third-party-mirror / eigen / 941ca8d83f776b9a07153d3abef2877907aa0555 / . / doc / TutorialAdvancedInitialization.dox

namespace Eigen { | |

/** \eigenManualPage TutorialAdvancedInitialization Advanced initialization | |

This page discusses several advanced methods for initializing matrices. It gives more details on the | |

comma-initializer, which was introduced before. It also explains how to get special matrices such as the | |

identity matrix and the zero matrix. | |

\eigenAutoToc | |

\section TutorialAdvancedInitializationCommaInitializer The comma initializer | |

Eigen offers a comma initializer syntax which allows the user to easily set all the coefficients of a matrix, | |

vector or array. Simply list the coefficients, starting at the top-left corner and moving from left to right | |

and from the top to the bottom. The size of the object needs to be specified beforehand. If you list too few | |

or too many coefficients, Eigen will complain. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_commainit_01.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_commainit_01.out | |

</td></tr></table> | |

Moreover, the elements of the initialization list may themselves be vectors or matrices. A common use is | |

to join vectors or matrices together. For example, here is how to join two row vectors together. Remember | |

that you have to set the size before you can use the comma initializer. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_AdvancedInitialization_Join.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_AdvancedInitialization_Join.out | |

</td></tr></table> | |

We can use the same technique to initialize matrices with a block structure. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_AdvancedInitialization_Block.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_AdvancedInitialization_Block.out | |

</td></tr></table> | |

The comma initializer can also be used to fill block expressions such as <tt>m.row(i)</tt>. Here is a more | |

complicated way to get the same result as in the first example above: | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_commainit_01b.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_commainit_01b.out | |

</td></tr></table> | |

\section TutorialAdvancedInitializationSpecialMatrices Special matrices and arrays | |

The Matrix and Array classes have static methods like \link DenseBase::Zero() Zero()\endlink, which can be | |

used to initialize all coefficients to zero. There are three variants. The first variant takes no arguments | |

and can only be used for fixed-size objects. If you want to initialize a dynamic-size object to zero, you need | |

to specify the size. Thus, the second variant requires one argument and can be used for one-dimensional | |

dynamic-size objects, while the third variant requires two arguments and can be used for two-dimensional | |

objects. All three variants are illustrated in the following example: | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_AdvancedInitialization_Zero.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_AdvancedInitialization_Zero.out | |

</td></tr></table> | |

Similarly, the static method \link DenseBase::Constant() Constant\endlink(value) sets all coefficients to \c value. | |

If the size of the object needs to be specified, the additional arguments go before the \c value | |

argument, as in <tt>MatrixXd::Constant(rows, cols, value)</tt>. The method \link DenseBase::Random() Random() | |

\endlink fills the matrix or array with random coefficients. The identity matrix can be obtained by calling | |

\link MatrixBase::Identity() Identity()\endlink; this method is only available for Matrix, not for Array, | |

because "identity matrix" is a linear algebra concept. The method | |

\link DenseBase::LinSpaced LinSpaced\endlink(size, low, high) is only available for vectors and | |

one-dimensional arrays; it yields a vector of the specified size whose coefficients are equally spaced between | |

\c low and \c high. The method \c LinSpaced() is illustrated in the following example, which prints a table | |

with angles in degrees, the corresponding angle in radians, and their sine and cosine. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_AdvancedInitialization_LinSpaced.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_AdvancedInitialization_LinSpaced.out | |

</td></tr></table> | |

This example shows that objects like the ones returned by LinSpaced() can be assigned to variables (and | |

expressions). Eigen defines utility functions like \link DenseBase::setZero() setZero()\endlink, | |

\link MatrixBase::setIdentity() \endlink and \link DenseBase::setLinSpaced() \endlink to do this | |

conveniently. The following example contrasts three ways to construct the matrix | |

\f$ J = \bigl[ \begin{smallmatrix} O & I \\ I & O \end{smallmatrix} \bigr] \f$: using static methods and | |

assignment, using static methods and the comma-initializer, or using the setXxx() methods. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_AdvancedInitialization_ThreeWays.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_AdvancedInitialization_ThreeWays.out | |

</td></tr></table> | |

A summary of all pre-defined matrix, vector and array objects can be found in the \ref QuickRefPage. | |

\section TutorialAdvancedInitializationTemporaryObjects Usage as temporary objects | |

As shown above, static methods as Zero() and Constant() can be used to initialize variables at the time of | |

declaration or at the right-hand side of an assignment operator. You can think of these methods as returning a | |

matrix or array; in fact, they return so-called \ref TopicEigenExpressionTemplates "expression objects" which | |

evaluate to a matrix or array when needed, so that this syntax does not incur any overhead. | |

These expressions can also be used as a temporary object. The second example in | |

the \ref GettingStarted guide, which we reproduce here, already illustrates this. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include QuickStart_example2_dynamic.cpp | |

</td> | |

<td> | |

\verbinclude QuickStart_example2_dynamic.out | |

</td></tr></table> | |

The expression <tt>m + MatrixXf::Constant(3,3,1.2)</tt> constructs the 3-by-3 matrix expression with all its coefficients | |

equal to 1.2 plus the corresponding coefficient of \a m. | |

The comma-initializer, too, can also be used to construct temporary objects. The following example constructs a random | |

matrix of size 2-by-3, and then multiplies this matrix on the left with | |

\f$ \bigl[ \begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr] \f$. | |

<table class="example"> | |

<tr><th>Example:</th><th>Output:</th></tr> | |

<tr><td> | |

\include Tutorial_AdvancedInitialization_CommaTemporary.cpp | |

</td> | |

<td> | |

\verbinclude Tutorial_AdvancedInitialization_CommaTemporary.out | |

</td></tr></table> | |

The \link CommaInitializer::finished() finished() \endlink method is necessary here to get the actual matrix | |

object once the comma initialization of our temporary submatrix is done. | |

*/ | |

} |