sll_m_gauss_legendre_integration Module Reference

Description

Gauss-Legendre integration.

Low-level mathematical utility that applies the Gauss-Legendre method to compute numeric integrals.

Derived types and interfaces
interface	sll_o_gauss_legendre_integrate_1d
	Compute numerical integration with Gauss-Legendre formula. More...

Functions/Subroutines
real(kind=f64) function	gauss_legendre_integral_1d (f, a, b, n)
	Gauss-Legendre Quadrature. More...
real(kind=f64) function, dimension(2, 1:npoints), public	sll_f_gauss_legendre_points_and_weights (npoints, a, b)
	Returns a 2d array of size (2,npoints) containing gauss-legendre points and weights in the interval [a,b]. More...
real(kind=f64) function, dimension(1:npoints), public	sll_f_gauss_legendre_points (npoints, a, b)
real(kind=f64) function, dimension(1:npoints), public	sll_f_gauss_legendre_weights (npoints, a, b)

Function/Subroutine Documentation

gauss_legendre_integral_1d()

real(kind=f64) function sll_m_gauss_legendre_integration::gauss_legendre_integral_1d ( procedure(function_1d_legendre)  f, real(kind=f64), intent(in)  a, real(kind=f64), intent(in)  b, integer(kind=i32), intent(in)  n  )

private

Gauss-Legendre Quadrature.

To integrate the function f(x) (real-valued and of a single, real-valued argument x) over the interval [a,b], we use the Gauss-Legendre formula

\[ \int_{-1}^1 f(x)dx \approx \sum_{k=1}^{n} w_k f(x_k) \]

where n represents the desired number of Gauss points.

the function maps the interval [-1,1] into the arbitrary interval [a,b].

To be considered is to split this function into degree-specific functions to avoid the select statement.

Parameters

	f	the function to be integrated
[in]	a	left-bound of the definition interval of f
[in]	b	right-bound of the definition interval of f
[in]	n	the desired number of Gauss points

Returns

The value of the integral

Definition at line 164 of file sll_m_gauss_legendre_integration.F90.

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sll_f_gauss_legendre_points()

real(kind=f64) function, dimension(1:npoints), public sll_m_gauss_legendre_integration::sll_f_gauss_legendre_points	(	integer(kind=i32), intent(in)	npoints,
		real(kind=f64), intent(in), optional	a,
		real(kind=f64), intent(in), optional	b
	)

Definition at line 300 of file sll_m_gauss_legendre_integration.F90.

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sll_f_gauss_legendre_points_and_weights()

real(kind=f64) function, dimension(2, 1:npoints), public sll_m_gauss_legendre_integration::sll_f_gauss_legendre_points_and_weights	(	integer(kind=i32), intent(in)	npoints,
		real(kind=f64), intent(in), optional	a,
		real(kind=f64), intent(in), optional	b
	)

Returns a 2d array of size (2,npoints) containing gauss-legendre points and weights in the interval [a,b].

Parameters

[in]	npoints	Number of gauss points.
[in]	a	OPTIONAL Minimum value of the interval.
[in]	b	OPTIONAL Maximun value of the interval.

Returns

array containing points (1,:) and weights (2,:) gauss_points(degree) returns a real 2D array with the values of the locations of the sll_m_gaussian points 'x_k' in the [-1,1] interval and their corresponding weights 'w_k'. Each column of the answer array contains the pair (x_k, w_k). Optionally, the user may provide the endpoints for the desired interval [a,b] where the gauss points should be mapped.

Definition at line 264 of file sll_m_gauss_legendre_integration.F90.

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sll_f_gauss_legendre_weights()

real(kind=f64) function, dimension(1:npoints), public sll_m_gauss_legendre_integration::sll_f_gauss_legendre_weights	(	integer(kind=i32), intent(in)	npoints,
		real(kind=f64), intent(in), optional	a,
		real(kind=f64), intent(in), optional	b
	)

Definition at line 334 of file sll_m_gauss_legendre_integration.F90.

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