Complex-step differentiation routines.

See also

1. J.R.R.A. Martins, P. Sturdza, J.J. Alonso, "The Complex-Step Derivative Approximation", ACM Transactions on Mathematical Software, Vol. 29, No. 3, September 2003, Pages 245262.

Interfaces

interface

• private function func(x) result(f)

  Arguments

  Type	Intent	Optional	Attributes		Name
  complex(kind=wp),	intent(in)			::	x

  Return Value complex(kind=wp)

Subroutines

public subroutine complex_step_derivative(f, x, h, dfdx)

Compute the first derivative using the complex-step method. This is Equation 6 from Reference [1].

Arguments

Type	Intent	Optional	Attributes		Name
procedure(func)				::	f
complex(kind=wp),	intent(in)			::	x
real(kind=wp),	intent(in)			::	h
real(kind=wp),	intent(out)			::	dfdx

private subroutine forward_diff(f, x, h, dfdx)

Compute the first derivative using a forward difference. This is Equation 1 from Reference [1].

Arguments

Type	Intent	Optional	Attributes		Name
procedure(func)				::	f
complex(kind=wp),	intent(in)			::	x
real(kind=wp),	intent(in)			::	h
real(kind=wp),	intent(out)			::	dfdx

private subroutine central_diff(f, x, h, dfdx)

Compute the first derivative using a 2-point central difference [-h,h].

Arguments

Type	Intent	Optional	Attributes		Name
procedure(func)				::	f
complex(kind=wp),	intent(in)			::	x
real(kind=wp),	intent(in)			::	h
real(kind=wp),	intent(out)			::	dfdx

private subroutine central_diff_4(f, x, h, dfdx)

Compute the first derivative using a 4-point central difference [-2h,-h,h,2h].

Arguments

Type	Intent	Optional	Attributes		Name
procedure(func)				::	f
complex(kind=wp),	intent(in)			::	x
real(kind=wp),	intent(in)			::	h
real(kind=wp),	intent(out)			::	dfdx

public subroutine complex_step_test()

Unit test for the complex_step module.

Arguments

None