tsgCoreOneDimensional.hpp File Reference

Algorithms and meta-data for the Gauuss, Chebyshev and custom rules. More...

#include "tsgIOHelpers.hpp"
#include "tsgLinearSolvers.hpp"
#include "tsgSequenceOptimizer.hpp"

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Classes
class	TasGrid::CustomTabulated
	Class providing manipulation of custom tabulated rules, file I/O and structured access to the points, weights, and meta-data. More...

Namespaces
	TasGrid
	Encapsulates the Tasmanian Sparse Grid module.
	TasGrid::OneDimensionalMeta
	Metadata for one dimensional rules, number of points, exactness, I/O, etc.
	TasGrid::OneDimensionalNodes
	Contains algorithms for generating Gauss,Chebyshev, and Fourier nodes and weights.

Functions
CustomTabulated	TasGrid::getSubrules (CustomTabulated &ct, int start_index, int stride, std::string description)
	Generates a subset of rules as a CustomTabulated object. The subset has a short description string given by description and takes the levels of the input ct starting from level start_index with distance stride between consecutive levels. More...
int	TasGrid::OneDimensionalMeta::getNumPoints (int level, TypeOneDRule rule)
	Return the number of points for the rule at the level, includes all global rules.
int	TasGrid::OneDimensionalMeta::getIExact (int level, TypeOneDRule rule)
	Return the exactness of the interpolation rule at the level, includes all global rules.
int	TasGrid::OneDimensionalMeta::getQExact (int level, TypeOneDRule rule)
	Return the exactness of the integration/quadrature rule at the level, includes all global rules.
bool	TasGrid::OneDimensionalMeta::isNonNested (TypeOneDRule rule)
	Return True if the rule does not have nested nodes, e.g., gauss-legendre.
bool	TasGrid::OneDimensionalMeta::isSequence (TypeOneDRule rule)
	Return True if the rule is nested and has single-node growth, fit for GridSequence, e.g., leja.
bool	TasGrid::OneDimensionalMeta::isGlobal (TypeOneDRule rule)
	Return True if the rule has basis with Lagrange polynomials with global support, fit for GridGlobal, e.g., clenshaw-curtis.
bool	TasGrid::OneDimensionalMeta::isSingleNodeGrowth (TypeOneDRule rule)
	Return True if the rule grows by one point per level.
bool	TasGrid::OneDimensionalMeta::isLocalPolynomial (TypeOneDRule rule)
	Return True if the rule has polynomial basis with local support, fit for GridLocalPolynomial, e.g., localp.
bool	TasGrid::OneDimensionalMeta::isWavelet (TypeOneDRule rule)
	Return True if the rule has wavelet basis with local support.
bool	TasGrid::OneDimensionalMeta::isFourier (TypeOneDRule rule)
	Return True if the rule has trigonometric basis.
const char *	TasGrid::OneDimensionalMeta::getHumanString (TypeOneDRule rule)
	Map the enumerate to a human readable string, used in printStats().
TypeDepth	TasGrid::OneDimensionalMeta::getControurType (TypeDepth type)
	Identifies the general contour, linear type_level, log-corrected type_curved, or hyperbolic type_hyperbolic. More...
bool	TasGrid::OneDimensionalMeta::isExactLevel (TypeDepth type)
	Returns true if the type indicates exactness with respect to raw levels.
bool	TasGrid::OneDimensionalMeta::isExactInterpolation (TypeDepth type)
	Returns true if the type indicates exactness with respect to interpolation.
bool	TasGrid::OneDimensionalMeta::isExactQuadrature (TypeDepth type)
	Returns true if the type indicates exactness with respect to integration.
TypeDepth	TasGrid::OneDimensionalMeta::getSelectionType (TypeDepth type)
	Identifies the selection type, level type_level, interpolation type_iptotal, or quadrature type_qptotal. More...
bool	TasGrid::OneDimensionalMeta::isTypeCurved (TypeDepth type)
	Return True if the multi-index selection type has log-correction term (need to use floating point indexing).
void	TasGrid::OneDimensionalNodes::getGaussLegendre (int m, std::vector< double > &w, std::vector< double > &x)
	Generate Gauss-Legendre weights w and points x for (input) number of points m.
void	TasGrid::OneDimensionalNodes::getChebyshev (int m, std::vector< double > &w, std::vector< double > &x)
	Generate Chebyshev weights w and points x for (input) number of points m.
void	TasGrid::OneDimensionalNodes::getGaussChebyshev1 (int m, std::vector< double > &w, std::vector< double > &x)
	Generate Gauss-Chebyshev type 1 weights w and points x for (input) number of points m.
void	TasGrid::OneDimensionalNodes::getGaussChebyshev2 (int m, std::vector< double > &w, std::vector< double > &x)
	Generate Gauss-Chebyshev type 2 weights w and points x for (input) number of points m.
void	TasGrid::OneDimensionalNodes::getGaussJacobi (int m, std::vector< double > &w, std::vector< double > &x, double alpha, double beta)
	Generate Gauss-Jacobi weights w and points x for (input) number of points m, using parameters alpha and beta.
void	TasGrid::OneDimensionalNodes::getGaussHermite (int m, std::vector< double > &w, std::vector< double > &x, double alpha)
	Generate Gauss-Hermite weights w and points x for (input) number of points m, using parameters alpha.
void	TasGrid::OneDimensionalNodes::getGaussLaguerre (int m, std::vector< double > &w, std::vector< double > &x, double alpha)
	Generate Gauss-Laguerre weights w and points x for (input) number of points m, using parameters alpha.
std::vector< double >	TasGrid::OneDimensionalNodes::getClenshawCurtisNodes (int level)
	Generate Clenshaw-Curtis nodes for the level.
double	TasGrid::OneDimensionalNodes::getClenshawCurtisWeight (int level, int point)
	Return the Clenshaw-Curtis weight for the level and node indexed by point.
std::vector< double >	TasGrid::OneDimensionalNodes::getClenshawCurtisNodesZero (int level)
	Generate Clenshaw-Curtis zero-boundary condition nodes for the level.
double	TasGrid::OneDimensionalNodes::getClenshawCurtisWeightZero (int level, int point)
	Return the Clenshaw-Curtis zero-boundary condition weight for the level and node indexed by point.
std::vector< double >	TasGrid::OneDimensionalNodes::getFejer2Nodes (int level)
	Generate Fejer type 2 nodes for the level.
double	TasGrid::OneDimensionalNodes::getFejer2Weight (int level, int point)
	Return the Fejer type 2 weight for the level and node indexed by point.
std::vector< double >	TasGrid::OneDimensionalNodes::getRLeja (int n)
	Generate the first n R-Leja nodes, starting with 1, -1, 0, ...
std::vector< double >	TasGrid::OneDimensionalNodes::getRLejaCentered (int n)
	Generate the first n R-Leja nodes, starting with 0, 1, -1, ...
std::vector< double >	TasGrid::OneDimensionalNodes::getRLejaShifted (int n)
	Generate the first n R-Leja nodes, starting with -0.5, 0.5, ...
std::vector< double >	TasGrid::OneDimensionalNodes::getFourierNodes (int level)
	Generate the Fourier nodes for the given level, uniformly distributed points with right-most point omitted due to periodicity.

Detailed Description

Algorithms and meta-data for the Gauuss, Chebyshev and custom rules.

Author

Miroslav Stoyanov

Contains core information about one dimensional rules, custom tabulated, Chebyshev and Gaussian rules. Also, generic I/O data.