87 lines
3.6 KiB
Plaintext
87 lines
3.6 KiB
Plaintext
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namespace Eigen {
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/** \page TopicCustomizing_NullaryExpr Matrix manipulation via nullary-expressions
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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.
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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.
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\section NullaryExpr_Circulant Example 1: circulant matrix
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To explore these possibilities let us start with the \em circulant example of the \ref TopicNewExpressionType "implementing new expression" topic.
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Let us recall that a circulant matrix is a matrix where each column is the same as the
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column to the left, except that it is cyclically shifted downwards.
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For example, here is a 4-by-4 circulant matrix:
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\f[ \begin{bmatrix}
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1 & 8 & 4 & 2 \\
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2 & 1 & 8 & 4 \\
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4 & 2 & 1 & 8 \\
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8 & 4 & 2 & 1
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\end{bmatrix} \f]
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A circulant matrix is uniquely determined by its first column. We wish
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to write a function \c makeCirculant which, given the first column,
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returns an expression representing the circulant matrix.
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For this exercise, the return type of \c makeCirculant will be a CwiseNullaryOp that we need to instantiate with:
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1 - a proper \c circulant_functor storing the input vector and implementing the adequate coefficient accessor \c operator(i,j)
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2 - a template instantiation of class Matrix conveying compile-time information such as the scalar type, sizes, and preferred storage layout.
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Calling \c ArgType the type of the input vector, we can construct the equivalent squared Matrix type as follows:
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\snippet make_circulant2.cpp square
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This little helper structure will help us to implement our \c makeCirculant function as follows:
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\snippet make_circulant2.cpp makeCirculant
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As usual, our function takes as argument a \c MatrixBase (see this \ref TopicFunctionTakingEigenTypes "page" for more details).
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Then, the CwiseNullaryOp object is constructed through the DenseBase::NullaryExpr static method with the adequate runtime sizes.
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Then, we need to implement our \c circulant_functor, which is a straightforward exercise:
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\snippet make_circulant2.cpp circulant_func
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We are now all set to try our new feature:
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\snippet make_circulant2.cpp main
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If all the fragments are combined, the following output is produced,
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showing that the program works as expected:
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\include make_circulant2.out
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This implementation of \c makeCirculant is much simpler than \ref TopicNewExpressionType "defining a new expression" from scratch.
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\section NullaryExpr_Indexing Example 2: indexing rows and columns
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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:
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\snippet nullary_indexing.out main1
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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):
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\snippet nullary_indexing.cpp functor
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Then, let's create an \c indexing(A,rows,cols) function creating the nullary expression:
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\snippet nullary_indexing.cpp function
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Finally, here is an example of how this function can be used:
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\snippet nullary_indexing.cpp main1
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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.
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\snippet nullary_indexing.cpp main2
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and the output is:
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\snippet nullary_indexing.out main2
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*/
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}
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