diff --git a/doc/C04_TutorialBlockOperations.dox b/doc/C04_TutorialBlockOperations.dox new file mode 100644 index 000000000..57a885852 --- /dev/null +++ b/doc/C04_TutorialBlockOperations.dox @@ -0,0 +1,294 @@ +namespace Eigen { + +/** \page TutorialBlockOperations Tutorial page 4 - Block operations + \ingroup Tutorial + +\li \b Previous: \ref TutorialArrayClass +\li \b Next: (not yet written) + +This tutorial explains the essentials of Block operations together with many examples. + +\b Table \b of \b contents + - \ref TutorialBlockOperationsWhatIs + - \ref TutorialBlockOperationsFixedAndDynamicSize + - \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 later. + +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, regarding 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 (m,n) whose origin is at (i,j) by using +the following syntax: + + + + + + + + + +
\b Block \b operationDefault \b versionOptimized version when the
size is known at compile time
Block of length (m,n), starting at (i,j)\code +MatrixXf m; +std::cout << m.block(i,j,m,n);\endcode \code +Matrix3f m; +std::cout << m.block(i,j);\endcode
+ +Therefore, if we want to print the values of a block inside a matrix we can simply write: + +
+\include Tutorial_BlockOperations_print_block.cpp + +Output: +\verbinclude Tutorial_BlockOperations_print_block.out +
+ + +In the previous example the \link DenseBase::block() .block() \endlink function was employed +to read the values inside matrix \p m . Blocks can also be used to perform operations and +assignments within matrices or arrays of different size: + + +
+\include Tutorial_BlockOperations_block_assignment.cpp + +Output: +\verbinclude Tutorial_BlockOperations_block_assignment.out +
+ + +Blocks can also be combined with matrices and arrays to create more complex expressions: + +\code + MatrixXf m(3,3), n(2,2); + MatrixXf p(3,3); + + m.block(0,0,2,2) = m.block(0,0,2,2) * n + p.block(1,1,2,2); +\endcode + +It is important to point out that \link DenseBase::block() .block() \endlink is the +general case for a block operation but there are many other useful block operations, +as described in the next section. + +\section TutorialBlockOperationsSyntax Block operation syntax +The following tables show a summary of Eigen's block operations and how they are applied to +fixed- and dynamic-sized Eigen objects. + +\subsection TutorialBlockOperationsSyntaxColumnRows Columns and rows +Other extremely useful block operations are \link DenseBase::col() .col() \endlink and +\link DenseBase::row() .row() \endlink which provide access to a +specific row or column. This is a special case in the sense that the syntax for fixed- and +dynamic-sized objects is exactly the same: + + + + + + + + + + + + + +
\b Block \b operationDefault versionOptimized version when the
size is known at compile time
ith row + \link DenseBase::row() * \endlink\code +MatrixXf m; +std::cout << m.row(i);\endcode \code +Matrix3f m; +std::cout << m.row(i);\endcode
jth column + \link DenseBase::col() * \endlink\code +MatrixXf m; +std::cout << m.col(j);\endcode \code +Matrix3f m; +std::cout << m.col(j);\endcode
+ +A simple example demonstrating these feature follows: + + +
+C++ code: +\include Tutorial_BlockOperations_colrow.cpp + +Output: +\include Tutorial_BlockOperations_colrow.out +
+ + +\b NOTE: the argument for \p col() and \p row() is the index of the column or row to be accessed, +starting at 0. Therefore, \p col(0) will access the first column and \p col(1) the second one. + + +\subsection TutorialBlockOperationsSyntaxCorners Corner-related operations + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
\b Block \b operationDefault versionOptimized version when the
size is known at compile time
Top-left m by n block \link DenseBase::topLeftCorner() * \endlink\code +MatrixXf m; +std::cout << m.topLeftCorner(m,n);\endcode \code +Matrix3f m; +std::cout << m.topLeftCorner();\endcode
Bottom-left m by n block + \link DenseBase::bottomLeftCorner() * \endlink\code +MatrixXf m; +std::cout << m.bottomLeftCorner(m,n);\endcode \code +Matrix3f m; +std::cout << m.bottomLeftCorner();\endcode
Top-right m by n block + \link DenseBase::topRightCorner() * \endlink\code +MatrixXf m; +std::cout << m.topRightCorner(m,n);\endcode \code +Matrix3f m; +std::cout << m.topRightCorner();\endcode
Bottom-right m by n block + \link DenseBase::bottomRightCorner() * \endlink\code +MatrixXf m; +std::cout << m.bottomRightCorner(m,n);\endcode \code +Matrix3f m; +std::cout << m.bottomRightCorner();\endcode
Block containing the first nth rows + \link DenseBase::topRows() * \endlink\code +MatrixXf m; +std::cout << m.topRows(n);\endcode \code +Matrix3f m; +std::cout << m.topRows();\endcode
Block containing the last nth rows + \link DenseBase::bottomRows() * \endlink\code +MatrixXf m; +std::cout << m.bottomRows(n);\endcode \code +Matrix3f m; +std::cout << m.bottomRows();\endcode
Block containing the first nth columns + \link DenseBase::leftCols() * \endlink\code +MatrixXf m; +std::cout << m.leftCols(n);\endcode \code +Matrix3f m; +std::cout << m.leftCols();\endcode
Block containing the last nth columns + \link DenseBase::rightCols() * \endlink\code +MatrixXf m; +std::cout << m.rightCols(n);\endcode \code +Matrix3f m; +std::cout << m.rightCols();\endcode
+ + +Here there is a simple example showing the power of the operations presented above: + + +
+C++ code: +\include Tutorial_BlockOperations_corner.cpp + +Output: +\include Tutorial_BlockOperations_corner.out +
+ + + + + + + + +\subsection TutorialBlockOperationsSyntaxVectors Block operations for vectors +Eigen also provides a set of block operations designed specifically for vectors: + + + + + + + + + + + + + + + + + +
\b Block \b operationDefault versionOptimized version when the
size is known at compile time
Block containing the first \p n th elements row + \link DenseBase::head() * \endlink\code +VectorXf v; +std::cout << v.head(n);\endcode \code +Vector3f v; +std::cout << v.head();\endcode
Block containing the last \p n th elements + \link DenseBase::tail() * \endlink\code +VectorXf v; +std::cout << v.tail(n);\endcode \code +Vector3f m; +std::cout << v.tail();\endcode
Block containing \p n elements, starting at position \p i + \link DenseBase::segment() * \endlink\code +VectorXf v; +std::cout << v.segment(i,n);\endcode \code +Vector3f m; +std::cout << v.segment(i);\endcode
+ + +An example is presented below: + +
+C++ code: +\include Tutorial_BlockOperations_vector.cpp + +Output: +\include Tutorial_BlockOperations_vector.out +
+ + +*/ + +} diff --git a/doc/examples/Tutorial_BlockOperations_block_assignment.cpp b/doc/examples/Tutorial_BlockOperations_block_assignment.cpp new file mode 100644 index 000000000..0419a500f --- /dev/null +++ b/doc/examples/Tutorial_BlockOperations_block_assignment.cpp @@ -0,0 +1,31 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + MatrixXf m(3,3), n(2,2); + + m << 1,2,3, + 4,5,6, + 7,8,9; + + // assignment through a block operation, + // block as rvalue + n = m.block(0,0,2,2); + + //print n + cout << "n = " << endl << n << endl << endl; + + + n << 1,1, + 1,1; + + // block as lvalue + m.block(0,0,2,2) = n; + + //print m + cout << "m = " << endl << m << endl; +} diff --git a/doc/examples/Tutorial_BlockOperations_colrow.cpp b/doc/examples/Tutorial_BlockOperations_colrow.cpp new file mode 100644 index 000000000..e639324b2 --- /dev/null +++ b/doc/examples/Tutorial_BlockOperations_colrow.cpp @@ -0,0 +1,15 @@ +#include +#include +using namespace Eigen; + +int main() +{ + MatrixXf m(3,3); + + m << 1,2,3, + 4,5,6, + 7,8,9; + + std::cout << "2nd Row: " + << m.row(1) << std::endl; +} diff --git a/doc/examples/Tutorial_BlockOperations_corner.cpp b/doc/examples/Tutorial_BlockOperations_corner.cpp new file mode 100644 index 000000000..96c6df62b --- /dev/null +++ b/doc/examples/Tutorial_BlockOperations_corner.cpp @@ -0,0 +1,27 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + MatrixXf m(4,4); + + m << 1, 2, 3, 4, + 5, 6, 7, 8, + 9, 10,11,12, + 13,14,15,16; + + //print first two columns + cout << "-- leftCols(2) --" << endl + << m.leftCols(2) << endl << endl; + + //print last two rows + cout << "-- bottomRows(2) --" << endl + << m.bottomRows(2) << endl << endl; + + //print top-left 2x3 corner + cout << "-- topLeftCorner(2,3) --" << endl + << m.topLeftCorner(2,3) << endl; +} diff --git a/doc/examples/Tutorial_BlockOperations_print_block.cpp b/doc/examples/Tutorial_BlockOperations_print_block.cpp new file mode 100644 index 000000000..a2d0db864 --- /dev/null +++ b/doc/examples/Tutorial_BlockOperations_print_block.cpp @@ -0,0 +1,14 @@ +#include +#include +using namespace Eigen; + +int main() +{ + MatrixXf m(3,3); + + m << 1,2,3, + 4,5,6, + 7,8,9; + + std::cout << m.block(0,0,2,2) << std::endl; +} diff --git a/doc/examples/Tutorial_BlockOperations_vector.cpp b/doc/examples/Tutorial_BlockOperations_vector.cpp new file mode 100644 index 000000000..211b55472 --- /dev/null +++ b/doc/examples/Tutorial_BlockOperations_vector.cpp @@ -0,0 +1,24 @@ +#include +#include + +using namespace std; +using namespace Eigen; + +int main() +{ + VectorXf v(6); + + v << 1, 2, 3, 4, 5, 6; + + //print first three elements + cout << "-- head(3) --" << endl + << v.head(3) << endl << endl; + + //print last three elements + cout << "-- tail(3) --" << endl + << v.tail(3) << endl << endl; + + //print between 2nd and 5th elem. inclusive + cout << "-- segment(1,4) --" << endl + << v.segment(1,4) << endl; +}