| 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 | |
| */ | |
| } | |