multiply.h File Reference

#include "operator.h"
#include "dg/functors.h"
#include "dg/blas1.h"
#include "tensor.h"

Go to the source code of this file.

Classes
struct	dg::TensorMultiply2d< value_type >
	\( y_i \leftarrow \lambda T_{ij} x_i + \mu y_i\) More...
struct	dg::TensorMultiply3d< value_type >
	\( y_i \leftarrow \lambda T_{ij} x_i + \mu y_i\) More...
struct	dg::InverseTensorMultiply2d< value_type >
	\( y_i \leftarrow \lambda T^{-1}_{ij} x_i + \mu y_i\) More...
struct	dg::InverseTensorMultiply3d< value_type >
	\( y_i \leftarrow \lambda T^{-1}_{ij} x_i + \mu y_i\) More...
struct	dg::TensorDot2d< value_type >
	\( y = \lambda\mu v_i T_{ij} w_j \) More...
struct	dg::TensorDot3d< value_type >
	\( y = \lambda \mu v_i T_{ij} w_j \) More...
struct	dg::TensorDeterminant2d< value_type >
	\( y = t_{00} t_{11} - t_{10}t_{01} \) More...
struct	dg::TensorDeterminant3d< value_type >
	\( y = t_{00} t_{11}t_{22} + t_{01}t_{12}t_{20} + t_{02}t_{10}t_{21} - t_{02}t_{11}t_{20} - t_{01}t_{10}t_{22} - t_{00}t_{12}t_{21} \) More...

Namespaces
namespace	dg
	This is the namespace for all functions and classes defined and used by the discontinuous Galerkin library.
namespace	dg::tensor
	Utility functions used in connection with the SparseTensor class.

Functions
template<class ContainerType0 , class ContainerType1 >
void	dg::tensor::scal (SparseTensor< ContainerType0 > &t, const ContainerType1 &mu)
	\( t^{ij} = \mu t^{ij} \ \forall i,j \) More...
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerTypeM , class ContainerType3 , class ContainerType4 >
void	dg::tensor::multiply2d (const ContainerTypeL &lambda, const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, const ContainerTypeM &mu, ContainerType3 &out0, ContainerType4 &out1)
	\( w^i = \sum_{i=0}^1 \lambda t^{ij}v_j + \mu w^i \text{ for } i\in \{0,1\}\) More...
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerTypeM , class ContainerType4 , class ContainerType5 , class ContainerType6 >
void	dg::tensor::multiply3d (const ContainerTypeL &lambda, const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, const ContainerType3 &in2, const ContainerTypeM &mu, ContainerType4 &out0, ContainerType5 &out1, ContainerType6 &out2)
	\( w^i = \sum_{i=0}^2\lambda t^{ij}v_j + \mu w^i \text{ for } i\in \{0,1,2\}\) More...
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerTypeM , class ContainerType3 , class ContainerType4 >
void	dg::tensor::inv_multiply2d (const ContainerTypeL &lambda, const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, const ContainerTypeM &mu, ContainerType3 &out0, ContainerType4 &out1)
	\( v_j = \sum_{i=0}^1\lambda (t^{-1})_{ji}w^i + \mu v_j \text{ for } i\in \{0,1\}\) More...
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerTypeM , class ContainerType4 , class ContainerType5 , class ContainerType6 >
void	dg::tensor::inv_multiply3d (const ContainerTypeL &lambda, const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, const ContainerType3 &in2, const ContainerTypeM &mu, ContainerType4 &out0, ContainerType5 &out1, ContainerType6 &out2)
	\( v_j = \sum_{i=0}^2\lambda(t^{-1})_{ji}w^i + \mu v_j \text{ for } i\in \{0,1,2\}\)i More...
template<class ContainerType >
ContainerType	dg::tensor::determinant2d (const SparseTensor< ContainerType > &t)
	\(\det_{2d}( t)\) More...
template<class ContainerType >
ContainerType	dg::tensor::determinant (const SparseTensor< ContainerType > &t)
	\(\det( t)\) More...
template<class ContainerType >
ContainerType	dg::tensor::volume2d (const SparseTensor< ContainerType > &t)
	\( \sqrt{\det_{2d}(t)}^{-1}\) More...
template<class ContainerType >
ContainerType	dg::tensor::volume (const SparseTensor< ContainerType > &t)
	\( \sqrt{\det(t)}^{-1}\) More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerType4 >
void	dg::tensor::multiply2d (const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, ContainerType3 &out0, ContainerType4 &out1)
	\( w^i = \sum_{i=0}^1 t^{ij}v_j \text{ for } i\in \{0,1\}\) More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerType4 , class ContainerType5 , class ContainerType6 >
void	dg::tensor::multiply3d (const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, const ContainerType3 &in2, ContainerType4 &out0, ContainerType5 &out1, ContainerType6 &out2)
	\( w^i = \sum_{i=0}^2 t^{ij}v_j \text{ for } i\in \{0,1,2\}\) More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerType4 >
void	dg::tensor::inv_multiply2d (const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, ContainerType3 &out0, ContainerType4 &out1)
	\( v_j = \sum_{i=0}^1(t^{-1})_{ji}w^i \text{ for } i\in \{0,1\}\) More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerType4 , class ContainerType5 , class ContainerType6 >
void	dg::tensor::inv_multiply3d (const SparseTensor< ContainerType0 > &t, const ContainerType1 &in0, const ContainerType2 &in1, const ContainerType3 &in2, ContainerType4 &out0, ContainerType5 &out1, ContainerType6 &out2)
	\( v_j = \sum_{i=0}^2(t^{-1})_{ji}w^i \text{ for } i\in \{0,1,2\}\)i More...
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerTypeM , class ContainerType4 , class ContainerType5 >
void	dg::tensor::scalar_product2d (get_value_type< ContainerType0 > alpha, const ContainerTypeL &lambda, const ContainerType0 &v0, const ContainerType1 &v1, const SparseTensor< ContainerType2 > &t, const ContainerTypeM &mu, const ContainerType3 &w0, const ContainerType4 &w1, get_value_type< ContainerType0 > beta, ContainerType5 &y)
	\( y = \alpha \lambda\mu \sum_{i=0}^1 v_it^{ij}w_j + \beta y \text{ for } i\in \{0,1\}\) More...
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerTypeM , class ContainerType4 , class ContainerType5 , class ContainerType6 , class ContainerType7 >
void	dg::tensor::scalar_product3d (get_value_type< ContainerType0 > alpha, const ContainerTypeL &lambda, const ContainerType0 &v0, const ContainerType1 &v1, const ContainerType2 &v2, const SparseTensor< ContainerType3 > &t, const ContainerTypeM &mu, const ContainerType4 &w0, const ContainerType5 &w1, const ContainerType6 &w2, get_value_type< ContainerType0 > beta, ContainerType7 &y)
	\( y = \alpha \lambda\mu \sum_{i=0}^2 v_it^{ij}w_j + \beta y \text{ for } i\in \{0,1,2\}\) More...

Detailed Description

Basic tensor functions (functions that involve sparse tensors)