integration Module Reference

Numerical integration. More...

Functions/Subroutines
real function, public	integrate (fkt, xl, xr, eps, plist, method)
	Numerical integration function. More...
recursive real function	qadaptive1d_recursive (fkt, oldS, xl, xr, tol, plist)
real function	qadaptive1d_iterative (fkt, oldS, xl, xr, tol, plist)
real function	qgauss1d (fkt, xl, xr, plist)
real function	qromberg (fkt, xl, xr, tol, plist)

Variables
integer, parameter	maxrec = 100
	maximal depth for recursion More...
real, dimension(3, maxrec)	stack
	stack for iterative algorithm More...

Detailed Description

Numerical integration.

Author

Tobias Illenseer

The module implements the Gauss and Romberg quadrature schemes.

Function/Subroutine Documentation

integrate()

real function, public integration::integrate	(		fkt,
		real, intent(in)	xl,
		real, intent(in)	xr,
		real, intent(in)	eps,
		real, dimension(:), intent(inout), optional	plist,
		integer, intent(in), optional	method
	)

Numerical integration function.

It computes an approximation for the definite integral of some function.

Returns

approximation for integral

Parameters

xl	[in] fkt function for integration
xl	[in] xl lower limit
xr	[in] xr upper limit
eps	[in] eps numerical precision
plist	[in] plist parameter list for function evaluation
method	[in] method quadrature scheme

The quadrature scheme could be one of

1. adaptive Gauss with recursion
2. adaptive Gauss with iteration
3. Romberg

Definition at line 124 of file integration.f90.

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qadaptive1d_iterative()

real function integration::qadaptive1d_iterative (   fkt, real, intent(in)  oldS, real, intent(in)  xl, real, intent(in)  xr, real, intent(in)  tol, real, dimension(:), intent(inout), optional  plist  )

private

Definition at line 259 of file integration.f90.

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qadaptive1d_recursive()

recursive real function integration::qadaptive1d_recursive (   fkt, real, intent(in)  oldS, real, intent(in)  xl, real, intent(in)  xr, real, intent(in)  tol, real, dimension(:), intent(inout), optional  plist  )

private

Definition at line 219 of file integration.f90.

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qgauss1d()

real function integration::qgauss1d (   fkt, real, intent(in)  xl, real, intent(in)  xr, real, dimension(:), intent(inout), optional  plist  )

private

Definition at line 339 of file integration.f90.

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qromberg()

real function integration::qromberg (   fkt, real, intent(in)  xl, real, intent(in)  xr, real  tol, real, dimension(:), intent(inout), optional  plist  )

private

Definition at line 379 of file integration.f90.

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Variable Documentation

maxrec

integer, parameter integration::maxrec = 100

private

maximal depth for recursion

Definition at line 45 of file integration.f90.

stack

real, dimension(3,maxrec) integration::stack

private

stack for iterative algorithm

Definition at line 112 of file integration.f90.