@BeginModule
@NewPage
@Name      = Fldcor
@Title     = Correlation in grid space
@Section   = Correlation and co.
@Class     = Correlation and co.
@Arguments = ifile1 ifile2 ofile
@Operators = fldcor
@EndModule


@BeginOperator_fldcor
@Title     = Correlation in grid space

@BeginDescription
The correlation coefficient is a quantity that gives the quality of a least 
squares fitting to the original data. This operator correlates all gridpoints
of two fields for each timestep. With
@IfMan

S(t) = {x, i_1(t,x) != missval and i_2(t,x) != missval}
@EndifMan
@IfDoc
@BeginDisplayMath
S(t) = \{x, i_1(t,x) \neq missval \wedge i_2(t,x) \neq missval\}
@EndDisplayMath
@EndifDoc
it is
@IfMan

o(t,1) = Cor{(i_1(t,x), i_2(t,x)), x_1 < x <= x_n}
@EndifMan
@IfDoc
@BeginDisplayMath
o(t,1) = \frac{\sum\limits_{x \in S(t)} i_1(t,x) i_2(t,x) w(x) - 
                      \overline{i_1(t,x)}\ \overline{i_2(t,x)}\sum\limits_{x \in S(t)} w(x) }
                   {\sqrt{ \left(\sum\limits_{x \in S(t)} i_1(t,x)^2 w(x) -
                      \overline{i_1(t,x)}^2 \sum\limits_{x \in S(t)} w(x) \right)
                           \left(\sum\limits_{x \in S(t)} i_2(t,x)^2 w(x) -
                      \overline{i_2(t,x)}^2 \sum\limits_{x \in S(t)} w(x) \right) }}
@EndDisplayMath
@EndifDoc
where @math{w(x)} are the area weights obtained by the input streams.
For every timestep @math{t} only those field elements @math{x} belong to the sample,
which have @math{i_1(t,x) \neq missval} and @math{i_2(t,x) \neq missval}.
@EndDescription
@EndOperator
