FEMAXX (Finite Element Maxwell Eigensolver): NR Namespace Reference


Functions
template<typename FunctionType, typename ScalarType>
ScalarType	adaptsim (FunctionType &func, ScalarType a, ScalarType b, ScalarType tol, int &info)
template<typename FunctionType, typename ScalarType>
ScalarType	adaptsimstp (FunctionType &func, ScalarType a, ScalarType b, ScalarType fa, ScalarType fm, ScalarType fb, ScalarType is, int &info)
void	polint (const vector< double > &xa, const vector< double > &ya, const double x, double &y, double &dy)
template<typename FunctionType>
double	trapzd (FunctionType &func, const double a, const double b, const int n)
template<typename FunctionType>
double	qtrap (FunctionType &func, double a, double b, double tol, int &info)
template<typename FunctionType>
double	qromb (FunctionType &func, double a, double b, double tol, int &info)
void	spline (const vector< double > &x, const vector< double > &y, const double yp1, const double ypn, vector< double > &y2)
void	splint (const vector< double > &xa, const vector< double > &ya, const vector< double > &y2a, const double x, double &y)
void	spline (const std::vector< double > &x, const std::vector< double > &y, const double yp1, const double ypn, std::vector< double > &y2)
void	splint (const std::vector< double > &xa, const std::vector< double > &ya, const std::vector< double > &y2a, const double x, double &y)

Function Documentation

template<typename FunctionType, typename ScalarType>

ScalarType NR::adaptsim	(	FunctionType &	func,
		ScalarType	a,
		ScalarType	b,
		ScalarType	tol,
		int &	info
	)

function Q = adaptsim(f,a,b,tol,trace,varargin) ADAPTSIM Numerically evaluate integral using adaptive % Simpson rule. % % Q = ADAPTSIM('F',A,B) approximates the integral of % F(X) from A to B to machine precision. 'F' is a % string containing the name of the function. The % function F must return a vector of output values if % given a vector of input values. % % Q = ADAPTSIM('F',A,B,TOL) integrates to a relative % error of TOL. % % Q = ADAPTSIM('F',A,B,TOL,TRACE) displays the left % end point of the current interval, the interval % length, and the partial integral. % % Q = ADAPTSIM('F',A,B,TOL,TRACE,P1,P2,...) allows % coefficients P1, ... to be passed directly to the % function F: G = F(X,P1,P2,...). To use default values % for TOL or TRACE, one may pass the empty matrix ([]). % % See also ADAPTSIMSTP. % % Walter Gander, 08/03/98 % Reference: Gander, Computermathematik, Birkhaeuser, 1992.

Definition at line 48 of file adaptsim.h.

References adaptsimstp().

Referenced by eval_gap_voltage().

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template<typename FunctionType, typename ScalarType>

ScalarType NR::adaptsimstp	(	FunctionType &	func,
		ScalarType	a,
		ScalarType	b,
		ScalarType	fa,
		ScalarType	fm,
		ScalarType	fb,
		ScalarType	is,
		int &	info
	)

ADAPTSIMSTP Recursive function used by ADAPTSIM. % % Q = ADAPTSIMSTP('F',A,B,FA,FM,FB,IS,TRACE) tries to % approximate the integral of F(X) from A to B to % an appropriate relative error. The argument 'F' is % a string containing the name of f. The remaining % arguments are generated by ADAPTSIM or by recursion. % % See also ADAPTSIM. % % Walter Gander, 08/03/98

Definition at line 94 of file adaptsim.h.

References Q.

Referenced by adaptsim().

void NR::polint	(	const vector< double > &	xa,
		const vector< double > &	ya,
		const double	x,
		double &	y,
		double &	dy
	)

Polynomial interpolation using Neville's algorithm.

Let n be the size of arrays xa and ya. If f(x) is the polynomial of degree n-1, such that f(xa[i]) = ya[i], i = 0..n-1, then y = f(x).

Parameters:

	xa	Vector of x values
	ya	Vector of corresponding y values, y_i = f(x_i)
	x	x to interpolate at
	y	Interpolated f(x)
	dy	Error estimate (the last dy added to y).

Definition at line 19 of file romberg.cpp.

Referenced by qromb().

template<typename FunctionType>

double NR::trapzd	(	FunctionType &	func,
		const double	a,
		const double	b,
		const int	n
	)

Compute the n-th stage of refinement of an extended trapezoidal rule.

Must be called with inceasing n, starting with n=1.

Parameters:

	func	Function to integrate, must implement operator()(double)
	a	Left boundary of integral interval
	b	Right boundary of integral interval
	n	n-th stage of refinement of trapezoidal rule

Returns:: Computed integral

Definition at line 50 of file romberg.h.

References x.

template<typename FunctionType>

double NR::qtrap	(	FunctionType &	func,
		double	a,
		double	b,
		double	tol,
		int &	info
	)

Caluculate Int(func(t), t=a..b) using trapezoidal rule.

Parameters:

	func	Function to integrate, must implement operator()(double)
	a	Left boundary of integral interval
	b	Right boundary of integral interval
	tol	Relative tolerance

Returns:: Computed integral

Definition at line 80 of file romberg.h.

template<typename FunctionType>

double NR::qromb	(	FunctionType &	func,
		double	a,
		double	b,
		double	tol,
		int &	info
	)

Caluculate Int(func(t), t=a..b) using Romberg integration.

Parameters:

	func	Function to integrate, must implement operator()(double)
	a
	b
	tol	Relative tolerance
	info	Status, 0 means no error

Returns:: Computed integral

Definition at line 112 of file romberg.h.

References polint().

Referenced by eval_gap_voltage().

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void NR::spline	(	const vector< double > &	x,
		const vector< double > &	y,
		const double	yp1,
		const double	ypn,
		vector< double > &	y2
	)

Definition at line 20 of file spline.cpp.

Referenced by CometGapFinder::CometGapFinder().

void NR::splint	(	const vector< double > &	xa,
		const vector< double > &	ya,
		const vector< double > &	y2a,
		const double	x,
		double &	y
	)

Definition at line 58 of file spline.cpp.

Referenced by CometGapFinder::get_gap().

void NR::spline	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		const double	yp1,
		const double	ypn,
		std::vector< double > &	y2
	)

NR Namespace Reference

Functions

Function Documentation