Lowlevel helper functions and classes

Collaboration diagram for Lowlevel helper functions and classes:

Classes
struct	dg::ClonePtr< Cloneable >
	Manager class that invokes the clone() method on the managed ptr when copied. More...

Functions
template<class T >
SquareMatrix< T >	dg::tensorproduct (const SquareMatrix< T > &op1, const SquareMatrix< T > &op2)
	Form the tensor product between two operators.
template<class T >
dg::SparseMatrix< int, T, thrust::host_vector >	dg::tensorproduct (unsigned N, const SquareMatrix< T > &op)
	Tensor product between Identity matrix and an operator.
template<class T >
dg::SparseMatrix< int, T, thrust::host_vector >	dg::sandwich (const SquareMatrix< T > &left, const dg::SparseMatrix< int, T, thrust::host_vector > &m, const SquareMatrix< T > &right)
	Multiply 1d matrices by diagonal block matrices from left and right.
template<class T >
dg::SparseMatrix< int, T, thrust::host_vector >	dg::tensorproduct (const dg::SparseMatrix< int, T, thrust::host_vector > &lhs, const dg::SparseMatrix< int, T, thrust::host_vector > &rhs)
	\( L\otimes R\) Form the tensor (Kronecker) product between two matrices
template<class T >
dg::SparseMatrix< int, T, thrust::host_vector >	dg::tensorproduct_cols (const dg::SparseMatrix< int, T, thrust::host_vector > &lhs, const dg::SparseMatrix< int, T, thrust::host_vector > &rhs)
	\( L\otimes R\) Form the tensor (Kronecker) product between two matrices in the column index

Detailed Description

Function Documentation

sandwich()

template<class T >

dg::SparseMatrix< int, T, thrust::host_vector > dg::sandwich	(	const SquareMatrix< T > &	left,
		const dg::SparseMatrix< int, T, thrust::host_vector > &	m,
		const SquareMatrix< T > &	right )

Multiply 1d matrices by diagonal block matrices from left and right.

computes (1xleft)m(1xright)

Template Parameters

T	value type

Parameters

left	The left hand side
m	The matrix
right	The right hand side

Returns

A newly allocated sparse matrix

tensorproduct() [1/3]

template<class T >

dg::SparseMatrix< int, T, thrust::host_vector > dg::tensorproduct	(	const dg::SparseMatrix< int, T, thrust::host_vector > &	lhs,
		const dg::SparseMatrix< int, T, thrust::host_vector > &	rhs )

\( L\otimes R\) Form the tensor (Kronecker) product between two matrices

The Kronecker product is formed by the triplets \(I = k n_r+l\), \( J = i N_r +j \), \( M_{IJ} = L_{ki}R_{lj}\)

Note

This function is "order preserving" in the sense that the order of row and column entries of lhs and rhs are preserved in the output. This is important for stencil computations.

Template Parameters

T	value type

Parameters

lhs	The left hand side matrix (duplicate entries lead to duplicate entries in result)
rhs	The right hand side matrix (duplicate entries lead to duplicate entries in result)

Returns

newly allocated matrix containing the tensor product

tensorproduct() [2/3]

template<class T >

SquareMatrix< T > dg::tensorproduct	(	const SquareMatrix< T > &	op1,
		const SquareMatrix< T > &	op2 )

Form the tensor product between two operators.

Computes C_{ijkl} = op1_{ij}op2_{kl}

Template Parameters

T	The value type

Parameters

op1	The left hand side
op2	The right hand side

Returns

The tensor product

tensorproduct() [3/3]

template<class T >

dg::SparseMatrix< int, T, thrust::host_vector > dg::tensorproduct	(	unsigned	N,
		const SquareMatrix< T > &	op )

Tensor product between Identity matrix and an operator.

\[ M = \begin{pmatrix} op & & & & & \\ & op & & & & \\ & & op & & & \\ & & & op & & \\ & & &...& & \end{pmatrix} \]

Can be used to create tensors that operate on each dg-vector entry

Template Parameters

T	value type

Parameters

N	Size of the identity (=number of times op is repeated in the matrix)
op	The SquareMatrix

Returns

A newly allocated sparse matrix (of size N*op.size() )

See also

fast_transform

tensorproduct_cols()

template<class T >

dg::SparseMatrix< int, T, thrust::host_vector > dg::tensorproduct_cols	(	const dg::SparseMatrix< int, T, thrust::host_vector > &	lhs,
		const dg::SparseMatrix< int, T, thrust::host_vector > &	rhs )

\( L\otimes R\) Form the tensor (Kronecker) product between two matrices in the column index

The Kronecker product in the columns is formed by the triplets \( J = i N_r +j \), \( M_{kJ} = L_{ki}R_{kj}\)

Note

This function is "order preserving" in the sense that the order of row and column entries of lhs and rhs are preserved in the output. This is important for stencil computations.

Template Parameters

T	value type

Parameters

lhs	The left hand side matrix (duplicate entries lead to duplicate entries in result)
rhs	The right hand side matrix (duplicate entries lead to duplicate entries in result)

Returns

newly allocated sparse matrix containing the tensor product