simplify and polish a bit the page 4 / block ops

doc/C03_TutorialArrayClass.dox

@@ -27,7 +27,7 @@ such as adding a constant to every coefficient in the array or multiplying two a
 
 \section TutorialArrayClassTypes Array types
 Array is a class template taking the same template parameters as Matrix.
-As with with, the first 3 template parameters are mandatory:
+As with Matrix, the first 3 template parameters are mandatory:
 \code
 Array<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>
 \endcode
@@ -123,7 +123,7 @@ have a \link ArrayBase::matrix() .matrix() \endlink method. As with all Eigen ex
 this doesn't have any runtime cost (provided that you let your compiler optimize).
 
 Both \link MatrixBase::array() .array() \endlink and \link ArrayBase::matrix() .matrix() \endlink 
-can be used as \b rvalues and as \b lvalues.
+can be used as rvalues and as lvalues.
 
 Mixing matrices and arrays in an expression is forbidden with Eigen. However,
 it is easy to convert from one to the other with \link MatrixBase::array() .array() \endlink and 

doc/C04_TutorialBlockOperations.dox

@@ -6,39 +6,18 @@ namespace Eigen {
 \li \b Previous: \ref TutorialArrayClass
 \li \b Next: \ref TutorialAdvancedInitialization
 
-This tutorial explains the essentials of Block operations together with many examples.
+This tutorial page explains the essentials of block operations.
+A block is a rectangular part of a matrix or array. Blocks expressions can be used both
+as rvalues and as lvalues. As usual with Eigen expressions, this abstraction has zero runtime cost
+provided that you let your compiler optimize.
 
 \b Table \b of \b contents
-  - \ref TutorialBlockOperationsWhatIs
-    - \ref TutorialBlockOperationsFixedAndDynamicSize
+  - \ref TutorialBlockOperationsUsing
   - \ref TutorialBlockOperationsSyntax
      - \ref TutorialBlockOperationsSyntaxColumnRows
      - \ref TutorialBlockOperationsSyntaxCorners
 
-
-\section TutorialBlockOperationsWhatIs What are Block operations?
-Block operations are a set of functions that provide an easy way to access a set of coefficients 
-inside a \b Matrix or \link ArrayBase Array \endlink. A typical example is accessing a single row or 
-column within a given matrix, as well as extracting a sub-matrix from the latter.
-
-Blocks are highly flexible and can be used both as \b rvalues and \b lvalues in expressions, simplifying 
-the task of writing combined expressions with Eigen.
-
-\subsection TutorialBlockOperationsFixedAndDynamicSize Block operations and compile-time optimizations
-As said earlier, a block operation is a way of accessing a group of coefficients inside a Matrix or 
-Array object. Eigen considers two different cases in order to provide compile-time optimization for 
-block operations, depending on whether the the size of the block to be accessed is known at compile time or not. 
-
-To deal with these two situations, for each type of block operation Eigen provides a default version that
-is able to work with run-time dependant block sizes and another one for block operations whose block size is
-known at compile-time.
-
-Even though both functions can be applied to fixed-size objects, it is advisable to use special block operations
-in this case, allowing Eigen to perform more optimizations at compile-time.
-
 \section TutorialBlockOperationsUsing Using block operations
-Block operations are implemented such that they are easy to use and combine with operators and other 
-matrices or arrays.
 
 The most general block operation in Eigen is called \link DenseBase::block() .block() \endlink.
 This function returns a block of size <tt>(p,q)</tt> whose origin is at <tt>(i,j)</tt> by using 
@@ -48,13 +27,11 @@ the following syntax:
 <tr><td align="center">\b Block \b operation</td>
 <td align="center">Default \b version</td>
 <td align="center">Optimized version when the<br>size is known at compile time</td></tr>
-<tr><td>Block of length <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td>
+<tr><td>Block of size <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td>
     <td>\code
-MatrixXf m;
-std::cout << m.block(i,j,p,q);\endcode </td>
+matrix.block(i,j,p,q);\endcode </td>
     <td>\code 
-Matrix3f m;
-std::cout << m.block<p,q>(i,j);\endcode </td>
+matrix.block<p,q>(i,j);\endcode </td>
 </tr>
 </table>