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+namespace Eigen {
+
+/** \eigenManualPage TutorialMatrixClass The Matrix class
+
+\eigenAutoToc
+
+In Eigen, all matrices and vectors are objects of the Matrix template class.
+Vectors are just a special case of matrices, with either 1 row or 1 column.
+
+\section TutorialMatrixFirst3Params The first three template parameters of Matrix
+
+The Matrix class takes six template parameters, but for now it's enough to
+learn about the first three first parameters. The three remaining parameters have default
+values, which for now we will leave untouched, and which we
+\ref TutorialMatrixOptTemplParams "discuss below".
+
+The three mandatory template parameters of Matrix are:
+\code
+Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>
+\endcode
+\li \c Scalar is the scalar type, i.e. the type of the coefficients.
+    That is, if you want a matrix of floats, choose \c float here.
+    See \ref TopicScalarTypes "Scalar types" for a list of all supported
+    scalar types and for how to extend support to new types.
+\li \c RowsAtCompileTime and \c ColsAtCompileTime are the number of rows
+    and columns of the matrix as known at compile time (see 
+    \ref TutorialMatrixDynamic "below" for what to do if the number is not
+    known at compile time).
+
+We offer a lot of convenience typedefs to cover the usual cases. For example, \c Matrix4f is
+a 4x4 matrix of floats. Here is how it is defined by Eigen:
+\code
+typedef Matrix<float, 4, 4> Matrix4f;
+\endcode
+We discuss \ref TutorialMatrixTypedefs "below" these convenience typedefs.
+
+\section TutorialMatrixVectors Vectors
+
+As mentioned above, in Eigen, vectors are just a special case of
+matrices, with either 1 row or 1 column. The case where they have 1 column is the most common;
+such vectors are called column-vectors, often abbreviated as just vectors. In the other case
+where they have 1 row, they are called row-vectors.
+
+For example, the convenience typedef \c Vector3f is a (column) vector of 3 floats. It is defined as follows by Eigen:
+\code
+typedef Matrix<float, 3, 1> Vector3f;
+\endcode
+We also offer convenience typedefs for row-vectors, for example:
+\code
+typedef Matrix<int, 1, 2> RowVector2i;
+\endcode
+
+\section TutorialMatrixDynamic The special value Dynamic
+
+Of course, Eigen is not limited to matrices whose dimensions are known at compile time.
+The \c RowsAtCompileTime and \c ColsAtCompileTime template parameters can take the special
+value \c Dynamic which indicates that the size is unknown at compile time, so must
+be handled as a run-time variable. In Eigen terminology, such a size is referred to as a
+\em dynamic \em size; while a size that is known at compile time is called a
+\em fixed \em size. For example, the convenience typedef \c MatrixXd, meaning
+a matrix of doubles with dynamic size, is defined as follows:
+\code
+typedef Matrix<double, Dynamic, Dynamic> MatrixXd;
+\endcode
+And similarly, we define a self-explanatory typedef \c VectorXi as follows:
+\code
+typedef Matrix<int, Dynamic, 1> VectorXi;
+\endcode
+You can perfectly have e.g. a fixed number of rows with a dynamic number of columns, as in:
+\code
+Matrix<float, 3, Dynamic>
+\endcode
+
+\section TutorialMatrixConstructors Constructors
+
+A default constructor is always available, never performs any dynamic memory allocation, and never initializes the matrix coefficients. You can do:
+\code
+Matrix3f a;
+MatrixXf b;
+\endcode
+Here,
+\li \c a is a 3-by-3 matrix, with a plain float[9] array of uninitialized coefficients,
+\li \c b is a dynamic-size matrix whose size is currently 0-by-0, and whose array of
+coefficients hasn't yet been allocated at all.
+
+Constructors taking sizes are also available. For matrices, the number of rows is always passed first.
+For vectors, just pass the vector size. They allocate the array of coefficients
+with the given size, but don't initialize the coefficients themselves:
+\code
+MatrixXf a(10,15);
+VectorXf b(30);
+\endcode
+Here,
+\li \c a is a 10x15 dynamic-size matrix, with allocated but currently uninitialized coefficients.
+\li \c b is a dynamic-size vector of size 30, with allocated but currently uninitialized coefficients.
+
+In order to offer a uniform API across fixed-size and dynamic-size matrices, it is legal to use these
+constructors on fixed-size matrices, even if passing the sizes is useless in this case. So this is legal:
+\code
+Matrix3f a(3,3);
+\endcode
+and is a no-operation.
+
+Finally, we also offer some constructors to initialize the coefficients of small fixed-size vectors up to size 4:
+\code
+Vector2d a(5.0, 6.0);
+Vector3d b(5.0, 6.0, 7.0);
+Vector4d c(5.0, 6.0, 7.0, 8.0);
+\endcode
+
+\section TutorialMatrixCoeffAccessors Coefficient accessors
+
+The primary coefficient accessors and mutators in Eigen are the overloaded parenthesis operators.
+For matrices, the row index is always passed first. For vectors, just pass one index.
+The numbering starts at 0. This example is self-explanatory:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr><td>
+\include tut_matrix_coefficient_accessors.cpp
+</td>
+<td>
+\verbinclude tut_matrix_coefficient_accessors.out
+</td></tr></table>
+
+Note that the syntax <tt> m(index) </tt>
+is not restricted to vectors, it is also available for general matrices, meaning index-based access
+in the array of coefficients. This however depends on the matrix's storage order. All Eigen matrices default to
+column-major storage order, but this can be changed to row-major, see \ref TopicStorageOrders "Storage orders".
+
+The operator[] is also overloaded for index-based access in vectors, but keep in mind that C++ doesn't allow operator[] to
+take more than one argument. We restrict operator[] to vectors, because an awkwardness in the C++ language
+would make matrix[i,j] compile to the same thing as matrix[j] !
+
+\section TutorialMatrixCommaInitializer Comma-initialization
+
+%Matrix and vector coefficients can be conveniently set using the so-called \em comma-initializer syntax.
+For now, it is enough to know this example:
+
+<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>
+
+
+The right-hand side can also contain matrix expressions as discussed in \ref TutorialAdvancedInitialization "this page".
+
+\section TutorialMatrixSizesResizing Resizing
+
+The current size of a matrix can be retrieved by \link EigenBase::rows() rows()\endlink, \link EigenBase::cols() cols() \endlink and \link EigenBase::size() size()\endlink. These methods return the number of rows, the number of columns and the number of coefficients, respectively. Resizing a dynamic-size matrix is done by the \link PlainObjectBase::resize(Index,Index) resize() \endlink method.
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include tut_matrix_resize.cpp </td>
+<td>\verbinclude tut_matrix_resize.out </td>
+</tr></table>
+
+The resize() method is a no-operation if the actual matrix size doesn't change; otherwise it is destructive: the values of the coefficients may change.
+If you want a conservative variant of resize() which does not change the coefficients, use \link PlainObjectBase::conservativeResize() conservativeResize()\endlink, see \ref TopicResizing "this page" for more details.
+
+All these methods are still available on fixed-size matrices, for the sake of API uniformity. Of course, you can't actually
+resize a fixed-size matrix. Trying to change a fixed size to an actually different value will trigger an assertion failure;
+but the following code is legal:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include tut_matrix_resize_fixed_size.cpp </td>
+<td>\verbinclude tut_matrix_resize_fixed_size.out </td>
+</tr></table>
+
+
+\section TutorialMatrixAssignment Assignment and resizing
+
+Assignment is the action of copying a matrix into another, using \c operator=. Eigen resizes the matrix on the left-hand side automatically so that it matches the size of the matrix on the right-hand size. For example:
+
+<table class="example">
+<tr><th>Example:</th><th>Output:</th></tr>
+<tr>
+<td>\include tut_matrix_assignment_resizing.cpp </td>
+<td>\verbinclude tut_matrix_assignment_resizing.out </td>
+</tr></table>
+
+Of course, if the left-hand side is of fixed size, resizing it is not allowed.
+
+If you do not want this automatic resizing to happen (for example for debugging purposes), you can disable it, see
+\ref TopicResizing "this page".
+
+
+\section TutorialMatrixFixedVsDynamic Fixed vs. Dynamic size
+
+When should one use fixed sizes (e.g. \c Matrix4f), and when should one prefer dynamic sizes (e.g. \c MatrixXf)?
+The simple answer is: use fixed
+sizes for very small sizes where you can, and use dynamic sizes for larger sizes or where you have to. For small sizes,
+especially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial
+to performance, as it allows Eigen to avoid dynamic memory allocation and to unroll
+loops. Internally, a fixed-size Eigen matrix is just a plain array, i.e. doing
+\code Matrix4f mymatrix; \endcode
+really amounts to just doing
+\code float mymatrix[16]; \endcode
+so this really has zero runtime cost. By contrast, the array of a dynamic-size matrix
+is always allocated on the heap, so doing
+\code MatrixXf mymatrix(rows,columns); \endcode
+amounts to doing
+\code float *mymatrix = new float[rows*columns]; \endcode
+and in addition to that, the MatrixXf object stores its number of rows and columns as
+member variables.
+
+The limitation of using fixed sizes, of course, is that this is only possible
+when you know the sizes at compile time. Also, for large enough sizes, say for sizes
+greater than (roughly) 32, the performance benefit of using fixed sizes becomes negligible.
+Worse, trying to create a very large matrix using fixed sizes inside a function could result in a
+stack overflow, since Eigen will try to allocate the array automatically as a local variable, and
+this is normally done on the stack.
+Finally, depending on circumstances, Eigen can also be more aggressive trying to vectorize
+(use SIMD instructions) when dynamic sizes are used, see \ref TopicVectorization "Vectorization".
+
+\section TutorialMatrixOptTemplParams Optional template parameters
+
+We mentioned at the beginning of this page that the Matrix class takes six template parameters,
+but so far we only discussed the first three. The remaining three parameters are optional. Here is
+the complete list of template parameters:
+\code
+Matrix<typename Scalar,
+       int RowsAtCompileTime,
+       int ColsAtCompileTime,
+       int Options = 0,
+       int MaxRowsAtCompileTime = RowsAtCompileTime,
+       int MaxColsAtCompileTime = ColsAtCompileTime>
+\endcode
+\li \c Options is a bit field. Here, we discuss only one bit: \c RowMajor. It specifies that the matrices
+      of this type use row-major storage order; by default, the storage order is column-major. See the page on
+      \ref TopicStorageOrders "storage orders". For example, this type means row-major 3x3 matrices:
+      \code
+      Matrix<float, 3, 3, RowMajor>
+      \endcode
+\li \c MaxRowsAtCompileTime and \c MaxColsAtCompileTime are useful when you want to specify that, even though
+      the exact sizes of your matrices are not known at compile time, a fixed upper bound is known at
+      compile time. The biggest reason why you might want to do that is to avoid dynamic memory allocation.
+      For example the following matrix type uses a plain array of 12 floats, without dynamic memory allocation:
+      \code
+      Matrix<float, Dynamic, Dynamic, 0, 3, 4>
+      \endcode
+
+\section TutorialMatrixTypedefs Convenience typedefs
+
+Eigen defines the following Matrix typedefs:
+\li MatrixNt for Matrix<type, N, N>. For example, MatrixXi for Matrix<int, Dynamic, Dynamic>.
+\li VectorNt for Matrix<type, N, 1>. For example, Vector2f for Matrix<float, 2, 1>.
+\li RowVectorNt for Matrix<type, 1, N>. For example, RowVector3d for Matrix<double, 1, 3>.
+
+Where:
+\li N can be any one of \c 2, \c 3, \c 4, or \c X (meaning \c Dynamic).
+\li t can be any one of \c i (meaning int), \c f (meaning float), \c d (meaning double),
+      \c cf (meaning complex<float>), or \c cd (meaning complex<double>). The fact that typedefs are only
+    defined for these five types doesn't mean that they are the only supported scalar types. For example,
+    all standard integer types are supported, see \ref TopicScalarTypes "Scalar types".
+
+
+*/
+
+}