#include <math_integral.h>

Collaboration diagram for ModuleBase::Integral:

Public Member Functions
	Integral ()

	~Integral ()

Static Public Member Functions
static void	Simpson_Integral (const int mesh, const double const func, const double const rab, double &asum)
	simpson integral.

static void	Simpson_Integral (const int mesh, const double *const func, const double dr, double &asum)
	simpson integral.

static void	Simpson_Integral_0toall (const int mesh, const double const func, const double const rab, double *const asum)
	simpson integral.

static void	Simpson_Integral_alltoinf (const int mesh, const double const func, const double const rab, double *const asum)
	simpson integral.

static double	simpson (const int n, const double *const f, const double dx)
	Numerical integration on an evenly-spaced grid using Simpson's rule.

static double	simpson (const int n, const double const f, const double const h)
	Numerical integration on an irregularly-spaced grid using Simpson's rule.

static void	Gauss_Legendre_grid_and_weight (const int n, double x, double weights)

static void	Gauss_Legendre_grid_and_weight (const double xmin, const double xmax, const int n, double x, double weights)

Static Public Attributes
static const double	Lebedev_Laikov_grid110_x [110]

static const double	Lebedev_Laikov_grid110_y [110]

static const double	Lebedev_Laikov_grid110_z [110]

static const double	Lebedev_Laikov_grid110_w [110]

Constructor & Destructor Documentation

◆ Integral()

ModuleBase::Integral::Integral ( )

◆ ~Integral()

ModuleBase::Integral::~Integral ( )

Member Function Documentation

◆ Gauss_Legendre_grid_and_weight() [1/2]

void ModuleBase::Integral::Gauss_Legendre_grid_and_weight	(	const double	xmin,
		const double	xmax,
		const int	n,
		double *	x,
		double *	weights
	)

static

◆ Gauss_Legendre_grid_and_weight() [2/2]

void ModuleBase::Integral::Gauss_Legendre_grid_and_weight	(	const int	n,
		double *	x,
		double *	weights
	)

static

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◆ simpson() [1/2]

double ModuleBase::Integral::simpson	(	const int	n,
		const double *const	f,
		const double *const	h
	)

static

Numerical integration on an irregularly-spaced grid using Simpson's rule.

Parameters

n	number of grid points
f	function values at grid points
h	grid spacing of length n-1, must be positive

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◆ simpson() [2/2]

double ModuleBase::Integral::simpson	(	const int	n,
		const double *const	f,
		const double	dx
	)

static

Numerical integration on an evenly-spaced grid using Simpson's rule.

Parameters

n	number of grid points
f	function values at grid points
dx	grid spacing

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◆ Simpson_Integral() [1/2]

void ModuleBase::Integral::Simpson_Integral	(	const int	mesh,
		const double *const	func,
		const double *const	rab,
		double &	asum
	)

static

simpson integral.

Parameters

mesh	[in] number of grid points (should be odd)
func	[in] function to be integrated
rab	[in] a list of interval
asum	[out] the final integral value

Author: Peize Lin

Date: 2017-10-02

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◆ Simpson_Integral() [2/2]

void ModuleBase::Integral::Simpson_Integral	(	const int	mesh,
		const double *const	func,
		const double	dr,
		double &	asum
	)

static

simpson integral.

Parameters

mesh	[in] number of grid points (should be odd)
func	[in] function to be integrated
dr	[in] interval
asum	[out] the final integral value

Author: Peize Lin

Date: 2017-10-02

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◆ Simpson_Integral_0toall()

void ModuleBase::Integral::Simpson_Integral_0toall	(	const int	mesh,
		const double *const	func,
		const double *const	rab,
		double *const	asum
	)

static

simpson integral.

Parameters

mesh	[in] number of grid points
func	[in] function to be integrated
rab	[in] a list of interval
asum	[out] a list of integral value. asum[i] = integral from 0 to i. The max index of asum is an even (mesh-1 or mesh).

Author: Peize Lin

Date: 2016-02-14

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◆ Simpson_Integral_alltoinf()

void ModuleBase::Integral::Simpson_Integral_alltoinf	(	const int	mesh,
		const double *const	func,
		const double *const	rab,
		double *const	asum
	)

static

simpson integral.

Parameters

mesh	[in] number of grid points
func	[in] function to be integrated
rab	[in] r(i) * dr(i)/di * di or (b-a)/2n
asum	[out] a list of integral value. sum[i] = integral from i to mesh-1.

Author: Peize Lin

Date: 2016-02-14

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Member Data Documentation

◆ Lebedev_Laikov_grid110_w

const double ModuleBase::Integral::Lebedev_Laikov_grid110_w

static

Initial value:

= {
048107465851397,   0.048107465851397,   0.048107465851397,   0.048107465851397,   0.048107465851397,   0.048107465851397,   0.123071735281670,   0.123071735281670,
123071735281670,   0.123071735281670,   0.123071735281670,   0.123071735281670,   0.123071735281670,   0.123071735281670,   0.103191734088330,   0.103191734088330,
103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,
103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,
103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.103191734088330,   0.124945096872513,   0.124945096872513,
124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,
124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,
124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.124945096872513,   0.120580249028528,   0.120580249028528,
120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,
120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,
120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.120580249028528,   0.121830917385521,   0.121830917385521,
121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,
121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,
121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521,   0.121830917385521
}

◆ Lebedev_Laikov_grid110_x

const double ModuleBase::Integral::Lebedev_Laikov_grid110_x

static

Initial value:

= {
000000000000000,  -1.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.577350269189626,  -0.577350269189626,
577350269189626,  -0.577350269189626,   0.577350269189626,  -0.577350269189626,   0.577350269189626,  -0.577350269189626,   0.185115635344736,  -0.185115635344736,
185115635344736,  -0.185115635344736,   0.185115635344736,  -0.185115635344736,   0.185115635344736,  -0.185115635344736,   0.185115635344736,  -0.185115635344736,
185115635344736,  -0.185115635344736,   0.185115635344736,  -0.185115635344736,   0.185115635344736,  -0.185115635344736,   0.965124035086594,  -0.965124035086594,
965124035086594,  -0.965124035086594,   0.965124035086594,  -0.965124035086594,   0.965124035086594,  -0.965124035086594,   0.690421048382292,  -0.690421048382292,
690421048382292,  -0.690421048382292,   0.690421048382292,  -0.690421048382292,   0.690421048382292,  -0.690421048382292,   0.690421048382292,  -0.690421048382292,
690421048382292,  -0.690421048382292,   0.690421048382292,  -0.690421048382292,   0.690421048382292,  -0.690421048382292,   0.215957291845848,  -0.215957291845848,
215957291845848,  -0.215957291845848,   0.215957291845848,  -0.215957291845848,   0.215957291845848,  -0.215957291845848,   0.395689473055942,  -0.395689473055942,
395689473055942,  -0.395689473055942,   0.395689473055942,  -0.395689473055942,   0.395689473055942,  -0.395689473055942,   0.395689473055942,  -0.395689473055942,
395689473055942,  -0.395689473055942,   0.395689473055942,  -0.395689473055942,   0.395689473055942,  -0.395689473055942,   0.828769981252592,  -0.828769981252592,
828769981252592,  -0.828769981252592,   0.828769981252592,  -0.828769981252592,   0.828769981252592,  -0.828769981252592,   0.478369028812150,  -0.478369028812150,
478369028812150,  -0.478369028812150,   0.878158910604066,  -0.878158910604066,   0.878158910604066,  -0.878158910604066,   0.478369028812150,  -0.478369028812150,
478369028812150,  -0.478369028812150,   0.878158910604066,  -0.878158910604066,   0.878158910604066,  -0.878158910604066,   0.000000000000000,   0.000000000000000,
000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000
}

◆ Lebedev_Laikov_grid110_y

const double ModuleBase::Integral::Lebedev_Laikov_grid110_y

static

Initial value:

= {
   0.000000000000000,   0.000000000000000,   1.000000000000000,  -1.000000000000000,   0.000000000000000,   0.000000000000000,   0.577350269189626,   0.577350269189626,
  -0.577350269189626,  -0.577350269189626,   0.577350269189626,   0.577350269189626,  -0.577350269189626,  -0.577350269189626,   0.185115635344736,   0.185115635344736,
  -0.185115635344736,  -0.185115635344736,   0.185115635344736,   0.185115635344736,  -0.185115635344736,  -0.185115635344736,   0.965124035086594,   0.965124035086594,
  -0.965124035086594,  -0.965124035086594,   0.965124035086594,   0.965124035086594,  -0.965124035086594,  -0.965124035086594,   0.185115635344736,   0.185115635344736,
  -0.185115635344736,  -0.185115635344736,   0.185115635344736,   0.185115635344736,  -0.185115635344736,  -0.185115635344736,   0.690421048382292,   0.690421048382292,
  -0.690421048382292,  -0.690421048382292,   0.690421048382292,   0.690421048382292,  -0.690421048382292,  -0.690421048382292,   0.215957291845848,   0.215957291845848,
  -0.215957291845848,  -0.215957291845848,   0.215957291845848,   0.215957291845848,  -0.215957291845848,  -0.215957291845848,   0.690421048382292,   0.690421048382292,
  -0.690421048382292,  -0.690421048382292,   0.690421048382292,   0.690421048382292,  -0.690421048382292,  -0.690421048382292,   0.395689473055942,   0.395689473055942,
  -0.395689473055942,  -0.395689473055942,   0.395689473055942,   0.395689473055942,  -0.395689473055942,  -0.395689473055942,   0.828769981252592,   0.828769981252592,
  -0.828769981252592,  -0.828769981252592,   0.828769981252592,   0.828769981252592,  -0.828769981252592,  -0.828769981252592,   0.395689473055942,   0.395689473055942,
  -0.395689473055942,  -0.395689473055942,   0.395689473055942,   0.395689473055942,  -0.395689473055942,  -0.395689473055942,   0.878158910604066,   0.878158910604066,
  -0.878158910604066,  -0.878158910604066,   0.478369028812150,   0.478369028812150,  -0.478369028812150,  -0.478369028812150,   0.000000000000000,   0.000000000000000,
   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.478369028812150,  -0.478369028812150,
   0.478369028812150,  -0.478369028812150,   0.878158910604066,  -0.878158910604066,   0.878158910604066,  -0.878158910604066
}

◆ Lebedev_Laikov_grid110_z

const double ModuleBase::Integral::Lebedev_Laikov_grid110_z

static

Initial value:

= {
000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   1.000000000000000,  -1.000000000000000,   0.577350269189626,   0.577350269189626,
577350269189626,   0.577350269189626,  -0.577350269189626,  -0.577350269189626,  -0.577350269189626,  -0.577350269189626,   0.965124035086594,   0.965124035086594,
965124035086594,   0.965124035086594,  -0.965124035086594,  -0.965124035086594,  -0.965124035086594,  -0.965124035086594,   0.185115635344736,   0.185115635344736,
185115635344736,   0.185115635344736,  -0.185115635344736,  -0.185115635344736,  -0.185115635344736,  -0.185115635344736,   0.185115635344736,   0.185115635344736,
185115635344736,   0.185115635344736,  -0.185115635344736,  -0.185115635344736,  -0.185115635344736,  -0.185115635344736,   0.215957291845848,   0.215957291845848,
215957291845848,   0.215957291845848,  -0.215957291845848,  -0.215957291845848,  -0.215957291845848,  -0.215957291845848,   0.690421048382292,   0.690421048382292,
690421048382292,   0.690421048382292,  -0.690421048382292,  -0.690421048382292,  -0.690421048382292,  -0.690421048382292,   0.690421048382292,   0.690421048382292,
690421048382292,   0.690421048382292,  -0.690421048382292,  -0.690421048382292,  -0.690421048382292,  -0.690421048382292,   0.828769981252592,   0.828769981252592,
828769981252592,   0.828769981252592,  -0.828769981252592,  -0.828769981252592,  -0.828769981252592,  -0.828769981252592,   0.395689473055942,   0.395689473055942,
395689473055942,   0.395689473055942,  -0.395689473055942,  -0.395689473055942,  -0.395689473055942,  -0.395689473055942,   0.395689473055942,   0.395689473055942,
395689473055942,   0.395689473055942,  -0.395689473055942,  -0.395689473055942,  -0.395689473055942,  -0.395689473055942,   0.000000000000000,   0.000000000000000,
000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.000000000000000,   0.878158910604066,   0.878158910604066,
  -0.878158910604066,  -0.878158910604066,   0.478369028812150,   0.478369028812150,  -0.478369028812150,  -0.478369028812150,   0.878158910604066,   0.878158910604066,
  -0.878158910604066,  -0.878158910604066,   0.478369028812150,   0.478369028812150,  -0.478369028812150,  -0.478369028812150
}

The documentation for this class was generated from the following files:

/home/runner/work/abacus-develop/abacus-develop/source/source_base/math_integral.h
/home/runner/work/abacus-develop/abacus-develop/source/source_base/math_integral.cpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Constructor & Destructor Documentation

◆ Integral()

◆ ~Integral()

Member Function Documentation

◆ Gauss_Legendre_grid_and_weight() [1/2]

◆ Gauss_Legendre_grid_and_weight() [2/2]

◆ simpson() [1/2]

◆ simpson() [2/2]

◆ Simpson_Integral() [1/2]

◆ Simpson_Integral() [2/2]

◆ Simpson_Integral_0toall()

◆ Simpson_Integral_alltoinf()

Member Data Documentation

◆ Lebedev_Laikov_grid110_w

◆ Lebedev_Laikov_grid110_x

◆ Lebedev_Laikov_grid110_y

◆ Lebedev_Laikov_grid110_z