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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 (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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