namespace Eigen { /** \page TutorialAdvancedInitialization Tutorial page 5 - Advanced initialization \ingroup Tutorial \li \b Previous: \ref TutorialBlockOperations \li \b Next: \ref TutorialLinearAlgebra 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. \b Table \b of \b contents - \ref TutorialAdvancedInitializationCommaInitializer - \ref TutorialAdvancedInitializationSpecialMatrices - \ref TutorialAdvancedInitializationTemporaryObjects \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.
Example:Output:
\include Tutorial_commainit_01.cpp \verbinclude Tutorial_commainit_01.out
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.
Example:Output:
\include Tutorial_AdvancedInitialization_Join.cpp \verbinclude Tutorial_AdvancedInitialization_Join.out
We can use the same technique to initialize matrices with a block structure.
Example:Output:
\include Tutorial_AdvancedInitialization_Block.cpp \verbinclude Tutorial_AdvancedInitialization_Block.out
The comma initializer can also be used to fill block expressions such as m.row(i). Here is a more complicated way to get the same result as in the first example above:
Example:Output:
\include Tutorial_commainit_01b.cpp \verbinclude Tutorial_commainit_01b.out
\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:
Example:Output:
\include Tutorial_AdvancedInitialization_Zero.cpp \verbinclude Tutorial_AdvancedInitialization_Zero.out
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 MatrixXd::Constant(rows, cols, value). 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.
Example:Output:
\include Tutorial_AdvancedInitialization_LinSpaced.cpp \verbinclude Tutorial_AdvancedInitialization_LinSpaced.out
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$: using static methods and assignment, using static methods and the comma-initializer, or using the setXxx() methods.
Example:Output:
\include Tutorial_AdvancedInitialization_ThreeWays.cpp \verbinclude Tutorial_AdvancedInitialization_ThreeWays.out
A summary of all pre-defined matrix, vector and array objects can be found in the \ref QuickRefPage. \section TutorialAdvancedInitializationTemporaryObjects Usage as temporary objects As shown above, static methods as Zero() and Constant() can be used to initialize variables at the time of declaration or at the right-hand side of an assignment operator. You can think of these methods as returning a matrix or array; in fact, they return so-called \ref TopicEigenExpressionTemplates "expression objects" which evaluate to a matrix or array when needed, so that this syntax does not incur any overhead. These expressions can also be used as a temporary object. The second example in the \ref GettingStarted guide, which we reproduce here, already illustrates this.
Example:Output:
\include QuickStart_example2_dynamic.cpp \verbinclude QuickStart_example2_dynamic.out
The expression m + MatrixXf::Constant(3,3,1.2) constructs the 3-by-3 matrix expression with all its coefficients equal to 1.2 plus the corresponding coefficient of \a m. The comma-initializer, too, can also be used to construct temporary objects. The following example constructs a random matrix of size 2-by-3, and then multiplies this matrix on the left with \f$ \bigl[ \begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix} \bigr] \f$.
Example:Output:
\include Tutorial_AdvancedInitialization_CommaTemporary.cpp \verbinclude Tutorial_AdvancedInitialization_CommaTemporary.out
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. \li \b Next: \ref TutorialLinearAlgebra */ }