boxdim_listepoints

Box dimension of a set of points computed with the box method.

Syntax

[boxdim,Nboxes,handlefig]=boxdim_listepoints(PointsList, Size, Ratio, Waitbar, reg, lrstr, optvarargin)

Inputs

PointsList :
N x M matrix. Set of points which box dimension is to be computated. Each line corresponds to a point, each column corresponds to a coordinate. N is the number of points. M is the number of coordinates (the dimension of the space). For example, if the points lie in an plane, M=2.

Size, Ratio :
Ratio defines the lengths of the sides of the reference box. It is a 1xM array. The successive boxes will be deduced from this first box by homotheties with ration Size(i). More precisely, the box at at the i - th iteration will have a length along the k - th axis equal to Ratio(k)*Size(i) For a graphical explanation about Size and Ratio, see Example 1

Waitbar :
1 if you want a waitbar to appear during the calculation, else 0

reg :
The way you choose the bounds. See the help on fl_regression for more information.

lrstr,optvarargin :
Regression parameters. They define the regression type. Type " help monolr" for more information

Outputs

boxdim :
The estimated box dimension

Nboxes :
Nboxes is a vector. Nboxes(i) is the number of non-empty boxes at the i - th iteration. A non-empty box is a box that contains at least one point of the graph of the function.

handlefig :
If reg~=0, a window appears to help you choosing the linearity bounds. handlefig is the handle of this figure.

bounds :
Bounds of linearity of log2(Nboxes) in function of log2(Size). Interesting if reg==1.

Optional arguments

All arguments except PointsList are optional. For example, the syntax : boxdim_classique(PointsList) is correct. If you don't want to precise an argument, you can also type []. The missing arguments take their default values :

Size=[1 1/2 1/4 ... 1/2048 1/4096]
Ratio =[1 1 ...]
Waitbar = 0
reg=0
lrstr='ls'

These default values are not always relevant, especially Size, so when you don't know how to define Size, try to use reg ~= 0 in order to precise manually the correct box sizes.

Examples

See Also

boxdim_classique, boxdim_binaire, fl_regression, normalize_list