fordiff Module

Module for numerical differentiation using complex step differentiation and finite difference methods

for real(kind=rk) and complex(kind=rk). Use -DREAL32 for real kind 4 and -DREAL64 for real kind 8. Default is real kind 8.


Uses

    • kinds
  • module~~fordiff~~UsesGraph module~fordiff fordiff kinds kinds module~fordiff->kinds

Used by

  • module~~fordiff~~UsedByGraph module~fordiff fordiff program~test1 test1 program~test1->module~fordiff program~test2 test2 program~test2->module~fordiff program~test3 test3 program~test3->module~fordiff program~test4 test4 program~test4->module~fordiff program~test5 test5 program~test5->module~fordiff program~test6 test6 program~test6->module~fordiff

Interfaces

public interface derivative

Derivative interface

  • private impure function complex_step_derivative_T0_T0(f, x, h) result(dfdx)

    Author
    Seyed Ali Ghasemi

    Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using complex step differentiation.

    Arguments

    Type IntentOptional Attributes Name
    private impure function f(z) result(fz)
    Arguments
    Type IntentOptional Attributes Name
    complex(kind=rk), intent(in) :: z

    scalar complex variable
    Return Value complex(kind=rk)

    scalar complex function
    real(kind=rk), intent(in) :: x

    scalar variable
    real(kind=rk), intent(in) :: h

    perturbation for complex step differentiation

    Return Value real(kind=rk)

    derivative of w.r.t.

  • private impure function complex_step_derivative_T0_T1(f, x, h) result(dfdx)

    Author
    Seyed Ali Ghasemi

    Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using complex step differentiation.

    Arguments

    Type IntentOptional Attributes Name
    private impure function f(z) result(fz)
    Arguments
    Type IntentOptional Attributes Name
    complex(kind=rk), intent(in), dimension(:) :: z

    vector complex variable
    Return Value complex(kind=rk)

    scalar complex function
    real(kind=rk), intent(in), dimension(:) :: x

    vector variable
    real(kind=rk), intent(in) :: h

    perturbation for complex step differentiation

    Return Value real(kind=rk), dimension(size(x))

    derivative of w.r.t.

  • private impure function complex_step_derivative_T1_T1(f, x, h) result(dfdx)

    Author
    Seyed Ali Ghasemi

    Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using complex step differentiation.

    Arguments

    Type IntentOptional Attributes Name
    private impure function f(z) result(fz)
    Arguments
    Type IntentOptional Attributes Name
    complex(kind=rk), intent(in), dimension(:) :: z

    vector complex variable
    Return Value complex(kind=rk), dimension(:), allocatable

    vector complex function
    real(kind=rk), intent(in), dimension(:) :: x

    vector variable
    real(kind=rk), intent(in) :: h

    perturbation for complex step differentiation

    Return Value real(kind=rk), dimension(:,:), allocatable

    derivative of w.r.t.

  • private impure function finite_difference_T0_T0(f, x, h, method) result(dfdx)

    Author
    Seyed Ali Ghasemi

    Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using finite difference methods (forward, backward, central).

    Arguments

    Type IntentOptional Attributes Name
    private impure function f(z) result(fz)
    Arguments
    Type IntentOptional Attributes Name
    real(kind=rk), intent(in) :: z

    scalar variable
    Return Value real(kind=rk)

    scalar function
    real(kind=rk), intent(in) :: x

    scalar variable
    real(kind=rk), intent(in) :: h

    perturbation for finite difference methods
    character(len=*), intent(in) :: method

    finite difference method (forward, backward, central)

    Return Value real(kind=rk)

    derivative of w.r.t.

  • private impure function finite_difference_T0_T1(f, x, h, method) result(dfdx)

    Author
    Seyed Ali Ghasemi

    Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using finite difference methods (forward, backward, central).

    Arguments

    Type IntentOptional Attributes Name
    private impure function f(z) result(fz)
    Arguments
    Type IntentOptional Attributes Name
    real(kind=rk), intent(in), dimension(:) :: z

    vector variable
    Return Value real(kind=rk)

    scalar function

    real(kind=rk), intent(in), dimension(:) :: x

    vector variable
    real(kind=rk), intent(in) :: h

    perturbation for finite difference methods
    character(len=*), intent(in) :: method

    finite difference method (forward, backward, central)

    Return Value real(kind=rk), dimension(size(x))

    derivative of w.r.t.

  • private impure function finite_difference_T1_T1(f, x, h, method) result(dfdx)

    Author
    Seyed Ali Ghasemi

    Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using finite difference methods (forward, backward, central).

    Arguments

    Type IntentOptional Attributes Name
    private impure function f(z) result(fz)
    Arguments
    Type IntentOptional Attributes Name
    real(kind=rk), intent(in), dimension(:) :: z

    vector variable
    Return Value real(kind=rk), dimension(:), allocatable

    vector function
    real(kind=rk), intent(in), dimension(:) :: x

    vector variable
    real(kind=rk), intent(in) :: h

    perturbation for finite difference methods
    character(len=*), intent(in) :: method

    finite difference method (forward, backward, central)

    Return Value real(kind=rk), dimension(:,:), allocatable

    derivative of w.r.t.


Functions

private impure function complex_step_derivative_T0_T0(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using complex step differentiation.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
complex(kind=rk), intent(in) :: z

scalar complex variable
Return Value complex(kind=rk)

scalar complex function
real(kind=rk), intent(in) :: x

scalar variable
real(kind=rk), intent(in) :: h

perturbation for complex step differentiation

Return Value real(kind=rk)

derivative of w.r.t.

private impure function complex_step_derivative_T0_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using complex step differentiation.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
complex(kind=rk), intent(in), dimension(:) :: z

vector complex variable
Return Value complex(kind=rk)

scalar complex function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for complex step differentiation

Return Value real(kind=rk), dimension(size(x))

derivative of w.r.t.

private impure function complex_step_derivative_T1_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using complex step differentiation.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
complex(kind=rk), intent(in), dimension(:) :: z

vector complex variable
Return Value complex(kind=rk), dimension(:), allocatable

vector complex function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for complex step differentiation

Return Value real(kind=rk), dimension(:,:), allocatable

derivative of w.r.t.

private impure function finite_difference_T0_T0(f, x, h, method) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using finite difference methods (forward, backward, central).

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: z

scalar variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in) :: x

scalar variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods
character(len=*), intent(in) :: method

finite difference method (forward, backward, central)

Return Value real(kind=rk)

derivative of w.r.t.

private impure function finite_difference_central_T0_T0(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using the central finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: z

scalar variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in) :: x

scalar variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk)

derivative of w.r.t.

private impure function finite_difference_forward_T0_T0(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using the forward finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: z

scalar variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in) :: x

scalar variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk)

derivative of w.r.t.

private impure function finite_difference_backward_T0_T0(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a scalar-valued variable using the backward finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: z

scalar variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in) :: x

scalar variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk)

derivative of w.r.t.

private impure function finite_difference_T0_T1(f, x, h, method) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using finite difference methods (forward, backward, central).

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk)

scalar function

real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods
character(len=*), intent(in) :: method

finite difference method (forward, backward, central)

Return Value real(kind=rk), dimension(size(x))

derivative of w.r.t.

private impure function finite_difference_central_T0_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using the central finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk), dimension(size(x))

derivative of w.r.t.

private impure function finite_difference_forward_T0_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using the forward finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk), dimension(size(x))

derivative of w.r.t.

private impure function finite_difference_backward_T0_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a scalar-valued function w.r.t. a vector-valued variable using the backward finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk)

scalar function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk), dimension(size(x))

derivative of w.r.t.

private impure function finite_difference_T1_T1(f, x, h, method) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using finite difference methods (forward, backward, central).

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk), dimension(:), allocatable

vector function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods
character(len=*), intent(in) :: method

finite difference method (forward, backward, central)

Return Value real(kind=rk), dimension(:,:), allocatable

derivative of w.r.t.

private impure function finite_difference_central_T1_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using the central finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk), dimension(:), allocatable

vector function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk), dimension(:,:), allocatable

derivative of w.r.t.

private impure function finite_difference_forward_T1_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using the forward finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk), dimension(:), allocatable

vector function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk), dimension(:,:), allocatable

derivative of w.r.t.

private impure function finite_difference_backward_T1_T1(f, x, h) result(dfdx)

Author
Seyed Ali Ghasemi

Calculates the derivative of a vector-valued function w.r.t. a vector-valued variable using the backward finite difference method.

Arguments

Type IntentOptional Attributes Name
private impure function f(z) result(fz)
Arguments
Type IntentOptional Attributes Name
real(kind=rk), intent(in), dimension(:) :: z

vector variable
Return Value real(kind=rk), dimension(:), allocatable

vector function
real(kind=rk), intent(in), dimension(:) :: x

vector variable
real(kind=rk), intent(in) :: h

perturbation for finite difference methods

Return Value real(kind=rk), dimension(:,:), allocatable

derivative of w.r.t.