moments_module Module Reference

Method of Moments module. More...

Public Member Functions
subroutine	wheeler_algorithm (m, xi, w)
	Wheeler algorithm. More...
subroutine	moments_correction (m, iter)
	Moments correction. More...
real *8 function	beta_function (z, w)
	Beta function. More...
real *8 function	gammln (xx)
	Gamma function logarithm. More...
subroutine	coefficient (nmax, c)
	Binomial Coefficient. More...

Public Attributes
integer	n_nodes
	Number of nodes for the quadrature. More...
integer, parameter	max_nmom = 20
	Maximum number of moments. More...
integer	n_mom
	Number of moments. More...

Detailed Description

Method of Moments module.

This module contains the procedures and the variables for the method of moments.

Date

22/10/2013

Author

Mattia de' Michieli Vitturi

Definition at line 11 of file moments.f90.

Member Function/Subroutine Documentation

real*8 function moments_module::beta_function	(	real*8, intent(in)	z,
		real*8, intent(in)	w
	)

Beta function.

This function evaluates the beta function B(z,w). This is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind).

Parameters

[in]	z	first parameter of the beta function
[in]	w	second parameter of the beta function

Date

22/10/2013

Author

Mattia de' Michieli Vitturi

Definition at line 316 of file moments.f90.

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subroutine moments_module::coefficient	(	integer, intent(in)	nmax,
		integer, dimension(0:nmax,0:nmax), intent(out)	c
	)

Binomial Coefficient.

This subroutine evaluates the binomial coefficients c(n,m) and stores the values in the matrix (array) c(n,m). The coefficient is used for the computation of the moments of the normal distribution. From: http://www-users.york.ac.uk/~hcb1/fortranY1/fortran90/array15.f90

Parameters

[in]	nmax	max index of the binomial coefficent
[out]	c	array of the binomial coefficients

Date

03/05/2014

Author

Mattia de' Michieli Vitturi

Definition at line 414 of file moments.f90.

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real*8 function moments_module::gammln

(

real*8

xx

)

Gamma function logarithm.

This function returns the logarithm of the gamma function, gammaln(A) = log(gamma(A)). Input must be nonnegative and real. Converted from Numerical Recipes.

Parameters

[in]

xx

argument of the function

Date

22/10/2013

Author

Mattia de' Michieli Vitturi

Definition at line 346 of file moments.f90.

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subroutine moments_module::moments_correction	(	real*8, dimension(:), intent(inout)	m,
		integer, intent(out)	iter
	)

Moments correction.

This subroutine compute uses the algorithm of McGraw for the correction of an unrealizable moment set. The subroutine first analyzes the moment set and then, if it is unrealizable, identifies the moemnt that has to be changed the least to make the set realizable. Modified from Marchisio and Fox 2013

Parameters

[in,out]	m	moments
[out]	iter	number of iterations required

Author

Mattia de' Michieli Vitturi

Date

22/10/2013

Definition at line 171 of file moments.f90.

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subroutine moments_module::wheeler_algorithm	(	real*8, dimension(n_mom), intent(in)	m,
		real*8, dimension(n_nodes), intent(out)	xi,
		real*8, dimension(n_nodes), intent(out)	w
	)

Wheeler algorithm.

This subroutine compute quadrature approximation with the Wheeler algorithm. Given the moments m from 0 to 2*n_nodes-1 it finds the nodes xi and the weights w. Modified from Marchisio and Fox 2013

Parameters

[in]	m	moments
[out]	xi	abscissas
[out]	w	weights

Date

22/10/2013

Author

Mattia de' Michieli Vitturi

Definition at line 41 of file moments.f90.

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Member Data Documentation

integer, parameter moments_module::max_nmom = 20

Maximum number of moments.

Definition at line 19 of file moments.f90.

integer moments_module::n_mom

Number of moments.

Definition at line 22 of file moments.f90.

integer moments_module::n_nodes

Number of nodes for the quadrature.

Definition at line 16 of file moments.f90.

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The documentation for this module was generated from the following file:

• src/moments.f90