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.

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)
	\( t^{ij} = \mu t^{ij} \ \forall i,j \)
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)
	\( w^i = \sum_{i=0}^1 \lambda t^{ij}v_j + \mu w^i \text{ for } i\in \{0,1\}\)
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)
	\( w^i = \sum_{i=0}^2\lambda t^{ij}v_j + \mu w^i \text{ for } i\in \{0,1,2\}\)
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)
	\( v_j = \sum_{i=0}^1\lambda (t^{-1})_{ji}w^i + \mu v_j \text{ for } i\in \{0,1\}\)
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
template<class ContainerType >
ContainerType	dg::tensor::determinant2d (const SparseTensor< ContainerType > &t)
	\(\det_{2d}( t)\)
template<class ContainerType >
ContainerType	dg::tensor::determinant (const SparseTensor< ContainerType > &t)
	\(\det( t)\)
template<class ContainerType >
ContainerType	dg::tensor::volume2d (const SparseTensor< ContainerType > &t)
	\( \sqrt{\det_{2d}(t)}^{-1}\)
template<class ContainerType >
ContainerType	dg::tensor::volume (const SparseTensor< ContainerType > &t)
	\( \sqrt{\det(t)}^{-1}\)
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)
	\( w^i = \sum_{i=0}^1 t^{ij}v_j \text{ for } i\in \{0,1\}\)
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)
	\( w^i = \sum_{i=0}^2 t^{ij}v_j \text{ for } i\in \{0,1,2\}\)
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)
	\( v_j = \sum_{i=0}^1(t^{-1})_{ji}w^i \text{ for } i\in \{0,1\}\)
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
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerTypeM , class ContainerType4 , class ContainerType5 , class value_type0 , class value_type1 >
void	dg::tensor::scalar_product2d (value_type0 alpha, const ContainerTypeL &lambda, const ContainerType0 &v0, const ContainerType1 &v1, const SparseTensor< ContainerType2 > &t, const ContainerTypeM &mu, const ContainerType3 &w0, const ContainerType4 &w1, value_type1 beta, ContainerType5 &y)
	\( y = \alpha \lambda\mu \sum_{i=0}^1 v_it^{ij}w_j + \beta y \text{ for } i\in \{0,1\}\)
template<class ContainerTypeL , class ContainerType0 , class ContainerType1 , class ContainerType2 , class ContainerType3 , class ContainerTypeM , class ContainerType4 , class ContainerType5 , class ContainerType6 , class ContainerType7 , class value_type0 , class value_type1 >
void	dg::tensor::scalar_product3d (value_type0 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, value_type1 beta, ContainerType7 &y)
	\( y = \alpha \lambda\mu \sum_{i=0}^2 v_it^{ij}w_j + \beta y \text{ for } i\in \{0,1,2\}\)

Detailed Description

Basic tensor functions (functions that involve sparse tensors)