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Structure functions of a vector field, histograms of increments

STFUN = **vsf**(F) computes the longitudinal and transverse structure
functions of the vector field F, and the histograms of the longitudinal
and transverse increments. If F is an array of fields, the structure
functions are (ensemble) averaged over the fields.
Longitudinal (resp. Transverse) structure functions of order n are the
moments of the vector increments as a function of the separation r,
<(v(x+r) - v(x))^n>, where v is the projection of the velocity along
(resp. perpendicular) to r, and the brackets <> denote both spatial
average and ensemble average (if F is an array of fields).
The structure STFUN contains the following fields:
- r : separation lengths (in mesh units)
- unitr: unit of separation length (e.g., 'mm')
- scaler : scale (in physical units) of a unit separation
- lsf, tsf : R-by-ORDER matrix containing the longitudinal and
transverse structure functions of order ORDER.
- lsfabs, tsfabs : idem as lsf and tsf, with absolute values.
- skew_long, skew_trans: long. and trans. skewness factor.
- flat_long, flat_trans: long. and trans. flatness factor.
- bin : bins for the histograms
- binwidth: width of a bin
- hlvi, htvi : (R x BINVEC) matrix containing the longitudinal and
transverse histograms of velocity increments.
- pdflvi, pdftvi: normalized long. and trans. histograms (PDF).
- history: remind from which field **vsf** has been called.
- n: nbre of points used in the computation.
- nfields: nbre of fields used in the computation (given by
LENGTH(V)).
The resulting structure STFUN may be displayed using vsf_disp.
STFUN = **vsf**(F, 'PropertyName', PropertyValue, ...) also specifies the
optional input arguments:
- 'bin', BIN : vector where velocity increments should be bined.
By default, 1000 bins are taken, chosen from the
rms of the first field.
- 'r', R : list of separations delta_r over which increments
are computed, given in mesh units (should be
smaller than the largest extent of the field).
If not specified, a default separation list is
used.
- 'maxorder', ORDER: maximum order of structure function (usually
between 4 and 8). ORDER=4 is taken by default
(although its convergence may not be
guaranteed).
- 'parallel' : parallelized computation (using parfor loop).
First open a matlab pool to use parallel
computing.
By default, **vsf** considers the values 0 as erroneous, and does not
include them in the histogram and in the computation of the S.F.
If however the values 0 are to be included, specify **vsf**(...,'0').

**Example**
% plot the 2nd order S.F. of a set of vector fields:
v = loadvec('*.vc7');
stfun = **vsf**(filterf(v,1),'maxorder',6);
loglog(stfun.r*stfun.scaler, stfun.lsf(:,2));

**Example**
stfun = **vsf**(loadvec('*.vc7'));
vsf_disp(stfun, 'hist', 'skew');

**See Also**
vsf_disp, ssf, histf, corrf, specf.
Published output in the Help browser
showdemo **vsf**

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