d2nat.d1nat: Probability Mass Function Calculator for Matrices
In stheoreme: Klimontovich's S-Theorem Algorithm Implementation and Data Preparation Tools

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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

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.

`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

Vitaly Efremov <vitaly.efremov@dcu.ie>

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.

crit.stheorem, cxds.stheorem, d1nat, utild2group

#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)