Namespace for all math specific code
More...

Namespaces
namespace	detail
	Implementations. Not intended to be used by a library user.

Classes
class	AssocLegendre
	Associated Legendre polynomial. More...

class	BindFirst
	Binds the first argument of a function of functor to a certain value. More...

class	BindSecond
	Binds the second argument of a function or functor to a certain value. More...

class	dense_matrix

class	IntAdaptiveRule
	Tag for an adaptive integration rule. More...

class	IntegrationBinder
	A binder for reducing an n-ary function to an n-1-ary function by integration over one variable. More...

class	IntGauss
	Gaussian integration rule. More...

class	IntMidPointRule
	Tag for the midpoint rule. More...

class	IntSimpsonRule
	Tag for the simpson rule. More...

class	IntTrapezoidalRule
	Tag for the trapezoidal rule. More...

class	iterate_not_found_exception
	Exception which is thrown if an iterate cannot be retrieved from the vector of iterates (unknowns) More...

struct	log_AssocLegendre
	Controls logging within the associated Legendre polynomial class. More...

struct	log_integrate
	Controls logging within the numerical integration routine. More...

struct	log_SphericalHarmonic_dTheta
	Controls logging for the derivative of spherical harmonics with respect to theta. More...

class	merseinne_twister_generator
	A pseudo-random number generator implementation using the merseinne twister MT 19937 cf. Makoto Matsumoto, Takuji Nishimura: Mersenne twister. "A 623-dimensionally equidistributed uniform pseudorandom number generator." ACM Transactions on Modeling and Computer Simulation 8, 1998. More...

class	normal_distribution

class	poisson_distribution
	A poisson (exponential) distribution of random numbers. More...

class	provided_solver_invalid_exception
	Exception which is thrown if a (linear) solver provided to some nonlinear solver is not valid (e.g. Nullpointer provided) More...

class	provided_updater_invalid_exception
	Exception which is thrown if an updater for a nonlinear solver is not valid (e.g. Nullpointer provided) More...

class	rand_generator_base
	The basic interface for pseudo-random number generators. More...

class	sparse_matrix
	Sparse matrix class based on a vector of binary trees for holding the entries. More...

class	spherical_harmonics_iterator
	Iteration over all spherical harmonics indices up to order L, with increasing indices l and m. More...

class	SphericalHarmonic
	A spherical harmonic. More...

class	SphericalHarmonic_dPhi
	Derivative of a spherical harmonic with respect to phi. More...

class	SphericalHarmonic_dTheta
	Derivative of a spherical harmonic with respect to theta. More...

class	SphericalHarmonic_dTheta_2
	Derivative of a spherical harmonic with respect to theta, alternative evaluation of theta-derivative. More...

class	std_rand_generator
	A pseudo-random number generator implementation based on std::rand() More...

class	truncated_solution_vector_size_exception
	Exception which is thrown if the size of a solution vector is truncated (too small or big) More...

class	uniform_distribution
	A uniform distribution of random numbers. More...

Typedefs
typedef detail::constants	constants
	Convenience typedef for accessing mathematical constants, e.g. viennashe::math::constants::pi. More...

Enumerations
enum	harmonics_iteration_type { ALL_HARMONICS_ITERATION_ID = 0 , EVEN_HARMONICS_ITERATION_ID , ODD_HARMONICS_ITERATION_ID }
	An enumeration of spherical harmonics types (all, even, odd) ViennaSHE supports. More...

Functions
template<typename NumericT >
NumericT	Bernoulli (NumericT x)
	The Bernoulli function f(x) = x / (exp(x) - 1). Avoids round-off errors near zero. More...

template<typename NumericT >
NumericT	Bernoulli_dx (NumericT x)
	Derivative of the Bernoulli function. f'(x) = [exp(x) - 1 - x exp(x)] / (exp(x) - 1)^2. Avoids round-off errors near zero. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntMidPointRule)
	Integration of a function using the mid point rule. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntTrapezoidalRule)
	Integration of a function using the trapezoidal rule. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntSimpsonRule)
	Integration of a function using the simpson rule. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 1 >)
	Integration of a function using the Gauss rule, 1 evaluation node. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 2 >)
	Integration of a function using the Gauss rule, 2 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 3 >)
	Integration of a function using the Gauss rule, 3 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 4 >)
	Integration of a function using the Gauss rule, 4 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 5 >)
	Integration of a function using the Gauss rule, 5 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 6 >)
	Integration of a function using the Gauss rule, 6 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 7 >)
	Integration of a function using the Gauss rule, 7 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 8 >)
	Integration of a function using the Gauss rule, 8 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 9 >)
	Integration of a function using the Gauss rule, 9 evaluation nodes. More...

template<typename T >
double	integrate (T const &f, double a, double b, IntGauss< 10 >)
	Integration of a function using the Gauss rule, 10 evaluation nodes. More...

template<typename T , typename U >
double	integrate (T const &f, double a, double b, IntAdaptiveRule< U > adaptiverule, long recursion_depth=0)
	Integration of a function using an adaptive integration rule based on bisection of the integration interval. More...

template<typename T , typename IntRuleTag >
double	integrate2D (double a1, double b1, double a2, double b2, T const &func2integrate, IntRuleTag)
	Convenience overload for two-dimensional integration. More...

template<typename VectorType >
VectorType::value_type	norm_2 (VectorType const &v)

template<typename VectorType >
VectorType	subtract (VectorType const &x, VectorType const &y)
	Helper routine for the generic vector subtraction z = x - y;. More...

template<typename NumericT , typename VectorT >
VectorT	row_normalize_system (sparse_matrix< NumericT > &system_matrix, VectorT &rhs)
	Normalizes an equation system such that all diagonal entries are non-negative, and such that all 2-norms of the rows are unity. More...

template<typename NumericT >
std::ostream &	operator<< (std::ostream &os, sparse_matrix< NumericT > const &system_matrix)
	Converts a sparse matrix (ublas, ViennaCL) to a string. Handy debugging facility. More...

template<typename NumericT , typename VectorType >
void	check_types (sparse_matrix< NumericT > const &system_matrix, VectorType const &x)

template<typename NumericT , typename VectorType >
VectorType	prod (sparse_matrix< NumericT > const &system_matrix, VectorType const &x)
	Computes A * x for a sparse A and a vector x. More...

double	factorial (long n)
	Compute the factorial. More...

double	doublefactorial (long n)
	Compute the double factorial, i.e. n(n-2)(n-4)... More...

Detailed Description

Namespace for all math specific code

Namespace containing mathematical tools.

Typedef Documentation

◆ constants

typedef detail::constants viennashe::math::constants

Convenience typedef for accessing mathematical constants, e.g. viennashe::math::constants::pi.

Definition at line 49 of file constants.hpp.

Enumeration Type Documentation

◆ harmonics_iteration_type

enum viennashe::math::harmonics_iteration_type

An enumeration of spherical harmonics types (all, even, odd) ViennaSHE supports.

Enumerator
ALL_HARMONICS_ITERATION_ID
EVEN_HARMONICS_ITERATION_ID
ODD_HARMONICS_ITERATION_ID

Definition at line 158 of file forwards.h.

Function Documentation

◆ Bernoulli()

template<typename NumericT >

NumericT viennashe::math::Bernoulli ( NumericT x )

The Bernoulli function f(x) = x / (exp(x) - 1). Avoids round-off errors near zero.

Definition at line 34 of file bernoulli.hpp.

◆ Bernoulli_dx()

template<typename NumericT >

NumericT viennashe::math::Bernoulli_dx ( NumericT x )

Derivative of the Bernoulli function. f'(x) = [exp(x) - 1 - x exp(x)] / (exp(x) - 1)^2. Avoids round-off errors near zero.

Definition at line 49 of file bernoulli.hpp.

◆ check_types()

template<typename NumericT , typename VectorType >

void viennashe::math::check_types	(	sparse_matrix< NumericT > const &	system_matrix,
		VectorType const &	x
	)

Definition at line 308 of file linalg_util.hpp.

◆ doublefactorial()

double viennashe::math::doublefactorial ( long n )

inline

Compute the double factorial, i.e. n(n-2)(n-4)...

Definition at line 52 of file spherical_harmonics.hpp.

◆ factorial()

double viennashe::math::factorial ( long n )

inline

Compute the factorial.

Definition at line 42 of file spherical_harmonics.hpp.

◆ integrate() [1/14]

template<typename T , typename U >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntAdaptiveRule< U >	adaptiverule,
		long	recursion_depth = `0`
	)

Integration of a function using an adaptive integration rule based on bisection of the integration interval.

Definition at line 283 of file integrator.hpp.

◆ integrate() [2/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 1 >
	)

Integration of a function using the Gauss rule, 1 evaluation node.

Definition at line 140 of file integrator.hpp.

◆ integrate() [3/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 10 >
	)

Integration of a function using the Gauss rule, 10 evaluation nodes.

Definition at line 263 of file integrator.hpp.

◆ integrate() [4/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 2 >
	)

Integration of a function using the Gauss rule, 2 evaluation nodes.

Definition at line 147 of file integrator.hpp.

◆ integrate() [5/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 3 >
	)

Integration of a function using the Gauss rule, 3 evaluation nodes.

Definition at line 157 of file integrator.hpp.

◆ integrate() [6/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 4 >
	)

Integration of a function using the Gauss rule, 4 evaluation nodes.

Definition at line 168 of file integrator.hpp.

◆ integrate() [7/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 5 >
	)

Integration of a function using the Gauss rule, 5 evaluation nodes.

Definition at line 181 of file integrator.hpp.

◆ integrate() [8/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 6 >
	)

Integration of a function using the Gauss rule, 6 evaluation nodes.

Definition at line 196 of file integrator.hpp.

◆ integrate() [9/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 7 >
	)

Integration of a function using the Gauss rule, 7 evaluation nodes.

Definition at line 211 of file integrator.hpp.

◆ integrate() [10/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 8 >
	)

Integration of a function using the Gauss rule, 8 evaluation nodes.

Definition at line 228 of file integrator.hpp.

◆ integrate() [11/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntGauss< 9 >
	)

Integration of a function using the Gauss rule, 9 evaluation nodes.

Definition at line 245 of file integrator.hpp.

◆ integrate() [12/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntMidPointRule
	)

Integration of a function using the mid point rule.

Definition at line 118 of file integrator.hpp.

◆ integrate() [13/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntSimpsonRule
	)

Integration of a function using the simpson rule.

Definition at line 133 of file integrator.hpp.

◆ integrate() [14/14]

template<typename T >

double viennashe::math::integrate	(	T const &	f,
		double	a,
		double	b,
		IntTrapezoidalRule
	)

Integration of a function using the trapezoidal rule.

Definition at line 126 of file integrator.hpp.

◆ integrate2D()

template<typename T , typename IntRuleTag >

double viennashe::math::integrate2D	(	double	a1,
		double	b1,
		double	a2,
		double	b2,
		T const &	func2integrate,
		IntRuleTag
	)

Convenience overload for two-dimensional integration.

\int_{a1}^{b1} \int_{a2}^{b2} func2integrate(x,y) dy dx

Template Parameters

IntRuleTag The integration rule to be used

Parameters

a1	Lower integration bound for the first variable
b1	Upper integration bound for the second variable
a2	Lower integration bound for the first variable
b2	Upper integration bound for the second variable
func2integrate	The integrand

Definition at line 357 of file integrator.hpp.

◆ norm_2()

template<typename VectorType >

VectorType::value_type viennashe::math::norm_2 ( VectorType const & v )

Definition at line 37 of file linalg_util.hpp.

◆ operator<<()

template<typename NumericT >

std::ostream & viennashe::math::operator<<	(	std::ostream &	os,
		sparse_matrix< NumericT > const &	system_matrix
	)

Converts a sparse matrix (ublas, ViennaCL) to a string. Handy debugging facility.

Definition at line 285 of file linalg_util.hpp.

◆ prod()

template<typename NumericT , typename VectorType >

VectorType viennashe::math::prod	(	sparse_matrix< NumericT > const &	system_matrix,
		VectorType const &	x
	)

Computes A * x for a sparse A and a vector x.

Does not apply expression template fancyness, but this is not a performance-critical routine anyway...

Definition at line 385 of file linalg_util.hpp.

◆ row_normalize_system()

template<typename NumericT , typename VectorT >

VectorT viennashe::math::row_normalize_system	(	sparse_matrix< NumericT > &	system_matrix,
		VectorT &	rhs
	)

Normalizes an equation system such that all diagonal entries are non-negative, and such that all 2-norms of the rows are unity.

Definition at line 202 of file linalg_util.hpp.

◆ subtract()

template<typename VectorType >

VectorType viennashe::math::subtract	(	VectorType const &	x,
		VectorType const &	y
	)

Helper routine for the generic vector subtraction z = x - y;.

Does not use any expression template magic. This, however, is okay, as this function is in no way performance critical.

Definition at line 51 of file linalg_util.hpp.

Namespaces

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ constants

Enumeration Type Documentation

◆ harmonics_iteration_type

Function Documentation

◆ Bernoulli()

◆ Bernoulli_dx()

◆ check_types()

◆ doublefactorial()

◆ factorial()

◆ integrate() [1/14]

◆ integrate() [2/14]

◆ integrate() [3/14]

◆ integrate() [4/14]

◆ integrate() [5/14]

◆ integrate() [6/14]

◆ integrate() [7/14]

◆ integrate() [8/14]

◆ integrate() [9/14]

◆ integrate() [10/14]

◆ integrate() [11/14]

◆ integrate() [12/14]

◆ integrate() [13/14]

◆ integrate() [14/14]

◆ integrate2D()

◆ norm_2()

◆ operator<<()

◆ prod()

◆ row_normalize_system()

◆ subtract()