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- namespace Eigen {
- /** \eigenManualPage TutorialBlockOperations Block operations
- This page explains the essentials of block operations.
- A block is a rectangular part of a matrix or array. Blocks expressions can be used both
- as rvalues and as lvalues. As usual with Eigen expressions, this abstraction has zero runtime cost
- provided that you let your compiler optimize.
- \eigenAutoToc
- \section TutorialBlockOperationsUsing Using block operations
- The most general block operation in Eigen is called \link DenseBase::block() .block() \endlink.
- There are two versions, whose syntax is as follows:
- <table class="manual">
- <tr><th>\b %Block \b operation</td>
- <th>Version constructing a \n dynamic-size block expression</th>
- <th>Version constructing a \n fixed-size block expression</th></tr>
- <tr><td>%Block of size <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td>
- <td>\code
- matrix.block(i,j,p,q);\endcode </td>
- <td>\code
- matrix.block<p,q>(i,j);\endcode </td>
- </tr>
- </table>
- As always in Eigen, indices start at 0.
- Both versions can be used on fixed-size and dynamic-size matrices and arrays.
- These two expressions are semantically equivalent.
- The only difference is that the fixed-size version will typically give you faster code if the block size is small,
- but requires this size to be known at compile time.
- The following program uses the dynamic-size and fixed-size versions to print the values of several blocks inside a
- matrix.
- <table class="example">
- <tr><th>Example:</th><th>Output:</th></tr>
- <tr><td>
- \include Tutorial_BlockOperations_print_block.cpp
- </td>
- <td>
- \verbinclude Tutorial_BlockOperations_print_block.out
- </td></tr></table>
- In the above example the \link DenseBase::block() .block() \endlink function was employed as a \em rvalue, i.e.
- it was only read from. However, blocks can also be used as \em lvalues, meaning that you can assign to a block.
- This is illustrated in the following example. This example also demonstrates blocks in arrays, which works exactly like the above-demonstrated blocks in matrices.
- <table class="example">
- <tr><th>Example:</th><th>Output:</th></tr>
- <tr><td>
- \include Tutorial_BlockOperations_block_assignment.cpp
- </td>
- <td>
- \verbinclude Tutorial_BlockOperations_block_assignment.out
- </td></tr></table>
- While the \link DenseBase::block() .block() \endlink method can be used for any block operation, there are
- other methods for special cases, providing more specialized API and/or better performance. On the topic of performance, all what
- matters is that you give Eigen as much information as possible at compile time. For example, if your block is a single whole column in a matrix,
- using the specialized \link DenseBase::col() .col() \endlink function described below lets Eigen know that, which can give it optimization opportunities.
- The rest of this page describes these specialized methods.
- \section TutorialBlockOperationsSyntaxColumnRows Columns and rows
- Individual columns and rows are special cases of blocks. Eigen provides methods to easily address them:
- \link DenseBase::col() .col() \endlink and \link DenseBase::row() .row()\endlink.
- <table class="manual">
- <tr><th>%Block operation</th>
- <th>Method</th>
- <tr><td>i<sup>th</sup> row
- \link DenseBase::row() * \endlink</td>
- <td>\code
- matrix.row(i);\endcode </td>
- </tr>
- <tr><td>j<sup>th</sup> column
- \link DenseBase::col() * \endlink</td>
- <td>\code
- matrix.col(j);\endcode </td>
- </tr>
- </table>
- The argument for \p col() and \p row() is the index of the column or row to be accessed. As always in Eigen, indices start at 0.
- <table class="example">
- <tr><th>Example:</th><th>Output:</th></tr>
- <tr><td>
- \include Tutorial_BlockOperations_colrow.cpp
- </td>
- <td>
- \verbinclude Tutorial_BlockOperations_colrow.out
- </td></tr></table>
- That example also demonstrates that block expressions (here columns) can be used in arithmetic like any other expression.
- \section TutorialBlockOperationsSyntaxCorners Corner-related operations
- Eigen also provides special methods for blocks that are flushed against one of the corners or sides of a
- matrix or array. For instance, \link DenseBase::topLeftCorner() .topLeftCorner() \endlink can be used to refer
- to a block in the top-left corner of a matrix.
- The different possibilities are summarized in the following table:
- <table class="manual">
- <tr><th>%Block \b operation</td>
- <th>Version constructing a \n dynamic-size block expression</th>
- <th>Version constructing a \n fixed-size block expression</th></tr>
- <tr><td>Top-left p by q block \link DenseBase::topLeftCorner() * \endlink</td>
- <td>\code
- matrix.topLeftCorner(p,q);\endcode </td>
- <td>\code
- matrix.topLeftCorner<p,q>();\endcode </td>
- </tr>
- <tr><td>Bottom-left p by q block
- \link DenseBase::bottomLeftCorner() * \endlink</td>
- <td>\code
- matrix.bottomLeftCorner(p,q);\endcode </td>
- <td>\code
- matrix.bottomLeftCorner<p,q>();\endcode </td>
- </tr>
- <tr><td>Top-right p by q block
- \link DenseBase::topRightCorner() * \endlink</td>
- <td>\code
- matrix.topRightCorner(p,q);\endcode </td>
- <td>\code
- matrix.topRightCorner<p,q>();\endcode </td>
- </tr>
- <tr><td>Bottom-right p by q block
- \link DenseBase::bottomRightCorner() * \endlink</td>
- <td>\code
- matrix.bottomRightCorner(p,q);\endcode </td>
- <td>\code
- matrix.bottomRightCorner<p,q>();\endcode </td>
- </tr>
- <tr><td>%Block containing the first q rows
- \link DenseBase::topRows() * \endlink</td>
- <td>\code
- matrix.topRows(q);\endcode </td>
- <td>\code
- matrix.topRows<q>();\endcode </td>
- </tr>
- <tr><td>%Block containing the last q rows
- \link DenseBase::bottomRows() * \endlink</td>
- <td>\code
- matrix.bottomRows(q);\endcode </td>
- <td>\code
- matrix.bottomRows<q>();\endcode </td>
- </tr>
- <tr><td>%Block containing the first p columns
- \link DenseBase::leftCols() * \endlink</td>
- <td>\code
- matrix.leftCols(p);\endcode </td>
- <td>\code
- matrix.leftCols<p>();\endcode </td>
- </tr>
- <tr><td>%Block containing the last q columns
- \link DenseBase::rightCols() * \endlink</td>
- <td>\code
- matrix.rightCols(q);\endcode </td>
- <td>\code
- matrix.rightCols<q>();\endcode </td>
- </tr>
- </table>
- Here is a simple example illustrating the use of the operations presented above:
- <table class="example">
- <tr><th>Example:</th><th>Output:</th></tr>
- <tr><td>
- \include Tutorial_BlockOperations_corner.cpp
- </td>
- <td>
- \verbinclude Tutorial_BlockOperations_corner.out
- </td></tr></table>
- \section TutorialBlockOperationsSyntaxVectors Block operations for vectors
- Eigen also provides a set of block operations designed specifically for the special case of vectors and one-dimensional arrays:
- <table class="manual">
- <tr><th> %Block operation</th>
- <th>Version constructing a \n dynamic-size block expression</th>
- <th>Version constructing a \n fixed-size block expression</th></tr>
- <tr><td>%Block containing the first \p n elements
- \link DenseBase::head() * \endlink</td>
- <td>\code
- vector.head(n);\endcode </td>
- <td>\code
- vector.head<n>();\endcode </td>
- </tr>
- <tr><td>%Block containing the last \p n elements
- \link DenseBase::tail() * \endlink</td>
- <td>\code
- vector.tail(n);\endcode </td>
- <td>\code
- vector.tail<n>();\endcode </td>
- </tr>
- <tr><td>%Block containing \p n elements, starting at position \p i
- \link DenseBase::segment() * \endlink</td>
- <td>\code
- vector.segment(i,n);\endcode </td>
- <td>\code
- vector.segment<n>(i);\endcode </td>
- </tr>
- </table>
- An example is presented below:
- <table class="example">
- <tr><th>Example:</th><th>Output:</th></tr>
- <tr><td>
- \include Tutorial_BlockOperations_vector.cpp
- </td>
- <td>
- \verbinclude Tutorial_BlockOperations_vector.out
- </td></tr></table>
- */
- }
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