| fractal.dim {RandomFields} | R Documentation |
The function estimates the fractal dimension of a process
fractal.dim(x, y = NULL, z = NULL, data,
grid=TRUE, gridtriple = FALSE,
bin= seq(min(ct$x[3, ]) / 2,
min((ct$x[2,]-ct$x[1,]) / 4, vario.n * min(ct$x[3,]) + 1),
min(ct$x[3,])),
vario.n=5,
sort=TRUE,
fft.m = c(65, 86), ## in
fft.max.length=Inf,
fft.max.regr=150000,
fft.shift = 50, # in
method=c("variogram", "fft"),
mode=c("plot", "interactive"),
pch=16, cex=0.2, cex.main=0.85,
PrintLevel = RFparameters()$Print,
height=3.5,
...)
x |
matrix of coordinates, or vector of x coordinates; if
x is not given a grid with unit grid length is assumed |
y |
vector of y coordinates |
z |
vector of z coordinates |
data |
the values measured. |
grid |
determines whether the vectors x,
y, and z should be
interpreted as a grid definition, see Details. grid
does not apply for T. |
gridtriple |
logical. Only relevant if grid=TRUE.
If gridtriple=TRUE
then x, y, and z are of the
form c(start,end,step); if
gridtriple=FALSE then x, y, and z
must be vectors of ascending values.
|
bin |
sequence of bin boundaries for the empirical variogram |
vario.n |
first vario.n value of the empirical variogram
are used for the regression fit that are not NA. |
sort |
If TRUE then the coordinates are permuted
such that the largest grid length is in x-direction; this is
of interest for algorithms that slice higher dimensional fields
into one-dimensional sections. |
fft.m |
numeric vector of two components; interval of frequencies for which the regression should be calculated; the interval is given in percent of the range of the frequencies in log scale. |
fft.max.length |
The first dimension of the data is cut into pieces
of length fft.max.length. For each piece the FFT is
calculated and then the average for all pieces is taken. The pieces
may overlap, see the parameter fft.shift. |
fft.max.regr |
If the fft.m is too large, parts of the
regression fit will take a very long time.
Therefore, the regression fit is calculated only if the number points
given by fft.m is less than fft.max.regr.
|
fft.shift |
This parameter is given in percent [of
fft.max.length] and defines the overlap of the pieces defined
by fft.max.length. If fft.shift=50 the WOSA estimator is
given; if fft.shift=100 no overlap exist. |
method |
list of implemented methods to calculate the fractal dimension; see Details |
mode |
character. A vector with components
'nographics', 'plot', or 'interactive':
|
pch |
vector or scalar; sign by which data are plotted. |
cex |
vector or scalar; size of pch. |
cex.main |
The size of the title in the regression plots. |
PrintLevel |
integer. If PrintLevel is 0 nothing is
printed. If PrintLevel=1 error messages are printed.
If PrintLevel=2 warnings and the regression results
are given. If PrintLevel>2 tracing information is given.
|
height |
height of the grahics window |
... |
graphical parameters |
The function calculates the fractal dimension by various methods:
The function returns a list with elements
vario,
fft corresponding to
the 2 methods given in the Details.
Each of the elements is itself a list that contains the
following elements.
x |
the x-coordinates used for the regression fit |
y |
the y-coordinates used for the regression fit |
regr |
the return list of the lm |
sm |
smoothed curve through the (x,y) points |
x.u |
NULL or the restricted x-coordinates given
by the user in the interactive plot |
y.u |
NULL or y-coordinates according to x.u |
regr.u |
NULL or the return list of
lm for x.u and y.u |
D |
the fractal dimension |
D.u |
NULL or the fractal dimension corresponding to the
user's regression line |
Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/institute
variogram method
fft