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Last data update: 2014.03.03

R: performs the computation of triplet and individual weights...

weight.famdep

R Documentation

performs the computation of triplet and individual weights for a pedigree under familial dependence

Description

computes the triplet and the individual weights of the E step of the EM algorithm for a pedigree in the case of familial dependence. It returns also the overall log-likelihood of the observations. This is an internal function not meant to be called by the user.

Usage

weight.famdep(id, dad, mom, status, probs, fyc, peel)

Arguments

`id`	individual ID of the pedigree,
`dad`	dad ID,
`mom`	mom ID,
`status`	symptom status: (2: symptomatic, 1: without symptoms, 0: missing),
`probs`	list of 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,
`peel`	a list of pedigree peeling containing connectors by peeling order and couples of parents

Details

the function calls the functions upward and downward which perform the required probability computations by processing the pedigree by nuclear family (or equivalently by connector) following the peeling order.

Value

the function returns a list of 3 elements:

`ww`	triplet weights: an array of `n` times 2 times `K+1` times `K+1` times `K+1`, see `e.step`,
`w`	individual weights: an array of `n` times 2 times `K+1`, see `e.step`,
`ll`	log-likelihood.

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.

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]]
#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))
#the function
weight.famdep(id,dad,mom,status,probs,fyc,peel)

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.famdep.Rd_%03d_medium.png", width=480, height=480)
> ### Name: weight.famdep
> ### Title: performs the computation of triplet and individual weights for a
> ###   pedigree under familial dependence
> ### Aliases: weight.famdep
> 
> ### ** 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]]
> #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))
> #the function
> weight.famdep(id,dad,mom,status,probs,fyc,peel)
$ww
, , 1, 1, 1

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.041095020 0.000000000
 [3,] 0.042341796 0.000000000
 [4,] 0.009962177 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.042075246 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.038299929 0.000000000
 [9,] 0.055497327 0.000000000
[10,] 0.000000000 0.017297297
[11,] 0.000000000 0.017297297
[12,] 0.008648649 0.008648649
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 1, 1

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.955064e-19 0.000000000
 [3,] 2.429267e-34 0.000000000
 [4,] 5.091975e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 2.411431e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.243711e-16 0.000000000
 [9,] 3.988249e-12 0.000000000
[10,] 0.000000e+00 0.017297297
[11,] 0.000000e+00 0.017297297
[12,] 8.648649e-03 0.008648649
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 1, 1

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.247323e-03 0.000000000
 [3,] 5.458718e-07 0.000000000
 [4,] 3.238017e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 2.595312e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 2.926764e-02 0.000000000
 [9,] 1.207024e-02 0.000000000
[10,] 0.000000e+00 0.017297297
[11,] 0.000000e+00 0.017297297
[12,] 8.648649e-03 0.008648649
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 1, 1

      [,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

, , 1, 2, 1

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.041095020 0.000000000
 [3,] 0.042341796 0.000000000
 [4,] 0.009962177 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.042075246 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.038299929 0.000000000
 [9,] 0.055497327 0.000000000
[10,] 0.000000000 0.011531532
[11,] 0.000000000 0.011531532
[12,] 0.005765766 0.005765766
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 2, 1

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.955064e-19 0.000000000
 [3,] 2.429267e-34 0.000000000
 [4,] 5.091975e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 2.411431e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.243711e-16 0.000000000
 [9,] 3.988249e-12 0.000000000
[10,] 0.000000e+00 0.011531532
[11,] 0.000000e+00 0.011531532
[12,] 5.765766e-03 0.005765766
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 2, 1

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.247323e-03 0.000000000
 [3,] 5.458718e-07 0.000000000
 [4,] 3.238017e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 2.595312e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 2.926764e-02 0.000000000
 [9,] 1.207024e-02 0.000000000
[10,] 0.000000e+00 0.011531532
[11,] 0.000000e+00 0.011531532
[12,] 5.765766e-03 0.005765766
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 2, 1

      [,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

, , 1, 3, 1

             [,1]       [,2]
 [1,] 0.000000000 0.00000000
 [2,] 0.041095020 0.00000000
 [3,] 0.042341796 0.00000000
 [4,] 0.009962177 0.00000000
 [5,] 0.000000000 0.00000000
 [6,] 0.042075246 0.00000000
 [7,] 0.000000000 0.00000000
 [8,] 0.038299929 0.00000000
 [9,] 0.055497327 0.00000000
[10,] 0.000000000 0.02882883
[11,] 0.000000000 0.02882883
[12,] 0.014414414 0.01441441
[13,] 0.000000000 0.00000000
[14,] 0.000000000 0.00000000

, , 2, 3, 1

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 1.955064e-19 0.00000000
 [3,] 2.429267e-34 0.00000000
 [4,] 5.091975e-16 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 2.411431e-04 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 1.243711e-16 0.00000000
 [9,] 3.988249e-12 0.00000000
[10,] 0.000000e+00 0.02882883
[11,] 0.000000e+00 0.02882883
[12,] 1.441441e-02 0.01441441
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 3, 3, 1

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 1.247323e-03 0.00000000
 [3,] 5.458718e-07 0.00000000
 [4,] 3.238017e-02 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 2.595312e-05 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 2.926764e-02 0.00000000
 [9,] 1.207024e-02 0.00000000
[10,] 0.000000e+00 0.02882883
[11,] 0.000000e+00 0.02882883
[12,] 1.441441e-02 0.01441441
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 4, 3, 1

      [,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

, , 1, 4, 1

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.044592468 0.000000000
 [3,] 0.045945354 0.000000000
 [4,] 0.010810022 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.045656118 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.016851969 0.000000000
 [9,] 0.024418824 0.000000000
[10,] 0.000000000 0.006756757
[11,] 0.000000000 0.006756757
[12,] 0.005405405 0.002702703
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 4, 1

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 2.121452e-19 0.000000000
 [3,] 2.636013e-34 0.000000000
 [4,] 5.525335e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 2.616659e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 5.472329e-17 0.000000000
 [9,] 1.754830e-12 0.000000000
[10,] 0.000000e+00 0.006756757
[11,] 0.000000e+00 0.006756757
[12,] 5.405405e-03 0.002702703
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 4, 1

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.353478e-03 0.000000000
 [3,] 5.923290e-07 0.000000000
 [4,] 3.513592e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 2.816189e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.287776e-02 0.000000000
 [9,] 5.310906e-03 0.000000000
[10,] 0.000000e+00 0.006756757
[11,] 0.000000e+00 0.006756757
[12,] 5.405405e-03 0.002702703
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 4, 1

      [,1]        [,2]
 [1,]    0 0.000000000
 [2,]    0 0.000000000
 [3,]    0 0.000000000
 [4,]    0 0.000000000
 [5,]    0 0.000000000
 [6,]    0 0.000000000
 [7,]    0 0.000000000
 [8,]    0 0.000000000
 [9,]    0 0.000000000
[10,]    0 0.010135135
[11,]    0 0.010135135
[12,]    0 0.006081081
[13,]    0 0.000000000
[14,]    0 0.000000000

, , 1, 1, 2

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.027396680 0.000000000
 [3,] 0.028227864 0.000000000
 [4,] 0.006641451 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.028050164 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.025533286 0.000000000
 [9,] 0.036998218 0.000000000
[10,] 0.000000000 0.011531532
[11,] 0.000000000 0.011531532
[12,] 0.005765766 0.005765766
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 1, 2

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.303376e-19 0.000000000
 [3,] 1.619511e-34 0.000000000
 [4,] 3.394650e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 1.607620e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 8.291408e-17 0.000000000
 [9,] 2.658833e-12 0.000000000
[10,] 0.000000e+00 0.011531532
[11,] 0.000000e+00 0.011531532
[12,] 5.765766e-03 0.005765766
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 1, 2

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 8.315485e-04 0.000000000
 [3,] 3.639145e-07 0.000000000
 [4,] 2.158678e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 1.730208e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.951176e-02 0.000000000
 [9,] 8.046827e-03 0.000000000
[10,] 0.000000e+00 0.011531532
[11,] 0.000000e+00 0.011531532
[12,] 5.765766e-03 0.005765766
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 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

, , 1, 2, 2

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.027396680 0.000000000
 [3,] 0.028227864 0.000000000
 [4,] 0.006641451 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.028050164 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.025533286 0.000000000
 [9,] 0.036998218 0.000000000
[10,] 0.000000000 0.007687688
[11,] 0.000000000 0.007687688
[12,] 0.003843844 0.003843844
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 2, 2

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.303376e-19 0.000000000
 [3,] 1.619511e-34 0.000000000
 [4,] 3.394650e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 1.607620e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 8.291408e-17 0.000000000
 [9,] 2.658833e-12 0.000000000
[10,] 0.000000e+00 0.007687688
[11,] 0.000000e+00 0.007687688
[12,] 3.843844e-03 0.003843844
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 2, 2

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 8.315485e-04 0.000000000
 [3,] 3.639145e-07 0.000000000
 [4,] 2.158678e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 1.730208e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.951176e-02 0.000000000
 [9,] 8.046827e-03 0.000000000
[10,] 0.000000e+00 0.007687688
[11,] 0.000000e+00 0.007687688
[12,] 3.843844e-03 0.003843844
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 2, 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

, , 1, 3, 2

             [,1]       [,2]
 [1,] 0.000000000 0.00000000
 [2,] 0.027396680 0.00000000
 [3,] 0.028227864 0.00000000
 [4,] 0.006641451 0.00000000
 [5,] 0.000000000 0.00000000
 [6,] 0.028050164 0.00000000
 [7,] 0.000000000 0.00000000
 [8,] 0.025533286 0.00000000
 [9,] 0.036998218 0.00000000
[10,] 0.000000000 0.01921922
[11,] 0.000000000 0.01921922
[12,] 0.009609610 0.00960961
[13,] 0.000000000 0.00000000
[14,] 0.000000000 0.00000000

, , 2, 3, 2

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 1.303376e-19 0.00000000
 [3,] 1.619511e-34 0.00000000
 [4,] 3.394650e-16 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 1.607620e-04 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 8.291408e-17 0.00000000
 [9,] 2.658833e-12 0.00000000
[10,] 0.000000e+00 0.01921922
[11,] 0.000000e+00 0.01921922
[12,] 9.609610e-03 0.00960961
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 3, 3, 2

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 8.315485e-04 0.00000000
 [3,] 3.639145e-07 0.00000000
 [4,] 2.158678e-02 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 1.730208e-05 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 1.951176e-02 0.00000000
 [9,] 8.046827e-03 0.00000000
[10,] 0.000000e+00 0.01921922
[11,] 0.000000e+00 0.01921922
[12,] 9.609610e-03 0.00960961
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 4, 3, 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

, , 1, 4, 2

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.029728312 0.000000000
 [3,] 0.030630236 0.000000000
 [4,] 0.007206681 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.030437412 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.011234646 0.000000000
 [9,] 0.016279216 0.000000000
[10,] 0.000000000 0.004504505
[11,] 0.000000000 0.004504505
[12,] 0.003603604 0.001801802
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 4, 2

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 1.414302e-19 0.000000000
 [3,] 1.757342e-34 0.000000000
 [4,] 3.683557e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 1.744439e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 3.648219e-17 0.000000000
 [9,] 1.169886e-12 0.000000000
[10,] 0.000000e+00 0.004504505
[11,] 0.000000e+00 0.004504505
[12,] 3.603604e-03 0.001801802
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 4, 2

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 9.023186e-04 0.000000000
 [3,] 3.948860e-07 0.000000000
 [4,] 2.342395e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 1.877460e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 8.585174e-03 0.000000000
 [9,] 3.540604e-03 0.000000000
[10,] 0.000000e+00 0.004504505
[11,] 0.000000e+00 0.004504505
[12,] 3.603604e-03 0.001801802
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 4, 2

      [,1]        [,2]
 [1,]    0 0.000000000
 [2,]    0 0.000000000
 [3,]    0 0.000000000
 [4,]    0 0.000000000
 [5,]    0 0.000000000
 [6,]    0 0.000000000
 [7,]    0 0.000000000
 [8,]    0 0.000000000
 [9,]    0 0.000000000
[10,]    0 0.006756757
[11,]    0 0.006756757
[12,]    0 0.004054054
[13,]    0 0.000000000
[14,]    0 0.000000000

, , 1, 1, 3

            [,1]       [,2]
 [1,] 0.00000000 0.00000000
 [2,] 0.06849170 0.00000000
 [3,] 0.07056966 0.00000000
 [4,] 0.01660363 0.00000000
 [5,] 0.00000000 0.00000000
 [6,] 0.07012541 0.00000000
 [7,] 0.00000000 0.00000000
 [8,] 0.06383321 0.00000000
 [9,] 0.09249555 0.00000000
[10,] 0.00000000 0.02882883
[11,] 0.00000000 0.02882883
[12,] 0.01441441 0.01441441
[13,] 0.00000000 0.00000000
[14,] 0.00000000 0.00000000

, , 2, 1, 3

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 3.258440e-19 0.00000000
 [3,] 4.048778e-34 0.00000000
 [4,] 8.486625e-16 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 4.019051e-04 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 2.072852e-16 0.00000000
 [9,] 6.647082e-12 0.00000000
[10,] 0.000000e+00 0.02882883
[11,] 0.000000e+00 0.02882883
[12,] 1.441441e-02 0.01441441
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 3, 1, 3

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 2.078871e-03 0.00000000
 [3,] 9.097863e-07 0.00000000
 [4,] 5.396694e-02 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 4.325520e-05 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 4.877940e-02 0.00000000
 [9,] 2.011707e-02 0.00000000
[10,] 0.000000e+00 0.02882883
[11,] 0.000000e+00 0.02882883
[12,] 1.441441e-02 0.01441441
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 4, 1, 3

      [,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

, , 1, 2, 3

            [,1]       [,2]
 [1,] 0.00000000 0.00000000
 [2,] 0.06849170 0.00000000
 [3,] 0.07056966 0.00000000
 [4,] 0.01660363 0.00000000
 [5,] 0.00000000 0.00000000
 [6,] 0.07012541 0.00000000
 [7,] 0.00000000 0.00000000
 [8,] 0.06383321 0.00000000
 [9,] 0.09249555 0.00000000
[10,] 0.00000000 0.01921922
[11,] 0.00000000 0.01921922
[12,] 0.00960961 0.00960961
[13,] 0.00000000 0.00000000
[14,] 0.00000000 0.00000000

, , 2, 2, 3

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 3.258440e-19 0.00000000
 [3,] 4.048778e-34 0.00000000
 [4,] 8.486625e-16 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 4.019051e-04 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 2.072852e-16 0.00000000
 [9,] 6.647082e-12 0.00000000
[10,] 0.000000e+00 0.01921922
[11,] 0.000000e+00 0.01921922
[12,] 9.609610e-03 0.00960961
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 3, 2, 3

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 2.078871e-03 0.00000000
 [3,] 9.097863e-07 0.00000000
 [4,] 5.396694e-02 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 4.325520e-05 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 4.877940e-02 0.00000000
 [9,] 2.011707e-02 0.00000000
[10,] 0.000000e+00 0.01921922
[11,] 0.000000e+00 0.01921922
[12,] 9.609610e-03 0.00960961
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 4, 2, 3

      [,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

, , 1, 3, 3

            [,1]       [,2]
 [1,] 0.00000000 0.00000000
 [2,] 0.06849170 0.00000000
 [3,] 0.07056966 0.00000000
 [4,] 0.01660363 0.00000000
 [5,] 0.00000000 0.00000000
 [6,] 0.07012541 0.00000000
 [7,] 0.00000000 0.00000000
 [8,] 0.06383321 0.00000000
 [9,] 0.09249555 0.00000000
[10,] 0.00000000 0.04804805
[11,] 0.00000000 0.04804805
[12,] 0.02402402 0.02402402
[13,] 0.00000000 0.00000000
[14,] 0.00000000 0.00000000

, , 2, 3, 3

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 3.258440e-19 0.00000000
 [3,] 4.048778e-34 0.00000000
 [4,] 8.486625e-16 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 4.019051e-04 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 2.072852e-16 0.00000000
 [9,] 6.647082e-12 0.00000000
[10,] 0.000000e+00 0.04804805
[11,] 0.000000e+00 0.04804805
[12,] 2.402402e-02 0.02402402
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 3, 3, 3

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 2.078871e-03 0.00000000
 [3,] 9.097863e-07 0.00000000
 [4,] 5.396694e-02 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 4.325520e-05 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 4.877940e-02 0.00000000
 [9,] 2.011707e-02 0.00000000
[10,] 0.000000e+00 0.04804805
[11,] 0.000000e+00 0.04804805
[12,] 2.402402e-02 0.02402402
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 4, 3, 3

      [,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

, , 1, 4, 3

             [,1]        [,2]
 [1,] 0.000000000 0.000000000
 [2,] 0.074320780 0.000000000
 [3,] 0.076575589 0.000000000
 [4,] 0.018016703 0.000000000
 [5,] 0.000000000 0.000000000
 [6,] 0.076093530 0.000000000
 [7,] 0.000000000 0.000000000
 [8,] 0.028086614 0.000000000
 [9,] 0.040698040 0.000000000
[10,] 0.000000000 0.011261261
[11,] 0.000000000 0.011261261
[12,] 0.009009009 0.004504505
[13,] 0.000000000 0.000000000
[14,] 0.000000000 0.000000000

, , 2, 4, 3

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 3.535754e-19 0.000000000
 [3,] 4.393355e-34 0.000000000
 [4,] 9.208891e-16 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 4.361098e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 9.120548e-17 0.000000000
 [9,] 2.924716e-12 0.000000000
[10,] 0.000000e+00 0.011261261
[11,] 0.000000e+00 0.011261261
[12,] 9.009009e-03 0.004504505
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 4, 3

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 2.255797e-03 0.000000000
 [3,] 9.872149e-07 0.000000000
 [4,] 5.855987e-02 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 4.693649e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 2.146294e-02 0.000000000
 [9,] 8.851510e-03 0.000000000
[10,] 0.000000e+00 0.011261261
[11,] 0.000000e+00 0.011261261
[12,] 9.009009e-03 0.004504505
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 4, 3

      [,1]       [,2]
 [1,]    0 0.00000000
 [2,]    0 0.00000000
 [3,]    0 0.00000000
 [4,]    0 0.00000000
 [5,]    0 0.00000000
 [6,]    0 0.00000000
 [7,]    0 0.00000000
 [8,]    0 0.00000000
 [9,]    0 0.00000000
[10,]    0 0.01689189
[11,]    0 0.01689189
[12,]    0 0.01013514
[13,]    0 0.00000000
[14,]    0 0.00000000

, , 1, 1, 4

            [,1]        [,2]
 [1,] 0.00000000 0.000000000
 [2,] 0.13698340 0.000000000
 [3,] 0.14113932 0.000000000
 [4,] 0.03320726 0.000000000
 [5,] 0.00000000 0.000000000
 [6,] 0.14025082 0.000000000
 [7,] 0.00000000 0.000000000
 [8,] 0.04255548 0.000000000
 [9,] 0.06166370 0.000000000
[10,] 0.00000000 0.020270270
[11,] 0.00000000 0.020270270
[12,] 0.01621622 0.008108108
[13,] 0.00000000 0.000000000
[14,] 0.00000000 0.000000000

, , 2, 1, 4

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 6.516880e-19 0.000000000
 [3,] 8.097557e-34 0.000000000
 [4,] 1.697325e-15 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 8.038102e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.381901e-16 0.000000000
 [9,] 4.431388e-12 0.000000000
[10,] 0.000000e+00 0.020270270
[11,] 0.000000e+00 0.020270270
[12,] 1.621622e-02 0.008108108
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 1, 4

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 4.157743e-03 0.000000000
 [3,] 1.819573e-06 0.000000000
 [4,] 1.079339e-01 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 8.651040e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 3.251960e-02 0.000000000
 [9,] 1.341138e-02 0.000000000
[10,] 0.000000e+00 0.020270270
[11,] 0.000000e+00 0.020270270
[12,] 1.621622e-02 0.008108108
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 1, 4

      [,1]       [,2]
 [1,]    0 0.00000000
 [2,]    0 0.00000000
 [3,]    0 0.00000000
 [4,]    0 0.00000000
 [5,]    0 0.00000000
 [6,]    0 0.00000000
 [7,]    0 0.00000000
 [8,]    0 0.00000000
 [9,]    0 0.00000000
[10,]    0 0.03040541
[11,]    0 0.03040541
[12,]    0 0.01824324
[13,]    0 0.00000000
[14,]    0 0.00000000

, , 1, 2, 4

            [,1]        [,2]
 [1,] 0.00000000 0.000000000
 [2,] 0.13698340 0.000000000
 [3,] 0.14113932 0.000000000
 [4,] 0.03320726 0.000000000
 [5,] 0.00000000 0.000000000
 [6,] 0.14025082 0.000000000
 [7,] 0.00000000 0.000000000
 [8,] 0.04255548 0.000000000
 [9,] 0.06166370 0.000000000
[10,] 0.00000000 0.013513514
[11,] 0.00000000 0.013513514
[12,] 0.01081081 0.005405405
[13,] 0.00000000 0.000000000
[14,] 0.00000000 0.000000000

, , 2, 2, 4

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 6.516880e-19 0.000000000
 [3,] 8.097557e-34 0.000000000
 [4,] 1.697325e-15 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 8.038102e-04 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 1.381901e-16 0.000000000
 [9,] 4.431388e-12 0.000000000
[10,] 0.000000e+00 0.013513514
[11,] 0.000000e+00 0.013513514
[12,] 1.081081e-02 0.005405405
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 3, 2, 4

              [,1]        [,2]
 [1,] 0.000000e+00 0.000000000
 [2,] 4.157743e-03 0.000000000
 [3,] 1.819573e-06 0.000000000
 [4,] 1.079339e-01 0.000000000
 [5,] 0.000000e+00 0.000000000
 [6,] 8.651040e-05 0.000000000
 [7,] 0.000000e+00 0.000000000
 [8,] 3.251960e-02 0.000000000
 [9,] 1.341138e-02 0.000000000
[10,] 0.000000e+00 0.013513514
[11,] 0.000000e+00 0.013513514
[12,] 1.081081e-02 0.005405405
[13,] 0.000000e+00 0.000000000
[14,] 0.000000e+00 0.000000000

, , 4, 2, 4

      [,1]       [,2]
 [1,]    0 0.00000000
 [2,]    0 0.00000000
 [3,]    0 0.00000000
 [4,]    0 0.00000000
 [5,]    0 0.00000000
 [6,]    0 0.00000000
 [7,]    0 0.00000000
 [8,]    0 0.00000000
 [9,]    0 0.00000000
[10,]    0 0.02027027
[11,]    0 0.02027027
[12,]    0 0.01216216
[13,]    0 0.00000000
[14,]    0 0.00000000

, , 1, 3, 4

            [,1]       [,2]
 [1,] 0.00000000 0.00000000
 [2,] 0.13698340 0.00000000
 [3,] 0.14113932 0.00000000
 [4,] 0.03320726 0.00000000
 [5,] 0.00000000 0.00000000
 [6,] 0.14025082 0.00000000
 [7,] 0.00000000 0.00000000
 [8,] 0.04255548 0.00000000
 [9,] 0.06166370 0.00000000
[10,] 0.00000000 0.03378378
[11,] 0.00000000 0.03378378
[12,] 0.02702703 0.01351351
[13,] 0.00000000 0.00000000
[14,] 0.00000000 0.00000000

, , 2, 3, 4

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 6.516880e-19 0.00000000
 [3,] 8.097557e-34 0.00000000
 [4,] 1.697325e-15 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 8.038102e-04 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 1.381901e-16 0.00000000
 [9,] 4.431388e-12 0.00000000
[10,] 0.000000e+00 0.03378378
[11,] 0.000000e+00 0.03378378
[12,] 2.702703e-02 0.01351351
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 3, 3, 4

              [,1]       [,2]
 [1,] 0.000000e+00 0.00000000
 [2,] 4.157743e-03 0.00000000
 [3,] 1.819573e-06 0.00000000
 [4,] 1.079339e-01 0.00000000
 [5,] 0.000000e+00 0.00000000
 [6,] 8.651040e-05 0.00000000
 [7,] 0.000000e+00 0.00000000
 [8,] 3.251960e-02 0.00000000
 [9,] 1.341138e-02 0.00000000
[10,] 0.000000e+00 0.03378378
[11,] 0.000000e+00 0.03378378
[12,] 2.702703e-02 0.01351351
[13,] 0.000000e+00 0.00000000
[14,] 0.000000e+00 0.00000000

, , 4, 3, 4

      [,1]       [,2]
 [1,]    0 0.00000000
 [2,]    0 0.00000000
 [3,]    0 0.00000000
 [4,]    0 0.00000000
 [5,]    0 0.00000000
 [6,]    0 0.00000000
 [7,]    0 0.00000000
 [8,]    0 0.00000000
 [9,]    0 0.00000000
[10,]    0 0.05067568
[11,]    0 0.05067568
[12,]    0 0.03040541
[13,]    0 0.00000000
[14,]    0 0.00000000

, , 1, 4, 4

      [,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, 4, 4

      [,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

, , 3, 4, 4

      [,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

, , 4, 4, 4

      [,1]       [,2]
 [1,]    0 0.00000000
 [2,]    0 0.00000000
 [3,]    0 0.00000000
 [4,]    0 0.00000000
 [5,]    0 0.00000000
 [6,]    0 0.00000000
 [7,]    0 0.00000000
 [8,]    0 0.00000000
 [9,]    0 0.00000000
[10,]    0 0.01801802
[11,]    0 0.01801802
[12,]    0 0.01801802
[13,]    0 0.00000000
[14,]    0 0.00000000


$w
, , 1

           [,1]       [,2]
 [1,] 0.0000000 0.17297297
 [2,] 0.9705420 0.00000000
 [3,] 0.9999871 0.00000000
 [4,] 0.2352769 0.00000000
 [5,] 0.0000000 0.17297297
 [6,] 0.9936920 0.00000000
 [7,] 0.1549550 0.07747748
 [8,] 0.5668389 0.00000000
 [9,] 0.8213604 0.00000000
[10,] 0.0000000 0.28228228
[11,] 0.0000000 0.28228228
[12,] 0.1681682 0.13213213
[13,] 0.1761261 0.08806306
[14,] 0.0000000 0.20337838

, , 2

              [,1]       [,2]
 [1,] 0.000000e+00 0.11531532
 [2,] 4.617279e-18 0.00000000
 [3,] 5.737205e-33 0.00000000
 [4,] 1.202573e-14 0.00000000
 [5,] 0.000000e+00 0.11531532
 [6,] 5.695081e-03 0.00000000
 [7,] 1.033033e-01 0.05165165
 [8,] 1.840692e-15 0.00000000
 [9,] 5.902609e-11 0.00000000
[10,] 0.000000e+00 0.28228228
[11,] 0.000000e+00 0.28228228
[12,] 1.681682e-01 0.13213213
[13,] 1.174174e-01 0.05870871
[14,] 0.000000e+00 0.13558559

, , 3

              [,1]      [,2]
 [1,] 0.000000e+00 0.2882883
 [2,] 2.945805e-02 0.0000000
 [3,] 1.289187e-05 0.0000000
 [4,] 7.647231e-01 0.0000000
 [5,] 0.000000e+00 0.2882883
 [6,] 6.129354e-04 0.0000000
 [7,] 2.582583e-01 0.1291291
 [8,] 4.331611e-01 0.0000000
 [9,] 1.786396e-01 0.