Dune::ACFem::Tensor::ProductTensor< LeftTensor, LeftIndices, RightTensor, RightIndices > Class Template Reference

Compute the component-wise product ".[i][j]" over selected indices: More...

Detailed Description

template<class LeftTensor, class LeftIndices, class RightTensor, class RightIndices>
class Dune::ACFem::Tensor::ProductTensor< LeftTensor, LeftIndices, RightTensor, RightIndices >

Compute the component-wise product ".[i][j]" over selected indices:

\[ (A .[i][j] B)_{k,a0,a1,b0,b1} := \sum_{i,j} delta_{i,j,k} A_{a0,i,a1} B_{b0,j,b1} := ( A_a0,k,a1 B_b0,k,b1 )_{k,a0,a1,b0,b1} \]

Here all indices are to be understood as (possibly empty) multi-indices, where i,j,k obviously must range over the same dimension signature.

• As indicated in the formula the component-wise product can be replaced by a contraction with a 3-(multi)-component identity tensor.
• If the product is only taken over a subset of the tensors ranks then the product dimensions are moved to the front, followed by the remaining degrees of freedom from A, followed by the remaining degrees of freedom of B.
• If the contraction indices are empty then the resulting tensor is just the dyadic product of A with B

Parameters

LeftTensor	Left operand.
LeftIndices	The positions of the contraction indices of the left operand.
RightTensor	Right operand.
RightIndices	The positions of the contraction indices of the right operand.

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The documentation for this class was generated from the following file:

• dune/acfem/tensors/operations/product.hh