Cartesian3d.h File Reference

#include <xtensor/xadapt.hpp>
#include <xtensor/xnoalias.hpp>
#include <xtensor/xrandom.hpp>
#include <xtensor/xtensor.hpp>
#include <xtensor/xview.hpp>
#include "config.h"
#include "detail.hpp"
#include "version.h"
#include "Cartesian3d.hpp"
#include "Cartesian3d_Array.hpp"

Go to the source code of this file.

Classes
class	GMatTensor::Cartesian3d::Array< N >
	Array of tensors: More...

Namespaces
namespace	GMatTensor
	Tensor products / operations.
namespace	GMatTensor::Cartesian3d
	Tensors and tensor operations for a(n) array of 3d tensors of different rank, defined in a Cartesian coordinate system.
namespace	GMatTensor::Cartesian3d::pointer
	API for individual tensors with pointer-only input.

Functions
array_type::tensor< double, 2 >	GMatTensor::Cartesian3d::Random2 ()
	Random 2nd-order tensor (for example for use in testing). More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::Random4 ()
	Random 4th-order tensor (for example for use in testing). More...
array_type::tensor< double, 2 >	GMatTensor::Cartesian3d::O2 ()
	2nd-order null tensor (all components equal to zero). More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::O4 ()
	4th-order null tensor (all components equal to zero). More...
array_type::tensor< double, 2 >	GMatTensor::Cartesian3d::I2 ()
	2nd-order identity tensor. More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::II ()
	Result of the dyadic product of two 2nd-order identity tensors (see I2()). More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::I4 ()
	Fourth order unit tensor. More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::I4rt ()
	Right-transposed fourth order unit tensor. More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::I4s ()
	Fourth order symmetric projection. More...
array_type::tensor< double, 4 >	GMatTensor::Cartesian3d::I4d ()
	Fourth order deviatoric projection. More...
template<class T >
auto	GMatTensor::Cartesian3d::Trace (const T &A)
	Trace or 2nd-order tensor. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::trace (const T &A, R &ret)
	Same as Trace() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Hydrostatic (const T &A)
	Hydrostatic part of a tensor. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::hydrostatic (const T &A, R &ret)
	Same as Hydrostatic() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Det (const T &A)
	Determinant. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::det (const T &A, R &ret)
	Same as Det() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::A2_ddot_B2 (const T &A, const T &B)
	Double tensor contraction. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::A2_ddot_B2 (const T &A, const T &B, R &ret)
	Same as A2_ddot_B2(const T& A, const T& B) but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::A2s_ddot_B2s (const T &A, const T &B)
	Same as A2_ddot_B2(const T& A, const T& B, R& ret) but for symmetric tensors. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::A2s_ddot_B2s (const T &A, const T &B, R &ret)
	Same as A2s_ddot_B2s(const T& A, const T& B) but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Norm_deviatoric (const T &A)
	Norm of the tensor's deviator: More...
template<class T , class R >
void	GMatTensor::Cartesian3d::norm_deviatoric (const T &A, R &ret)
	Same as Norm_deviatoric() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Deviatoric (const T &A)
	Deviatoric part of a tensor: More...
template<class T , class R >
void	GMatTensor::Cartesian3d::deviatoric (const T &A, R &ret)
	Same as Deviatoric() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Sym (const T &A)
	Symmetric part of a tensor: More...
template<class T , class R >
void	GMatTensor::Cartesian3d::sym (const T &A, R &ret)
	Same as Sym() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Inv (const T &A)
	Inverse. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::inv (const T &A, R &ret)
	Same as Inv() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::Logs (const T &A)
	Logarithm. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::logs (const T &A, R &ret)
	Same as Logs() but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::A2_dot_A2T (const T &A)
	Dot-product (single tensor contraction) More...
template<class T , class R >
void	GMatTensor::Cartesian3d::A2_dot_A2T (const T &A, R &ret)
	Same as A2_dot_A2T(const T& A) but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::A2_dot_B2 (const T &A, const T &B)
	Dot-product (single tensor contraction) More...
template<class T , class R >
void	GMatTensor::Cartesian3d::A2_dot_B2 (const T &A, const T &B, R &ret)
	Same as A2_dot_B2(const T& A, const T& B) but writes to externally allocated output. More...
template<class T >
auto	GMatTensor::Cartesian3d::A2_dyadic_B2 (const T &A, const T &B)
	Dyadic product. More...
template<class T , class R >
void	GMatTensor::Cartesian3d::A2_dyadic_B2 (const T &A, const T &B, R &ret)
	Same as A2_dyadic_B2(const T& A, const T& B) but writes to externally allocated output. More...
template<class T , class U >
auto	GMatTensor::Cartesian3d::A4_ddot_B2 (const T &A, const U &B)
	Double tensor contraction. More...
template<class T , class U , class R >
void	GMatTensor::Cartesian3d::A4_ddot_B2 (const T &A, const U &B, R &ret)
	Same as A4_ddot_B2(const T& A, const U& B) but writes to externally allocated output. More...
template<class T , class U >
auto	GMatTensor::Cartesian3d::A4_dot_B2 (const T &A, const U &B)
	Tensor contraction. More...
template<class T , class U , class R >
void	GMatTensor::Cartesian3d::A4_dot_B2 (const T &A, const U &B, R &ret)
	Same as A4_dot_B2(const T& A, const U& B) but writes to externally allocated output. More...
template<class T >
size_t	GMatTensor::Cartesian3d::underlying_size_A2 (const T &A)
	Size of the underlying array. More...
template<class T >
size_t	GMatTensor::Cartesian3d::underlying_size_A4 (const T &A)
	Size of the underlying array. More...
template<class T >
auto	GMatTensor::Cartesian3d::underlying_shape_A2 (const T &A) -> std::array< size_t, detail::impl_A2< T, 3 >::rank >
	Shape of the underlying array. More...
template<class T >
auto	GMatTensor::Cartesian3d::underlying_shape_A4 (const T &A) -> std::array< size_t, detail::impl_A4< T, 3 >::rank >
	Shape of the underlying array. More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::O2 (T *ret)
	See Cartesian3d::O2() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::O4 (T *ret)
	See Cartesian3d::O4() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::I2 (T *ret)
	See Cartesian3d::I2() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::II (T *ret)
	See Cartesian3d::II() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::I4 (T *ret)
	See Cartesian3d::I4() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::I4rt (T *ret)
	See Cartesian3d::I4rt() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::I4s (T *ret)
	See Cartesian3d::I4s() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::I4d (T *ret)
	See Cartesian3d::I4d() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Trace (const T *A)
	See Cartesian3d::Trace() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Hydrostatic (const T *A)
	See Cartesian3d::Hydrostatic() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Det (const T *A)
	See Cartesian3d::Det() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::sym (const T *A, T *ret)
	See Cartesian3d::Sym() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Inv (const T *A, T *ret)
	See Cartesian3d::Inv(), returns Cartesian3d::Det() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Hydrostatic_deviatoric (const T *A, T *ret)
	Returns Cartesian3d::Hydrostatic() and computes Cartesian3d::Deviatoric() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Deviatoric_ddot_deviatoric (const T *A)
	Double tensor contraction of the tensor's deviator. More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::Norm_deviatoric (const T *A)
	See Cartesian3d::Norm_deviatoric() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::A2_ddot_B2 (const T *A, const T *B)
	See Cartesian3d::A2_ddot_B2() More...
template<class T >
T	GMatTensor::Cartesian3d::pointer::A2s_ddot_B2s (const T *A, const T *B)
	See Cartesian3d::A2s_ddot_B2s() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A2_dyadic_B2 (const T *A, const T *B, T *ret)
	See Cartesian3d::A2_dyadic_B2() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A4_dot_B2 (const T *A, const T *B, T *ret)
	See Cartesian3d::A4_dot_B2() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A2_dot_B2 (const T *A, const T *B, T *ret)
	See Cartesian3d::A2_dot_B2() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A2_dot_A2T (const T *A, T *ret)
	See Cartesian3d::A2_dot_A2T() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A4_ddot_B2 (const T *A, const T *B, T *ret)
	See Cartesian3d::A4_ddot_B2() More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A4_ddot_B4_ddot_C4 (const T *A, const T *B, const T *C, T *ret)
	Product. More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::A2_dot_B2_dot_C2T (const T *A, const T *B, const T *C, T *ret)
	Product. More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::eigs (const T *A, T *vec, T *val)
	Get eigenvalues/-vectors such that. More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::from_eigs (const T *vec, const T *val, T *ret)
	Reconstruct tensor from eigenvalues/-vectors (reverse operation of eigs()) Symmetric tensors only, no assertion. More...
template<class T >
void	GMatTensor::Cartesian3d::pointer::logs (const T *A, T *ret)
	See Cartesian3d::Logs() More...

Detailed Description

Copyright

Copyright 2020. Tom de Geus. All rights reserved.

License: This project is released under the MIT License.

Definition in file Cartesian3d.h.