Functionality related to computing quadrature nodes and weights. More...

Classes
class	ClenshawCurtis
	Quadrature handler for Clenshaw-Curtis quadrature. More...

class	GaussLegendre
	Quadrature handler for Gauss-Legendre quadrature. More...

class	GaussLobatto
	Quadrature handler for Gauss-Lobatto quadrature. More...

class	GaussRadau
	Quadrature handler for Gauss-Radau quadrature. More...

class	IQuadrature
	Interface for quadrature handlers. More...

class	Polynomial
	Representation of a polynomial including differentiation, integration and root finding. More...

class	Uniform
	Quadrature handler for uniform distributed nodes. More...

Enumerations
enum	QuadratureType : int { QuadratureType::GaussLegendre = 0, QuadratureType::GaussLobatto = 1, QuadratureType::GaussRadau = 2, QuadratureType::ClenshawCurtis = 3, QuadratureType::Uniform = 4, QuadratureType::UNDEFINED = -1 }
	Quadrature type descriptors. More...

Functions
template<typename scalar >
static Polynomial< scalar >	build_polynomial (const size_t node, const vector< scalar > &nodes)

template<typename scalar >
static Matrix< scalar >	compute_q_matrix (const vector< scalar > &from, const vector< scalar > &to)
	Compute quadrature matrix \( Q \) between two sets of nodes. More...

template<typename scalar >
static Matrix< scalar >	compute_q_matrix (const vector< scalar > &nodes)
	Compute quadrature matrix \( Q \) for one set of nodes. More...

template<typename scalar >
static Matrix< scalar >	compute_q_matrix (const Matrix< scalar > &s_mat)
	Compute quadrature matrix \( Q \) from a given node-to-node quadrature matrix \( S \). More...

template<typename scalar >
static Matrix< scalar >	compute_s_matrix (const Matrix< scalar > &q_mat)
	Compute node-to-node quadrature matrix \( S \) from a given quadrature matrix \( Q \). More...

template<typename scalar >
static Matrix< scalar >	compute_s_matrix (const vector< scalar > &from, const vector< scalar > &to)
	Compute node-to-node quadrature matrix \( S \) from two given sets of nodes. More...

template<typename scalar >
static vector< scalar >	compute_q_vec (const vector< scalar > &nodes)
	Compute vector \( q \) for integration from \( 0 \) to \( 1 \) for given set of nodes. More...

template<typename precision = pfasst::time_precision>
shared_ptr< IQuadrature< precision > >	quadrature_factory (const size_t nnodes, const QuadratureType qtype)
	Instantiates quadrature handler for given number of nodes and type descriptor. More...

template<typename precision = pfasst::time_precision>
vector< precision >	compute_nodes (size_t nnodes, QuadratureType qtype)
	Compute quadrature nodes for given quadrature type descriptor. More...

template<typename precision = time_precision>
Matrix< precision >	compute_interp (vector< precision > dst, vector< precision > src)

Detailed Description

Functionality related to computing quadrature nodes and weights.

Note: Please note, that all quadrature nodes are in the range \( [0, 1] \).

Enumeration Type Documentation

enum pfasst::quadrature::QuadratureType : int

strong

Quadrature type descriptors.

Since: v0.3.0

Enumerator
GaussLegendre	Gauss-Legendre quadrature
GaussLobatto	Gauss-Lobatto quadrature
GaussRadau	Gauss-Radau quadrature
ClenshawCurtis	Clenshaw-Curtis quadrature
Uniform	Uniform quadrature.
UNDEFINED

Definition at line 32 of file interface.hpp.

Function Documentation

template<typename scalar >

static Polynomial<scalar> pfasst::quadrature::build_polynomial	(	const size_t	node,
		const vector< scalar > &	nodes
	)

static

Definition at line 43 of file interface.hpp.

Referenced by compute_q_matrix(), and compute_q_vec().

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template<typename precision = time_precision>

Matrix<precision> pfasst::quadrature::compute_interp	(	vector< precision >	dst,
		vector< precision >	src
	)

Todo:: write documentation

Template Parameters

precision numerical type of the interpolation (e.g. double)

Definition at line 95 of file quadrature.hpp.

template<typename precision = pfasst::time_precision>

vector<precision> pfasst::quadrature::compute_nodes	(	size_t	nnodes,
		QuadratureType	qtype
	)

Compute quadrature nodes for given quadrature type descriptor.

Template Parameters

precision numerical type of the nodes (e.g. double)

Parameters

[in]	nnodes	number of quadrature nodes to compute
[in]	qtype	type descriptor of the quadrature nodes

Returns: std::vector of quadrature nodes of given type

See also: pfasst::quadrature::QuadratureType for valid types; pfasst::quadrature::quadrature_factory for further details

Definition at line 84 of file quadrature.hpp.

template<typename scalar >

static Matrix<scalar> pfasst::quadrature::compute_q_matrix	(	const vector< scalar > &	from,
		const vector< scalar > &	to
	)

static

Compute quadrature matrix \( Q \) between two sets of nodes.

Computing the quadrature matrix \( Q \) for polynomial-based integration from one set of quadrature nodes (from) to another set of quadrature nodes (to).

Template Parameters

scalar precision of quadrature (i.e. double)

Parameters

[in]	from	first set of quadrature nodes
[in]	to	second set of quadrature nodes

Returns: quadrature matrix \( Q \) with to.size() rows and from.size() colums

Precondition: For correctness of the algorithm it is assumed, that both sets of nodes are in the range \( [0, 1] \).

Since: v0.3.0

Definition at line 80 of file interface.hpp.

References build_polynomial(), pfasst::quadrature::Polynomial< CoeffT >::evaluate(), and pfasst::quadrature::Polynomial< CoeffT >::integrate().

Referenced by pfasst::quadrature::IQuadrature< precision >::compute_weights().

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template<typename scalar >

static Matrix<scalar> pfasst::quadrature::compute_q_matrix ( const vector< scalar > & nodes )

static

Compute quadrature matrix \( Q \) for one set of nodes.

Template Parameters

scalar precision of quadrature (i.e. double)

Parameters

[in] nodes quadrature nodes to compute \( Q \) matrix for

Since: v0.3.0

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 113 of file interface.hpp.

template<typename scalar >

static Matrix<scalar> pfasst::quadrature::compute_q_matrix ( const Matrix< scalar > & s_mat )

static

Compute quadrature matrix \( Q \) from a given node-to-node quadrature matrix \( S \).

Template Parameters

scalar precision of quadrature (i.e. double)

Parameters

[in] s_mat \( S \) matrix to compute \( Q \) from

See also: pfasst::quadrature::compute_s_matrix

Since: v0.3.0

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 131 of file interface.hpp.

Referenced by compute_s_matrix().

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template<typename scalar >

static vector<scalar> pfasst::quadrature::compute_q_vec ( const vector< scalar > & nodes )

static

Compute vector \( q \) for integration from \( 0 \) to \( 1 \) for given set of nodes.

This equals to the last row of the quadrature matrix \( Q \) for the given set of nodes.

Template Parameters

scalar precision of quadrature (i.e. double)

Parameters

[in] nodes quadrature nodes to compute \( Q \) matrix for

Precondition: For correctness of the algorithm it is assumed, that the nodes are in the range \( [0, 1] \).

Since: v0.3.0

Definition at line 200 of file interface.hpp.

References build_polynomial(), pfasst::quadrature::Polynomial< CoeffT >::evaluate(), and pfasst::quadrature::Polynomial< CoeffT >::integrate().

Referenced by pfasst::quadrature::IQuadrature< precision >::compute_weights().

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template<typename scalar >

static Matrix<scalar> pfasst::quadrature::compute_s_matrix ( const Matrix< scalar > & q_mat )

static

Compute node-to-node quadrature matrix \( S \) from a given quadrature matrix \( Q \).

The \( S \) matrix provides a node-to-node quadrature where the \( i \)-th row of \( S \) represents a quadrature from the \( i-1 \)-th node to the \( i \)-th node.

The procedure is simply subtracting the \( i-1 \)-th row of \( Q \) from the \( i \)-th row of \( Q \).

Template Parameters

scalar precision of quadrature (i.e. double)

Parameters

[in] q_mat \( Q \) matrix to compute \( S \) of

Returns: \( S \) matrix

Since: v0.3.0

Definition at line 158 of file interface.hpp.

Referenced by pfasst::quadrature::IQuadrature< precision >::compute_weights().

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template<typename scalar >

static Matrix<scalar> pfasst::quadrature::compute_s_matrix	(	const vector< scalar > &	from,
		const vector< scalar > &	to
	)

static

Compute node-to-node quadrature matrix \( S \) from two given sets of nodes.

Template Parameters

scalar precision of quadrature (i.e. double)

Parameters

[in]	from	first set of quadrature nodes
[in]	to	second set of quadrature nodes

Since: v0.3.0

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 181 of file interface.hpp.

References compute_q_matrix().

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template<typename precision = pfasst::time_precision>

shared_ptr<IQuadrature<precision> > pfasst::quadrature::quadrature_factory	(	const size_t	nnodes,
		const QuadratureType	qtype
	)

Instantiates quadrature handler for given number of nodes and type descriptor.

Template Parameters

precision numerical type of the nodes (e.g. double)

Parameters

[in]	nnodes	number of quadrature nodes
[in]	qtype	type descriptor of the quadrature

Returns: instance of pfasst::quadrature::IQuadrature of specified type with desired number of nodes

Exceptions

pfasst::ValueError if qtype is not a valid quadrature type descriptor

Definition at line 53 of file quadrature.hpp.

Referenced by pfasst::examples::advection_diffusion::run_mpi_pfasst(), pfasst::examples::scalar::run_scalar_sdc(), pfasst::examples::advection_diffusion::run_serial_mlsdc(), pfasst::examples::advection_diffusion::run_vanilla_sdc(), and pfasst::examples::vdp::run_vdp_sdc().

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Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

Function Documentation