Write topic page for storage orders.

4 files changed, 110 insertions, 11 deletions

diff --git a/doc/I08_StorageOrders.dox b/doc/I08_StorageOrders.dox
deleted file mode 100644
index 0ceb771d3..000000000
--- a/doc/I08_StorageOrders.dox
+++ /dev/null
@@ -1,11 +0,0 @@
-namespace Eigen {
-
-/** \page TopicStorageOrders Storage orders
-
-
-TODO: write this dox page!
-
-Is linked from the tutorial on the Matrix class.
-
-*/
-}
diff --git a/doc/I15_StorageOrders.dox b/doc/I15_StorageOrders.dox
new file mode 100644
index 000000000..6b56ca8f8
--- /dev/null
+++ b/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.
+
+*/
+}
diff --git a/doc/Overview.dox b/doc/Overview.dox
index a4c4cde5d..04bc075f0 100644
--- a/doc/Overview.dox
+++ b/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
diff --git a/doc/snippets/TopicStorageOrders_example.cpp b/doc/snippets/TopicStorageOrders_example.cpp
new file mode 100644
index 000000000..0623ef0c2
--- /dev/null
+++ b/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;
+