deal.II version GIT relicensing-2238-gc05b561aad 2024-12-10 20:50:00+00:00
|
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/kokkos.h>
#include <deal.II/base/numbers.h>
#include <deal.II/base/table_indices.h>
#include <deal.II/base/template_constraints.h>
#include <deal.II/base/tensor_accessors.h>
#include <Kokkos_Array.hpp>
#include <adolc/adouble.h>
#include <cmath>
#include <ostream>
#include <type_traits>
Go to the source code of this file.
Classes | |
class | Tensor< 0, dim, Number > |
class | Tensor< rank_, dim, Number > |
Functions | |
Output functions for Tensor objects | |
template<int rank_, int dim, typename Number > | |
std::ostream & | operator<< (std::ostream &out, const Tensor< rank_, dim, Number > &p) |
template<int dim, typename Number > | |
std::ostream & | operator<< (std::ostream &out, const Tensor< 0, dim, Number > &p) |
Vector space operations on Tensor objects | |
template<int dim, typename Number , typename Other > | |
constexpr ProductType< Other, Number >::type | operator* (const Other &object, const Tensor< 0, dim, Number > &t) |
template<int dim, typename Number , typename Other > | |
constexpr ProductType< Number, Other >::type | operator* (const Tensor< 0, dim, Number > &t, const Other &object) |
template<int dim, typename Number , typename OtherNumber > | |
constexpr ProductType< Number, OtherNumber >::type | operator* (const Tensor< 0, dim, Number > &src1, const Tensor< 0, dim, OtherNumber > &src2) |
template<int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< 0, dim, typename ProductType< Number, typename EnableIfScalar< OtherNumber >::type >::type > | operator/ (const Tensor< 0, dim, Number > &t, const OtherNumber &factor) |
template<int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< 0, dim, typename ProductType< Number, OtherNumber >::type > | operator+ (const Tensor< 0, dim, Number > &p, const Tensor< 0, dim, OtherNumber > &q) |
template<int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< 0, dim, typename ProductType< Number, OtherNumber >::type > | operator- (const Tensor< 0, dim, Number > &p, const Tensor< 0, dim, OtherNumber > &q) |
template<int rank, int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< rank, dim, typename ProductType< Number, typename EnableIfScalar< OtherNumber >::type >::type > | operator* (const Tensor< rank, dim, Number > &t, const OtherNumber &factor) |
template<int rank, int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< rank, dim, typename ProductType< typename EnableIfScalar< Number >::type, OtherNumber >::type > | operator* (const Number &factor, const Tensor< rank, dim, OtherNumber > &t) |
template<int rank, int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< rank, dim, typename ProductType< Number, typename EnableIfScalar< OtherNumber >::type >::type > | operator/ (const Tensor< rank, dim, Number > &t, const OtherNumber &factor) |
template<int rank, int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< rank, dim, typename ProductType< Number, OtherNumber >::type > | operator+ (const Tensor< rank, dim, Number > &p, const Tensor< rank, dim, OtherNumber > &q) |
template<int rank, int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< rank, dim, typename ProductType< Number, OtherNumber >::type > | operator- (const Tensor< rank, dim, Number > &p, const Tensor< rank, dim, OtherNumber > &q) |
template<int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< 0, dim, typename ProductType< Number, OtherNumber >::type > | schur_product (const Tensor< 0, dim, Number > &src1, const Tensor< 0, dim, OtherNumber > &src2) |
template<int rank, int dim, typename Number , typename OtherNumber > | |
constexpr Tensor< rank, dim, typename ProductType< Number, OtherNumber >::type > | schur_product (const Tensor< rank, dim, Number > &src1, const Tensor< rank, dim, OtherNumber > &src2) |
Contraction operations and the outer product for tensor objects | |
template<int dim, typename Number > | |
Number | l1_norm (const Tensor< 2, dim, Number > &t) |
template<int dim, typename Number > | |
Number | linfty_norm (const Tensor< 2, dim, Number > &t) |
|
inline |
|
inlineconstexpr |
|
inlineconstexpr |
|
constexpr |
|
constexpr |
|
constexpr |
|
constexpr |
|
inlineconstexpr |
Multiplication of a tensor of general rank with a scalar number from the right.
Only multiplication with a scalar number type (i.e., a floating point number, a complex floating point number, etc.) is allowed, see the documentation of EnableIfScalar for details.
|
inlineconstexpr |
Multiplication of a tensor of general rank with a scalar number from the left.
Only multiplication with a scalar number type (i.e., a floating point number, a complex floating point number, etc.) is allowed, see the documentation of EnableIfScalar for details.
|
inlineconstexpr |
Division of a tensor of general rank with a scalar number. See the discussion on operator*() above for more information about template arguments and the return type.
|
inlineconstexpr |
|
inlineconstexpr |
|
inlineconstexpr |
|
inlineconstexpr |
Entrywise multiplication of two tensor objects of general rank.
This multiplication is also called "Hadamard-product" (c.f. https://en.wikipedia.org/wiki/Hadamard_product_(matrices)), and generates a new tensor of size <rank, dim>:
\[ \text{result}_{i, j} = \text{left}_{i, j}\circ \text{right}_{i, j} \]
rank | The rank of both tensors. |
The dot product (single contraction) for tensors. This function return a tensor of rank \((\text{rank}_1 + \text{rank}_2 - 2)\) that is the contraction of the last index of a tensor src1
of rank rank_1
with the first index of a tensor src2
of rank rank_2:
\[ \text{result}_{i_1,\ldots,i_{r1},j_1,\ldots,j_{r2}} = \sum_{k} \text{left}_{i_1,\ldots,i_{r1}, k} \text{right}_{k, j_1,\ldots,j_{r2}} \]
operator*()
performs a double contraction. The origin of the difference in how operator*()
is implemented between Tensor and SymmetricTensor is that for the former, the product between two Tensor objects of same rank and dimension results in another Tensor object – that it, operator*()
corresponds to the multiplicative group action within the group of tensors. On the other hand, there is no corresponding multiplicative group action with the set of symmetric tensors because, in general, the product of two symmetric tensors is a nonsymmetric tensor. As a consequence, for a mathematician, it is clear that operator*()
for symmetric tensors must have a different meaning: namely the dot or scalar product that maps two symmetric tensors of rank 2 to a scalar. This corresponds to the double-dot (colon) operator whose meaning is then extended to the product of any two even-ranked symmetric tensors.rank_1==rank_2==1
, then a scalar number is returned as an unwrapped number type. Return the \(l_1\) norm of the given rank-2 tensor, where \(\|\mathbf T\|_1 = \max_j \sum_i |T_{ij}|\) (maximum of the sums over columns).