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)

template<typename T>
void	GetCoefsIntegrateLegendre32Template (T a, T b, std::vector< T > xp, std::vector< T > wp)

Variables
const double	coefficients_xleg5 [5]
	Nodes of the 5-point Gauss-Legendre quadrature.

const double	coefficients_wleg5 [5]
	Weights of the 5-point Gauss-Legendre quadrature.

const double	coefficients_xleg10 [10]
	Nodes of the 10-point Gauss-Legendre quadrature.

const double	coefficients_wleg10 [10]
	Weights of the 10-point Gauss-Legendre quadrature.

const double	coefficients_xleg32 [32]
	Nodes of the 32-point Gauss-Legendre quadrature.

const double	coefficients_wleg32 [32]
	Weights of the 32-point Gauss-Legendre quadrature.

const double	coefficients_xleg40 [40]
	Nodes of the 40-point Gauss-Legendre quadrature.

const double	coefficients_wleg40 [40]
	Weights of the 40-point Gauss-Legendre quadrature.

const double	coefficients_xlag32 [32]
	Nodes of the 32-point Gauss-Laguerre quadrature.

const double	coefficients_wlag32 [32]
	Weights of the 32-point Gauss-Laguerre quadrature.

const double	coefficients_xleg32_zeroone [32]
	Nodes of the 32-point Gauss-Legendre quadrature in the interval [0,1].

const double	coefficients_wleg32_zeroone [32]
	Weights of the 32-point Gauss-Legendre quadrature in the interval [0,1].

Detailed Description

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

Function Documentation

◆ GetCoefs2DLaguerre32Legendre32()

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 < \infty, 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 51 of file NumericalIntegration.cpp.

◆ GetCoefs2DLegendre32Legendre32()

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 77 of file NumericalIntegration.cpp.

◆ GetCoefsIntegrateLaguerre32()

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 < \infty using the 32-point Gauss-Laguerre quadrature.

Parameters

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

Definition at line 183 of file NumericalIntegration.cpp.

◆ GetCoefsIntegrateLegendre10()

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 122 of file NumericalIntegration.cpp.

◆ GetCoefsIntegrateLegendre32()

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-Laguerre nodes.
[out]	w	Gauss-Laguerre weights.

Definition at line 101 of file NumericalIntegration.cpp.

◆ GetCoefsIntegrateLegendre32Template()

template<typename T>

void thermalfist::NumericalIntegration::GetCoefsIntegrateLegendre32Template	(	T	a,
		T	b,
		std::vector< T > *	xp,
		std::vector< T > *	wp )

Template version. 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 289 of file NumericalIntegration.h.

◆ GetCoefsIntegrateLegendre40()

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

	a	< x <
	b	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 162 of file NumericalIntegration.cpp.

◆ GetCoefsIntegrateLegendre5()

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 142 of file NumericalIntegration.cpp.

◆ Integrate2DLaguerre32Legendre32()

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

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

Parameters

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

Returns: Result of the integration.

Integrate a 2D function from 0 to infinity using Gauss-Laguerre integration with 32 points and from ay to by using Gauss-Legendre integration with 32 points.

Parameters

func	The function to integrate, taking two double arguments.
ay	The lower bound for the Gauss-Legendre integration.
by	The upper bound for the Gauss-Legendre integration.

Returns: The result of the integration.

Definition at line 23 of file NumericalIntegration.cpp.

Variable Documentation

◆ coefficients_wlag32

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

Initial value:

= { 0.114187105768, 0.266065216898, 0.418793137325, 0.572532846500,
727648788381, 0.884536719340, 1.04361887589, 1.20534927415,
37022133852, 1.53877725647, 1.71161935269, 1.88942406345,
07295934025, 2.26310663400, 2.46088907249, 2.66750812640,
88439209292, 3.11326132704, 3.35621769260, 3.61586985648,
89551304495, 4.19939410471, 4.53311497853, 4.90427028761,
32350097202, 5.80633321423, 6.37661467416, 7.07352658071,
96769350930, 9.20504033128, 11.1630130908, 15.3901804153 }

Weights of the 32-point Gauss-Laguerre quadrature.

Definition at line 129 of file NumericalIntegration.h.

◆ coefficients_wleg10

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.

◆ coefficients_wleg32

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

Initial value:

= { 0.00701861000947, 0.0162743947309, 0.0253920653093, 0.0342738629130,
0428358980222, 0.0509980592624, 0.0586840934785, 0.0658222227764,
0723457941088, 0.0781938957871, 0.0833119242269, 0.0876520930044,
0911738786958, 0.0938443990808, 0.0956387200793, 0.0965400885147,
0965400885147, 0.0956387200793, 0.0938443990808, 0.0911738786958,
0876520930044, 0.0833119242269, 0.0781938957871, 0.0723457941088,
0658222227764, 0.0586840934785, 0.0509980592624, 0.0428358980222,
0342738629130, 0.0253920653093, 0.0162743947309, 0.00701861000947 }

Weights of the 32-point Gauss-Legendre quadrature.

Definition at line 73 of file NumericalIntegration.h.

◆ coefficients_wleg32_zeroone

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

Initial value:

= { 0.00350930500474, 0.00813719736545, 0.0126960326546,
0171369314565, 0.0214179490111, 0.0254990296312, 0.0293420467393,
0329111113882, 0.0361728970544, 0.0390969478935, 0.0416559621135,
0438260465022, 0.0455869393479, 0.0469221995404, 0.0478193600396,
0482700442574, 0.0482700442574, 0.0478193600396, 0.0469221995404,
0455869393479, 0.0438260465022, 0.0416559621135, 0.0390969478935,
0361728970544, 0.0329111113882, 0.0293420467393, 0.0254990296312,
0214179490111, 0.0171369314565, 0.0126960326546, 0.00813719736545,
00350930500474 }

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

Definition at line 156 of file NumericalIntegration.h.

◆ coefficients_wleg40

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

Initial value:

= { 0.00452127709853, 0.0104982845312, 0.0164210583819, 0.0222458491942,
0279370069800, 0.0334601952825, 0.0387821679745, 0.0438709081857,
0486958076351, 0.0532278469839, 0.0574397690994, 0.0613062424929,
0648040134566, 0.0679120458152, 0.0706116473913, 0.0728865823958,
0747231690580, 0.0761103619006, 0.0770398181642, 0.0775059479784,
0775059479784, 0.0770398181642, 0.0761103619006, 0.0747231690580,
0728865823958, 0.0706116473913, 0.0679120458152, 0.0648040134566,
0613062424929, 0.0574397690994, 0.0532278469839, 0.0486958076351,
0438709081857, 0.0387821679745, 0.0334601952825, 0.0279370069800,
0222458491942, 0.0164210583819, 0.0104982845312, 0.00452127709853 }

Weights of the 40-point Gauss-Legendre quadrature.

Definition at line 101 of file NumericalIntegration.h.

◆ coefficients_wleg5

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.

◆ coefficients_xlag32

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

Initial value:

= { 0.0444893658333, 0.234526109520, 0.576884629302, 1.07244875382,
72240877644, 2.52833670643, 3.49221327302, 4.61645676975,
90395850417, 7.35812673319, 8.98294092421, 10.7830186325,
7636979867, 14.9311397555, 17.2924543367, 19.8558609403,
6308890132, 25.6286360225, 28.8621018163, 32.3466291540,
1004948058, 40.1457197715, 44.5092079958, 49.2243949873,
3337213334, 59.8925091621, 65.9753772879, 72.6876280907,
1874469779, 88.7353404179, 98.8295428683, 111.751398098 }

Nodes of the 32-point Gauss-Laguerre quadrature.

Definition at line 116 of file NumericalIntegration.h.

◆ coefficients_xleg10

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.

◆ coefficients_xleg32

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.

◆ coefficients_xleg32_zeroone

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

Initial value:

= { 0.00136806907526, 0.00719424422737, 0.0176188722062,
0325469620311, 0.0518394221170, 0.0753161931337, 0.102758102016,
133908940630, 0.168477866535, 0.206142121380, 0.246550045534,
289324361935, 0.334065698859, 0.380356318874, 0.427764019209,
475846167156, 0.524153832844, 0.572235980791, 0.619643681126,
665934301141, 0.710675638065, 0.753449954466, 0.793857878620,
831522133465, 0.866091059370, 0.897241897984, 0.924683806866,
948160577883, 0.967453037969, 0.982381127794, 0.992805755773,
998631930925 }

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

Definition at line 142 of file NumericalIntegration.h.

◆ coefficients_xleg40

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.

◆ coefficients_xleg5

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.

Functions

Variables

Detailed Description

Function Documentation

◆ GetCoefs2DLaguerre32Legendre32()

◆ GetCoefs2DLegendre32Legendre32()

◆ GetCoefsIntegrateLaguerre32()

◆ GetCoefsIntegrateLegendre10()

◆ GetCoefsIntegrateLegendre32()

◆ GetCoefsIntegrateLegendre32Template()

◆ GetCoefsIntegrateLegendre40()

◆ GetCoefsIntegrateLegendre5()

◆ Integrate2DLaguerre32Legendre32()

Variable Documentation

◆ coefficients_wlag32

◆ coefficients_wleg10

◆ coefficients_wleg32

◆ coefficients_wleg32_zeroone

◆ coefficients_wleg40

◆ coefficients_wleg5

◆ coefficients_xlag32

◆ coefficients_xleg10

◆ coefficients_xleg32

◆ coefficients_xleg32_zeroone

◆ coefficients_xleg40

◆ coefficients_xleg5