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Diffstat (limited to 'doc/TutorialReductionsVisitorsBroadcasting.dox')
| -rw-r--r-- | doc/TutorialReductionsVisitorsBroadcasting.dox | 14 |
1 files changed, 6 insertions, 8 deletions
diff --git a/doc/TutorialReductionsVisitorsBroadcasting.dox b/doc/TutorialReductionsVisitorsBroadcasting.dox index 6d25ff0ea..f5322b4a6 100644 --- a/doc/TutorialReductionsVisitorsBroadcasting.dox +++ b/doc/TutorialReductionsVisitorsBroadcasting.dox @@ -101,17 +101,16 @@ row and column position are to be stored. These variables should be of type \verbinclude Tutorial_ReductionsVisitorsBroadcasting_visitors.out </td></tr></table> -Note that both functions also return the value of the minimum or maximum coefficient if needed, -as if it was a typical reduction operation. +Both functions also return the value of the minimum or maximum coefficient. \section TutorialReductionsVisitorsBroadcastingPartialReductions Partial reductions Partial reductions are reductions that can operate column- or row-wise on a Matrix or Array, applying the reduction operation on each column or row and -returning a column or row-vector with the corresponding values. Partial reductions are applied +returning a column or row vector with the corresponding values. Partial reductions are applied with \link DenseBase::colwise() colwise() \endlink or \link DenseBase::rowwise() rowwise() \endlink. A simple example is obtaining the maximum of the elements -in each column in a given matrix, storing the result in a row-vector: +in each column in a given matrix, storing the result in a row vector: <table class="example"> <tr><th>Example:</th><th>Output:</th></tr> @@ -133,8 +132,7 @@ The same operation can be performed row-wise: \verbinclude Tutorial_ReductionsVisitorsBroadcasting_rowwise.out </td></tr></table> -<b>Note that column-wise operations return a 'row-vector' while row-wise operations -return a 'column-vector'</b> +<b>Note that column-wise operations return a row vector, while row-wise operations return a column vector.</b> \subsection TutorialReductionsVisitorsBroadcastingPartialReductionsCombined Combining partial reductions with other operations It is also possible to use the result of a partial reduction to do further processing. @@ -176,7 +174,7 @@ The concept behind broadcasting is similar to partial reductions, with the diffe constructs an expression where a vector (column or row) is interpreted as a matrix by replicating it in one direction. -A simple example is to add a certain column-vector to each column in a matrix. +A simple example is to add a certain column vector to each column in a matrix. This can be accomplished with: <table class="example"> @@ -253,7 +251,7 @@ is a new matrix whose size is the same as matrix <tt>m</tt>: \f[ \f] - <tt>(m.colwise() - v).colwise().squaredNorm()</tt> is a partial reduction, computing the squared norm column-wise. The result of -this operation is a row-vector where each coefficient is the squared Euclidean distance between each column in <tt>m</tt> and <tt>v</tt>: \f[ +this operation is a row vector where each coefficient is the squared Euclidean distance between each column in <tt>m</tt> and <tt>v</tt>: \f[ \mbox{(m.colwise() - v).colwise().squaredNorm()} = \begin{bmatrix} 1 & 505 & 32 & 50 |