https://github.com/cran/BDgraph
Revision c17dc94109f661b2a40cc99b32bfc6bbd93e9077 authored by Reza Mohammadi on 19 March 2019, 22:53:32 UTC, committed by cran-robot on 19 March 2019, 22:53:32 UTC
1 parent 123fcf5
Tip revision: c17dc94109f661b2a40cc99b32bfc6bbd93e9077 authored by Reza Mohammadi on 19 March 2019, 22:53:32 UTC
version 2.56
version 2.56
Tip revision: c17dc94
gm_rj.cpp
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Copyright (C) 2012 - 2019 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> |
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
#include "matrix.h"
#include "rgwish.h"
#include "copula.h"
extern "C" {
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Computing alpha (probability of acceptance) in RJ-MCMC algorithm
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void log_alpha_rjmcmc( double *log_alpha_ij, double log_ratio_g_prior[], int *selected_edge_i,
int *selected_edge_j, int G[], double Ds[],
double sigma[], double sigma21[], double sigma22[], double sigmaj12[], double sigmaj22[],
double K[], double K21[], double K121[], double Kj12[],
double K12xK22_inv[], double Kj12xK22_inv[], double sigma11_inv[],
double sigma21xsigma11_inv[], int *b, int *p )
{
int one = 1, two = 2, dim = *p, dim1 = dim + 1, p1 = dim - 1, p2 = dim - 2;
double alpha = 1.0, beta = 0.0, alpha1 = -1.0, beta1 = 1.0;
char transT = 'T', transN = 'N', sideL = 'L';
int ij = *selected_edge_j * dim + *selected_edge_i;
int jj = *selected_edge_j * dim1;
double Dsij = Ds[ ij ];
double Dsjj = Ds[ jj ];
sub_matrices1( &sigma[0], &sigmaj12[0], &sigmaj22[0], selected_edge_j, &dim );
// sigma[-j,-j] - ( sigma[-j, j] %*% sigma[j, -j] ) / sigma[j,j]
// Kj22_inv <- sigmaj22 = sigmaj22 - sigmaj12 * sigmaj12 / sigmaj11
double sigmajj_inv = - 1.0 / sigma[jj];
F77_NAME(dsyr)( &sideL, &p1, &sigmajj_inv, &sigmaj12[0], &one, &sigmaj22[0], &p1 );
// For (i,j) = 0 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
sub_row_mins( K, &Kj12[0], selected_edge_j, &dim ); // Kj12 = K[j, -j]
Kj12[ *selected_edge_i ] = 0.0; // Kj12[1,i] = 0
// Kj12xK22_inv = Kj12 %*% Kj22_inv here sigmaj22 instead of Kj22_inv
F77_NAME(dsymv)( &sideL, &p1, &alpha, &sigmaj22[0], &p1, &Kj12[0], &one, &beta, &Kj12xK22_inv[0], &one );
// K022 = Kj12xK22_inv %*% t(Kj12)
double K022 = F77_NAME(ddot)( &p1, &Kj12xK22_inv[0], &one, &Kj12[0], &one );
// For (i,j) = 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
sub_cols_mins( K, &K21[0], selected_edge_i, selected_edge_j, &dim ); // K21 = K[-e, e]
sub_matrices_inv( &sigma[0], &sigma11_inv[0], &sigma21[0], &sigma22[0], selected_edge_i, selected_edge_j, &dim );
// sigma21xsigma11_inv = sigma21 %*% sigma11_inv
F77_NAME(dgemm)( &transN, &transN, &p2, &two, &two, &alpha, &sigma21[0], &p2, &sigma11_inv[0], &two, &beta, &sigma21xsigma11_inv[0], &p2 );
// sigma22 = sigma22 - sigma21xsigma11_inv %*% t( sigma21 )
F77_NAME(dgemm)( &transN, &transT, &p2, &p2, &two, &alpha1, &sigma21xsigma11_inv[0], &p2, &sigma21[0], &p2, &beta1, &sigma22[0], &p2 );
// K12xK22_inv = t( K21 ) %*% K22_inv here sigam12 = K22_inv
F77_NAME(dgemm)( &transT, &transN, &two, &p2, &p2, &alpha, &K21[0], &p2, &sigma22[0], &p2, &beta, &K12xK22_inv[0], &two );
// K121 = K12xK22_inv %*% K21
F77_NAME(dgemm)( &transN, &transN, &two, &two, &p2, &alpha, &K12xK22_inv[0], &two, &K21[0], &p2, &beta, &K121[0], &two );
// Finished (i,j) = 1- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
double a11 = K[*selected_edge_i * dim1] - K121[0];
double sum_diag = Dsjj * ( K022 - K121[3] ) - Dsij * ( K121[1] + K121[2] );
// nu_star = b + sum( Gf[,i] * Gf[,j] )
int nu_star = *b;
for( int k = 0; k < dim; k++ )
nu_star += G[*selected_edge_i * dim + k] * G[*selected_edge_j * dim + k];
nu_star = 0.5 * nu_star;
// *log_alpha_ij = 0.5 * ( log( static_cast<double>( 2.0 ) ) + log( static_cast<double>( Dsjj ) ) - log( static_cast<double>( a11 ) ) ) +
*log_alpha_ij = - log_ratio_g_prior[ ij ] + 0.5 * log( 2.0 * Dsjj / a11 ) +
lgammafn( nu_star + 0.5 ) - lgammafn( nu_star ) - 0.5 * ( Dsij * Dsij * a11 / Dsjj + sum_diag );
if( G[ ij ] == 0 ) *log_alpha_ij = - *log_alpha_ij;
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Reversible Jump MCMC for Gaussian Graphical models
// for D = I_p
// it is for Bayesian model averaging
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void ggm_rjmcmc_ma( int *iter, int *burnin, int G[], double g_prior[], double Ts[], double K[],
int *p, double *threshold, double K_hat[], int p_links[],
int *b, int *b_star, double Ds[], int *print )
{
int print_c = *print, iteration = *iter, burn_in = *burnin;
int selected_edge, selected_edge_i, selected_edge_j, ip, i, j, ij, counter;
int dim = *p, pxp = dim * dim, p1 = dim - 1, p2 = dim - 2, p2x2 = p2 * 2;
int qp = dim * ( dim - 1 ) / 2;
double log_alpha_ij;
// - - allocation for log_alpha_ij
vector<double> K121( 4 );
vector<double> Kj12( p1 ); // K[j, -j]
vector<double> sigmaj12( p1 ); // sigma[-j, j]
vector<double> sigmaj22( p1 * p1 ); // sigma[-j, -j]
vector<double> Kj12xK22_inv( p1 );
vector<double> K21( p2x2 ); // K[-e, e]
vector<double> sigma21( p2x2 ); // sigma[-e, e]
vector<double> sigma22( ( dim - 2 ) * ( dim - 2 ) ); // sigma[-e, -e]
vector<double> sigma11_inv( 4 ); // inv( sigma[e, e] )
vector<double> sigma21xsigma11_inv( p2x2 );
vector<double> K12xK22_inv( p2x2 );
// - - for rgwish_sigma
vector<double> sigma_start( pxp );
vector<double> inv_C( pxp );
vector<double> beta_star( dim );
vector<double> sigma_i( dim );
vector<double> sigma_start_N_i( dim ); // For dynamic memory used
vector<double> sigma_N_i( pxp ); // For dynamic memory used
vector<int> N_i( dim ); // For dynamic memory used
// - - - - - - - - - - - - - -
vector<double> sigma( pxp );
vector<double> copyK( pxp );
memcpy( ©K[0], K, sizeof( double ) * pxp );
inverse( ©K[0], &sigma[0], &dim );
// Count size of notes
vector<int> size_node( dim, 0 );
for( i = 0; i < dim; i++ )
{
ip = i * dim;
for( j = 0; j < dim; j++ ) size_node[ i ] += G[ ip + j ];
}
// For finding the index of selected edge
vector<int> index_row( qp );
vector<int> index_col( qp );
counter = 0;
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = g_prior[ j * dim + i ];
if( ( ij != 0.0 ) or ( ij != 1.0 ) )
{
index_row[ counter ] = i;
index_col[ counter ] = j;
counter++;
}
}
int sub_qp = counter;
vector<double> log_ratio_g_prior( pxp );
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = j * dim + i;
log_ratio_g_prior[ ij ] = log( static_cast<double>( g_prior[ ij ] / ( 1 - g_prior[ ij ] ) ) );
}
// - - Main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
GetRNGstate();
for( int i_mcmc = 0; i_mcmc < iteration; i_mcmc++ )
{
if( ( i_mcmc + 1 ) % print_c == 0 ) Rprintf( " Iteration %d \n", i_mcmc + 1 );
// - - - STEP 1: selecting edge and calculating alpha - - - - - - - - - - - - - - - - - - - - - - -|
// Randomly selecting one edge: NOTE qp = p * ( p - 1 ) / 2
selected_edge = static_cast<int>( unif_rand() * sub_qp );
selected_edge_i = index_row[ selected_edge ];
selected_edge_j = index_col[ selected_edge ];
// - - - STEP 1: calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
log_alpha_rjmcmc( &log_alpha_ij, &log_ratio_g_prior[0], &selected_edge_i, &selected_edge_j, G, Ds,
&sigma[0], &sigma21[0], &sigma22[0], &sigmaj12[0], &sigmaj22[0],
&K[0], &K21[0], &K121[0], &Kj12[0],
&K12xK22_inv[0], &Kj12xK22_inv[0], &sigma11_inv[0], &sigma21xsigma11_inv[0],
b, &dim );
// - - - End of calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Selecting an edge and updating G (graph)
if( log( static_cast<double>( unif_rand() ) ) < log_alpha_ij )
{
ij = selected_edge_j * dim + selected_edge_i;
G[ ij ] = 1 - G[ ij ];
G[ selected_edge_i * dim + selected_edge_j ] = G[ ij ];
if( G[ ij ] )
{
++size_node[ selected_edge_i ];
++size_node[ selected_edge_j ];
}else{
--size_node[ selected_edge_i ];
--size_node[ selected_edge_j ];
}
}
// - - - STEP 2: Sampling from G-Wishart for new graph - - - - - - - - - - - - - - - - - - - - - - |
rgwish_sigma( G, &size_node[0], Ts, K, &sigma[0], b_star, &dim, threshold, &sigma_start[0], &inv_C[0], &beta_star[0], &sigma_i[0], sigma_start_N_i, sigma_N_i, N_i );
// - - - saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
if( i_mcmc >= burn_in )
for( i = 0; i < pxp ; i++ )
{
K_hat[ i ] += K[ i ];
p_links[ i ] += G[ i ];
}
// - - - End of saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
}
PutRNGstate();
// - - - End of main loop for reversible jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - |
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Reversible Jump MCMC for Gaussian Graphical models
// for D = I_p
// it is for maximum a posterior probability estimation (MAP)
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void ggm_rjmcmc_map( int *iter, int *burnin, int G[], double g_prior[], double Ts[], double K[],
int *p, double *threshold,
int all_graphs[], double all_weights[], double K_hat[],
char *sample_graphs[], double graph_weights[], int *size_sample_g,
int *b, int *b_star, double Ds[], int *print )
{
int print_c = *print, iteration = *iter, burn_in = *burnin, count_all_g = 0;
int selected_edge, selected_edge_i, selected_edge_j, size_sample_graph = *size_sample_g;
int ip, i, j, ij, counter, dim = *p, pxp = dim * dim, p1 = dim - 1, p2 = dim - 2, p2x2 = p2 * 2;
int qp = dim * ( dim - 1 ) / 2;
double log_alpha_ij;
string string_g;
vector<string> sample_graphs_C( iteration - burn_in );
bool this_one;
// - - - allocation for log_alpha_ij
vector<double> K121( 4 );
vector<double> Kj12( p1 ); // K[j, -j]
vector<double> sigmaj12( p1 ); // sigma[-j, j]
vector<double> sigmaj22( p1 * p1 ); // sigma[-j, -j]
vector<double> Kj12xK22_inv( p1 );
vector<double> K21( p2x2 ); // K[-e, e]
vector<double> sigma21( p2x2 ); // sigma[-e, e]
vector<double> sigma22( ( dim - 2 ) * ( dim - 2 ) ); // sigma[-e, -e]
vector<double> sigma11_inv( 4 ); // inv( sigma[e, e] )
vector<double> sigma21xsigma11_inv( p2x2 );
vector<double> K12xK22_inv( p2x2 );
// - - for rgwish_sigma
vector<double> sigma_start( pxp );
vector<double> inv_C( pxp );
vector<double> beta_star( dim );
vector<double> sigma_i( dim );
vector<double> sigma_start_N_i( dim ); // For dynamic memory used
vector<double> sigma_N_i( pxp ); // For dynamic memory used
vector<int> N_i( dim ); // For dynamic memory used
// - - - - - - - - - - - - - -
vector<char> char_g( qp ); // char string_g[pp];
vector<double> sigma( pxp );
vector<double> copyK( pxp );
memcpy( ©K[0], K, sizeof( double ) * pxp );
inverse( ©K[0], &sigma[0], &dim );
// Count size of notes
vector<int> size_node( dim, 0 );
for( i = 0; i < dim; i++ )
{
ip = i * dim;
for( j = 0; j < dim; j++ ) size_node[ i ] += G[ ip + j ];
}
vector<int> index_row( qp );
vector<int> index_col( qp );
counter = 0;
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = g_prior[ j * dim + i ];
if( ( ij != 0.0 ) or ( ij != 1.0 ) )
{
index_row[ counter ] = i;
index_col[ counter ] = j;
counter++;
}
}
int sub_qp = counter;
vector<double> log_ratio_g_prior( pxp );
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = j * dim + i;
log_ratio_g_prior[ ij ] = log( static_cast<double>( g_prior[ ij ] / ( 1 - g_prior[ ij ] ) ) );
}
// - - - Main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
GetRNGstate();
for( int i_mcmc = 0; i_mcmc < iteration; i_mcmc++ )
{
if( ( i_mcmc + 1 ) % print_c == 0 ) Rprintf( " Iteration %d \n", i_mcmc + 1 );
// STEP 1: selecting edge and calculating alpha
// Randomly selecting one edge: NOTE qp = p * ( p - 1 ) / 2
selected_edge = static_cast<int>( unif_rand() * sub_qp );
selected_edge_i = index_row[ selected_edge ];
selected_edge_j = index_col[ selected_edge ];
// - - - STEP 1: calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
log_alpha_rjmcmc( &log_alpha_ij, &log_ratio_g_prior[0], &selected_edge_i, &selected_edge_j, G, Ds,
&sigma[0], &sigma21[0], &sigma22[0], &sigmaj12[0], &sigmaj22[0],
&K[0], &K21[0], &K121[0], &Kj12[0],
&K12xK22_inv[0], &Kj12xK22_inv[0], &sigma11_inv[0], &sigma21xsigma11_inv[0],
b, &dim );
// - - - End of calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Selecting an edge and updating G (graph)
if( log( static_cast<double>( unif_rand() ) ) < log_alpha_ij )
{
ij = selected_edge_j * dim + selected_edge_i;
G[ ij ] = 1 - G[ ij ];
G[ selected_edge_i * dim + selected_edge_j ] = G[ ij ];
if( G[ ij ] )
{
++size_node[ selected_edge_i ];
++size_node[ selected_edge_j ];
}else{
--size_node[ selected_edge_i ];
--size_node[ selected_edge_j ];
}
}
// - - - STEP 2: Sampling from G-Wishart for new graph - - - - - - - - - - - - - - - - - - - - - - |
rgwish_sigma( G, &size_node[0], Ts, K, &sigma[0], b_star, &dim, threshold, &sigma_start[0], &inv_C[0], &beta_star[0], &sigma_i[0], sigma_start_N_i, sigma_N_i, N_i );
// - - - saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
if( i_mcmc >= burn_in )
{
counter = 0;
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
char_g[ counter++ ] = G[ j * dim + i ] + '0';
for( i = 0; i < pxp ; i++ ) K_hat[ i ] += K[ i ];
string_g = string( char_g.begin(), char_g.end() );
this_one = false;
for( i = 0; i < size_sample_graph; i++ )
if( sample_graphs_C[ i ] == string_g )
{
graph_weights[ i ]++; // += all_weights[count_all_g];
all_graphs[ count_all_g ] = i;
this_one = true;
break;
}
if( !this_one || size_sample_graph == 0 )
{
sample_graphs_C[ size_sample_graph ] = string_g;
graph_weights[ size_sample_graph ] = all_weights[ count_all_g ];
all_graphs[ count_all_g ] = size_sample_graph;
size_sample_graph++;
}
count_all_g++;
}
// - - - End of saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
}
PutRNGstate();
// - - - End of main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - |
for( i = 0; i < ( iteration - burn_in ); i++ )
{
sample_graphs_C[ i ].copy( sample_graphs[ i ], qp, 0 );
sample_graphs[ i ][ qp ] = '\0';
}
*size_sample_g = size_sample_graph;
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Reversible Jump MCMC for Gaussian copula Graphical models
// for D = I_p
// it is for Bayesian model averaging
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void gcgm_rjmcmc_ma( int *iter, int *burnin, int G[], double g_prior[], double Ts[], double K[],
int *p, double *threshold,
double Z[], int R[], int not_continuous[], int *n, int *gcgm,
double K_hat[], int p_links[],
int *b, int *b_star, double D[], double Ds[], int *print )
{
int print_c = *print, iteration = *iter, burn_in = *burnin;
int selected_edge, counter, selected_edge_i, selected_edge_j;
int ip, i, j, ij, dim = *p, pxp = dim * dim, p1 = dim - 1, p2 = dim - 2, p2x2 = p2 * 2;
int qp = dim * ( dim - 1 ) / 2;
double log_alpha_ij;
// - - allocation for log_alpha_ij
vector<double> K121( 4 );
vector<double> Kj12( p1 ); // K[j, -j]
vector<double> sigmaj12( p1 ); // sigma[-j, j]
vector<double> sigmaj22( p1 * p1 ); // sigma[-j, -j]
vector<double> Kj12xK22_inv( p1 );
vector<double> K21( p2x2 ); // K[-e, e]
vector<double> sigma21( p2x2 ); // sigma[-e, e]
vector<double> sigma22( ( dim - 2 ) * ( dim - 2 ) ); // sigma[-e, -e]
vector<double> sigma11_inv( 4 ); // inv( sigma[e, e] )
vector<double> sigma21xsigma11_inv( p2x2 );
vector<double> K12xK22_inv( p2x2 );
// - - for rgwish_sigma - - - - - - - - -
vector<double> sigma_start( pxp );
vector<double> inv_C( pxp );
vector<double> beta_star( dim );
vector<double> sigma_i( dim );
vector<double> sigma_start_N_i( dim ); // For dynamic memory used
vector<double> sigma_N_i( pxp ); // For dynamic memory used
vector<int> N_i( dim ); // For dynamic memory used
// - - for copula - - - - - - - - - - - -
vector<double> S( pxp );
vector<double> inv_Ds( pxp );
vector<double> copy_Ds( pxp );
// - - - - - - - - - - - - - - - - - - - -
vector<double> sigma( pxp );
vector<double> copyK( pxp );
memcpy( ©K[0], K, sizeof( double ) * pxp );
inverse( ©K[0], &sigma[0], &dim );
// Count size of notes
vector<int> size_node( dim, 0 );
for( i = 0; i < dim; i++ )
{
ip = i * dim;
for( j = 0; j < dim; j++ ) size_node[ i ] += G[ ip + j ];
}
// For finding the index of selected edge
vector<int> index_row( qp );
vector<int> index_col( qp );
counter = 0;
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = g_prior[ j * dim + i ];
if( ( ij != 0.0 ) or ( ij != 1.0 ) )
{
index_row[ counter ] = i;
index_col[ counter ] = j;
counter++;
}
}
int sub_qp = counter;
vector<double> log_ratio_g_prior( pxp );
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = j * dim + i;
log_ratio_g_prior[ ij ] = log( static_cast<double>( g_prior[ ij ] / ( 1 - g_prior[ ij ] ) ) );
}
// - - - Main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
GetRNGstate();
for( int i_mcmc = 0; i_mcmc < iteration; i_mcmc++ )
{
if( ( i_mcmc + 1 ) % print_c == 0 ) Rprintf( " Iteration %d \n", i_mcmc + 1 );
// - - - STEP 1: copula - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
get_Ds( K, Z, R, not_continuous, D, Ds, &S[0], gcgm, n, &dim );
get_Ts( Ds, Ts, &inv_Ds[0], ©_Ds[0], &dim );
// - - - STEP 2: calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
// Randomly selecting one edge: NOTE qp = p * ( p - 1 ) / 2
selected_edge = static_cast<int>( unif_rand() * sub_qp );
selected_edge_i = index_row[ selected_edge ];
selected_edge_j = index_col[ selected_edge ];
// - - - STEP 2: calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
log_alpha_rjmcmc( &log_alpha_ij, &log_ratio_g_prior[0], &selected_edge_i, &selected_edge_j, G, Ds,
&sigma[0], &sigma21[0], &sigma22[0], &sigmaj12[0], &sigmaj22[0],
&K[0], &K21[0], &K121[0], &Kj12[0],
&K12xK22_inv[0], &Kj12xK22_inv[0], &sigma11_inv[0], &sigma21xsigma11_inv[0],
b, &dim );
// - - - End of calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Selecting an edge and updating G (graph)
if( log( static_cast<double>( unif_rand() ) ) < log_alpha_ij )
{
ij = selected_edge_j * dim + selected_edge_i;
G[ ij ] = 1 - G[ ij ];
G[ selected_edge_i * dim + selected_edge_j ] = G[ ij ];
if( G[ ij ] )
{
++size_node[ selected_edge_i ];
++size_node[ selected_edge_j ];
}else{
--size_node[ selected_edge_i ];
--size_node[ selected_edge_j ];
}
}
// - - - STEP 2: Sampling from G-Wishart for new graph - - - - - - - - - - - - - - - - - - - - - - |
rgwish_sigma( G, &size_node[0], Ts, K, &sigma[0], b_star, &dim, threshold, &sigma_start[0], &inv_C[0], &beta_star[0], &sigma_i[0], sigma_start_N_i, sigma_N_i, N_i );
// - - - saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
if( i_mcmc >= burn_in )
for( i = 0; i < pxp ; i++ )
{
K_hat[ i ] += K[ i ];
p_links[ i ] += G[ i ];
}
// - - - End of saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
}
PutRNGstate();
// - - - End of main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - |
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Reversible Jump MCMC for Gaussian copula Graphical models
// for D = I_p
// it is for maximum a posterior probability estimation (MAP)
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void gcgm_rjmcmc_map( int *iter, int *burnin, int G[], double g_prior[], double Ts[], double K[],
int *p, double *threshold,
double Z[], int R[], int not_continuous[], int *n, int *gcgm,
int all_graphs[], double all_weights[], double K_hat[],
char *sample_graphs[], double graph_weights[], int *size_sample_g,
int *b, int *b_star, double D[], double Ds[], int *print )
{
int print_c = *print, iteration = *iter, burn_in = *burnin, count_all_g = 0;
int selected_edge, counter, selected_edge_i, selected_edge_j, size_sample_graph = *size_sample_g;
int ip, i, j, ij, dim = *p, pxp = dim * dim, p1 = dim - 1, p2 = dim - 2, p2x2 = p2 * 2;
int qp = dim * ( dim - 1 ) / 2;
bool this_one;
double log_alpha_ij;
string string_g;
vector<string> sample_graphs_C( iteration - burn_in );
// - - - allocation for log_alpha_ij
vector<double> K121( 4 );
vector<double> Kj12( p1 ); // K[j, -j]
vector<double> sigmaj12( p1 ); // sigma[-j, j]
vector<double> sigmaj22( p1 * p1 ); // sigma[-j, -j]
vector<double> Kj12xK22_inv( p1 );
vector<double> K21( p2x2 ); // K[-e, e]
vector<double> sigma21( p2x2 ); // sigma[-e, e]
vector<double> sigma22( ( dim - 2 ) * ( dim - 2 ) ); // sigma[-e, -e]
vector<double> sigma11_inv( 4 ); // inv( sigma[e, e] )
vector<double> sigma21xsigma11_inv( p2x2 );
vector<double> K12xK22_inv( p2x2 );
// - - for rgwish_sigma - - - - - - - - -
vector<double> sigma_start( pxp );
vector<double> inv_C( pxp );
vector<double> beta_star( dim );
vector<double> sigma_i( dim );
vector<double> sigma_start_N_i( dim ); // For dynamic memory used
vector<double> sigma_N_i( pxp ); // For dynamic memory used
vector<int> N_i( dim ); // For dynamic memory used
// - - for copula - - - - - - - - - - - -
vector<double> S( pxp );
vector<double> inv_Ds( pxp );
vector<double> copy_Ds( pxp );
// - - - - - - - - - - -- - - - - - - - -
vector<char> char_g( qp ); // char string_g[pp];
vector<double> sigma( pxp );
vector<double> copyK( pxp );
memcpy( ©K[0], K, sizeof( double ) * pxp );
inverse( ©K[0], &sigma[0], &dim );
// Count size of notes
vector<int> size_node( dim, 0 );
for( i = 0; i < dim; i++ )
{
ip = i * dim;
for( j = 0; j < dim; j++ ) size_node[ i ] += G[ ip + j ];
}
// For finding the index of selected edge
vector<int> index_row( qp );
vector<int> index_col( qp );
counter = 0;
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = g_prior[ j * dim + i ];
if( ( ij != 0.0 ) or ( ij != 1.0 ) )
{
index_row[ counter ] = i;
index_col[ counter ] = j;
counter++;
}
}
int sub_qp = counter;
vector<double> log_ratio_g_prior( pxp );
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = j * dim + i;
log_ratio_g_prior[ ij ] = log( static_cast<double>( g_prior[ ij ] / ( 1 - g_prior[ ij ] ) ) );
}
// - - Main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
GetRNGstate();
for( int i_mcmc = 0; i_mcmc < iteration; i_mcmc++ )
{
if( ( i_mcmc + 1 ) % print_c == 0 ) Rprintf( " Iteration %d \n", i_mcmc + 1 );
// - - - STEP 1: copula - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
get_Ds( K, Z, R, not_continuous, D, Ds, &S[0], gcgm, n, &dim );
get_Ts( Ds, Ts, &inv_Ds[0], ©_Ds[0], &dim );
// - - - STEP 2: calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
// Randomly selecting one edge: NOTE qp = p * ( p - 1 ) / 2
selected_edge = static_cast<int>( unif_rand() * sub_qp );
selected_edge_i = index_row[ selected_edge ];
selected_edge_j = index_col[ selected_edge ];
// - - - STEP 2: calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
log_alpha_rjmcmc( &log_alpha_ij, &log_ratio_g_prior[0], &selected_edge_i, &selected_edge_j, G, Ds,
&sigma[0], &sigma21[0], &sigma22[0], &sigmaj12[0], &sigmaj22[0],
&K[0], &K21[0], &K121[0], &Kj12[0],
&K12xK22_inv[0], &Kj12xK22_inv[0], &sigma11_inv[0], &sigma21xsigma11_inv[0],
b, &dim );
// - - - End of calculating log_alpha_ij - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Selecting an edge and updating G (graph)
if( log( static_cast<double>( unif_rand() ) ) < log_alpha_ij )
{
ij = selected_edge_j * dim + selected_edge_i;
G[ ij ] = 1 - G[ ij ];
G[ selected_edge_i * dim + selected_edge_j ] = G[ ij ];
if( G[ ij ] )
{
++size_node[ selected_edge_i ];
++size_node[ selected_edge_j ];
}else{
--size_node[ selected_edge_i ];
--size_node[ selected_edge_j ];
}
}
// - - - STEP 2: Sampling from G-Wishart for new graph - - - - - - - - - - - - - - - - - - - - - - |
rgwish_sigma( G, &size_node[0], Ts, K, &sigma[0], b_star, &dim, threshold, &sigma_start[0], &inv_C[0], &beta_star[0], &sigma_i[0], sigma_start_N_i, sigma_N_i, N_i );
// - - - saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
if( i_mcmc >= burn_in )
{
counter = 0;
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
char_g[ counter++ ] = G[ j * dim + i ] + '0';
for( i = 0; i < pxp ; i++ ) K_hat[ i ] += K[ i ];
string_g = string( char_g.begin(), char_g.end() );
this_one = false;
for( i = 0; i < size_sample_graph; i++ )
if( sample_graphs_C[ i ] == string_g )
{
graph_weights[ i ]++; // += all_weights[count_all_g];
all_graphs[ count_all_g ] = i;
this_one = true;
break;
}
if( !this_one || size_sample_graph == 0 )
{
sample_graphs_C[ size_sample_graph ] = string_g;
graph_weights[ size_sample_graph ] = all_weights[ count_all_g ];
all_graphs[ count_all_g ] = size_sample_graph;
size_sample_graph++;
}
count_all_g++;
}
// - - - End of saving result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
}
PutRNGstate();
// - - End of main loop for Reversible Jump MCMC - - - - - - - - - - - - - - - - - - - - - - - - - |
for( i = 0; i < ( iteration - burn_in ); i++ )
{
sample_graphs_C[ i ].copy(sample_graphs[ i ], qp, 0);
sample_graphs[ i ][ qp ] = '\0';
}
*size_sample_g = size_sample_graph;
}
} // End of exturn "C"
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