp is to define \em procedural matrices such as constant or random matrices as returned by the Ones(), Zero(), Constant(), Identity() and Random() methods. | |

Nevertheless, with some imagination it is possible to accomplish very sophisticated matrix manipulation with minimal efforts such that \ref TopicNewExpressionType "implementing new expression" is rarely needed. | |

\section NullaryExpr_Circulant Example 1: circulant matrix | |

To explore these possibilities let us start with the \em circulant example of the \ref TopicNewExpressionType "implementing new expression" topic. | |

Let us recall that 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 this exercise, the return type of \c makeCirculant will be a CwiseNullaryOp that we need to instantiate with: | |

1 - a proper \c circulant_functor storing the input vector and implementing the adequate coefficient accessor \c operator(i,j) | |

2 - a template instantiation of class Matrix conveying compile-time information such as the scalar type, sizes, and preferred storage layout. | |

Calling \c ArgType the type of the input vector, we can construct the equivalent squared Matrix type as follows: | |

\snippet make_circulant2.cpp square | |

This little helper structure will help us to implement our \c makeCirculant function as follows: | |

\snippet make_circulant2.cpp makeCirculant | |

As usual, our function takes as argument a \c MatrixBase (see this \ref TopicFunctionTakingEigenTypes "page" for more details). | |

Then, the CwiseNullaryOp object is constructed through the DenseBase::NullaryExpr static method with the adequate runtime sizes. | |

Then, we need to implement our \c circulant_functor, which is a straightforward exercise: | |

\snippet make_circulant2.cpp circulant_func | |

We are now all set to try our new feature: | |

\snippet make_circulant2.cpp main | |

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

showing that the program works as expected: | |

\include make_circulant2.out | |

This implementation of \c makeCirculant is much simpler than \ref TopicNewExpressionType "defining a new expression" from scratch. | |

\section NullaryExpr_Indexing Example 2: indexing rows and columns | |

The goal here is to mimic MatLab's ability to index a matrix through two vectors of indices referencing the rows and columns to be picked respectively, like this: | |

\snippet nullary_indexing.out main1 | |

To this end, let us first write a nullary-functor storing references to the input matrix and to the two arrays of indices, and implementing the required \c operator()(i,j): | |

\snippet nullary_indexing.cpp functor | |

Then, let's create an \c indexing(A,rows,cols) function creating the nullary expression: | |

\snippet nullary_indexing.cpp function | |

Finally, here is an example of how this function can be used: | |

\snippet nullary_indexing.cpp main1 | |

This straightforward implementation is already quite powerful as the row or column index arrays can also be expressions to perform offsetting, modulo, striding, reverse, etc. | |

\snippet nullary_indexing.cpp main2 | |

and the output is: | |

\snippet nullary_indexing.out main2 | |

*/ | |

} | |