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## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Copyright (C) 2012 - 2022 Reza Mohammadi |
# |
# This file is part of BDgraph package. |
# |
# BDgraph is free software: you can redistribute it and/or modify it under |
# the terms of the GNU General Public License as published by the Free |
# Software Foundation; see <https://cran.r-project.org/web/licenses/GPL-3>.|
# |
# Maintainer: Reza Mohammadi <a.mohammadi@uva.nl> |
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Data generator according to the graph structure |
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
bdgraph.sim = function( p = 10, graph = "random", n = 0, type = "Gaussian",
prob = 0.2, size = NULL, mean = 0, class = NULL,
cut = 4, b = 3, D = diag( p ), K = NULL, sigma = NULL,
q = exp( -1 ), beta = 1, vis = FALSE, rewire = 0.05,
range.mu = c( 3, 5 ), range.dispersion = c( 0.01, 0.1 ),
nu = 1 )
{
if( p < 2 ) stop( "'p' must be greater than 1" )
if( ( prob < 0 ) | ( prob > 1 ) ) stop( "'prob' must be between ( 0, 1 )" )
if( cut < 2 ) stop( "'cut' must be greater than 1" )
if( b <= 2 ) stop( "'b' must be greater than 2" )
if( ( rewire < 0 ) | ( rewire > 1 ) ) stop( "'rewire' must be between ( 0, 1 )" )
if( length( range.mu ) != 2 ) stop( "'range.mu' must be a vector with length 2" )
if( length( range.dispersion ) != 2 ) stop( "'range.dispersion' must be a vector with length 2" )
if( inherits( graph, "graph" ) ) graph = unclass( graph )
if( is.matrix( graph ) & is.matrix( K ) ) if( nrow( graph ) != nrow( K ) ) stop( "'graph' and 'K' have non-conforming size" )
if( !is.null( size ) )
if( ( sum( size ) < 0 ) | ( sum( size ) > ( p * ( p - 1 ) / 2 ) ) ) stop( "'size' must be between ( 0, p*(p-1)/2 )" )
if( is.matrix( K ) )
{
if( !isSymmetric( K ) ) stop( "'K' must be a positive definite matrix" )
graph <- "fixed"
p <- nrow( K )
}
if( type == "normal" ) type = "Gaussian"
if( type == "non-normal" ) type = "non-Gaussian"
#if( type == "discrete" ) type = "count"
if( ( type == "categorical" ) & ( cut == 2 ) ) type = "binary"
if( is.matrix( graph ) )
{
if( !isSymmetric( graph ) ) stop( "'graph' must be symmetric matrix" )
p = nrow( graph )
if( ( graph != 0 ) && ( graph != 1 ) ) stop( "Elements of matrix 'graph' must be 0 or 1" )
G <- graph
graph <- "fixed"
}
# - - build the graph structure - - - - - - - - - - - - - - - - - - - - - -|
if( !any( graph == c( "fixed", "AR1", "AR2", "circle" ) ) )
G <- BDgraph::graph.sim( p = p, graph = graph, prob = prob, size = size, class = class, rewire = rewire )
if( graph == "AR1" )
{
sigma = matrix( 0, p, p )
for( i in 1 : ( p - 1 ) )
for( j in ( i + 1 ) : p )
sigma[ i, j ] = ( 0.7 ) ^ abs( i - j )
sigma = sigma + t( sigma ) + diag( p )
K = solve( sigma )
G = 1 * ( abs( K ) > 0.02 )
}
if( graph == "AR2" )
{
K = stats::toeplitz( c( 1, 0.5, 0.25, rep( 0, p - 3 ) ) )
G = 1 * ( abs( K ) > 0.02 )
}
if( graph == "circle" )
{
K <- stats::toeplitz( c( 1, 0.5, rep( 0, p - 2 ) ) )
K[ 1, p ] <- 0.4
K[ p, 1 ] <- 0.4
G = 1 * ( abs( K ) > 0.02 )
}
# - - generate multivariate data according to the graph structure - - - - -|
if( n != 0 )
{
if( !is.null( sigma ) ) K <- solve( sigma )
if( is.matrix( K ) )
{
G = 1 * ( abs( K ) > 0.02 )
diag( G ) = 0
# if( is.null( sigma ) ) sigma <- solve( K )
if( is.null( sigma ) )
sigma = stats::cov2cor( solve( K ) )
}else{
# - - Generate precision matrix according to the graph structure - |
if( !isSymmetric( D ) )
stop( "'D' must be a positive definite matrix" )
Ti = chol( solve( D ) )
diag( G ) = 0
K = matrix( 0, p, p )
threshold = 1e-8 # for "rgwish_c" function in C++
result = .C( "rgwish_c", as.integer(G), as.double(Ti), K = as.double(K),
as.integer(b), as.integer(p), as.double(threshold), PACKAGE = "BDgraph" )
K = matrix( result $ K, p, p )
# sigma = solve( K )
sigma = stats::cov2cor( solve( K ) )
K = solve( sigma )
}
# - - generate multivariate normal data - - - - - - - - - - - - - - - -|
d <- BDgraph::rmvnorm( n = n, mean = mean, sigma = sigma )
# - - generate multivariate mixed data - - - - - - - - - - - - - - - - |
not.cont = numeric( p )
if( type == "mixed" )
{
# generating mixed data which are 'count', 'ordinal', 'non-Gaussian',
# 'binary', and 'Gaussian', respectively.
ps = floor( p / 5 )
# generating count data
col_number <- c( 1:ps )
prob <- stats::pnorm( d[ , col_number ] )
d[ , col_number ] <- stats::qpois( p = prob, lambda = 10 )
not.cont[ 1:ps ] = 1
# generating ordinal data
col_number <- c( ( ps + 1 ):( 2 * ps ) )
prob <- stats::pnorm( d[ , col_number ] )
d[ , col_number ] <- stats::qpois( p = prob, lambda = 2 )
not.cont[ c( ( ps + 1 ):( 2 * ps ) ) ] = 1
# generating non-Gaussian data
col_number <- c( ( 2 * ps + 1 ):( 3 * ps ) )
prob <- stats::pnorm( d[ , col_number ] )
d[ ,col_number ] <- stats::qexp( p = prob, rate = 10 )
# for binary data
col_number <- c( ( 3 * ps + 1 ):( 4 * ps ) )
prob <- stats::pnorm( d[ , col_number ] )
d[ , col_number ] <- stats::qbinom( p = prob, size = 1, prob = 0.5 )
not.cont[ c( ( 3 * ps + 1 ):( 4 * ps ) ) ] = 1
}
# - - generate multivariate continuous non-Gaussian data - - - - - - - |
if( type == "non-Gaussian" )
{
# generating multivariate continuous non-Gaussian data
prob <- stats::pnorm( d )
d <- stats::qexp( p = prob, rate = 10 )
}
# - - To generate multivariate data from T-distribution - - - - - - - |
if( type == "t" )
{
tau_gamma = stats::rgamma( n, shape = nu / 2, rate = nu / 2 )
d = mean + d / sqrt( tau_gamma )
}
if ( type == "alternative-t" )
{
taugamma = stats::rgamma( n * p, shape = nu / 2, rate = nu / 2 )
taugamma = matrix( taugamma, n, p )
d = mean + d / sqrt( taugamma )
}
# - - generate multivariate count data - - - - - - - - - - - - - - - - |
if( type == "categorical" )
{
not.cont[ 1:p ] = 1
runif_m = matrix( stats::runif( cut * p ), nrow = p, ncol = cut )
marginals = apply( runif_m, 1, function( x ) { stats::qnorm( cumsum( x / sum( x ) )[ -length( x ) ] ) } )
if( cut == 2 )
marginals = matrix( marginals, nrow = 1, ncol = p )
for( j in 1:p )
{
breaks <- c( min( d[ , j ] ) - 1, marginals[ , j ], max( d[ , j ] ) + 1 )
d[ , j ] <- as.integer( cut( d[ , j ], breaks = breaks, right = FALSE ) )
}
d = d - 1
}
if( type == "binary" )
{
not.cont[ 1:p ] = 1
if( p > 16 )
stop( "'p' must be less than 16, for option 'type = \"binary\"'" )
## Generate clique factors
clique_factors = generate_clique_factors( ug = G )
d = sample_ug( n = n, ug = G, clique_factors = clique_factors )
d = d - 1
}
if((type == "dweibull") | (type == "dw"))
{
if(length(q ) == 1) q = rep(q , time = p)
if(length(beta) == 1) beta = rep(beta, time = p)
# q & beta can be a vector of length p (one for each Y variable)
if(is.vector(q ) && (length(q ) != p)) stop("'q', as a vector, has non-conforming size with 'p'" )
if(is.vector(beta) && (length(beta) != p)) stop("'beta', as a vector, has non-conforming size with 'p'")
# or an n x p matrix (in the case of covariates)
if(is.matrix(q ) && any(dim( q ) != c(n, p))) stop("'q', as a matrix, has non-conforming size with 'n' and 'p'")
if(is.matrix(beta) && any(dim( beta) != c(n, p))) stop("'beta', as a matrix, has non-conforming size with 'n' and 'p'")
not.cont[1:p] = 1
Y_data <- matrix(c(0, 1), nrow = n, ncol = p)
# To detect binary variables
# while( any( apply( Y_data, 2, function( x ) { all( x %in% 0:1 ) } ) ) == TRUE ) {
Z = tmvtnorm::rtmvnorm(n = n, mean = rep(mean, p), sigma = sigma, lower = rep(-5, length = p), upper = rep(5, length = p))
pnorm_Z = stats::pnorm(Z)
if(is.matrix(q) && is.matrix(beta))
for(j in 1:p)
Y_data[, j] = BDgraph::qdweibull(pnorm_Z[, j], q = q[, j], beta = beta[, j], zero = TRUE)
if(is.vector(q) && is.vector(beta))
for(j in 1:p)
Y_data[, j] = BDgraph::qdweibull( pnorm_Z[, j], q = q[j], beta = beta[j], zero = TRUE)
if( any( apply( Y_data, 2, function( x ) { all( x %in% 0 : 1 ) } ) ) ) cat( " Some of the variables are binary \n" )
d = Y_data
}
if( ( type == "nbinom" ) | ( type == "NB" ) )
{
not.cont[ 1:p ] = 1
Y.star <- matrix( c( 0, 1 ), nrow = n, ncol = p )
# To detect binary variables
while ( any( apply( Y.star, 2, function( x ) { all( x %in% 0:1 ) } ) ) == TRUE )
{
d = tmvtnorm::rtmvnorm( n = n, mean = rep( mean, p ), sigma = sigma,
lower = rep( -5, length = p ), upper = rep( 5, length = p ) )
#mu <- stats::runif( n = p, min = 0.5, max = 5 )
#size <- stats::runif( n = p, min = 0.1, max = 3 )
mu = stats::runif( n = p, min = range.mu[ 1 ], max = range.mu[ 2 ] )
size = stats::runif( n = p, min = range.dispersion[ 1 ], max = range.dispersion[ 2 ] )
for(j in 1 : p )
Y.star[ , j ] = stats::qnbinom( stats::pnorm( d[ , j ] ), size = size[ j ],
mu = mu[ j ], lower.tail = TRUE, log.p = FALSE )
# cat( "any binary variables ", any( apply( Y , 2, function( x ) { all( x %in% 0:1 ) }) ) , "\n" )
}
d = Y.star
}
if( ( type == "pois" ) | ( type == "count" ) )
{
not.cont[ 1:p ] = 1
Y.star = matrix( c( 0, 1 ), nrow = n, ncol = p )
while( any( apply( Y.star, 2, function( x ) { all( x %in% 0:1 ) } ) ) == TRUE ) ##detect binary variables
{
d = tmvtnorm::rtmvnorm( n = n, mean = rep( mean, p ), sigma = sigma,
lower = rep( -5, length = p ), upper = rep( 5, length = p ) )
#lambda = stats::runif( n = p, min = 2, max = 3 )
#lambda = stats::runif( n = p, min = 2, max = 5 )
lambda = stats::runif( n = p, min = range.mu[ 1 ], max = range.mu[ 2 ] )
for(j in 1 : p )
Y.star[ , j ] = stats::qpois( stats::pnorm( d[ , j ] ), lambda = lambda[ j ], lower.tail = TRUE, log.p = FALSE )
}
d = Y.star
}
}
# - - Saving the result - - - - - - - - - - - - - - - - - - - - - - - - - -|
if( n != 0 )
{
if( type != "dw" ){
simulation <- list( G = G, graph = graph, data = d, sigma = sigma, K = K, type = type, not.cont = not.cont )
}else{
simulation <- list( G = G, graph = graph, data = d, sigma = sigma, K = K, type = type, not.cont = not.cont,
beta = beta, q = q )
}
}else{
simulation <- list( G = G, graph = graph )
}
# - - graph visualization - - - - - - - - - - - - - - - - - - - - - - - - -|
if( vis == TRUE )
BDgraph::plot.graph( G, main = "Graph structure" )
class( simulation ) <- "sim"
return( simulation )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Print function for simulation data
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
print.sim = function( x, ... )
{
p = ncol( x $ G )
sum_G = sum( x $ G )
cat( paste( " graph generated by bdgraph.sim" ), fill = TRUE )
if( !is.null( x $ type ) )
{
cat( paste( " Data type =", x $ type ), fill = TRUE )
cat( paste( " Sample size =", nrow( x $ data ) ), fill = TRUE )
}
cat( paste( " Graph type =", x $ graph ), fill = TRUE )
cat( paste( " Number of nodes =", p ), fill = TRUE )
cat( paste( " Graph size =", sum_G / 2 ), fill = TRUE )
cat( paste( " Sparsity =", round( BDgraph::sparsity( x ), 4 ) ), fill = TRUE )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# plot for class "sim" from bdgraph.sim function
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
plot.sim = function( x, ... )
{
BDgraph::plot.graph( x, ... )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
# Function for exact sampling from binary data
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
sample_ug = function( n = 1, ug = diag( 3 ), clique_factors = NULL )
{
p = ncol( ug ) # p smaller than 17 check
if( p > 16 )
stop( "number of nodes must be smaller than 16" )
ug[ lower.tri( ug, diag = TRUE ) ] = 0
if( is.null( clique_factors ) )
clique_factors = generate_clique_factors( ug )
prob = calc_joint_dist( ug, clique_factors )
noc = length( prob )
ind = sample( 1:noc, n, replace = TRUE, prob = prob )
oc = sapply( 1:noc, function( x ){ as.integer( intToBits( x ) ) } )
oc = 2 - t( oc[ 1:p, ] )
data = oc[ ind, ]
return( data )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
generate_clique_factors = function( ug )
{
ug[ lower.tri( ug, diag = TRUE ) ] = 0
p = ncol( ug )
edges = which( ug == 1, arr.ind = T )
a = igraph::make_undirected_graph( c( t( edges ) ), p )
cliques = igraph::max_cliques( a )
clique_factors = vector( 'list', length( cliques ) )
for ( i in 1:length( cliques ) )
{
clq = cliques[[i]]
clique_factors[[i]] = stats::runif( 2 ^ length( clq ) )
}
return( clique_factors )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
calc_joint_dist = function( ug, clique_factors )
{
p = ncol( ug )
oc = sapply( 1:( 2 ^ p ), function( x ){ as.integer( intToBits( x ) ) } )
oc = 2 - t( oc[ 1:p, ] )
edges = which( ug == 1, arr.ind = T )
a = igraph::make_undirected_graph( c( t( edges ) ), p )
joint_dist = rep( 1, 2 ^ p )
cliques = igraph::max_cliques( a )
for ( i in 1:length( cliques ) )
{
clq = cliques[[i]]
k = length( clq )
temp = sapply( 1:( 2 ^ k ), function( x ){ as.integer( intToBits( x ) ) } )
clq_oc = 2 - t( temp[1:k, ] )
clq_factor = clique_factors[[i]]
for ( j in 1:nrow( clq_oc ) )
{
oc_col_clq = oc[ , clq ]
if( is.null( dim( oc_col_clq ) ) )
oc_col_clq = matrix( oc_col_clq, nrow = length( oc_col_clq ), ncol = 1 )
ind = apply( oc_col_clq, 1, identical, clq_oc[ j, ] )
joint_dist[ind] = joint_dist[ ind ] * clq_factor[ j ]
}
}
joint_dist = joint_dist / sum( joint_dist )
return( joint_dist )
}
## - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
|
