1 namespace Eigen { 2 3 /** \eigenManualPage TutorialAdvancedInitialization Advanced initialization 4 5 This page discusses several advanced methods for initializing matrices. It gives more details on the 6 comma-initializer, which was introduced before. It also explains how to get special matrices such as the 7 identity matrix and the zero matrix. 8 9 \eigenAutoToc 10 11 \section TutorialAdvancedInitializationCommaInitializer The comma initializer 12 13 Eigen offers a comma initializer syntax which allows the user to easily set all the coefficients of a matrix, 14 vector or array. Simply list the coefficients, starting at the top-left corner and moving from left to right 15 and from the top to the bottom. The size of the object needs to be specified beforehand. If you list too few 16 or too many coefficients, Eigen will complain. 17 18 <table class="example"> 19 <tr><th>Example:</th><th>Output:</th></tr> 20 <tr><td> 21 \include Tutorial_commainit_01.cpp 22 </td> 23 <td> 24 \verbinclude Tutorial_commainit_01.out 25 </td></tr></table> 26 27 Moreover, the elements of the initialization list may themselves be vectors or matrices. A common use is 28 to join vectors or matrices together. For example, here is how to join two row vectors together. Remember 29 that you have to set the size before you can use the comma initializer. 30 31 <table class="example"> 32 <tr><th>Example:</th><th>Output:</th></tr> 33 <tr><td> 34 \include Tutorial_AdvancedInitialization_Join.cpp 35 </td> 36 <td> 37 \verbinclude Tutorial_AdvancedInitialization_Join.out 38 </td></tr></table> 39 40 We can use the same technique to initialize matrices with a block structure. 41 42 <table class="example"> 43 <tr><th>Example:</th><th>Output:</th></tr> 44 <tr><td> 45 \include Tutorial_AdvancedInitialization_Block.cpp 46 </td> 47 <td> 48 \verbinclude Tutorial_AdvancedInitialization_Block.out 49 </td></tr></table> 50 51 The comma initializer can also be used to fill block expressions such as <tt>m.row(i)</tt>. Here is a more 52 complicated way to get the same result as in the first example above: 53 54 <table class="example"> 55 <tr><th>Example:</th><th>Output:</th></tr> 56 <tr><td> 57 \include Tutorial_commainit_01b.cpp 58 </td> 59 <td> 60 \verbinclude Tutorial_commainit_01b.out 61 </td></tr></table> 62 63 64 \section TutorialAdvancedInitializationSpecialMatrices Special matrices and arrays 65 66 The Matrix and Array classes have static methods like \link DenseBase::Zero() Zero()\endlink, which can be 67 used to initialize all coefficients to zero. There are three variants. The first variant takes no arguments 68 and can only be used for fixed-size objects. If you want to initialize a dynamic-size object to zero, you need 69 to specify the size. Thus, the second variant requires one argument and can be used for one-dimensional 70 dynamic-size objects, while the third variant requires two arguments and can be used for two-dimensional 71 objects. All three variants are illustrated in the following example: 72 73 <table class="example"> 74 <tr><th>Example:</th><th>Output:</th></tr> 75 <tr><td> 76 \include Tutorial_AdvancedInitialization_Zero.cpp 77 </td> 78 <td> 79 \verbinclude Tutorial_AdvancedInitialization_Zero.out 80 </td></tr></table> 81 82 Similarly, the static method \link DenseBase::Constant() Constant\endlink(value) sets all coefficients to \c value. 83 If the size of the object needs to be specified, the additional arguments go before the \c value 84 argument, as in <tt>MatrixXd::Constant(rows, cols, value)</tt>. The method \link DenseBase::Random() Random() 85 \endlink fills the matrix or array with random coefficients. The identity matrix can be obtained by calling 86 \link MatrixBase::Identity() Identity()\endlink; this method is only available for Matrix, not for Array, 87 because "identity matrix" is a linear algebra concept. The method 88 \link DenseBase::LinSpaced LinSpaced\endlink(size, low, high) is only available for vectors and 89 one-dimensional arrays; it yields a vector of the specified size whose coefficients are equally spaced between 90 \c low and \c high. The method \c LinSpaced() is illustrated in the following example, which prints a table 91 with angles in degrees, the corresponding angle in radians, and their sine and cosine. 92 93 <table class="example"> 94 <tr><th>Example:</th><th>Output:</th></tr> 95 <tr><td> 96 \include Tutorial_AdvancedInitialization_LinSpaced.cpp 97 </td> 98 <td> 99 \verbinclude Tutorial_AdvancedInitialization_LinSpaced.out 100 </td></tr></table> 101 102 This example shows that objects like the ones returned by LinSpaced() can be assigned to variables (and 103 expressions). Eigen defines utility functions like \link DenseBase::setZero() setZero()\endlink, 104 \link MatrixBase::setIdentity() \endlink and \link DenseBase::setLinSpaced() \endlink to do this 105 conveniently. The following example contrasts three ways to construct the matrix 106 \f$ J = \bigl[ \begin{smallmatrix} O & I \\ I & O \end{smallmatrix} \bigr] \f$: using static methods and 107 assignment, using static methods and the comma-initializer, or using the setXxx() methods. 108 109 <table class="example"> 110 <tr><th>Example:</th><th>Output:</th></tr> 111 <tr><td> 112 \include Tutorial_AdvancedInitialization_ThreeWays.cpp 113 </td> 114 <td> 115 \verbinclude Tutorial_AdvancedInitialization_ThreeWays.out 116 </td></tr></table> 117 118 A summary of all pre-defined matrix, vector and array objects can be found in the \ref QuickRefPage. 119 120 121 \section TutorialAdvancedInitializationTemporaryObjects Usage as temporary objects 122 123 As shown above, static methods as Zero() and Constant() can be used to initialize variables at the time of 124 declaration or at the right-hand side of an assignment operator. You can think of these methods as returning a 125 matrix or array; in fact, they return so-called \ref TopicEigenExpressionTemplates "expression objects" which 126 evaluate to a matrix or array when needed, so that this syntax does not incur any overhead. 127 128 These expressions can also be used as a temporary object. The second example in 129 the \ref GettingStarted guide, which we reproduce here, already illustrates this. 130 131 <table class="example"> 132 <tr><th>Example:</th><th>Output:</th></tr> 133 <tr><td> 134 \include QuickStart_example2_dynamic.cpp 135 </td> 136 <td> 137 \verbinclude QuickStart_example2_dynamic.out 138 </td></tr></table> 139 140 The expression <tt>m + MatrixXf::Constant(3,3,1.2)</tt> constructs the 3-by-3 matrix expression with all its coefficients 141 equal to 1.2 plus the corresponding coefficient of \a m. 142 143 The comma-initializer, too, can also be used to construct temporary objects. The following example constructs a random 144 matrix of size 2-by-3, and then multiplies this matrix on the left with 145 \f$ \bigl[ \begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr] \f$. 146 147 <table class="example"> 148 <tr><th>Example:</th><th>Output:</th></tr> 149 <tr><td> 150 \include Tutorial_AdvancedInitialization_CommaTemporary.cpp 151 </td> 152 <td> 153 \verbinclude Tutorial_AdvancedInitialization_CommaTemporary.out 154 </td></tr></table> 155 156 The \link CommaInitializer::finished() finished() \endlink method is necessary here to get the actual matrix 157 object once the comma initialization of our temporary submatrix is done. 158 159 160 */ 161 162 } 163
