Write topic page for storage orders.

Eigen/src/Core/BandMatrix.h

@@ -181,9 +181,9 @@ class BandMatrixBase : public EigenBase<Derived>
   * \param Supers Number of super diagonal
   * \param Subs Number of sub diagonal
   * \param _Options A combination of either \b RowMajor or \b ColMajor, and of \b SelfAdjoint
-  *                 The former controls storage order, and defaults to column-major. The latter controls
-  *                 whether the matrix represent a selfadjoint matrix in which case either Supers of Subs
-  *                 have to be null.
+  *                 The former controls \ref TopicStorageOrders "storage order", and defaults to
+  *                 column-major. The latter controls whether the matrix represents a selfadjoint 
+  *                 matrix in which case either Supers of Subs have to be null.
   *
   * \sa class TridiagonalMatrix
   */

Eigen/src/Core/DenseBase.h

@@ -185,8 +185,8 @@ template<typename Derived> class DenseBase
     /** \returns the outer size.
       *
       * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
-      * with respect to the storage order, i.e., the number of columns for a column-major matrix,
-      * and the number of rows for a row-major matrix. */
+      * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
+      * column-major matrix, and the number of rows for a row-major matrix. */
     Index outerSize() const
     {
       return IsVectorAtCompileTime ? 1
@@ -196,8 +196,8 @@ template<typename Derived> class DenseBase
     /** \returns the inner size.
       *
       * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
-      * with respect to the storage order, i.e., the number of rows for a column-major matrix,
-      * and the number of columns for a row-major matrix. */
+      * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a 
+      * column-major matrix, and the number of columns for a row-major matrix. */
     Index innerSize() const
     {
       return IsVectorAtCompileTime ? this->size()

Eigen/src/Core/Map.h

@@ -44,7 +44,7 @@
   * data is laid out contiguously in memory. You can however override this by explicitly specifying
   * inner and outer strides.
   *
-  * Here's an example of simply mapping a contiguous array as a column-major matrix:
+  * Here's an example of simply mapping a contiguous array as a \ref TopicStorageOrders "column-major" matrix:
   * \include Map_simple.cpp
   * Output: \verbinclude Map_simple.out
   *
@@ -74,7 +74,7 @@
   *
   * This class is the return type of Matrix::Map() but can also be used directly.
   *
-  * \sa Matrix::Map()
+  * \sa Matrix::Map(), \ref TopicStorageOrders
   */
 
 namespace internal {

Eigen/src/Core/Matrix.h

@@ -45,7 +45,7 @@
   * The remaining template parameters are optional -- in most cases you don't have to worry about them.
   * \tparam _Options \anchor matrix_tparam_options A combination of either \b RowMajor or \b ColMajor, and of either
   *                 \b AutoAlign or \b DontAlign.
-  *                 The former controls storage order, and defaults to column-major. The latter controls alignment, which is required
+  *                 The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
   *                 for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
   * \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
   * \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
@@ -107,7 +107,8 @@
   * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
   * </dl>
   *
-  * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy
+  * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy, 
+  * \ref TopicStorageOrders 
   */
 
 namespace internal {

Eigen/src/Core/Stride.h

@@ -51,7 +51,7 @@
   * \include Map_general_stride.cpp
   * Output: \verbinclude Map_general_stride.out
   *
-  * \sa class InnerStride, class OuterStride
+  * \sa class InnerStride, class OuterStride, \ref TopicStorageOrders
   */
 template<int _OuterStrideAtCompileTime, int _InnerStrideAtCompileTime>
 class Stride

Eigen/src/Core/util/Constants.h

@@ -56,7 +56,8 @@ const int Infinity = -1;
   * for a matrix, this means that the storage order is row-major.
   * If this bit is not set, the storage order is column-major.
   * For an expression, this determines the storage order of
-  * the matrix created by evaluation of that expression. */
+  * the matrix created by evaluation of that expression. 
+  * \sa \ref TopicStorageOrders */
 const unsigned int RowMajorBit = 0x1;
 
 /** \ingroup flags

doc/I08_StorageOrders.dox

@@ -1,11 +0,0 @@
-namespace Eigen {
-
-/** \page TopicStorageOrders Storage orders
-
-
-TODO: write this dox page!
-
-Is linked from the tutorial on the Matrix class.
-
-*/
-}

doc/I15_StorageOrders.dox

@@ -0,0 +1,91 @@
+namespace Eigen {
+
+/** \page TopicStorageOrders Storage orders
+
+There are two different storage orders for matrices and two-dimensional arrays: column-major and row-major.
+This page explains these storage orders and how to specify which one should be used.
+
+<b>Table of contents</b>
+  - \ref TopicStorageOrdersIntro
+  - \ref TopicStorageOrdersInEigen
+  - \ref TopicStorageOrdersWhich
+
+
+\section TopicStorageOrdersIntro Column-major and row-major storage
+
+The entries of a matrix form a two-dimensional grid. However, when the matrix is stored in memory, the entries
+have to somehow be laid out linearly. There are two main ways to do this, by row and by column.
+
+We say that a matrix is stored in \b row-major order if it is stored row by row. The entire first row is
+stored first, followed by the entire second row, and so on. Consider for example the matrix
+
+\f[
+A = \begin{bmatrix}
+8 & 2 & 2 & 9 \\
+9 & 1 & 4 & 4 \\
+3 & 5 & 4 & 5
+\end{bmatrix}.
+\f]
+
+If this matrix is stored in row-major order, then the entries are laid out in memory as follows:
+
+\code 8 2 2 9 9 1 4 4 3 5 4 5 \endcode
+
+On the other hand, a matrix is stored in \b column-major order if it is stored column by column, starting with
+the entire first column, followed by the entire second column, and so on. If the above matrix is stored in
+column-major order, it is laid out as follows:
+
+\code 8 9 3 2 1 5 2 4 4 9 4 5 \endcode
+
+This example is illustrated by the following Eigen code. It uses the PlainObjectBase::data() function, which
+returns a pointer to the memory location of the first entry of the matrix.
+
+<table class="example">
+<tr><th>Example</th><th>Output</th></tr>
+<tr><td>
+\include TopicStorageOrders_example.cpp
+</td>
+<td>
+\verbinclude TopicStorageOrders_example.out
+</td></tr></table>
+
+
+\section TopicStorageOrdersInEigen Storage orders in Eigen
+
+The storage order of a matrix or a two-dimensional array can be set by specifying the \c Options template
+parameter for Matrix or Array. As \ref TutorialMatrixClass explains, the %Matrix class template has six
+template parameters, of which three are compulsory (\c Scalar, \c RowsAtCompileTime and \c ColsAtCompileTime)
+and three are optional (\c Options, \c MaxRowsAtCompileTime and \c MaxColsAtCompileTime). If the \c Options
+parameter is set to \c RowMajor, then the matrix or array is stored in row-major order; if it is set to 
+\c ColMajor, then it is stored in column-major order. This mechanism is used in the above Eigen program to
+specify the storage order.
+
+If the storage order is not specified, then Eigen normally defaults to storing the entry in column-major
+order. This is also the case if one of the convenience typedefs (\c Matrix3f, \c ArrayXXd, etc.) is
+used. However, it is possible to change the default to row-major order by defining the 
+\c EIGEN_DEFAULT_TO_ROW_MAJOR \ref TopicPreprocessorDirectives "preprocessor directive".
+
+Matrices and arrays using one storage order can be assigned to matrices and arrays using the other storage
+order, as happens in the above program when \c Arowmajor is initialized using \c Acolmajor. Eigen will reorder
+the entries automatically. More generally, row-major and column-major matrices can be mixed in an expression
+as we want.
+
+
+\section TopicStorageOrdersWhich Which storage order to choose?
+
+So, which storage order should you use in your program? There is no simple answer to this question; it depends
+on your application. Here are some points to keep in mind:
+
+  - Your users may expect you to use a specific storage order. Alternatively, you may use other libraries than
+    Eigen, and these other libraries may expect a certain storage order. In these cases it may be easiest and
+    fastest to use this storage order in your whole program.
+  - Algorithms that traverse a matrix row by row will go faster when the matrix is stored in row-major order
+    because of better data locality. Similarly, column-by-column traversal is faster for column-major
+    matrices. It may be worthwhile to experiment a bit to find out what is faster for your particular
+    application.
+  - The default in Eigen is column-major. Naturally, most of the development and testing of the Eigen library
+    is thus done with column-major matrices. This means that, even though we aim to support column-major and
+    row-major storage orders transparently, the Eigen library may well work best with column-major matrices.
+
+*/
+}

doc/Overview.dox

@@ -34,6 +34,7 @@ For a first contact with Eigen, the best place is to have a look at the \ref Get
     - \ref TopicLinearAlgebraDecompositions
     - \ref TopicCustomizingEigen
     - \ref TopicPreprocessorDirectives
+    - \ref TopicStorageOrders
     - \ref TopicInsideEigenExample
     - \ref TopicWritingEfficientProductExpression
     - \ref TopicClassHierarchy

doc/snippets/TopicStorageOrders_example.cpp

@@ -0,0 +1,18 @@
+Matrix<int, 3, 4, ColMajor> Acolmajor;
+Acolmajor << 8, 2, 2, 9,
+             9, 1, 4, 4,
+	     3, 5, 4, 5;
+cout << "The matrix A:" << endl;
+cout << Acolmajor << endl << endl; 
+
+cout << "In memory (column-major):" << endl;
+for (int i = 0; i < Acolmajor.size(); i++)
+  cout << *(Acolmajor.data() + i) << "  ";
+cout << endl << endl;
+
+Matrix<int, 3, 4, RowMajor> Arowmajor = Acolmajor;
+cout << "In memory (row-major):" << endl;
+for (int i = 0; i < Arowmajor.size(); i++)
+  cout << *(Arowmajor.data() + i) << "  ";
+cout << endl;
+