mo_moment::mixed_central_moment Interface Reference

R-s mixed central moment between vectors. More...

Public Member Functions
real(sp) function	mixed_central_moment_sp (x, y, r, s, mask)
real(dp) function	mixed_central_moment_dp (x, y, r, s, mask)

Detailed Description

R-s mixed central moment between vectors.

Calculates the r,s-th mixed central moment between two vectors:

\[\mu_{r-s} = \sum_i\frac{(x_i-\bar{x})^r(y_i-\bar{y})^s}{N}\]

Note that covariace(x,y) = mixed_central_moment(x,y,1,1)

If an optinal mask is given, the average is only over those locations that correspond to true values in the mask. \(x\) can be single or double precision. The result will have the same numerical precision.

Example

 vec1 = (/ 1., 2, 3., -999., 5., 6. /)
 vec2 = (/ 1.3, 2.7, 3.9, 5.1, 6., 8. /)
 m   = mixed_central_moment(vec1, vec2, 2, 2, mask=((vec1 >= 0.) .and. (vec2 >= 0.)))

See also example in test directory.

Literature

1. LH Benedict & RD Gould, Towards better uncertainty estimates for turbulence statistics, Experiments in Fluids 22, 129-136, 1996

Parameters

[in]	real(sp/dp) :: x(:)	First 1D-array
[in]	real(sp/dp) :: y(:)	Second 1D-array
[in]	integer(i4) :: r	Order of x
[in]	integer(i4) :: s	Order of y
[in]	logical, optional :: mask(:)	1D-array of logical values with size(x). If present, only those locations in dat corresponding to the true values in mask are used.

Return values

real(sp/dp) :: mixed_central_moment

r,s-th mixed central moment between x and y

Note

Input values must be floating points.

Author

Matthias Cuntz

Date

Nov 2011

Definition at line 401 of file mo_moment.f90.

Member Function/Subroutine Documentation

mixed_central_moment_dp()

real(dp) function mo_moment::mixed_central_moment::mixed_central_moment_dp	(	real(dp), dimension(:), intent(in)	x,
		real(dp), dimension(:), intent(in)	y,
		integer(i4), intent(in)	r,
		integer(i4), intent(in)	s,
		logical, dimension(:), intent(in), optional	mask
	)

Definition at line 1164 of file mo_moment.f90.

mixed_central_moment_sp()

real(sp) function mo_moment::mixed_central_moment::mixed_central_moment_sp	(	real(sp), dimension(:), intent(in)	x,
		real(sp), dimension(:), intent(in)	y,
		integer(i4), intent(in)	r,
		integer(i4), intent(in)	s,
		logical, dimension(:), intent(in), optional	mask
	)

Definition at line 1214 of file mo_moment.f90.

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

• src/mo_moment.f90