Description

Rectangle integration.

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

Derived types and interfaces
interface	sll_o_rectangle_integrate_1d
	Integrate numerically with Gauss-Lobatto formula. More...

Functions/Subroutines
real(kind=f64) function	rectangle_integral_1d (f, x, n)
	Integrate with rectangle formula. More...

real(kind=f64) function, dimension(n)	rectangle_weights (n, x)
	Returns a 1d array of size (n) containing rectangle integration weights in the interval [x(1),x(n)]. More...

Function/Subroutine Documentation

real(kind=f64) function sll_m_rectangle_integration::rectangle_integral_1d	(	procedure(function_1d)	f,
		real(kind=f64), dimension(n)	x,
		integer(kind=i32), intent(in)	n
	)

private

Integrate with rectangle formula.

To integrate the function \( f(x) \) , we use the rectangle formula

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

where n and x represents the desired number of points and their positions.

Parameters

	f	the function to be integrated
[in]	x	positions of points
[in]	n	the number of points

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real(kind=f64) function, dimension(n) sll_m_rectangle_integration::rectangle_weights	(	integer(kind=i32), intent(in)	n,
		real(kind=f64), dimension(n)	x
	)

private

Returns a 1d array of size (n) containing rectangle integration weights in the interval [x(1),x(n)].

Parameters

[in]	n	Number of gauss points.
[in]	x	Point poisitions in interval.