Description

A fast, automatic and robust discretized spline smoothing of uniformly sampled data of arbitrary dimension. Non finite values (NaN or Inf) are treated as missing. Without a smoothing parameter, it is determined by minimizing the generalized cross-validation score. Vector fields or multicomponent data are given as a cell array of their components. The author's original help, kept in the source, lists the details and eight examples.

Syntax

z = smoothn(y)

Automatic smoothing.

z = smoothn(y,s)

Smoothing parameter s, the larger the smoother.

z = smoothn(y,W,s)

With nonnegative weights W of the size of y.

z = smoothn({Vx,Vy})

Smooth a vector field.

z = smoothn(y,'robust')

Minimize the influence of outliers.

opt = struct('TolZ',1e-3,'MaxIter',100,'Spacing',[1 2]);
[z,s,exitflag] = smoothn(y,opt)

Termination of the iteration and spacing of the grid.

Input

`y`	`N-D double, or cell array of the components of a vector field`
`s`	`smoothing parameter, a positive scalar, [] for automatic`
`W`	`weights, 0 for a missing value`
`opt`	`struct of options, the last argument`

Options

`TolZ`	`termination tolerance on z, in ]0,1[ (default 1e-2)`
`MaxIter`	`maximum number of iterations (default 100)`
`Initial`	`initial value of the iteration (default y)`
`Weight`	`weight function of the robust smoothing, 'bisquare' (default), 'talworth' or 'cauchy'`
`Spacing`	`spacing [d1 d2 ...] of the grid in each dimension`
`Order`	`order 0, 1 or 2 of the smoothing (default 2)`

Flags

robust robust smoothing

Output

`z`	`smoothed data`
`s`	`the smoothing parameter used`
`exitflag`	`true if the iteration converged`

References

D. Garcia, Robust smoothing of gridded data in one and higher dimensions with missing values, Computational Statistics & Data Analysis, 2010;54:1167-1178, doi:10.1016/j.csda.2009.09.020

D. Garcia, A fast all-in-one method for automated post-processing of PIV data, Exp Fluids, 2011;50:1247-1259, doi:10.1007/s00348-010-0985-y

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/smoothn.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.