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Spatial correlation function and integral scale of a scalar field

COR = **corrf**(F, DIM) returns the correlation function and the integral
scale of the scalar field F along the dimension DIM (with DIM=1, 2,
or 'x','y', for correlation along the 'X' or 'Y' direction). If F is an
array of scalar fields, COR returns the average of the correlation
functions of each field.
For DIM='x', the correlation function is defined as
f(r) = < F(x,y) F(x+r,y) >,
where <..> is the spatial average (over x and y) and ensemble average
(over all the fields F).
The integral scale of the correlation f(r) is defined as
IS = integral_(from r=0)_(to r=r_max) f(r) dr / f(0),
where r_max is the maximum separation r. However, if the correlation
f(r) does not decrease enough down to 0, the integral does not converge
and IS is ill defined. It is therefore necessary to introduction a
truncation scale in the integral. This truncation scale r_t is defined
here as the scale at which f(r) decreases below a certain threshold.
Five integral scales are computed by **corrf**, corresponding to the
following thresholds:
IS0: r_t is such that f(r_t) = 0
IS1: r_t '' f(r_t) = 0.1*f(0)
IS2: r_t '' f(r_t) = 0.2*f(0)
IS5: r_t '' f(r_t) = 0.5*f(0)
ISinf: r_t is given by the maximum separation r.
COR is a structure which contains the following fields:
r: separation length
f: correlation function
unitr: unit of separation length
unitf: unit of correlation function
namef: name of correlation function
isinf: integral scale, computed as the integral of f up to the
maximum separation r.
r5: scale at which f(r5)=0.5 (linearly interpolated)
is5: integral scale, computed as the integral of f from 0 to r5
r2, is2, r1, is1, r0, is0 : idem as r5, is5, for crossovers
at 0.2, 0.1 and 0 respectively
COR = **corrf**(F, DIM, 'norm') normalizes the correlation function, so
that f = 1 at r = 0.
For a vector field V, **corrf**(vec2scal(V,'ux'),'x') and
**corrf**(vec2scal(V,'uy'),'y') are the longitudinal correlation functions,
and **corrf**(vec2scal(V,'ux'),'y') and **corrf**(vec2scal(V,'uy'),'x') are the
transverse ones.
Note that the convergence of the correlation function is not garanteed,
especially at large separations r, for which very few data points are
available to compute the correlation.
If the crossover scales are not defined (i.e. if the correlation
function does not decrease enough for large r), NaNs (not a number)
are returned, and a warning is issued. Use **corrf**(...,'nowarning') to
ignore these warnings.
COR = **corrf**(..., 'verbose') also displays the computation in progress.
If no output argument, the correlation function is plotted.

**Example**
v = loadvec('B00001.VEC');
cor = **corrf**(vec2scal(v,'vx'),'x');
plot(cor.r, cor.f, 'o-');

**See Also**
vec2scal, tempcorrf, statf, histf, vsf, specf.
Published output in the Help browser
showdemo **corrf**

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