1 namespace Eigen { 2 3 /** \eigenManualPage TutorialBlockOperations Block operations 4 5 This page explains the essentials of block operations. 6 A block is a rectangular part of a matrix or array. Blocks expressions can be used both 7 as rvalues and as lvalues. As usual with Eigen expressions, this abstraction has zero runtime cost 8 provided that you let your compiler optimize. 9 10 \eigenAutoToc 11 12 \section TutorialBlockOperationsUsing Using block operations 13 14 The most general block operation in Eigen is called \link DenseBase::block() .block() \endlink. 15 There are two versions, whose syntax is as follows: 16 17 <table class="manual"> 18 <tr><th>\b %Block \b operation</td> 19 <th>Version constructing a \n dynamic-size block expression</th> 20 <th>Version constructing a \n fixed-size block expression</th></tr> 21 <tr><td>%Block of size <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td> 22 <td>\code 23 matrix.block(i,j,p,q);\endcode </td> 24 <td>\code 25 matrix.block<p,q>(i,j);\endcode </td> 26 </tr> 27 </table> 28 29 As always in Eigen, indices start at 0. 30 31 Both versions can be used on fixed-size and dynamic-size matrices and arrays. 32 These two expressions are semantically equivalent. 33 The only difference is that the fixed-size version will typically give you faster code if the block size is small, 34 but requires this size to be known at compile time. 35 36 The following program uses the dynamic-size and fixed-size versions to print the values of several blocks inside a 37 matrix. 38 39 <table class="example"> 40 <tr><th>Example:</th><th>Output:</th></tr> 41 <tr><td> 42 \include Tutorial_BlockOperations_print_block.cpp 43 </td> 44 <td> 45 \verbinclude Tutorial_BlockOperations_print_block.out 46 </td></tr></table> 47 48 In the above example the \link DenseBase::block() .block() \endlink function was employed as a \em rvalue, i.e. 49 it was only read from. However, blocks can also be used as \em lvalues, meaning that you can assign to a block. 50 51 This is illustrated in the following example. This example also demonstrates blocks in arrays, which works exactly like the above-demonstrated blocks in matrices. 52 53 <table class="example"> 54 <tr><th>Example:</th><th>Output:</th></tr> 55 <tr><td> 56 \include Tutorial_BlockOperations_block_assignment.cpp 57 </td> 58 <td> 59 \verbinclude Tutorial_BlockOperations_block_assignment.out 60 </td></tr></table> 61 62 While the \link DenseBase::block() .block() \endlink method can be used for any block operation, there are 63 other methods for special cases, providing more specialized API and/or better performance. On the topic of performance, all what 64 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, 65 using the specialized \link DenseBase::col() .col() \endlink function described below lets Eigen know that, which can give it optimization opportunities. 66 67 The rest of this page describes these specialized methods. 68 69 \section TutorialBlockOperationsSyntaxColumnRows Columns and rows 70 71 Individual columns and rows are special cases of blocks. Eigen provides methods to easily address them: 72 \link DenseBase::col() .col() \endlink and \link DenseBase::row() .row()\endlink. 73 74 <table class="manual"> 75 <tr><th>%Block operation</th> 76 <th>Method</th> 77 <tr><td>i<sup>th</sup> row 78 \link DenseBase::row() * \endlink</td> 79 <td>\code 80 matrix.row(i);\endcode </td> 81 </tr> 82 <tr><td>j<sup>th</sup> column 83 \link DenseBase::col() * \endlink</td> 84 <td>\code 85 matrix.col(j);\endcode </td> 86 </tr> 87 </table> 88 89 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. 90 91 <table class="example"> 92 <tr><th>Example:</th><th>Output:</th></tr> 93 <tr><td> 94 \include Tutorial_BlockOperations_colrow.cpp 95 </td> 96 <td> 97 \verbinclude Tutorial_BlockOperations_colrow.out 98 </td></tr></table> 99 100 That example also demonstrates that block expressions (here columns) can be used in arithmetic like any other expression. 101 102 103 \section TutorialBlockOperationsSyntaxCorners Corner-related operations 104 105 Eigen also provides special methods for blocks that are flushed against one of the corners or sides of a 106 matrix or array. For instance, \link DenseBase::topLeftCorner() .topLeftCorner() \endlink can be used to refer 107 to a block in the top-left corner of a matrix. 108 109 The different possibilities are summarized in the following table: 110 111 <table class="manual"> 112 <tr><th>%Block \b operation</td> 113 <th>Version constructing a \n dynamic-size block expression</th> 114 <th>Version constructing a \n fixed-size block expression</th></tr> 115 <tr><td>Top-left p by q block \link DenseBase::topLeftCorner() * \endlink</td> 116 <td>\code 117 matrix.topLeftCorner(p,q);\endcode </td> 118 <td>\code 119 matrix.topLeftCorner<p,q>();\endcode </td> 120 </tr> 121 <tr><td>Bottom-left p by q block 122 \link DenseBase::bottomLeftCorner() * \endlink</td> 123 <td>\code 124 matrix.bottomLeftCorner(p,q);\endcode </td> 125 <td>\code 126 matrix.bottomLeftCorner<p,q>();\endcode </td> 127 </tr> 128 <tr><td>Top-right p by q block 129 \link DenseBase::topRightCorner() * \endlink</td> 130 <td>\code 131 matrix.topRightCorner(p,q);\endcode </td> 132 <td>\code 133 matrix.topRightCorner<p,q>();\endcode </td> 134 </tr> 135 <tr><td>Bottom-right p by q block 136 \link DenseBase::bottomRightCorner() * \endlink</td> 137 <td>\code 138 matrix.bottomRightCorner(p,q);\endcode </td> 139 <td>\code 140 matrix.bottomRightCorner<p,q>();\endcode </td> 141 </tr> 142 <tr><td>%Block containing the first q rows 143 \link DenseBase::topRows() * \endlink</td> 144 <td>\code 145 matrix.topRows(q);\endcode </td> 146 <td>\code 147 matrix.topRows<q>();\endcode </td> 148 </tr> 149 <tr><td>%Block containing the last q rows 150 \link DenseBase::bottomRows() * \endlink</td> 151 <td>\code 152 matrix.bottomRows(q);\endcode </td> 153 <td>\code 154 matrix.bottomRows<q>();\endcode </td> 155 </tr> 156 <tr><td>%Block containing the first p columns 157 \link DenseBase::leftCols() * \endlink</td> 158 <td>\code 159 matrix.leftCols(p);\endcode </td> 160 <td>\code 161 matrix.leftCols<p>();\endcode </td> 162 </tr> 163 <tr><td>%Block containing the last q columns 164 \link DenseBase::rightCols() * \endlink</td> 165 <td>\code 166 matrix.rightCols(q);\endcode </td> 167 <td>\code 168 matrix.rightCols<q>();\endcode </td> 169 </tr> 170 </table> 171 172 Here is a simple example illustrating the use of the operations presented above: 173 174 <table class="example"> 175 <tr><th>Example:</th><th>Output:</th></tr> 176 <tr><td> 177 \include Tutorial_BlockOperations_corner.cpp 178 </td> 179 <td> 180 \verbinclude Tutorial_BlockOperations_corner.out 181 </td></tr></table> 182 183 184 \section TutorialBlockOperationsSyntaxVectors Block operations for vectors 185 186 Eigen also provides a set of block operations designed specifically for the special case of vectors and one-dimensional arrays: 187 188 <table class="manual"> 189 <tr><th> %Block operation</th> 190 <th>Version constructing a \n dynamic-size block expression</th> 191 <th>Version constructing a \n fixed-size block expression</th></tr> 192 <tr><td>%Block containing the first \p n elements 193 \link DenseBase::head() * \endlink</td> 194 <td>\code 195 vector.head(n);\endcode </td> 196 <td>\code 197 vector.head<n>();\endcode </td> 198 </tr> 199 <tr><td>%Block containing the last \p n elements 200 \link DenseBase::tail() * \endlink</td> 201 <td>\code 202 vector.tail(n);\endcode </td> 203 <td>\code 204 vector.tail<n>();\endcode </td> 205 </tr> 206 <tr><td>%Block containing \p n elements, starting at position \p i 207 \link DenseBase::segment() * \endlink</td> 208 <td>\code 209 vector.segment(i,n);\endcode </td> 210 <td>\code 211 vector.segment<n>(i);\endcode </td> 212 </tr> 213 </table> 214 215 216 An example is presented below: 217 <table class="example"> 218 <tr><th>Example:</th><th>Output:</th></tr> 219 <tr><td> 220 \include Tutorial_BlockOperations_vector.cpp 221 </td> 222 <td> 223 \verbinclude Tutorial_BlockOperations_vector.out 224 </td></tr></table> 225 226 */ 227 228 } 229
