You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
239 lines
8.0 KiB
239 lines
8.0 KiB
namespace Eigen {
|
|
|
|
/** \page TutorialBlockOperations Tutorial page 4 - %Block operations
|
|
\ingroup Tutorial
|
|
|
|
\li \b Previous: \ref TutorialArrayClass
|
|
\li \b Next: \ref TutorialAdvancedInitialization
|
|
|
|
This tutorial 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.
|
|
|
|
\b Table \b of \b contents
|
|
- \ref TutorialBlockOperationsUsing
|
|
- \ref TutorialBlockOperationsSyntaxColumnRows
|
|
- \ref TutorialBlockOperationsSyntaxCorners
|
|
- \ref TutorialBlockOperationsSyntaxVectors
|
|
|
|
|
|
\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>
|
|
|
|
\li \b Next: \ref TutorialAdvancedInitialization
|
|
|
|
*/
|
|
|
|
}
|