Quad Class Reference

Generates quadrature rules. More...

#include <quad.h>

Classes
struct	QuadRule
	Rule structure that stores quadrature points, weights and indices. More...

Public Member Functions
	Quad (char *grid_type, char *fs_type, int ndim, int param, double alpha=0.0, double betta=1.0)
	Constructor: initializes the rule type, sparseness type, dimensionality, level or ppd parameter, and two optional parameters for quadrature rule. More...
	Quad (Array1D< string > &grid_types, char *fs_type, Array1D< int > &param, Array1D< double > &alphas, Array1D< double > &bettas)
	Constructor, overloaded for dimension-unisotropy: initializes the dimension-specific rule types, sparseness type, dimension-specific ppd or level, and two optional parameters for quadrature rule per each dimension. More...
	Quad ()
	Constructor: empty. More...
	~Quad ()
	Destructor. More...
void	init ()
	Initialization function. More...
void	SetAlpha (double alpha)
	Set the parameter alpha. More...
void	SetBeta (double betta)
	Set the parameter beta. More...
void	SetDomain (Array1D< double > &aa, Array1D< double > &bb)
	Set the domain endpoints (for compact support domains) More...
void	SetDomain (Array1D< double > &aa)
	Set the domain endpoint (for semi-infinite domains) More...
void	GetDomain (Array1D< double > &aa, Array1D< double > &bb) const
	Get the domain endpoints (for compact support domains) More...
void	GetDomain (Array1D< double > &aa) const
	Get the domain endpoint (for semi-infinite domains) More...
void	SetRule (Array2D< double > &q, Array1D< double > &w)
	Set the rule externally (only quadrature points and weights) More...
void	SetRule (Array2D< double > &q, Array1D< double > &w, Array2D< int > &ind)
	Set the rule externally (quadrature points, weights and indices) Dummy function for backward compatibility. More...
void	SetRule ()
	Set the rule externally (quadrature points, weights, indices, and the level) More...
void	GetRule (Array2D< double > &q, Array1D< double > &w)
	Get the quadrature rule. More...
void	GetRule (Array2D< double > &q, Array1D< double > &w, Array2D< int > &ind)
	Get the quadrature rule with indexing Dummy function for backward compatibility. More...
void	SetQdpts (Array2D< double > &q)
	Externally set quadrature points. More...
void	SetWghts (Array1D< double > &w)
	Externally set the weights. More...
void	GetQdpts (Array2D< double > &q)
	Externally set the indices. More...
void	GetWghts (Array1D< double > &w)
	Get the weights. More...
void	SetLevel (int param)
	Get the indices. More...
void	nextLevel ()
	Compute the indices of the next-level points. More...
int	GetNQ ()
	Get the number of quadrature points. More...
void	SetVerbosity (int verbosity)
	Set the verbosity level. More...

Private Member Functions
	Quad (const Quad &)
	Dummy copy constructor, which should not be used as it is currently not well defined. More...
void	MultiplyTwoRules (QuadRule *rule1, QuadRule *rule2, QuadRule *rule_prod)
	Multiply two rules (full tensor product) More...
void	MultiplyManyRules (int nrules, QuadRule *rules, QuadRule *rule_prod)
	Multiply many rules (full tensor product) More...
void	MultiplyManyRules_ (int nrules, QuadRule *rules, QuadRule *rule_prod)
void	AddTwoRules (QuadRule *rule1, QuadRule *rule2, QuadRule *rule_sum)
	Add two rules. More...
void	SubtractTwoRules (QuadRule *rule1, QuadRule *rule2, QuadRule *rule_sum)
	Subtract two rules. More...
void	create1DRule (string gridtype, Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Compute 1D rules. More...
void	create1DRule_CC (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Clenshaw-Curtis (includes the endpoints) More...
void	create1DRule_LU (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Legendre-Uniform. More...
void	create1DRule_HG (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr)
	Gauss-Hermite. More...
void	create1DRule_NC (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Newton-Cotes (i.e. equispaced, includes the endpoints) More...
void	create1DRule_NCO (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Newton-Cotes open (i.e. excludes the endpoints) More...
void	create1DRule_CCO (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Clenshaw-Curtis open (i.e. excludes the endpoints) More...
void	create1DRule_JB (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Jacobi-Beta. More...
void	create1DRule_LG (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr)
	Gamma-Laguerre. More...
void	create1DRule_SW (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr)
	Stieltjes-Wigert. More...
void	create1DRule_pdf (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Custom rule given the recursive coefficients of the corresponding orthogonal polynomials. More...
void	create1DRule_GP3 (Array1D< double > &qdpts, Array1D< double > &wghts, int ngr, double a, double b)
	Gauss-Patterson starting with Legendre-Uniform 3. More...
void	getMultiIndexLevel (Array2D< int > &multiIndexLevel, int level, int ndim)
	Auxilliary function: get the level of the multi-index. More...
void	compressRule (QuadRule *rule)
	Compress the rule, i.e. merge repeating points. More...

Private Attributes
Array1D< double >	aa_
	The left endpoints of the domain. More...
Array1D< double >	bb_
	the right endpoints of the domain More...
int	quadverbose_
	Verbosity level. More...
double	alpha_
	The first parameter of the rule, if any. More...
double	beta_
	The second parameter of the rule, if any. More...
Array1D< double >	alphas_
	The first parameter of the rule, if any. More...
Array1D< double >	betas_
	The second parameter of the rule, if any. More...
QuadRule	rule_
	The quadrature rule structure. More...
int	ndim_
	The dimensionality. More...
int	nlevel_
	The current level, working variable for hierarchical construction. More...
int	maxlevel_
	The level for sparse rules, or the number of grid points per dim for full product rules. More...
Array1D< int >	param_
Array2D< int >	npts_all
	Working arrays. More...
Array2D< int >	npts_1_all
Array2D< QuadRule >	qr_all
Array2D< QuadRule >	qr_1_all
int	growth_rule_
	Growth rule: exponential(0) or linear(1) More...
Array1D< int >	growth_rules_
	Growth rules: exponential(0) or linear(1) More...
string	grid_type_
	Grid type: 'CC','CCO','NC','NCO','LU', 'HG', 'JB', 'LG', 'SW', 'pdf', or 'GP3'. More...
Array1D< string >	grid_types_
	Vector of grid types: 'CC','CCO','NC','NCO','LU', 'HG', 'JB', 'LG', 'SW', 'pdf', or 'GP3'. More...
string	fs_type_
	Sparseness type (full or sparse) More...

Detailed Description

Generates quadrature rules.

Note

Besides quadrature rules corresponding to PC bases (i.e. LU, HG, LG, SW, JB), Clenshaw-Curtis(CC) and Newton-Cotes(NC) as well as their Open (with no endpoints) versions (CCO, NCO) are implemented. Also, Gauss-Patterson (GP3) and custom (pdf) rules are added.

Constructor & Destructor Documentation

Quad() [1/4]

Quad::Quad	(	char *	grid_type,
		char *	fs_type,
		int	ndim,
		int	param,
		double	alpha = 0.0,
		double	betta = 1.0
	)

Constructor: initializes the rule type, sparseness type, dimensionality, level or ppd parameter, and two optional parameters for quadrature rule.

Note

Options for the arguments are: grid_type : LU, HG, LG, SW, JB, CC, CCO, NC, NCO, GP3, pdf fs_type : full, sparse ndim : integer dimensionality param : integer points-per-dimension (if full), or level (if sparse) alpha : parameter #1 for the corresponding PC type (e.g. LG requires one parameter) betta : parameter #2 for the corresponding PC type (e.g. JB requires two parameters)

Quad() [2/4]

Quad::Quad	(	Array1D< string > &	grid_types,
		char *	fs_type,
		Array1D< int > &	param,
		Array1D< double > &	alphas,
		Array1D< double > &	bettas
	)

Constructor, overloaded for dimension-unisotropy: initializes the dimension-specific rule types, sparseness type, dimension-specific ppd or level, and two optional parameters for quadrature rule per each dimension.

Note

Options for the arguments are: grid_types : array with entry options LU, HG, LG, SW, JB, CC, CCO, NC, NCO, GP3, pdf fs_type : full, sparse param : integer array for points-per-dimension (if full), or an array with first element indicating the level (if sparse) alpha : array of parameters #1 for the corresponding PC type (e.g. LG requires one parameter) bettas : array of parameters #2 for the corresponding PC type (e.g. JB requires two parameters)

Quad() [3/4]

Quad::Quad ( )

inline

Constructor: empty.

~Quad()

Quad::~Quad ( )

inline

Destructor.

Quad() [4/4]

Quad::Quad ( const Quad &  )

inlineprivate

Dummy copy constructor, which should not be used as it is currently not well defined.

Member Function Documentation

AddTwoRules()

void Quad::AddTwoRules ( QuadRule *  rule1, QuadRule *  rule2, QuadRule *  rule_sum  )

private

Add two rules.

compressRule()

void Quad::compressRule ( QuadRule *  rule )

private

Compress the rule, i.e. merge repeating points.

create1DRule()

void Quad::create1DRule ( string  gridtype, Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Compute 1D rules.

create1DRule_CC()

void Quad::create1DRule_CC ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Clenshaw-Curtis (includes the endpoints)

Note

Heavily adopted from http://people.sc.fsu.edu/~jburkardt/cpp_src/sparse_grid_cc/sparse_grid_cc.html (distributed under LGPL)

create1DRule_CCO()

void Quad::create1DRule_CCO ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Clenshaw-Curtis open (i.e. excludes the endpoints)

Note

Heavily adopted from http://people.sc.fsu.edu/~jburkardt/cpp_src/sparse_grid_cc/sparse_grid_cc.html (distributed under LGPL)

create1DRule_GP3()

void Quad::create1DRule_GP3 ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Gauss-Patterson starting with Legendre-Uniform 3.

Note

Hardwired reading of quadrature points and weights

create1DRule_HG()

void Quad::create1DRule_HG ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr  )

private

Gauss-Hermite.

create1DRule_JB()

void Quad::create1DRule_JB ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Jacobi-Beta.

create1DRule_LG()

void Quad::create1DRule_LG ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr  )

private

Gamma-Laguerre.

create1DRule_LU()

void Quad::create1DRule_LU ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Legendre-Uniform.

create1DRule_NC()

void Quad::create1DRule_NC ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Newton-Cotes (i.e. equispaced, includes the endpoints)

create1DRule_NCO()

void Quad::create1DRule_NCO ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Newton-Cotes open (i.e. excludes the endpoints)

create1DRule_pdf()

void Quad::create1DRule_pdf ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr, double  a, double  b  )

private

Custom rule given the recursive coefficients of the corresponding orthogonal polynomials.

Todo:

Recursive coefficients are given in a file 'ab.dat'; will need to make this more friendly

create1DRule_SW()

void Quad::create1DRule_SW ( Array1D< double > &  qdpts, Array1D< double > &  wghts, int  ngr  )

private

Stieltjes-Wigert.

GetDomain() [1/2]

void Quad::GetDomain ( Array1D< double > &  aa ) const

inline

Get the domain endpoint (for semi-infinite domains)

GetDomain() [2/2]

void Quad::GetDomain ( Array1D< double > &  aa, Array1D< double > &  bb  ) const

inline

Get the domain endpoints (for compact support domains)

getMultiIndexLevel()

void Quad::getMultiIndexLevel ( Array2D< int > &  multiIndexLevel, int  level, int  ndim  )

private

Auxilliary function: get the level of the multi-index.

GetNQ()

int Quad::GetNQ ( )

inline

Get the number of quadrature points.

GetQdpts()

void Quad::GetQdpts ( Array2D< double > &  q )

inline

Externally set the indices.

Get quadrature points

GetRule() [1/2]

void Quad::GetRule	(	Array2D< double > &	q,
		Array1D< double > &	w
	)

Get the quadrature rule.

GetRule() [2/2]

void Quad::GetRule ( Array2D< double > &  q, Array1D< double > &  w, Array2D< int > &  ind  )

inline

Get the quadrature rule with indexing Dummy function for backward compatibility.

GetWghts()

void Quad::GetWghts ( Array1D< double > &  w )

inline

Get the weights.

init()

void Quad::init

(

)

Initialization function.

MultiplyManyRules()

void Quad::MultiplyManyRules ( int  nrules, QuadRule *  rules, QuadRule *  rule_prod  )

private

Multiply many rules (full tensor product)

MultiplyManyRules_()

void Quad::MultiplyManyRules_ ( int  nrules, QuadRule *  rules, QuadRule *  rule_prod  )

private

MultiplyTwoRules()

void Quad::MultiplyTwoRules ( QuadRule *  rule1, QuadRule *  rule2, QuadRule *  rule_prod  )

private

Multiply two rules (full tensor product)

nextLevel()

void Quad::nextLevel

(

)

Compute the indices of the next-level points.

SetAlpha()

void Quad::SetAlpha ( double  alpha )

inline

Set the parameter alpha.

SetBeta()

void Quad::SetBeta ( double  betta )

inline

Set the parameter beta.

SetDomain() [1/2]

void Quad::SetDomain

(

Array1D< double > &

aa

)

Set the domain endpoint (for semi-infinite domains)

SetDomain() [2/2]

void Quad::SetDomain	(	Array1D< double > &	aa,
		Array1D< double > &	bb
	)

Set the domain endpoints (for compact support domains)

SetLevel()

void Quad::SetLevel ( int  param )

inline

Get the indices.

Set the level parameter

SetQdpts()

void Quad::SetQdpts ( Array2D< double > &  q )

inline

Externally set quadrature points.

SetRule() [1/3]

void Quad::SetRule

(

)

Set the rule externally (quadrature points, weights, indices, and the level)

Set the rule (the function that builds quadrature points/weights/indices)

SetRule() [2/3]

void Quad::SetRule	(	Array2D< double > &	q,
		Array1D< double > &	w
	)

Set the rule externally (only quadrature points and weights)

SetRule() [3/3]

void Quad::SetRule ( Array2D< double > &  q, Array1D< double > &  w, Array2D< int > &  ind  )

inline

Set the rule externally (quadrature points, weights and indices) Dummy function for backward compatibility.

SetVerbosity()

void Quad::SetVerbosity ( int  verbosity )

inline

Set the verbosity level.

Note

Currently, the values of 0, 1 and 2 are implemented

SetWghts()

void Quad::SetWghts ( Array1D< double > &  w )

inline

Externally set the weights.

SubtractTwoRules()

void Quad::SubtractTwoRules ( QuadRule *  rule1, QuadRule *  rule2, QuadRule *  rule_sum  )

private

Subtract two rules.

Member Data Documentation

aa_

Array1D<double> Quad::aa_

private

The left endpoints of the domain.

alpha_

double Quad::alpha_

private

The first parameter of the rule, if any.

alphas_

Array1D<double> Quad::alphas_

private

The first parameter of the rule, if any.

bb_

Array1D<double> Quad::bb_

private

the right endpoints of the domain

beta_

double Quad::beta_

private

The second parameter of the rule, if any.

betas_

Array1D<double> Quad::betas_

private

The second parameter of the rule, if any.

fs_type_

string Quad::fs_type_

private

Sparseness type (full or sparse)

grid_type_

string Quad::grid_type_

private

Grid type: 'CC','CCO','NC','NCO','LU', 'HG', 'JB', 'LG', 'SW', 'pdf', or 'GP3'.

grid_types_

Array1D<string> Quad::grid_types_

private

Vector of grid types: 'CC','CCO','NC','NCO','LU', 'HG', 'JB', 'LG', 'SW', 'pdf', or 'GP3'.

growth_rule_

int Quad::growth_rule_

private

Growth rule: exponential(0) or linear(1)

growth_rules_

Array1D<int> Quad::growth_rules_

private

Growth rules: exponential(0) or linear(1)

maxlevel_

int Quad::maxlevel_

private

The level for sparse rules, or the number of grid points per dim for full product rules.

ndim_

int Quad::ndim_

private

The dimensionality.

nlevel_

int Quad::nlevel_

private

The current level, working variable for hierarchical construction.

npts_1_all

Array2D<int> Quad::npts_1_all

private

npts_all

Array2D<int> Quad::npts_all

private

Working arrays.

param_

Array1D<int> Quad::param_

private

qr_1_all

Array2D<QuadRule> Quad::qr_1_all

private

qr_all

Array2D<QuadRule> Quad::qr_all

private

quadverbose_

int Quad::quadverbose_

private

Verbosity level.

Note

Currently the values of 0, 1 or 2 are implemented.

rule_

QuadRule Quad::rule_

private

The quadrature rule structure.

---

The documentation for this class was generated from the following files:

• quad.h
• quad.cpp