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vsf
Structure functions of a vector field, histograms of increments

Description
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 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. 
 
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 for which field vsf has been called. 
 
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). 
 
By default, vsf considers the values 0 as erroneous, and does not 
include them in the histogram. If however the values 0 are to be 
included, specify vsf(...,'0'); 
 
Example
 
   stfun = vsf(filterf(loadset,1),'maxorder',6); 
   vsf_disp(stfun, 'hist', 'skew'); 
 
See Also
vsf_disp, histf, corrf. 

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