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Finish doc page on aliasing.

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Jitse Niesen
2010-12-27 15:06:55 +00:00
parent dc3618a557
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4 changed files with 62 additions and 2 deletions
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doc/I11_Aliasing.dox
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@@ -152,8 +152,50 @@ not necessary to evaluate the right-hand side explicitly.
\section TopicAliasingMatrixMult Aliasing and matrix multiplication
Synopsis: %Matrix multiplication assumes aliasing by default. Use noalias() to improve performance if there is
no aliasing.
Matrix multiplication is the only operation in Eigen that assumes aliasing by default. Thus, if \c matA is a
matrix, then the statement <tt>matA = matA * matA;</tt> is safe. All other operations in Eigen assume that
there are no aliasing problems, either because the result is assigned to a different matrix or because it is a
component-wise operation.
<table class="example">
<tr><th>Example</th><th>Output</th></tr>
<tr><td>
\include TopicAliasing_mult1.cpp
</td>
<td>
\verbinclude TopicAliasing_mult1.out
</td></tr></table>
However, this comes at a price. When executing the expression <tt>matA = matA * matA</tt>, Eigen evaluates the
product in a temporary matrix which is assigned to \c matA after the computation. This is fine. But Eigen does
the same when the product is assigned to a different matrix (e.g., <tt>matB = matA * matA</tt>). In that case,
it is more efficient to evaluate the product directly into \c matB instead of evaluating it first into a
temporary matrix and copying that matrix to \c matB.
The user can indicate with the \link MatrixBase::noalias() noalias()\endlink function that there is no
aliasing, as follows: <tt>matB.noalias() = matA * matA</tt>. This allows Eigen to evaluate the matrix product
<tt>matA * matA</tt> directly into \c matB.
<table class="example">
<tr><th>Example</th><th>Output</th></tr>
<tr><td>
\include TopicAliasing_mult2.cpp
</td>
<td>
\verbinclude TopicAliasing_mult2.out
</td></tr></table>
Of course, you should not use \c noalias() when there is in fact aliasing taking place. If you do, then you
may get wrong results:
<table class="example">
<tr><th>Example</th><th>Output</th></tr>
<tr><td>
\include TopicAliasing_mult3.cpp
</td>
<td>
\verbinclude TopicAliasing_mult3.out
</td></tr></table>
\section TopicAliasingSummary Summary