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- 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
- */
- }
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