Integrates a function using the trapezoidal rule. More...
Public Member Functions | |
| integer function | calc_int_eqd (var, step_size, var_int) |
| equidistant version More... | |
| integer function | calc_int_reg (var, x, var_int) |
| regular version More... | |
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.
- Returns
- ierr
Definition at line 160 of file num_utilities.f90.
Member Function/Subroutine Documentation
◆ calc_int_eqd()
| 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
-
[in,out] var_int integrated variable [in] var variable to be integrated [in] step_size step size of abscissa
Definition at line 327 of file num_utilities.f90.
Here is the call graph for this function:◆ calc_int_reg()
| 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
-
[in,out] var_int integrated variable [in] var variable to be integrated [in] x abscissa
Definition at line 286 of file num_utilities.f90.
Here is the call graph for this function:The documentation for this interface was generated from the following file:
- /opt/PB3D/Modules/num_utilities.f90