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