calculus_m Module
- Jabir Ali Ouassou
-
- Foundation
- 135 statements
- Source File
This module defines some functions that perform common calculus operations, including differentiating, integrating, and interpolating discretized data.
Uses
Functions
public pure function mean_array_re(x) result(r)
Calculates the mean value of a real-valued array.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Real-valued array |
Return Value real(kind=wp)
Mean value
public pure function mean_array_cx(x) result(r)
Calculates the mean value of a complex-valued array.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=wp), | intent(in), | dimension(:) | :: | x |
Complex-valued array |
Return Value complex(kind=wp)
Mean value
public pure function differentiate_array_re(x, y) result(r)
Calculates the numerical derivative of an array y wrt. x using central differences at the interior points and forward/backward differences at the exterior points. All three approaches yield two-point approximations of the derivatives, thus the mesh spacing does not have to be uniform.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| real(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
Return Value real(kind=wp), dimension(size(x))
Derivative dy/dx
public pure function differentiate_array_cx(x, y) result(r)
Complex version of differentiate_array_re.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| complex(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
Return Value complex(kind=wp), dimension(size(x))
Derivative dy/dx
public pure function integrate_array_re(x, y) result(r)
Calculates the integral of an array y wrt. x using the trapezoid method. The mesh spacing does not necessarily have to be uniform.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| real(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
Return Value real(kind=wp)
Integral ∫y(x)·dx
public pure function integrate_array_cx(x, y) result(r)
Complex version of integrate_array_re.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| complex(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
Return Value complex(kind=wp)
Integral ∫y(x)·dx
public function integrate_range_re(x, y, a, b) result(r)
Constructs a piecewise hermitian cubic interpolation of an array y(x) from discrete numerical data, and then integrates the interpolation in the range (a, b). The mesh spacing does not have to be uniform.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| real(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in) | :: | a |
Left endpoint |
||
| real(kind=wp), | intent(in) | :: | b |
Right endpoint |
Return Value real(kind=wp)
Integral ∫y(x)·dx
public function integrate_range_cx(x, y, a, b) result(r)
Complex version of integrate_range_re.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| complex(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in) | :: | a |
Left endpoint |
||
| real(kind=wp), | intent(in) | :: | b |
Right endpoint |
Return Value complex(kind=wp)
Integral ∫y(x)·dx
public function interpolate_array_re(x, y, p) result(r)
Constructs a piecewise hermitian cubic interpolation of an array y(x) based on discrete numerical data and evaluates the interpolation at p. Note that the mesh spacing does not necessarily have to be uniform.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| real(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in), | dimension(:) | :: | p |
Point array p |
Return Value real(kind=wp), dimension(size(p))
Interpolation y(p)
public function interpolate_array_cx(x, y, p) result(r)
Complex version of interpolate_array_re.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| complex(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in), | dimension(:) | :: | p |
Point array p |
Return Value complex(kind=wp), dimension(size(p))
Interpolation y(p)
public function interpolate_point_re(x, y, p) result(r)
Wrapper for interpolate_array_re that accepts scalar arguments.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| real(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in) | :: | p |
Single point p |
Return Value real(kind=wp)
Interpolation y(p)
public function interpolate_point_cx(x, y, p) result(r)
Complex version of interpolate_point_re.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| complex(kind=wp), | intent(in), | dimension(size(x)) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in) | :: | p |
Single point p |
Return Value complex(kind=wp)
Interpolation y(p)
public pure function interpolate_point_matrix_re(x, y, p) result(r)
Interpolates a matrix function using Catmull-Rom splines.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
Variable x |
|
| real(kind=wp), | intent(in), | dimension(:, :, :) | :: | y |
Function y(x) |
|
| real(kind=wp), | intent(in) | :: | p |
Single point p |
Return Value real(kind=wp), dimension(size(y, 1), size(y, 2))
Interpolation y(p)
Subroutines
public pure subroutine linspace_array_re(array, first, last)
Populates an array with elements from first to last, inclusive.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(out), | dimension(:) | :: | array |
Output array to populate |
|
| real(kind=wp), | intent(in) | :: | first |
Value of first element |
||
| real(kind=wp), | intent(in) | :: | last |
Value of last element |