thermalfist::NumericalIntegration Namespace Reference

Contains various Gauss-Legendre and Gauss-Laguerre quadratures used in numerical integrations. More...

Functions
double	Integrate2DLaguerre32Legendre32 (double(*func)(double, double), double ay, double by)
void	GetCoefs2DLaguerre32Legendre32 (double ay, double by, std::vector< double > *xlag, std::vector< double > *wlag, std::vector< double > *xleg, std::vector< double > *wleg)
void	GetCoefs2DLegendre32Legendre32 (double ax, double bx, double ay, double by, std::vector< double > *xleg1, std::vector< double > *wleg1, std::vector< double > *xleg2, std::vector< double > *wleg2)
void	GetCoefsIntegrateLegendre32 (double a, double b, std::vector< double > *x, std::vector< double > *w)
void	GetCoefsIntegrateLegendre10 (double a, double b, std::vector< double > *x, std::vector< double > *w)
void	GetCoefsIntegrateLegendre5 (double a, double b, std::vector< double > *x, std::vector< double > *w)
void	GetCoefsIntegrateLegendre40 (double a, double b, std::vector< double > *x, std::vector< double > *w)
void	GetCoefsIntegrateLaguerre32 (std::vector< double > *x, std::vector< double > *w)

Variables
const double	coefficients_xleg5 [5]
	Nodes of the 5-point Gauss-Legendre quadrature. More...
const double	coefficients_wleg5 [5]
	Weights of the 5-point Gauss-Legendre quadrature. More...
const double	coefficients_xleg10 [10]
	Nodes of the 10-point Gauss-Legendre quadrature. More...
const double	coefficients_wleg10 [10]
	Weights of the 10-point Gauss-Legendre quadrature. More...
const double	coefficients_xleg32 [32]
	Nodes of the 32-point Gauss-Legendre quadrature. More...
const double	coefficients_wleg32 [32]
	Weights of the 32-point Gauss-Legendre quadrature. More...
const double	coefficients_xleg40 [40]
	Nodes of the 40-point Gauss-Legendre quadrature. More...
const double	coefficients_wleg40 [40]
	Weights of the 40-point Gauss-Legendre quadrature. More...
const double	coefficients_xlag32 [32]
	Nodes of the 32-point Gauss-Laguerre quadrature. More...
const double	coefficients_wlag32 [32]
	Weights of the 32-point Gauss-Laguerre quadrature. More...
const double	coefficients_xleg32_zeroone [32]
	Nodes of the 32-point Gauss-Legendre quadrature in the interval [0,1]. More...
const double	coefficients_wleg32_zeroone [32]
	Weights of the 32-point Gauss-Legendre quadrature in the interval [0,1]. More...

Detailed Description

Contains various Gauss-Legendre and Gauss-Laguerre quadratures used in numerical integrations.

Function Documentation

void thermalfist::NumericalIntegration::GetCoefs2DLaguerre32Legendre32	(	double	ay,
		double	by,
		std::vector< double > *	xlag,
		std::vector< double > *	wlag,
		std::vector< double > *	xleg,
		std::vector< double > *	wleg
	)

Populates the nodes and weights for integrating a function f(x,y) in the range 0 < x < , ay <= y <= by using the combined 32-point Gauss-Laguerre and the 32-point Gauss-Legendre quadrature.

Parameters

[in]	ay	Left limit of integration for variable y.
[in]	by	Right limit of integration for variable y.
[out]	xlag	Gauss-Laguerre nodes for the variable x.
[out]	wlag	Gauss-Laguerre weights for the variable x.
[out]	xleg	Gauss-Legendre nodes for the variable y.
[out]	wleg	Gauss-Legendre weights for the variable y.

Definition at line 42 of file NumericalIntegration.cpp.

void thermalfist::NumericalIntegration::GetCoefs2DLegendre32Legendre32	(	double	ax,
		double	bx,
		double	ay,
		double	by,
		std::vector< double > *	xleg1,
		std::vector< double > *	wleg1,
		std::vector< double > *	xleg2,
		std::vector< double > *	wleg2
	)

Populates the nodes and weights for integrating a function f(x,y) in the range ax < x < bx, ay <= y <= by using two 32-point Gauss-Legendre quadratures.

Parameters

[in]	ax	Left limit of integration for variable x.
[in]	bx	Right limit of integration for variable x.
[in]	ay	Left limit of integration for variable y.
[in]	by	Right limit of integration for variable y.
[out]	xlag	Gauss-Legendre nodes for the variable x.
[out]	wlag	Gauss-Legendre weights for the variable x.
[out]	xleg	Gauss-Legendre nodes for the variable y.
[out]	wleg	Gauss-Legendre weights for the variable y.

Definition at line 68 of file NumericalIntegration.cpp.

void thermalfist::NumericalIntegration::GetCoefsIntegrateLaguerre32	(	std::vector< double > *	x,
		std::vector< double > *	w
	)

Populates the nodes and weights for integrating a function f(x) in the range 0 < x < using the 32-point Gauss-Laguerre quadrature.

Parameters

[out]	x	Gauss-Legendre nodes.
[out]	w	Gauss-Legendre weights.

Definition at line 174 of file NumericalIntegration.cpp.

void thermalfist::NumericalIntegration::GetCoefsIntegrateLegendre10	(	double	a,
		double	b,
		std::vector< double > *	x,
		std::vector< double > *	w
	)

Populates the nodes and weights for integrating a function f(x) in the range ax < x < bx using the 10-point Gauss-Legendre quadrature.

Parameters

[in]	a	Left limit of integration.
[in]	b	Right limit of integration
[out]	x	Gauss-Legendre nodes.
[out]	w	Gauss-Legendre weights.

Definition at line 113 of file NumericalIntegration.cpp.

void thermalfist::NumericalIntegration::GetCoefsIntegrateLegendre32	(	double	a,
		double	b,
		std::vector< double > *	x,
		std::vector< double > *	w
	)

Populates the nodes and weights for integrating a function f(x) in the range ax < x < bx using the 32-point Gauss-Legendre quadrature.

Parameters

[in]	a	Left limit of integration.
[in]	b	Right limit of integration
[out]	x	Gauss-Legendre nodes.
[out]	w	Gauss-Legendre weights.

Definition at line 92 of file NumericalIntegration.cpp.

void thermalfist::NumericalIntegration::GetCoefsIntegrateLegendre40	(	double	a,
		double	b,
		std::vector< double > *	x,
		std::vector< double > *	w
	)

Populates the nodes and weights for integrating a function f(x) in the range

Parameters

	ax	< x <
	bx	using the 40-point Gauss-Legendre quadrature.
[in]	a	Left limit of integration.
[in]	b	Right limit of integration
[out]	x	Gauss-Legendre nodes.
[out]	w	Gauss-Legendre weights.

Definition at line 153 of file NumericalIntegration.cpp.

void thermalfist::NumericalIntegration::GetCoefsIntegrateLegendre5	(	double	a,
		double	b,
		std::vector< double > *	x,
		std::vector< double > *	w
	)

Populates the nodes and weights for integrating a function f(x) in the range ax < x < bx using the 5-point Gauss-Legendre quadrature.

Parameters

[in]	a	Left limit of integration.
[in]	b	Right limit of integration
[out]	x	Gauss-Legendre nodes.
[out]	w	Gauss-Legendre weights.

Definition at line 133 of file NumericalIntegration.cpp.

double thermalfist::NumericalIntegration::Integrate2DLaguerre32Legendre32	(	double(*)(double, double)	func,
		double	ay,
		double	by
	)

Integrates a function f(x,y) in range 0 < x < , ay <= y <= by using the combined 32-point Gauss-Laguerre and the 32-point Gauss-Legendre quadrature.

Parameters

func	A point to a function to be integrate.
ay	Left limit of integration for variable y.
by	Right limit of integration for variable y.

Returns

Result of the integration.

Definition at line 14 of file NumericalIntegration.cpp.

Variable Documentation

const double thermalfist::NumericalIntegration::coefficients_wlag32[32]

Initial value:

= { 0.114187105768, 0.266065216898, 0.418793137325, 0.572532846500,
      0.727648788381, 0.884536719340, 1.04361887589, 1.20534927415,
      1.37022133852, 1.53877725647, 1.71161935269, 1.88942406345,
      2.07295934025, 2.26310663400, 2.46088907249, 2.66750812640,
      2.88439209292, 3.11326132704, 3.35621769260, 3.61586985648,
      3.89551304495, 4.19939410471, 4.53311497853, 4.90427028761,
      5.32350097202, 5.80633321423, 6.37661467416, 7.07352658071,
      7.96769350930, 9.20504033128, 11.1630130908, 15.3901804153 }

Weights of the 32-point Gauss-Laguerre quadrature.

Definition at line 129 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_wleg10[10]

Initial value:

= { 0.0666713443087, 0.149451349151, 0.219086362516, 0.269266719310,
      0.295524224715, 0.295524224715, 0.269266719310, 0.219086362516,
      0.149451349151, 0.0666713443087 }

Weights of the 10-point Gauss-Legendre quadrature.

Definition at line 52 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_wleg32[32]

Initial value:

= { 0.00701861000947, 0.0162743947309, 0.0253920653093, 0.0342738629130,
      0.0428358980222, 0.0509980592624, 0.0586840934785, 0.0658222227764,
      0.0723457941088, 0.0781938957871, 0.0833119242269, 0.0876520930044,
      0.0911738786958, 0.0938443990808, 0.0956387200793, 0.0965400885147,
      0.0965400885147, 0.0956387200793, 0.0938443990808, 0.0911738786958,
      0.0876520930044, 0.0833119242269, 0.0781938957871, 0.0723457941088,
      0.0658222227764, 0.0586840934785, 0.0509980592624, 0.0428358980222,
      0.0342738629130, 0.0253920653093, 0.0162743947309, 0.00701861000947 }

Weights of the 32-point Gauss-Legendre quadrature.

Definition at line 73 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_wleg32_zeroone[32]

Initial value:

= { 0.00350930500474, 0.00813719736545, 0.0126960326546,
      0.0171369314565, 0.0214179490111, 0.0254990296312, 0.0293420467393,
      0.0329111113882, 0.0361728970544, 0.0390969478935, 0.0416559621135,
      0.0438260465022, 0.0455869393479, 0.0469221995404, 0.0478193600396,
      0.0482700442574, 0.0482700442574, 0.0478193600396, 0.0469221995404,
      0.0455869393479, 0.0438260465022, 0.0416559621135, 0.0390969478935,
      0.0361728970544, 0.0329111113882, 0.0293420467393, 0.0254990296312,
      0.0214179490111, 0.0171369314565, 0.0126960326546, 0.00813719736545,
      0.00350930500474 }

Weights of the 32-point Gauss-Legendre quadrature in the interval [0,1].

Definition at line 156 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_wleg40[40]

Initial value:

= { 0.00452127709853, 0.0104982845312, 0.0164210583819, 0.0222458491942,
      0.0279370069800, 0.0334601952825, 0.0387821679745, 0.0438709081857,
      0.0486958076351, 0.0532278469839, 0.0574397690994, 0.0613062424929,
      0.0648040134566, 0.0679120458152, 0.0706116473913, 0.0728865823958,
      0.0747231690580, 0.0761103619006, 0.0770398181642, 0.0775059479784,
      0.0775059479784, 0.0770398181642, 0.0761103619006, 0.0747231690580,
      0.0728865823958, 0.0706116473913, 0.0679120458152, 0.0648040134566,
      0.0613062424929, 0.0574397690994, 0.0532278469839, 0.0486958076351,
      0.0438709081857, 0.0387821679745, 0.0334601952825, 0.0279370069800,
      0.0222458491942, 0.0164210583819, 0.0104982845312, 0.00452127709853 }

Weights of the 40-point Gauss-Legendre quadrature.

Definition at line 101 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_wleg5[5]

Initial value:

= { 0.236926885056, 0.478628670499, 0.568888888889, 0.478628670499,
      0.236926885056 }

Weights of the 5-point Gauss-Legendre quadrature.

Definition at line 37 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_xlag32[32]

Initial value:

= { 0.0444893658333, 0.234526109520, 0.576884629302, 1.07244875382,
      1.72240877644, 2.52833670643, 3.49221327302, 4.61645676975,
      5.90395850417, 7.35812673319, 8.98294092421, 10.7830186325,
      12.7636979867, 14.9311397555, 17.2924543367, 19.8558609403,
      22.6308890132, 25.6286360225, 28.8621018163, 32.3466291540,
      36.1004948058, 40.1457197715, 44.5092079958, 49.2243949873,
      54.3337213334, 59.8925091621, 65.9753772879, 72.6876280907,
      80.1874469779, 88.7353404179, 98.8295428683, 111.751398098 }

Nodes of the 32-point Gauss-Laguerre quadrature.

Definition at line 116 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_xleg10[10]

Initial value:

= { -0.973906528517, -0.865063366689, -0.679409568299, -0.433395394129,
      -0.148874338982, 0.148874338982, 0.433395394129, 0.679409568299,
      0.865063366689, 0.973906528517 }

Nodes of the 10-point Gauss-Legendre quadrature.

Definition at line 44 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_xleg32[32]

Initial value:

= { -0.997263861849, -0.985611511545, -0.964762255588, -0.934906075938,
      -0.896321155766, -0.849367613733, -0.794483795968, -0.732182118740,
      -0.663044266930, -0.587715757241, -0.506899908932, -0.421351276131,
      -0.331868602282, -0.239287362252, -0.144471961583, -0.048307665688,
      0.048307665688, 0.144471961583, 0.239287362252, 0.331868602282,
      0.421351276131, 0.506899908932, 0.587715757241, 0.663044266930,
      0.732182118740, 0.794483795968, 0.849367613733, 0.896321155766,
      0.934906075938, 0.964762255588, 0.985611511545, 0.997263861849 }

Nodes of the 32-point Gauss-Legendre quadrature.

Definition at line 60 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_xleg32_zeroone[32]

Initial value:

= { 0.00136806907526, 0.00719424422737, 0.0176188722062,
      0.0325469620311, 0.0518394221170, 0.0753161931337, 0.102758102016,
      0.133908940630, 0.168477866535, 0.206142121380, 0.246550045534,
      0.289324361935, 0.334065698859, 0.380356318874, 0.427764019209,
      0.475846167156, 0.524153832844, 0.572235980791, 0.619643681126,
      0.665934301141, 0.710675638065, 0.753449954466, 0.793857878620,
      0.831522133465, 0.866091059370, 0.897241897984, 0.924683806866,
      0.948160577883, 0.967453037969, 0.982381127794, 0.992805755773,
      0.998631930925 }

Nodes of the 32-point Gauss-Legendre quadrature in the interval [0,1].

Definition at line 142 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_xleg40[40]

Initial value:

= { -0.998237709711, -0.990726238699, -0.977259949984, -0.957916819214,
      -0.932812808279, -0.902098806969, -0.865959503212, -0.824612230833,
      -0.778305651427, -0.727318255190, -0.671956684614, -0.612553889668,
      -0.549467125095, -0.483075801686, -0.413779204372, -0.341994090826,
      -0.268152185007, -0.192697580701, -0.116084070675, -0.038772417506,
      0.038772417506, 0.116084070675, 0.192697580701, 0.268152185007,
      0.341994090826, 0.413779204372, 0.483075801686, 0.549467125095,
      0.612553889668, 0.671956684614, 0.727318255190, 0.778305651427,
      0.824612230833, 0.865959503212, 0.902098806969, 0.932812808279,
      0.957916819214, 0.977259949984, 0.990726238699, 0.998237709711 }

Nodes of the 40-point Gauss-Legendre quadrature.

Definition at line 86 of file NumericalIntegration.h.

const double thermalfist::NumericalIntegration::coefficients_xleg5[5]

Initial value:

= { -0.906179845939, -0.538469310106,
      0., 0.538469310106, 0.906179845939 }

Nodes of the 5-point Gauss-Legendre quadrature.

Definition at line 30 of file NumericalIntegration.h.