stheoreme (version 1.2)

d2nat.d1nat: Probability Mass Function Calculator for Matrices

Description

Function d2nat.d1nat is applied to a pair of matrices and generates then the pair of corresponding probability mass functions by calling d1nat

Usage

d2nat.d1nat(d2arr0, d2arr1, band = c(0, 0), brks = 64, method = "default")

Arguments

d2arr0

sample matrix

d2arr1

sample matrix

band

two border values to set a range of considered values in matrices. The default c(0,0) sets full entire range i.e. range(d2arr0, d2arr1)

brks

value giving a number of bins (in a same manner as the number of cells for the histogram). The default value sets the number of bins automatically equal to 64.

method

specifies selection of matrix elements method='default' simply to call d1nat and apply it to ensemble of all matrix elements as to 1d vector of outcomes

method='cols' to create 1d array with elements being the mean values of original matrix columns and then simply to call d1nat function

method='rows' to create 1d array with elements being the mean values of original matrix rows and then simply to call d1nat function

Value

f0

probability vector representing state0 of a system

f1

probability vector representing state1 of a system

midpoints

vector of the centres of bins where probability values are calculated

Details

It works similarly to d1nat function but for pair of matrices. It is recommended for use as a data preparation step before following Klimontovich's S-theorem based analysis. For instance, it can be used for image analysis.

References

A.N.Herega. On One Criterion of the Relative Degree of Ordering in Images. Technical Physics, 2010, Vol.55, No.5, pp.741-742.

G.B.Bagci, U.Tirnakli. Self-organization in dissipative optical lattices. CHAOS. 19, 033113. 2009.

See Also

crit.stheorem, cxds.stheorem, d1nat, utild2group

Examples

#two modelling arrays: random with randomness distorted by power
s0<-array(runif(256,0,1)^2, c(16,16))
s1<-array(runif(512,0,1)^3, c(16,8))

b<-d2nat.d1nat(d2arr0=s0,d2arr1=s1); b
b<-d2nat.d1nat(s0,s1,brks=256); b
b<-d2nat.d1nat(s0,s1,brks=18,band=c(0.1,0.5),method='rows'); b

#example of 3-step data analysis with Klimontovich's S-theorem
# step a. Split matrices to regions with radius 1, create new matrices 
# of region means 
a<-utild2group(s0, s1, radius=1)
# step b. Create probability vectors
b<-d1nat(a$group0,a$group1,brks=8,band=c(0.1,0.8))
# step c. Compare samples with Klimontovich's S-theorem
crit.stheorem(b$f0,b$f1)
cxds.stheorem(b$f0,b$f1)