Tensor-Vector operations

\( v^i = T^{ij} w_j\) More...

Collaboration diagram for Tensor-Vector operations:

Namespaces
namespace	dg::tensor
	Utility functions used in connection with the SparseTensor class.

Classes
struct	dg::SparseTensor< container >
	Class for 2x2 and 3x3 matrices sharing elements. More...

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

\( v^i = T^{ij} w_j\)

Function Documentation

determinant()

template<class ContainerType >

ContainerType dg::tensor::determinant

(

const SparseTensor< ContainerType > &

t

)

\(\det( t)\)

Compute the determinant of a 3d tensor: \( \det(t) := t_{00}t_{11}t_{22} + t_{01}t_{12}t_{20} + \ldots - t_{22}t_{10}t_{01}\).

Parameters

t	the input tensor

Returns

the determinant of t

Note

This function is just a shortcut for a call to dg::blas1::evaluate

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

determinant2d()

template<class ContainerType >

ContainerType dg::tensor::determinant2d

(

const SparseTensor< ContainerType > &

t

)

\(\det_{2d}( t)\)

Compute the minor determinant of a tensor \( \det_{2d}(t) := t_{00}t_{01}-t_{10}t_{11}\).

Parameters

t	the input tensor

Returns

the upper left minor determinant of t

Note

This function is just a shortcut for a call to dg::blas1::evaluate

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

inv_multiply2d() [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 )

\( v_j = \sum_{i=0}^1\lambda (t^{-1})_{ji}w^i + \mu v_j \text{ for } i\in \{0,1\}\)

Multiply the inverse of a tensor t with a vector in 2d. Ignore the 3rd dimension in t. The inverse of t is computed inplace.

Parameters

t	input Tensor
lambda	(input) (may be a vector or an actual number like 0 or 1)
in0	(input) first component of w (may alias out0)
in1	(input) second component of w (may alias out1)
mu	(input) (may be a vector or an actual number like 0 or 1)
out0	(output) first component of v (may alias in0)
out1	(output) second component of v (may alias in1)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

inv_multiply2d() [2/2]

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 )

\( v_j = \sum_{i=0}^1(t^{-1})_{ji}w^i \text{ for } i\in \{0,1\}\)

Multiply the inverse of a tensor t with a vector in 2d. Ignore the 3rd dimension in t. The inverse of t is computed inplace.

Parameters

t	input Tensor
in0	(input) first component of w (may alias out0)
in1	(input) second component of w (may alias out1)
out0	(output) first component of v (may alias in0)
out1	(output) second component of v (may alias in1)

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

inv_multiply3d() [1/2]

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

Multiply the inverse of a tensor with a vector in 3d. The inverse of t is computed inplace.

Parameters

t	input Tensor
lambda	(input) (may be a vector or an actual number like 0 or 1)
in0	(input) first component of w (may alias out0)
in1	(input) second component of w (may alias out1)
in2	(input) third component of w (may alias out2)
mu	(input) (may be a vector or an actual number like 0 or 1)
out0	(output) first component of v (may alias in0)
out1	(output) second component of v (may alias in1)
out2	(output) third component of v (may alias in2)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

inv_multiply3d() [2/2]

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

Multiply the inverse of a tensor with a vector in 3d. The inverse of t is computed inplace.

Parameters

t	input Tensor
in0	(input) first component of w (may alias out0)
in1	(input) second component of w (may alias out1)
in2	(input) third component of w (may alias out2)
out0	(output) first component of v (may alias in0)
out1	(output) second component of v (may alias in1)
out2	(output) third component of v (may alias in2)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

multiply2d() [1/2]

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 )

\( w^i = \sum_{i=0}^1 \lambda t^{ij}v_j + \mu w^i \text{ for } i\in \{0,1\}\)

Multiply a tensor with a vector in 2d. Ignore the 3rd dimension in t.

Parameters

t	input Tensor
lambda	(input)
in0	(input) first component of v (may alias out0)
in1	(input) second component of v (may alias out1)
mu	(input)
out0	(output) first component of w (may alias in0)
out1	(output) second component of w (may alias in1)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

multiply2d() [2/2]

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 )

\( w^i = \sum_{i=0}^1 t^{ij}v_j \text{ for } i\in \{0,1\}\)

Multiply a tensor with a vector in 2d. Ignore the 3rd dimension in t.

Parameters

t	input Tensor
in0	(input) first component of v (may alias out0)
in1	(input) second component of v (may alias out1)
out0	(output) first component of w (may alias in0)
out1	(output) second component of w (may alias in1)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

multiply3d() [1/2]

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 )

\( w^i = \sum_{i=0}^2\lambda t^{ij}v_j + \mu w^i \text{ for } i\in \{0,1,2\}\)

Multiply a tensor with a vector in 3d.

Parameters

t	input Tensor
lambda	(input) (may be a vector or an actual number like 0 or 1)
in0	(input) first component of v (may alias out0)
in1	(input) second component of v (may alias out1)
in2	(input) third component of v (may alias out2)
mu	(input) (may be a vector or an actual number like 0 or 1)
out0	(output) first component of w (may alias in0)
out1	(output) second component of w (may alias in1)
out2	(output) third component of w (may alias in2)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

multiply3d() [2/2]

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 )

\( w^i = \sum_{i=0}^2 t^{ij}v_j \text{ for } i\in \{0,1,2\}\)

Multiply a tensor with a vector in 3d.

Parameters

t	input Tensor
in0	(input) first component of v (may alias out0)
in1	(input) second component of v (may alias out1)
in2	(input) third component of v (may alias out2)
out0	(output) first component of w (may alias in0)
out1	(output) second component of w (may alias in1)
out2	(output) third component of w (may alias in2)

Note

This function is just a shortcut for a call to dg::blas1::subroutine

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

scal()

template<class ContainerType0 , class ContainerType1 >

void dg::tensor::scal	(	SparseTensor< ContainerType0 > &	t,
		const ContainerType1 &	mu )

\( t^{ij} = \mu t^{ij} \ \forall i,j \)

Scale tensor with a Scalar or a Vector

Parameters

t	input (contains result on output)
mu	all elements in t are scaled with mu

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

scalar_product2d()

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 )

\( y = \alpha \lambda\mu \sum_{i=0}^1 v_it^{ij}w_j + \beta y \text{ for } i\in \{0,1\}\)

Ignore the 3rd dimension in t.

Parameters

alpha	scalar input prefactor
lambda	second input prefactor
v0	(input) first component of v (may alias w0)
v1	(input) second component of v (may alias w1)
t	input Tensor
mu	third input prefactor
w0	(input) first component of w (may alias v0)
w1	(input) second component of w (may alias v1)
beta	scalar output prefactor
y	(output)

Note

This function is just a shortcut for a call to dg::blas1::evaluate

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

scalar_product3d()

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 )

\( y = \alpha \lambda\mu \sum_{i=0}^2 v_it^{ij}w_j + \beta y \text{ for } i\in \{0,1,2\}\)

Parameters

alpha	scalar input prefactor
lambda	second input prefactor
v0	(input) first component of v (may alias w0)
v1	(input) second component of v (may alias w1)
v2	(input) third component of v (may alias w1)
t	input Tensor
mu	third input prefactor
w0	(input) first component of w (may alias v0)
w1	(input) second component of w (may alias v1)
w2	(input) third component of w (may alias v1)
beta	scalar output prefactor
y	(output)

Note

This function is just a shortcut for a call to dg::blas1::evaluate

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

volume()

template<class ContainerType >

ContainerType dg::tensor::volume

(

const SparseTensor< ContainerType > &

t

)

\( \sqrt{\det(t)}^{-1}\)

Compute the sqrt of the inverse determinant of a 3d tensor. This is a convenience function that is equivalent to

ContainerType vol=determinant(t);
dg::blas1::transform(vol, vol, dg::InvSqrt<>());

Note

The function is called volume because when you apply it to the inverse metric tensor of our grids then you obtain the volume

\[ \sqrt{g} = 1 / \sqrt{ \det( g^{-1})}\]

ContainerType vol = dg::tensor::volume( g.metric());

Parameters

t	the input tensor

Returns

the inverse square root of the determinant of t

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system

volume2d()

template<class ContainerType >

ContainerType dg::tensor::volume2d

(

const SparseTensor< ContainerType > &

t

)

\( \sqrt{\det_{2d}(t)}^{-1}\)

Compute the sqrt of the inverse minor determinant of a tensor. This is a convenience function that is equivalent to

ContainerType vol=determinant2d(t);
dg::blas1::transform(vol, vol, dg::InvSqrt<>());

Note

The function is called volume because when you apply it to the inverse metric tensor of our grids then you obtain the volume

\[ \sqrt{g} = 1 / \sqrt{ \det( g^{-1})}\]

ContainerType vol = volume2d( g.metric());

Parameters

t	the input tensor

Returns

the inverse square root of the determinant of t

Template Parameters

ContainerType

Any class for which a specialization of TensorTraits exists and which fulfills the requirements of the there defined data and execution policies derived from AnyVectorTag and AnyPolicyTag. Among others dg::HVec (serial), dg::DVec (cuda / omp), dg::MHVec (mpi + serial) or dg::MDVec (mpi + cuda / omp) std::vector<dg::DVec> (vector of shared device vectors), std::array<double, 4> (array of 4 doubles) or std::map < std::string, dg::DVec> ( a map of named vectors) double (scalar) and other primitive types ... If there are several ContainerTypes in the argument list, then TensorTraits must exist for all of them

See also

See The dg dispatch system for a detailed explanation of our type dispatch system