diff options
author | Benoit Jacob <jacob.benoit.1@gmail.com> | 2010-10-18 08:44:27 -0400 |
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committer | Benoit Jacob <jacob.benoit.1@gmail.com> | 2010-10-18 08:44:27 -0400 |
commit | 1c15a6d96f5bdd6e758552725ea316167aa5ebe3 (patch) | |
tree | 64e1d682afb5fb1efe7e7633550038ae55b9dd9f | |
parent | 4b0fb968ea9c138df74203f8695ece58edc680b0 (diff) |
improvements in tutorial page 4 : block operations
-rw-r--r-- | doc/C04_TutorialBlockOperations.dox | 68 | ||||
-rw-r--r-- | doc/examples/Tutorial_BlockOperations_block_assignment.cpp | 18 | ||||
-rw-r--r-- | doc/examples/Tutorial_BlockOperations_colrow.cpp | 11 | ||||
-rw-r--r-- | doc/examples/Tutorial_BlockOperations_print_block.cpp | 12 |
4 files changed, 52 insertions, 57 deletions
diff --git a/doc/C04_TutorialBlockOperations.dox b/doc/C04_TutorialBlockOperations.dox index b45cbfbc8..ce6bc4717 100644 --- a/doc/C04_TutorialBlockOperations.dox +++ b/doc/C04_TutorialBlockOperations.dox @@ -21,13 +21,12 @@ provided that you let your compiler optimize. \section TutorialBlockOperationsUsing Using block operations 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>. There are two versions, whose syntax is as follows: <table class="tutorial_code" align="center"> <tr><td align="center">\b %Block \b operation</td> -<td align="center">Default version</td> -<td align="center">Optimized version when the<br>size is known at compile time</td></tr> +<td align="center">Version constructing a dynamic-size block expression</td> +<td align="center">Version constructing a fixed-size block expression</td></tr> <tr><td>%Block of size <tt>(p,q)</tt>, starting at <tt>(i,j)</tt></td> <td>\code matrix.block(i,j,p,q);\endcode </td> @@ -36,13 +35,14 @@ matrix.block<p,q>(i,j);\endcode </td> </tr> </table> -The default version is a method which takes four arguments. It can always be used. The optimized version -takes two template arguments (the size of the block) and two normal arguments (the position of the block). -It can only be used if the size of the block is known at compile time, but it may be faster than the -non-optimized version, especially if the size of the block is small. Both versions can be used on fixed-size -and dynamic-size matrices and arrays. +As always in Eigen, indices start at 0. -The following program uses the default and optimized versions to print the values of several blocks inside a +Both versions can be used on fixed-size and dynamic-size matrices and arrays. +These two expressions are semantically equivalent. +The only difference is that the fixed-size version will typically give you faster code if the block size is small, +but requires this size to be known at compile time. + +The following program uses the dynamic-size and fixed-size versions to print the values of several blocks inside a matrix. <table class="tutorial_code"><tr><td> @@ -53,15 +53,10 @@ Output: \verbinclude Tutorial_BlockOperations_print_block.out </td></tr></table> -In the above example the \link DenseBase::block() .block() \endlink function was employed -to read the values inside matrix \p m . However, blocks can also be used as lvalues, meaning that you can -assign to a block. +In the above example the \link DenseBase::block() .block() \endlink function was employed as a \em rvalue, i.e. +it was only read from. However, blocks can also be used as \em lvalues, meaning that you can assign to a block. -This is illustrated in the following example, which uses arrays instead of matrices. The coefficients of the -5-by-5 array \c n are first all set to 0.6, but then the 3-by-3 block in the middle is set to the values in -\c m . The penultimate line shows that blocks can be combined with matrices and arrays to create more complex -expressions. Blocks of an array are an array expression, and thus the multiplication here is coefficient-wise -multiplication. +This is illustrated in the following example. This example also demonstrates blocks in arrays, which works exactly like the above-demonstrated blocks in matrices. <table class="tutorial_code"><tr><td> \include Tutorial_BlockOperations_block_assignment.cpp @@ -71,38 +66,34 @@ Output: \verbinclude Tutorial_BlockOperations_block_assignment.out </td></tr></table> -The \link DenseBase::block() .block() \endlink method is used for general block operations, but there are -other methods for special cases. These are described in the rest of this page. +While the \link DenseBase::block() .block() \endlink method can be used for any block operation, there are +other methods for special cases, providing more specialized API and/or better performance. On the topic of performance, all what +matters is that you give Eigen as much information as possible at compile time. For example, if your block is a single whole column in a matrix, +using the specialized \link DenseBase::col() .col() \endlink function described below lets Eigen know that, which can give it optimization opportunities. +The rest of this page describes these specialized methods. \section TutorialBlockOperationsSyntaxColumnRows Columns and rows -Individual columns and rows are special cases of blocks. Eigen provides methods to easily access them: -\link DenseBase::col() .col() \endlink and \link DenseBase::row() .row()\endlink. There is no syntax variant -for an optimized version. +Individual columns and rows are special cases of blocks. Eigen provides methods to easily address them: +\link DenseBase::col() .col() \endlink and \link DenseBase::row() .row()\endlink. <table class="tutorial_code" align="center"> <tr><td align="center">\b %Block \b operation</td> -<td align="center">Default version</td> -<td align="center">Optimized version when the<br>size is known at compile time</td></tr> +<td align="center">Method</td> <tr><td>i<sup>th</sup> row \link DenseBase::row() * \endlink</td> <td>\code matrix.row(i);\endcode </td> - <td>\code -matrix.row(i);\endcode </td> </tr> <tr><td>j<sup>th</sup> column \link DenseBase::col() * \endlink</td> <td>\code matrix.col(j);\endcode </td> - <td>\code -matrix.col(j);\endcode </td> </tr> </table> -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. +The argument for \p col() and \p row() is the index of the column or row to be accessed. As always in Eigen, indices start at 0. <table class="tutorial_code"><tr><td> C++ code: @@ -113,22 +104,21 @@ Output: \verbinclude Tutorial_BlockOperations_colrow.out </td></tr></table> +That example also demonstrates that block expressions (here columns) can be used in arithmetic like any other expression. + \section TutorialBlockOperationsSyntaxCorners Corner-related operations Eigen also provides special methods for blocks that are flushed against one of the corners or sides of a matrix or array. For instance, \link DenseBase::topLeftCorner() .topLeftCorner() \endlink can be used to refer -to a block in the top-left corner of a matrix. Use <tt>matrix.topLeftCorner(p,q)</tt> to access the block -consisting of the coefficients <tt>matrix(i,j)</tt> with \c i < \c p and \c j < \c q. As an other -example, blocks consisting of whole rows flushed against the top side of the matrix can be accessed by -\link DenseBase::topRows() .topRows() \endlink. +to a block in the top-left corner of a matrix. The different possibilities are summarized in the following table: <table class="tutorial_code" align="center"> <tr><td align="center">\b %Block \b operation</td> -<td align="center">Default version</td> -<td align="center">Optimized version when the<br>size is known at compile time</td></tr> +<td align="center">Version constructing a dynamic-size block expression</td> +<td align="center">Version constructing a fixed-size block expression</td></tr> <tr><td>Top-left p by q block \link DenseBase::topLeftCorner() * \endlink</td> <td>\code matrix.topLeftCorner(p,q);\endcode </td> @@ -200,12 +190,12 @@ Output: \section TutorialBlockOperationsSyntaxVectors Block operations for vectors -Eigen also provides a set of block operations designed specifically for vectors and one-dimensional arrays: +Eigen also provides a set of block operations designed specifically for the special case of vectors and one-dimensional arrays: <table class="tutorial_code" align="center"> <tr><td align="center">\b %Block \b operation</td> -<td align="center">Default version</td> -<td align="center">Optimized version when the<br>size is known at compile time</td></tr> +<td align="center">Version constructing a dynamic-size block expression</td> +<td align="center">Version constructing a fixed-size block expression</td></tr> <tr><td>%Block containing the first \p n elements \link DenseBase::head() * \endlink</td> <td>\code diff --git a/doc/examples/Tutorial_BlockOperations_block_assignment.cpp b/doc/examples/Tutorial_BlockOperations_block_assignment.cpp index 56ca69a6e..76f49f2fb 100644 --- a/doc/examples/Tutorial_BlockOperations_block_assignment.cpp +++ b/doc/examples/Tutorial_BlockOperations_block_assignment.cpp @@ -6,13 +6,13 @@ using namespace Eigen; int main() { - Array33f m; - m << 1,2,3, - 4,5,6, - 7,8,9; - Array<float,5,5> n = Array<float,5,5>::Constant(0.6); - n.block(1,1,3,3) = m; - cout << "n = " << endl << n << endl << endl; - Array33f res = n.block(0,0,3,3) * m; - cout << "res =" << endl << res << endl; + Array22f m; + m << 1,2, + 3,4; + Array44f a = Array44f::Constant(0.6); + cout << "Here is the array a:" << endl << a << endl << endl; + a.block<2,2>(1,1) = m; + cout << "Here is now a with m copied into its central 2x2 block:" << endl << a << endl << endl; + a.block(0,0,2,3) = a.block(2,1,2,3); + cout << "Here is now a with bottom-right 2x3 block copied into top-left 2x2 block:" << endl << a << endl << endl; } diff --git a/doc/examples/Tutorial_BlockOperations_colrow.cpp b/doc/examples/Tutorial_BlockOperations_colrow.cpp index e98263057..2e7eb009b 100644 --- a/doc/examples/Tutorial_BlockOperations_colrow.cpp +++ b/doc/examples/Tutorial_BlockOperations_colrow.cpp @@ -1,14 +1,17 @@ #include <Eigen/Dense> #include <iostream> +using namespace std; + int main() { Eigen::MatrixXf m(3,3); m << 1,2,3, 4,5,6, 7,8,9; - std::cout << "2nd Row: " << m.row(1) << std::endl; - m.col(0) += m.col(2); - std::cout << "m after adding third column to first:\n"; - std::cout << m << std::endl; + cout << "Here is the matrix m:" << endl << m << endl; + cout << "2nd Row: " << m.row(1) << endl; + m.col(2) += 3 * m.col(0); + cout << "After adding 3 times the first column into the third column, the matrix m is:\n"; + cout << m << endl; } diff --git a/doc/examples/Tutorial_BlockOperations_print_block.cpp b/doc/examples/Tutorial_BlockOperations_print_block.cpp index 0fdefecdf..edea4aefe 100644 --- a/doc/examples/Tutorial_BlockOperations_print_block.cpp +++ b/doc/examples/Tutorial_BlockOperations_print_block.cpp @@ -1,6 +1,8 @@ #include <Eigen/Dense> #include <iostream> +using namespace std; + int main() { Eigen::MatrixXf m(4,4); @@ -8,11 +10,11 @@ int main() 5, 6, 7, 8, 9,10,11,12, 13,14,15,16; - std::cout << "Block in the middle" << std::endl; - std::cout << m.block<2,2>(1,1) << std::endl << std::endl; - for (int i = 1; i < 4; ++i) + cout << "Block in the middle" << endl; + cout << m.block<2,2>(1,1) << endl << endl; + for (int i = 1; i <= 3; ++i) { - std::cout << "Block of size " << i << std::endl; - std::cout << m.block(0,0,i,i) << std::endl << std::endl; + cout << "Block of size " << i << "x" << i << endl; + cout << m.block(0,0,i,i) << endl << endl; } } |