Last data update: 2014.03.03

 R: performs the computation of unnormalized triplet and...
weight.nucR Documentation

performs the computation of unnormalized triplet and individuals weights for a nuclear family in the pedigree

Description

the weighting algorithm proceeds by nuclear family, the function weight.nuc computes the unnormalized triplet and individuals weights for a nuclear family in the pedigree. This is an internal function not meant to be called by the user.

Usage

weight.nuc(connect, spouse.connect, children.connect, status, 
probs, fyc, p.ybarF.c, ww, w, res.upward)

Arguments

connect

a connector in the pedigree,

spouse.connect

spouse of the connector,

children.connect

children of the connector,

status

vector of symptom status of the whole pedigree,

probs

all probability parameters of the model,

fyc

a matrix of n times K+1 given the density of observations of each individual if allocated to class k, where n is the number of individuals and K is the total number of latent classes in the model,

p.ybarF.c

a array of dimension n times 2 times K+1 giving the probability of observations above the individual, depending on his status and his class and conditionally on his class,

ww

unnormalized triplet weights, an array of n times 2 times K+1 times K+1 times K+1, where n is the number of individuals and K is the total number of latent classes in the model, see e.step,

w

unnormalized individual weights, an array of n times 2 times K+1, see e.step,

res.upward

result of the upward step of the weighting algorithm, see upward,

Details

updated ww and w are computed for the current nuclear family.

Value

the function returns a list of 2 elements:

ww

unnormalized triplet weights, an array of n times 2 times K+1 times K+1 times K+1, see e.step,

w

unnormalized individual weights, an array of n times 2 times K+1, see e.step.

References

TAYEB et al.: Solving Genetic Heterogeneity in Extended Families by Identifying Sub-types of Complex Diseases. Computational Statistics, 2011, DOI: 10.1007/s00180-010-0224-2.

See Also

See also downward

Examples

#data
data(ped.cont)
data(peel)
fam <- ped.cont[,1]
id <- ped.cont[fam==1,2]
dad <- ped.cont[fam==1,3]
mom <- ped.cont[fam==1,4]
status <- ped.cont[fam==1,6]
y <- ped.cont[fam==1,7:ncol(ped.cont)]
peel <- peel[[1]]
#standardize id to be 1, 2, 3, ...
id.origin <- id
standard <- function(vec) ifelse(vec%in%id.origin,which(id.origin==vec),0)
id <- apply(t(id),2,standard)
dad <- apply(t(dad),2,standard)
mom <- apply(t(mom),2,standard)
peel$couple <- cbind(apply(t(peel$couple[,1]),2,standard),
                     apply(t(peel$couple[,2]),2,standard))
for(generat in 1:peel$generation)
peel$peel.connect[generat,] <- apply(t(peel$peel.connect[generat,]),2,standard)
#the first nuclear family
generat <- peel$generation
connect <- peel$peel.connect[generat,]
connect <- connect[connect>0]
spouse.connect <- peel$couple[peel$couple[,1]==connect,2]
children.connect <- union(id[dad==connect],id[mom==connect])
#probs and param
data(probs)
data(param.cont)
#densities of the observations
fyc <- matrix(1,nrow=length(id),ncol=length(probs$p)+1)
fyc[status==2,1:length(probs$p)] <- t(apply(y[status==2,],1,dens.norm,
                                            param.cont,NULL))
#triplet and individual weights
ww <- array(0,dim=c(length(id),rep(2,3),rep(length(probs$p)+1,3)))
w <- array(0,dim=c(length(id),2,length(probs$p)+1))
#probability of the observations below
p.ybarF.c <- array(1,dim=c(length(id),2,length(probs$p)+1))
p.ybarF.c[connect,,] <- p.post.found(connect,status,probs,fyc)
#the upward step
res.upward <- upward(id,dad,mom,status,probs,fyc,peel)
#the function
weight.nuc(connect,spouse.connect,children.connect,status,probs,fyc,
           p.ybarF.c,ww,w,res.upward)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LCAextend)
Loading required package: boot
Loading required package: mvtnorm
Loading required package: rms
Loading required package: Hmisc
Loading required package: lattice

Attaching package: 'lattice'

The following object is masked from 'package:boot':

    melanoma

Loading required package: survival

Attaching package: 'survival'

The following object is masked from 'package:boot':

    aml

Loading required package: Formula
Loading required package: ggplot2

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

    format.pval, round.POSIXt, trunc.POSIXt, units

Loading required package: SparseM

Attaching package: 'SparseM'

The following object is masked from 'package:base':

    backsolve

Loading required package: kinship2
Loading required package: Matrix
Loading required package: quadprog
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LCAextend/weight.nuc.Rd_%03d_medium.png", width=480, height=480)
> ### Name: weight.nuc
> ### Title: performs the computation of unnormalized triplet and individuals
> ###   weights for a nuclear family in the pedigree
> ### Aliases: weight.nuc
> 
> ### ** Examples
> 
> #data
> data(ped.cont)
> data(peel)
> fam <- ped.cont[,1]
> id <- ped.cont[fam==1,2]
> dad <- ped.cont[fam==1,3]
> mom <- ped.cont[fam==1,4]
> status <- ped.cont[fam==1,6]
> y <- ped.cont[fam==1,7:ncol(ped.cont)]
> peel <- peel[[1]]
> #standardize id to be 1, 2, 3, ...
> id.origin <- id
> standard <- function(vec) ifelse(vec%in%id.origin,which(id.origin==vec),0)
> id <- apply(t(id),2,standard)
> dad <- apply(t(dad),2,standard)
> mom <- apply(t(mom),2,standard)
> peel$couple <- cbind(apply(t(peel$couple[,1]),2,standard),
+                      apply(t(peel$couple[,2]),2,standard))
> for(generat in 1:peel$generation)
+ peel$peel.connect[generat,] <- apply(t(peel$peel.connect[generat,]),2,standard)
> #the first nuclear family
> generat <- peel$generation
> connect <- peel$peel.connect[generat,]
> connect <- connect[connect>0]
> spouse.connect <- peel$couple[peel$couple[,1]==connect,2]
> children.connect <- union(id[dad==connect],id[mom==connect])
> #probs and param
> data(probs)
> data(param.cont)
> #densities of the observations
> fyc <- matrix(1,nrow=length(id),ncol=length(probs$p)+1)
> fyc[status==2,1:length(probs$p)] <- t(apply(y[status==2,],1,dens.norm,
+                                             param.cont,NULL))
> #triplet and individual weights
> ww <- array(0,dim=c(length(id),rep(2,3),rep(length(probs$p)+1,3)))
> w <- array(0,dim=c(length(id),2,length(probs$p)+1))
> #probability of the observations below
> p.ybarF.c <- array(1,dim=c(length(id),2,length(probs$p)+1))
> p.ybarF.c[connect,,] <- p.post.found(connect,status,probs,fyc)
> #the upward step
> res.upward <- upward(id,dad,mom,status,probs,fyc,peel)
> #the function
> weight.nuc(connect,spouse.connect,children.connect,status,probs,fyc,
+            p.ybarF.c,ww,w,res.upward)
$ww
, , 1, 1, 1, 1, 1

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, , 2, 1, 1, 1, 1

              [,1]         [,2]
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 [4,] 0.000000e+00 0.000000e+00
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 [7,] 0.000000e+00 0.000000e+00
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 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 1.975685e-20 9.878427e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 1, 1, 1

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, , 2, 2, 1, 1, 1

              [,1]         [,2]
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 [9,] 0.000000e+00 0.000000e+00
[10,] 3.951371e-20 1.975685e-20
[11,] 3.951371e-20 1.975685e-20
[12,] 1.975685e-20 9.878427e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 2, 1, 1

      [,1] [,2]
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, , 2, 1, 2, 1, 1

              [,1]         [,2]
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[11,] 0.000000e+00 0.000000e+00
[12,] 1.317124e-20 6.585618e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 2, 1, 1

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, , 2, 2, 2, 1, 1

              [,1]         [,2]
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 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 2.634247e-20 1.317124e-20
[11,] 2.634247e-20 1.317124e-20
[12,] 1.317124e-20 6.585618e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 3, 1, 1

      [,1] [,2]
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, , 2, 1, 3, 1, 1

              [,1]         [,2]
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 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
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 [7,] 0.000000e+00 0.000000e+00
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 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 3.292809e-20 1.646404e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 3, 1, 1

      [,1] [,2]
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, , 2, 2, 3, 1, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 6.585618e-20 3.292809e-20
[11,] 6.585618e-20 3.292809e-20
[12,] 3.292809e-20 1.646404e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 4, 1, 1

      [,1] [,2]
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, , 2, 1, 4, 1, 1

      [,1]         [,2]
 [1,]    0 0.000000e+00
 [2,]    0 0.000000e+00
 [3,]    0 0.000000e+00
 [4,]    0 0.000000e+00
 [5,]    0 0.000000e+00
 [6,]    0 0.000000e+00
 [7,]    0 0.000000e+00
 [8,]    0 0.000000e+00
 [9,]    0 0.000000e+00
[10,]    0 0.000000e+00
[11,]    0 0.000000e+00
[12,]    0 1.852205e-20
[13,]    0 0.000000e+00
[14,]    0 0.000000e+00

, , 1, 2, 4, 1, 1

      [,1] [,2]
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, , 2, 2, 4, 1, 1

      [,1]         [,2]
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 [9,]    0 0.000000e+00
[10,]    0 2.315256e-20
[11,]    0 2.315256e-20
[12,]    0 9.261025e-21
[13,]    0 0.000000e+00
[14,]    0 0.000000e+00

, , 1, 1, 1, 2, 1

      [,1] [,2]
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, , 2, 1, 1, 2, 1

              [,1]         [,2]
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[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
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[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 1, 2, 1

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, , 2, 2, 1, 2, 1

              [,1]         [,2]
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[11,] 2.634247e-20 1.317124e-20
[12,] 1.317124e-20 6.585618e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 2, 2, 1

      [,1] [,2]
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, , 2, 1, 2, 2, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
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 [4,] 0.000000e+00 0.000000e+00
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 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 8.780824e-21 4.390412e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 2, 2, 1

      [,1] [,2]
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, , 2, 2, 2, 2, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 1.756165e-20 8.780824e-21
[11,] 1.756165e-20 8.780824e-21
[12,] 8.780824e-21 4.390412e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 3, 2, 1

      [,1] [,2]
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, , 2, 1, 3, 2, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
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, , 1, 2, 3, 2, 1

      [,1] [,2]
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, , 2, 2, 3, 2, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
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[10,] 4.390412e-20 2.195206e-20
[11,] 4.390412e-20 2.195206e-20
[12,] 2.195206e-20 1.097603e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 4, 2, 1

      [,1] [,2]
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, , 2, 1, 4, 2, 1

      [,1]         [,2]
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[11,]    0 0.000000e+00
[12,]    0 1.234803e-20
[13,]    0 0.000000e+00
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, , 1, 2, 4, 2, 1

      [,1] [,2]
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, , 2, 2, 4, 2, 1

      [,1]         [,2]
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 [3,]    0 0.000000e+00
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[10,]    0 1.543504e-20
[11,]    0 1.543504e-20
[12,]    0 6.174017e-21
[13,]    0 0.000000e+00
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, , 1, 1, 1, 3, 1

      [,1] [,2]
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, , 2, 1, 1, 3, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
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[12,] 3.292809e-20 1.646404e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 1, 3, 1

      [,1] [,2]
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, , 2, 2, 1, 3, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
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 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 6.585618e-20 3.292809e-20
[11,] 6.585618e-20 3.292809e-20
[12,] 3.292809e-20 1.646404e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 2, 3, 1

      [,1] [,2]
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, , 2, 1, 2, 3, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
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 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 2.195206e-20 1.097603e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 2, 3, 1

      [,1] [,2]
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, , 2, 2, 2, 3, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
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 [7,] 0.000000e+00 0.000000e+00
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 [9,] 0.000000e+00 0.000000e+00
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[11,] 4.390412e-20 2.195206e-20
[12,] 2.195206e-20 1.097603e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 3, 3, 1

      [,1] [,2]
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, , 2, 1, 3, 3, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
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[12,] 5.488015e-20 2.744007e-20
[13,] 0.000000e+00 0.000000e+00
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, , 1, 2, 3, 3, 1

      [,1] [,2]
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, , 2, 2, 3, 3, 1

              [,1]         [,2]
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 [2,] 0.000000e+00 0.000000e+00
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[12,] 5.488015e-20 2.744007e-20
[13,] 0.000000e+00 0.000000e+00
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, , 1, 1, 4, 3, 1

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, , 2, 1, 4, 3, 1

      [,1]         [,2]
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, , 1, 2, 4, 3, 1

      [,1] [,2]
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, , 2, 2, 4, 3, 1

      [,1]         [,2]
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, , 1, 1, 1, 4, 1

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, , 2, 1, 1, 4, 1

             [,1]         [,2]
 [1,] 0.00000e+00 0.000000e+00
 [2,] 0.00000e+00 0.000000e+00
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, , 1, 2, 1, 4, 1

      [,1] [,2]
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, , 2, 2, 1, 4, 1

              [,1]         [,2]
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[11,] 4.630512e-20 2.315256e-20
[12,] 1.852205e-20 9.261025e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 2, 4, 1

      [,1] [,2]
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, , 2, 1, 2, 4, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
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[12,] 2.469607e-20 1.234803e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 2, 4, 1

      [,1] [,2]
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, , 2, 2, 2, 4, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
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[11,] 3.087008e-20 1.543504e-20
[12,] 1.234803e-20 6.174017e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 3, 4, 1

      [,1] [,2]
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, , 2, 1, 3, 4, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
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 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 6.174017e-20 3.087008e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 3, 4, 1

      [,1] [,2]
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, , 2, 2, 3, 4, 1

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 7.717521e-20 3.858760e-20
[11,] 7.717521e-20 3.858760e-20
[12,] 3.087008e-20 1.543504e-20
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 4, 4, 1

      [,1] [,2]
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, , 2, 1, 4, 4, 1

      [,1] [,2]
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, , 1, 2, 4, 4, 1

      [,1] [,2]
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, , 2, 2, 4, 4, 1

      [,1] [,2]
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, , 1, 1, 1, 1, 2

      [,1] [,2]
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 [7,]    0    0
 [8,]    0    0
 [9,]    0    0
[10,]    0    0
[11,]    0    0
[12,]    0    0
[13,]    0    0
[14,]    0    0

, , 2, 1, 1, 1, 2

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 1.975685e-20 9.878427e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 1, 1, 2

      [,1] [,2]
 [1,]    0    0
 [2,]    0    0
 [3,]    0    0
 [4,]    0    0
 [5,]    0    0
 [6,]    0    0
 [7,]    0    0
 [8,]    0    0
 [9,]    0    0
[10,]    0    0
[11,]    0    0
[12,]    0    0
[13,]    0    0
[14,]    0    0

, , 2, 2, 1, 1, 2

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 3.951371e-20 1.975685e-20
[11,] 3.951371e-20 1.975685e-20
[12,] 1.975685e-20 9.878427e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 2, 1, 2

      [,1] [,2]
 [1,]    0    0
 [2,]    0    0
 [3,]    0    0
 [4,]    0    0
 [5,]    0    0
 [6,]    0    0
 [7,]    0    0
 [8,]    0    0
 [9,]    0    0
[10,]    0    0
[11,]    0    0
[12,]    0    0
[13,]    0    0
[14,]    0    0

, , 2, 1, 2, 1, 2

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 0.000000e+00 0.000000e+00
[11,] 0.000000e+00 0.000000e+00
[12,] 1.317124e-20 6.585618e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 2, 2, 1, 2

      [,1] [,2]
 [1,]    0    0
 [2,]    0    0
 [3,]    0    0
 [4,]    0    0
 [5,]    0    0
 [6,]    0    0
 [7,]    0    0
 [8,]    0    0
 [9,]    0    0
[10,]    0    0
[11,]    0    0
[12,]    0    0
[13,]    0    0
[14,]    0    0

, , 2, 2, 2, 1, 2

              [,1]         [,2]
 [1,] 0.000000e+00 0.000000e+00
 [2,] 0.000000e+00 0.000000e+00
 [3,] 0.000000e+00 0.000000e+00
 [4,] 0.000000e+00 0.000000e+00
 [5,] 0.000000e+00 0.000000e+00
 [6,] 0.000000e+00 0.000000e+00
 [7,] 0.000000e+00 0.000000e+00
 [8,] 0.000000e+00 0.000000e+00
 [9,] 0.000000e+00 0.000000e+00
[10,] 2.634247e-20 1.317124e-20
[11,] 2.634247e-20 1.317124e-20
[12,] 1.317124e-20 6.585618e-21
[13,] 0.000000e+00 0.000000e+00
[14,] 0.000000e+00 0.000000e+00

, , 1, 1, 3, 1, 2

      [,1] [,2]
 [1,]    0    0
 [2,]    0    0
 [3,]    0    0
 [4,]    0    0
 [5,]    0    0
 [6,]    0    0
 [7,]    0    0
 [8,]    0    0
 [9,]    0    0
[10,]    0    0
[11,]    0    0
[12,]    0    0
[13,]    0    0
[14,]    0    0

, , 2, 1, 3, 1, 2


Created & Maintained by Osamu Ogasawara (osamu.ogasawara@gmail.com) and IMSBIO