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...
struct	dg::Buffer< T >
	a manager class that invokes the copy constructor on the managed ptr when copied (deep copy) More...

Functions
template<class Matrix >
Matrix	dg::transpose (const Matrix &src)
	Generic matrix transpose method. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::dx_symm (int n, int N, real_type h, bc bcx)
	Create and assemble a host Matrix for the centered 1d single derivative. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::dx_plus (int n, int N, real_type h, bc bcx)
	Create and assemble a host Matrix for the forward 1d single derivative. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::dx_minus (int n, int N, real_type h, bc bcx)
	Create and assemble a host Matrix for the backward 1d single derivative. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::jump (int n, int N, real_type h, bc bcx)
	Create and assemble a host Matrix for the jump terms in 1d. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::dx_normed (int n, int N, real_type h, bc bcx, direction dir)
	Create and assemble a host Matrix for normed derivative in 1d. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::dx (const RealGridX1d< real_type > &g, bc bcx, direction dir=centered)
	Create and assemble a host Matrix for the derivative in 1d. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::dx (const RealGridX1d< real_type > &g, direction dir=centered)
	Create and assemble a host Matrix for the derivative in 1d. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::jump (const RealGridX1d< real_type > &g, bc bcx)
	Create and assemble a host Matrix for the jump in 1d. More...
template<class real_type >
EllSparseBlockMat< real_type >	dg::create::jump (const RealGridX1d< real_type > &g)
	Create and assemble a host Matrix for the jump in 1d. More...
template<class real_type >
Operator< real_type >	dg::create::delta (unsigned n)
	Create the unit matrix. More...
template<class real_type >
Operator< real_type >	dg::create::pipj (unsigned n)
	Create the S-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::pipj_inv (unsigned n)
	Create the T-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::pidxpj (unsigned n)
	Create the D-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::rirj (unsigned n)
	Create the R-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::rilj (unsigned n)
	Create the RL-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::lirj (unsigned n)
	Create the LR-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::lilj (unsigned n)
	Create the L-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::ninj (unsigned n)
	Create the N-matrix. More...
template<class real_type >
Operator< real_type >	dg::create::weights (const DLT< real_type > &dlt)
	Construct a diagonal operator with weights. More...
template<class real_type >
Operator< real_type >	dg::create::inv_weights (const DLT< real_type > &dlt)
	Construct a diagonal operator with inverse weights. More...
template<class T >
Operator< T >	dg::tensorproduct (const Operator< T > &op1, const Operator< T > &op2)
	Form the tensor product between two operators. More...
template<class T >
cusp::coo_matrix< int, T, cusp::host_memory >	dg::tensorproduct (unsigned N, const Operator< T > &op)
	Tensor product between Identity matrix and an operator. More...
template<class T >
cusp::coo_matrix< int, T, cusp::host_memory >	dg::sandwich (const Operator< T > &left, const cusp::coo_matrix< int, T, cusp::host_memory > &m, const Operator< T > &right)
	Multiply 1d matrices by diagonal block matrices from left and right. More...
template<class T >
cusp::csr_matrix< int, T, cusp::host_memory >	dg::tensorproduct (const cusp::csr_matrix< int, T, cusp::host_memory > &lhs, const cusp::csr_matrix< int, T, cusp::host_memory > &rhs)
	\( L\otimes R\) Form the tensor (Kronecker) product between two matrices More...

Detailed Description

Function Documentation

delta()

template<class real_type >

Operator< real_type > dg::create::delta

(

unsigned

n

)

Create the unit matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

dx() [1/2]

template<class real_type >

EllSparseBlockMat< real_type > dg::create::dx	(	const RealGridX1d< real_type > &	g,
		bc	bcx,
		direction	dir = centered
	)

Create and assemble a host Matrix for the derivative in 1d.

Parameters

g	1D grid with X-point topology
bcx	boundary condition
dir	The direction of the first derivative

Returns

Host Matrix

dx() [2/2]

template<class real_type >

EllSparseBlockMat< real_type > dg::create::dx	(	const RealGridX1d< real_type > &	g,
		direction	dir = centered
	)

Create and assemble a host Matrix for the derivative in 1d.

Take the boundary condition from the grid

Parameters

g	1D grid with X-point topology
dir	The direction of the first derivative

Returns

Host Matrix

dx_minus()

template<class real_type >

EllSparseBlockMat< real_type > dg::create::dx_minus	(	int	n,
		int	N,
		real_type	h,
		bc	bcx
	)

Create and assemble a host Matrix for the backward 1d single derivative.

Parameters

n	Number of Legendre nodes per cell
N	Vector size ( number of cells)
h	cell size ( used to compute normalisation)
bcx	boundary condition

Returns

Host Matrix

dx_normed()

template<class real_type >

EllSparseBlockMat< real_type > dg::create::dx_normed	(	int	n,
		int	N,
		real_type	h,
		bc	bcx,
		direction	dir
	)

Create and assemble a host Matrix for normed derivative in 1d.

Parameters

n	Number of Legendre nodes per cell
N	Vector size ( number of cells)
h	cell size ( used to compute normalisation)
bcx	boundary condition
dir	The direction of the first derivative

Returns

Host Matrix

dx_plus()

template<class real_type >

EllSparseBlockMat< real_type > dg::create::dx_plus	(	int	n,
		int	N,
		real_type	h,
		bc	bcx
	)

Create and assemble a host Matrix for the forward 1d single derivative.

Parameters

n	Number of Legendre nodes per cell
N	Vector size ( number of cells)
h	cell size ( used to compute normalisation)
bcx	boundary condition

Returns

Host Matrix

dx_symm()

template<class real_type >

EllSparseBlockMat< real_type > dg::create::dx_symm	(	int	n,
		int	N,
		real_type	h,
		bc	bcx
	)

Create and assemble a host Matrix for the centered 1d single derivative.

The matrix isn't symmetric due to the normalisation T.

Parameters

n	Number of Legendre nodes per cell
N	Vector size ( number of cells)
h	cell size (used to compute normalisation)
bcx	boundary condition

Returns

Host Matrix

inv_weights()

template<class real_type >

Operator< real_type > dg::create::inv_weights

(

const DLT< real_type > &

dlt

)

Construct a diagonal operator with inverse weights.

Parameters

dlt

Returns

new operator

jump() [1/3]

template<class real_type >

EllSparseBlockMat< real_type > dg::create::jump

(

const RealGridX1d< real_type > &

g

)

Create and assemble a host Matrix for the jump in 1d.

Take the boundary condition from the grid

Parameters

g	1D grid with X-point topology

Returns

Host Matrix

jump() [2/3]

template<class real_type >

EllSparseBlockMat< real_type > dg::create::jump	(	const RealGridX1d< real_type > &	g,
		bc	bcx
	)

Create and assemble a host Matrix for the jump in 1d.

Parameters

g	1D grid with X-point topology
bcx	boundary condition

Returns

Host Matrix

jump() [3/3]

template<class real_type >

EllSparseBlockMat< real_type > dg::create::jump	(	int	n,
		int	N,
		real_type	h,
		bc	bcx
	)

Create and assemble a host Matrix for the jump terms in 1d.

Parameters

n	Number of Legendre nodes per cell
N	Vector size ( number of cells)
h	cell size ( used to compute normalisation)
bcx	boundary condition

Returns

Host Matrix

lilj()

template<class real_type >

Operator< real_type > dg::create::lilj

(

unsigned

n

)

Create the L-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

lirj()

template<class real_type >

Operator< real_type > dg::create::lirj

(

unsigned

n

)

Create the LR-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

ninj()

template<class real_type >

Operator< real_type > dg::create::ninj

(

unsigned

n

)

Create the N-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

pidxpj()

template<class real_type >

Operator< real_type > dg::create::pidxpj

(

unsigned

n

)

Create the D-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

pipj()

template<class real_type >

Operator< real_type > dg::create::pipj

(

unsigned

n

)

Create the S-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

pipj_inv()

template<class real_type >

Operator< real_type > dg::create::pipj_inv

(

unsigned

n

)

Create the T-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

rilj()

template<class real_type >

Operator< real_type > dg::create::rilj

(

unsigned

n

)

Create the RL-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

rirj()

template<class real_type >

Operator< real_type > dg::create::rirj

(

unsigned

n

)

Create the R-matrix.

Parameters

n	# of polynomial coefficients

Returns

Operator

sandwich()

template<class T >

cusp::coo_matrix< int, T, cusp::host_memory > dg::sandwich	(	const Operator< T > &	left,
		const cusp::coo_matrix< int, T, cusp::host_memory > &	m,
		const Operator< 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 cusp matrix

tensorproduct() [1/3]

template<class T >

cusp::csr_matrix< int, T, cusp::host_memory > dg::tensorproduct	(	const cusp::csr_matrix< int, T, cusp::host_memory > &	lhs,
		const cusp::csr_matrix< int, T, cusp::host_memory > &	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 cusp matrix containing the tensor product

Note

use cusp::add and cusp::multiply to add and multiply matrices.

tensorproduct() [2/3]

template<class T >

Operator< T > dg::tensorproduct	(	const Operator< T > &	op1,
		const Operator< 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 >

cusp::coo_matrix< int, T, cusp::host_memory > dg::tensorproduct	(	unsigned	N,
		const Operator< 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 Operator

Returns

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

See also

fast_transform

transpose()

template<class Matrix >

Matrix dg::transpose

(

const Matrix &

src

)

Generic matrix transpose method.

Template Parameters

Matrix

one of any cusp matrix any MPIDistMatrix with a cusp matrix as template parameter

Parameters

src	the marix to transpose

Returns

the matrix that acts as the transpose of src

weights()

template<class real_type >

Operator< real_type > dg::create::weights

(

const DLT< real_type > &

dlt

)

Construct a diagonal operator with weights.

Parameters

dlt

Returns

new operator