integration Module

Utility module containing generic integration routines

Contents

Variables

use_compensated_sum

Interfaces

trapezoidal_integration rectangular_integration local_sum

Functions

real_local_sum complex_local_sum real_trapezoidal_integration complex_trapezoidal_integration real_rectangular_integration complex_rectangular_integration

Variables

Type	Visibility	Attributes		Name		Initial
logical,	private,	parameter	::	use_compensated_sum	=	.true.

Interfaces

public interface trapezoidal_integration

• private function real_trapezoidal_integration(x, y) result(integral)

  Apply the trapezium rule to integrate y over the domain of x.

  Arguments

  Type	Intent	Optional	Attributes		Name
  real,	intent(in),		dimension(:)	::	x
  real,	intent(in),		dimension(:)	::	y

  Return Value real

• private function complex_trapezoidal_integration(x, y) result(integral)

  Apply the trapezium rule to integrate y over the domain of x.

  Arguments

  Type	Intent	Optional	Attributes		Name
  real,	intent(in),		dimension(:)	::	x
  complex,	intent(in),		dimension(:)	::	y

  Return Value complex

public interface rectangular_integration

• private function real_rectangular_integration(x, y) result(integral)

  Apply the (left) rectangular rule to integrate y over the domain of x.

  Arguments

  Type	Intent	Optional	Attributes		Name
  real,	intent(in),		dimension(:)	::	x
  real,	intent(in),		dimension(:)	::	y

  Return Value real

• private function complex_rectangular_integration(x, y) result(integral)

  Apply the (left) rectangular rule to integrate y over the domain of x.

  Arguments

  Type	Intent	Optional	Attributes		Name
  real,	intent(in),		dimension(:)	::	x
  complex,	intent(in),		dimension(:)	::	y

  Return Value complex

private interface local_sum

• private pure function real_local_sum(array) result(total)

  A wrapper routine to perform a sum. Used to provide a single point at which we choose a summation method

  Arguments

  Type	Intent	Optional	Attributes		Name
  real,	intent(in),		dimension(:)	::	array

  Return Value real

• private pure function complex_local_sum(array) result(total)

  A wrapper routine to perform a sum. Used to provide a single point at which we choose a summation method

  Arguments

  Type	Intent	Optional	Attributes		Name
  complex,	intent(in),		dimension(:)	::	array

  Return Value complex

Functions

private pure function real_local_sum(array) result(total)

A wrapper routine to perform a sum. Used to provide a single point at which we choose a summation method

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in),		dimension(:)	::	array

Return Value real

private pure function complex_local_sum(array) result(total)

A wrapper routine to perform a sum. Used to provide a single point at which we choose a summation method

Arguments

Type	Intent	Optional	Attributes		Name
complex,	intent(in),		dimension(:)	::	array

Return Value complex

private function real_trapezoidal_integration(x, y) result(integral)

Apply the trapezium rule to integrate y over the domain of x.

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in),		dimension(:)	::	x
real,	intent(in),		dimension(:)	::	y

Return Value real

private function complex_trapezoidal_integration(x, y) result(integral)

Apply the trapezium rule to integrate y over the domain of x.

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in),		dimension(:)	::	x
complex,	intent(in),		dimension(:)	::	y

Return Value complex

private function real_rectangular_integration(x, y) result(integral)

Apply the (left) rectangular rule to integrate y over the domain of x.

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in),		dimension(:)	::	x
real,	intent(in),		dimension(:)	::	y

Return Value real

private function complex_rectangular_integration(x, y) result(integral)

Apply the (left) rectangular rule to integrate y over the domain of x.

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in),		dimension(:)	::	x
complex,	intent(in),		dimension(:)	::	y

Return Value complex