Integrates a function using the trapezoidal rule. More...

Public Member Functions
integer function	calc_int_eqd (var, step_size, var_int)
	equidistant version
integer function	calc_int_reg (var, x, var_int)
	regular version

Detailed Description

Integrates a function using the trapezoidal rule.

This function can be defined on an equidistant grid or a regular one:

For an equidistant grid,
\[\int_1^n f(x) dx = \sum_{k=1}^{n-1} {\left(f(k+1)+f(k)\right) \frac{\Delta_x}{2}},\]
is used, with \(n\) the number of points, which are assumed to be equidistant with a given step size \(Delta_x\).
For a regular grid,
\[\int_1^n f(x) dx = \sum_{k=1}^{n-1} {\left(f(k+1)+f(k)\right) \frac{x(k+1)-x(k)}{2}}, \]
is used, with \(n\) the number of points.
- Therefore, \(n\) points have to be specified as well as \(n\) values for the function to be integrated.
- They have to be given in ascending order but the step size does not have to be constant.
- This yields the following difference formula:
  \[\int_1^n f(x) dx = \int_1^{n-1} f(x) dx + \left(f(n)+f(n-1)\right) \frac{x(n)-x(n-1)}{2},\]
  which is used here

Note: For periodic function, the trapezoidal rule works well only if the last point of the grid is included, i.e. the point where the function is equal to the first point.

Definition at line 160 of file num_utilities.f90.

Member Function/Subroutine Documentation

integer function num_utilities::calc_int::calc_int_eqd	(	real(dp), dimension(:), intent(in)	var,
		real(dp), intent(in)	step_size,
		real(dp), dimension(:), intent(inout)	var_int )

equidistant version

Parameters

Definition at line 326 of file num_utilities.f90.

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integer function num_utilities::calc_int::calc_int_reg	(	real(dp), dimension(:), intent(in)	var,
		real(dp), dimension(:), intent(in)	x,
		real(dp), dimension(:), intent(inout)	var_int )

regular version

Parameters

Definition at line 285 of file num_utilities.f90.

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The documentation for this interface was generated from the following file: