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5 In %Eigen, aliasing refers to assignment statement in which the same matrix (or array or vector) appears on the
46 Aliasing occurs more naturally when trying to shrink a matrix. For example, the expressions <tt>vec =
68 [with OtherDerived = Eigen::Transpose<Eigen::Matrix<int, 2, 2, 0, 2, 2> >, Derived = Eigen::Matrix<int, 2, 2, 0, 2, 2>]:
81 to evaluate the right-hand side fully into a temporary matrix/array and then assign it to the left-hand
100 \link DenseBase::transposeInPlace() transposeInPlace() \endlink which replaces a matrix by its transpose.
126 In the special case where a matrix or vector is shrunk using an expression like <tt>vec = vec.head(n)</tt>,
132 As explained above, it may be dangerous if the same matrix or array occurs on both the left-hand side and the
134 explicitly. However, applying component-wise operations (such as matrix addition, scalar multiplication and
138 eval() \endlink even though the same matrix appears on both sides of the assignments.
150 the (i,j) entry of the matrix or array on the left-hand side and not on any other entries. In that case it is
154 \section TopicAliasingMatrixMult Aliasing and matrix multiplication
156 Matrix multiplication is the only operation in %Eigen that assumes aliasing by default. Thus, if \c matA is a
157 matrix, then the statement <tt>matA = matA * matA;</tt> is safe. All other operations in %Eigen assume that
158 there are no aliasing problems, either because the result is assigned to a different matrix or because it is a
171 product in a temporary matrix which is assigned to \c matA after the computation. This is fine. But %Eigen does
172 the same when the product is assigned to a different matrix (e.g., <tt>matB = matA * matA</tt>). In that case,
174 temporary matrix and copying that matrix to \c matB.
177 aliasing, as follows: <tt>matB.noalias() = matA * matA</tt>. This allows %Eigen to evaluate the matrix product
204 Aliasing occurs when the same matrix or array coefficients appear both on the left- and the right-hand side of
206 - Aliasing is harmless with coefficient-wise computations; this includes scalar multiplication and matrix or