transformE: Equitable transform

In celphin/Equitable: Equitable Transform

Equitable transform

Description

Creates an equitable transform and returns information regarding it

Usage

transformE(
  d,
  Ave = TRUE,
  cAve = FALSE,
  Zero = FALSE,
  zero = NULL,
  diagonal = TRUE,
  imageplot = FALSE,
  old = NULL
)

Arguments

d	2D data to be transformed
Ave	Include a new column with Row averages "TRUE"(Default) or "FALSE"
cAve	Include a new row with Column averages "TRUE" or "FALSE"(Default)
Zero	if TRUE subtract a zero from data set. Default FALSE
zero	Value to be subtracted off of all data when transforming Default=0
diagonal	Include diagonals of matrices when transforming "TRUE"(Default) or "FALSE"
imageplot	TRUE plots image of data Default FALSE
old	Default NULL (could use old transform slopes to mask new slope transform)

Value

Output from the TransformE function

Running Td<-transformE(d) gives Td that contains several variables (see summary(Td))

(access variables via Td$variable_name ).

Td$smat is original data set :view using imagenan(Td$smat)

Equitable Transform: Td$ET.x matrix of transformed data :view using imagenan(Td$ET.x)

least squared Transform: Td$l.s.x :view using imagenan(Td$l.s.x)

Equitable Transform based only on average column: Td$Ave.ET.x (assumes Ave=TRUE)

l.s. prefix indicates LEAST SQUARES result

s=slope, b=intercept sse =std error of slope bse=std error of intercept

r2=coef. of determination N: # of points in fit pslope: prob. for no correlation

node== indication if fit is due to a node p_par:sequences approximately parallel

zero: subtracted value

Examples of LEAST SQUARES variables:

l.s.s l.s.sse

l.s.b l.s.bse l.s.r2 l.s.N l.s.pslope l.s.node l.s.p_par l.s.zero

# e.g. view using imagenan(Td$l.s.s)

l.s.x= Least squared transform std. dev. errors at each point: l.s.xsd

l.s.Es l.s.Eb l.s.Ep : masked matrices of best values included slope=Es intercept=Eb prob= Ep

E prefix indicates EQUITABLE result

Equitable slopes: E.s intercepts: E.b

errors: E.rtestxsd, E.rtestbsd

#view using imagenan(Td$E.s)

with convergence information (E.rtestxm,E.rtestbm) Values of r^2 after convergence functions

E.numrun: # runs to get convergence

first iteration slopes/intercepts: (E.s1,E.b1) with std. dev. errors (E.sd1, E.bsd1)

E.s E.numrun E.rtestxm E.rtestxsd E.s1 E.sd1 E.sN E.snode

E.b E.numrun E.rtestbm E.rtestbsd E.b1 E.bsd1 E.bN

ET.x: Equitable tranform () with std. dev. errors at each point: ET.xsd

ET.N: number of points averaged to get point

ET.x ET.xsd ET.N

ET.Es ET.Eb ET.Ep : masked matrices included slope=Es interceprt=Eb prob= Ep

Ave.ET.x Ave.ET.xsd Ave.ET.N Ave.ET.Es Ave.ET.Eb Ave.ET.Ep

transform based on only average column: masked matrices included

Examples

# Find a transform using a signal with no noise and then
# add noise and show the results for a noisy data set.
# A researcher with a data set can simply use transformE and plotsummary
#  on their data set placed in variable d
# d is an example (4) of a two dimensional separable signal
d<-eg4(3,3)
Td<-transformE(d, Ave=TRUE)  #Run and equitable transform on the data
#creates summary plots of the data comparing sequences in various ways
plotsummary(Td)
               #add noise to this signal data set
#find the std dev of the overall signal and add normally distributed noise
# that has a std. dev that is some fraction (fac) of this signal std dev
#let the fraction be 1/2 the standard deviaiton of the signal
#add to signal a normal distribution of noise with this std dev.
d_noise<-d+rnorm(prod(dim(d)),mean=0,sd=1/2*sd(d,na.rm=TRUE))
      # Once you have a data set (named d_noise) and
      #you want to find if there is an underlying pattern, run the transform
#Ave= TRUE includes an additional sequence of averages, if not desired set to FALSE
Td_noise<-transformE(d_noise, Ave=TRUE)
 #summary plots of the transform data compared to the thwe original
plotsummary(Td_noise)
 # if you want to include units for the rows columns and data add in the units
plotsummary(Td_noise,row_unit="Year", col_unit="Day Number",z_unit="Temperature")
#shows statistics relative to Signal :Cnonly run this if you already have a signal
runstatsNS(Td,Td_noise)
#shows signal along with noisy data and transforms
#plotsummary puts togetwher numerous calls to plotsome, and plotsquares
plotsummary(Td_noise,Td)
#shows signal along with noisy data and transforms
plotsummary(Td_noise,Td)
#plotsummary puts togetwher numerous calls to plotsome, and plotsquares

plotsummary(Td_noise,Td,row_unit="Year", col_unit="Day Number",z_unit="Temperature")
plotsummary(Td_noise,Td,row_unit="Year", col_unit="Day Number",z_unit="Temperature")

#if you already know the "signal" (in d), create the separable
# Transforms into Td
      #Any of the above stepts could be run with data sets
      # having less than about 450 sequences
      # other examples include eg0, eg1,eg2,eg3,e4,eg5, eg6,eg7,eg8,egrand
      #resolutions of these examples can be altered by changing rmult and cmult
d<-eg5(1,1)
d<-eg5(2,2)
d<-eg5(5,5)
d<-eg5(15,15)
d<-eg5(1,15)
d<-eg5(15,1)

celphin/Equitable documentation built on Jan. 23, 2023, 11:02 p.m.