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BRUG_BDMCMC.cpp
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BRUG_BDMCMC.cpp
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/***************************************************************************************
* Copyright (C) 2020 Chan Ga Ming Angus
*
* Maintainer: Chan Ga Ming Angus <chan.ga.ming.angus@gmail.com>
***************************************************************************************/
// Compile with:
// g++ BRUG_BDMCMC.cpp -llapack -lblas -std=c++11 -o BRUG_BDMCMC
/***************************************************************************************
* Reference
****************************************************************************************
* Title: BDgraph source code
* Author: Reza Mohammadi, Ernst C. Wit
* Date: 2012 - 2020
* Code version: 2.63
* Availability: https://github.com/cran/BDgraph
*
***************************************************************************************/
#include <iostream>
#include <fstream>
#include <omp.h>
#include <string>
#include <vector>
#include <random>
#include <cmath>
#include <cstring>
#include <getopt.h>
using namespace std;
extern "C" void daxpy_(int* N, double* DA, double* DX, int* INCX, double* DY, int* INCY);
extern "C" void dtrmm_(char* SIDE, char* UPLO, char* TRANSA, char* DIAG, int* M, int* N, double* ALPHA, double* A, int* LDA, double* B, int* LDB);
extern "C" void dtrsm_(char* SIDE, char* UPLO, char* TRANSA, char* DIAG, int* M, int* N, double* ALPHA, double* A, int* LDA, double* B, int* LDB);
extern "C" void dgemm_(char* TRANSA, char* TRANSB, int* M, int* N, int *K, double *ALPHA, double *A, int *LDA, double *B, int *LDB, double *BETA, double* C, int* LDC);
extern "C" void dposv_(char* UPLO, int* N, int* NRHS, double* A, int* LDA, double* B, int* LDB, int* INFO);
extern "C" void dsymv_(char* UPLO, int* N, double* ALPHA, double* A, int* LDA, double* X, int* INCX, double* BETA, double* Y, int* INCY);
extern "C" void dsyr_(char* UPLO, int* N, double* ALPHA, double* X, int* INCX, double* A, int* LDA);
extern "C" double ddot_(int* N, double* DX, int* INCX, double* DY, int* INCY);
extern "C" void dpotrf_(char* UPLO, int* N, double* A, int* LDA, int* INFO);
// Write a function to update \beta_lm
void update_beta(double beta0[], double beta1[], int G[], double X[], int p, int L, int ns[])
{
int lm = 0;
default_random_engine generator;
for (int i=1; i<p; i++) // all potential edges.
for (int j = 0; j<i; j++)
{
int ij = i*p + j;
// Update beta0
//prior N(-1000, 1.0)
//MH N(beta^{t-1}, 0.1)
double beta_old = beta0[lm];
normal_distribution<double> N(beta_old,0.1); //Can change the sd later.
double beta_new = N(generator);
double logr = (pow(beta_old + 1000, 2.0) - pow(beta_new + 1000, 2.0))/2; //assuming prior of -1000 for beta0
for (int l=0; l<L; l++) //groups
{
double x = X[l];
logr += ns[l]*(G[l*p*p + ij]*(beta_new - beta_old) - log(1 + exp(beta_new + beta1[lm]*x)) + log(1 + exp(beta_old + beta1[lm]*x)));
}
if (logr > log((double)rand()/RAND_MAX)) beta0[lm] = beta_new;
// Update beta1
//prior N(0, 1.0)
//MH N(beta^{t-1}, 0.1)
beta_old = beta1[lm];
normal_distribution<double> N_2(beta_old,0.01); //Can change the sd later.
beta_new = N_2(generator);
//prior
logr = (pow(beta_old, 2.0) - pow(beta_new, 2.0))/2; // assume \sigma = 1.0?
for (int l=0; l<L; l++) //groups
{
double x = X[l];
logr += ns[l]*(G[l*p*p + ij]*(beta_new - beta_old)*x - log(1 + exp(beta0[lm] + beta_new*x)) + log(1 + exp(beta0[lm] + beta_new*x)));
}
if (logr > log((double)rand()/RAND_MAX)) beta1[lm] = beta_new;
lm++;
}
}
int factorial(int n)
{
int result = 1;
for( int i=2; i<=n; i++) result *= i;
return(result);
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Determinant of a symmetric possitive-definite matrix ( A )
// > > > > > > > > > WARNING: Matrix you pass is overwritten < < < < < < < < <
// For any symmetric PD Matrix A, we have: |A| = |T| ^ 2, where T is cholesky decomposition of A.
// Thus, |T| = \prod_{i = 1}^p T_{ii}.
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
double determinant( double A[], int dim )
{
char uplo = 'U';
int info, dim1 = dim + 1;
dpotrf_( &uplo, &dim, &A[0], &dim, &info );
double result = 1;
for( int i = 0; i < dim; i++ ) result *= A[ i * dim1 ];
return ( result * result );
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Part of function "gnorm"
// which is for calculating Normalizing constant of G-Wishart distribution
// based on Monto Carlo algorithm
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void log_exp_mc( int G[], int nu[], int b_c, double H[], int check_H, int mc_iter, int dim, double f_T[] )
{
int iter, i, j, ij, h, r, pxp = dim * dim;
double sumPsi, sumPsiH, sumPsiHi, sumPsiHj;
double max_numeric_limits_ld = numeric_limits<double>::max() / 1000;
double min_numeric_limits_ld = numeric_limits<double>::min() * 1000;
vector<double> psi( pxp, 0.0 );
//GetRNGstate();
default_random_engine generator;
normal_distribution<double> rnorm( 0.0, 1.0 );
if( check_H == 1 )
{
for( iter = 0; iter < mc_iter; iter++ )
{
for( i = 0; i < dim; i++ )
{
gamma_distribution<double> rgamma( ( b_c + nu[ i ] ) / 2.0, 2.0 );
psi[ i * dim + i ] = sqrt( rgamma(generator));
//psi[i * dim + i] = sqrt( rchisq( b_c + nu[i] ) );
}
for( i = 0; i < dim - 1; i++ )
for( j = i + 1; j < dim; j++ )
{
ij = j * dim + i;
//if( G[ij] == 1 ) psi[ij] = rnorm( 0, 1 ); else psi[ij] = 0.0;
psi[ ij ] = ( G[ ij ] == 1 ) ? rnorm(generator) : 0.0;
}
for( i = 0; i < dim - 1; i++ )
for( j = i + 1; j < dim; j++ )
{
ij = j * dim + i;
if( G[ ij ] == 0 )
{
psi[ ij ] = 0.0; // it's not necessary
if( i > 0 )
{
sumPsi = 0.0;
//sum( psi[ 1 : ( i - 1 ), i ] * psi[ 1 : ( i - 1 ), j ] )
// for( h = 0; h < ( i - 1 ); h++ )
for( h = 0; h < i; h++ )
{
if( sumPsi > max_numeric_limits_ld ) sumPsi = max_numeric_limits_ld;
if( sumPsi > min_numeric_limits_ld ) sumPsi = min_numeric_limits_ld;
sumPsi += ( psi[ i * dim + h ] * psi[ j * dim + h ] );
}
//psi[i, j] <- - sum( psi[ 1 : ( i - 1 ), i ] * psi[ 1 : ( i - 1 ), j ] ) / psi[i, i]
psi[ ij ] = - sumPsi / psi[ i * dim + i ];
}
if( psi[ ij ] > max_numeric_limits_ld ) psi[ ij ] = max_numeric_limits_ld;
if( psi[ ij ] > min_numeric_limits_ld ) psi[ ij ] = min_numeric_limits_ld;
//f_T[k] <- f_T[k] + psi[i, j] ^ 2
f_T[ iter ] += ( psi[ ij ] * psi[ ij ] );
}
}
// checking Inf values
if( f_T[ iter ] > max_numeric_limits_ld ) f_T[ iter ] = max_numeric_limits_ld;
}
}else{
for( iter = 0; iter < mc_iter; iter++ )
{
for( i = 0; i < dim; i++ )
{
gamma_distribution<double> rgamma( ( b_c + nu[ i ] ) / 2.0, 2.0 );
psi[ i * dim + i ] = sqrt(rgamma( generator ));
//psi[i * dim + i] = sqrt( rchisq( b_c + nu[i] ) );
}
for( i = 0; i < dim - 1; i++ )
for( j = i + 1; j < dim; j++ )
{
ij = j * dim + i;
//if( G[ij] == 1 ) psi[ij] = rnorm( 0, 1 ); elsepsi[ij] = 0.0;
psi[ ij ] = ( G[ ij ] == 1 ) ? rnorm(generator) : 0.0;
}
for( i = 0; i < dim - 1; i++ )
for( j = i + 1; j < dim; j++ )
{
ij = j * dim + i;
if( G[ ij ] == 0 )
{
//psi[i, j] = - sum( psi[ i, i : ( j - 1 ) ] * H[ i : ( j - 1 ), j ] )
sumPsiH = 0.0;
for( h = i; h < j; h++ )
{
if( sumPsiH > max_numeric_limits_ld ) sumPsiH = max_numeric_limits_ld;
if( sumPsiH > min_numeric_limits_ld ) sumPsiH = min_numeric_limits_ld;
sumPsiH += ( psi[ h * dim + i ] * H[ j * dim + h ] );
}
psi[ ij ] = - sumPsiH;
if( i > 0 ) //if( i > 1 )
for( r = 0; r < i; r++ ) //for( r in 1 : ( i - 1 ) )
{
//sum( psi[ r, r : i ] * H[ r : i, i ] )
sumPsiHi = 0.0;
for( h = r; h < i + 1; h++ )
{
if( sumPsiHi > max_numeric_limits_ld ) sumPsiHi = max_numeric_limits_ld;
if( sumPsiHi > min_numeric_limits_ld ) sumPsiHi = min_numeric_limits_ld;
sumPsiHi += ( psi[ h * dim + r ] * H[ i * dim + h ] );
}
//sum( psi[ r, r : j ] * H[ r : j, j ] ) )
sumPsiHj = 0.0;
for( h = r; h < j + 1; h++ )
sumPsiHj += ( psi[ h * dim + r ] * H[ j * dim + h ] );
//psi[i, j] <- psi[i, j] - ( ( sum( psi[ r, r : i ] * H[ r : i, i ] ) ) * ( sum( psi[ r, r : j ] * H[ r : j, j ] ) ) ) / ( psi[i, i] )
psi[ ij ] -= ( sumPsiHi * sumPsiHj ) / psi[ i * dim + i ];
}
if( psi[ ij ] > max_numeric_limits_ld ) psi[ ij ] = max_numeric_limits_ld;
if( psi[ ij ] > min_numeric_limits_ld ) psi[ ij ] = min_numeric_limits_ld;
//f_T[k] <- f_T[k] + psi[i, j] ^ 2
f_T[ iter ] += ( psi[ ij ] * psi[ ij ] );
}
}
// checking Inf values
if( f_T[ iter ] > max_numeric_limits_ld ) f_T[ iter ] = max_numeric_limits_ld;
}
}
//PutRNGstate();
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// inverse function for symmetric positive-definite matrices (p x p)
// WARNING: Matrix you pass is overwritten with the result
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void inverse( double A[], double A_inv[], int dim )
{
int info;
char uplo = 'U';
// creating an identity matrix
#pragma omp parallel for
for( int i = 0; i < dim; i++ )
for( int j = 0; j < dim; j++ )
A_inv[ j * dim + i ] = ( i == j );
// LAPACK function: computes solution to A * X = B, where A is symmetric positive definite matrix
//F77_NAME(dposv)( &uplo, &dim, &dim, A, &dim, A_inv, &dim, &info FCONE );
dposv_(&uplo, &dim, &dim, A, &dim, A_inv, &dim, &info);
}
double gnorm(int G[], int b, double D[], int p, int iter)
{
double result;
// get Ti
vector<double> Ti(p*p);
char uplo = 'U'; int info;
inverse(D, &Ti[0], p);
dpotrf_( &uplo, &p, &Ti[0], &p, &info );
vector<double> H(p*p);
int check_H = 1;
for (int i=0; i<p; i++)
for (int j=0; j<p; j++)
H[i*p + j] = Ti[i*p + j]/Ti[i*p+i];
int qp = p*(p-1)/2;
for (int i=1; i<p; i++)
{
for (int j=0; j<i; j++)
{
if(H[i*p + j] != 0)
{
check_H = 0;
break;
}
}
if (check_H == 0) break;
}
vector<int> nu(p, 0);
for (int i=0; i<p; i++) for (int j=i; j<p; j++) nu[i] += G[i*p + j];
int size_graph = 0; for (int i=0; i<p; i++) size_graph += nu[i];
if (size_graph == qp)
{
double sum_lgamma_bnu = 0;
for (int i=0; i<p; i++) sum_lgamma_bnu += lgamma((b + nu[i])/(double)2);
result = ( (double)size_graph / 2 ) * log( M_PI ) + ( (double)p * ( b + p - 1 ) / 2 ) * log( 2 ) +
sum_lgamma_bnu - ( ( b + p - 1 ) / (double)2 ) * log( determinant( D, p ) );
}
else if(size_graph == 0)
{
double sum_log_diag_D = 0;
for (int i=0; i<p; i++) sum_log_diag_D += log(D[i*(p+1)]);
result = ( (double)p * b / 2 ) * log( 2 ) + p * lgamma( (double)b / 2 ) - ( (double)b / 2 ) * sum_log_diag_D;
}
else
{
vector<double> f_T(iter);
log_exp_mc(G, &nu[0], b, &H[0], check_H, iter, p, &f_T[0]);
double log_Ef_T = 0;
for (int i=0; i<iter; i++) log_Ef_T += exp(-f_T[i]/2)/iter;
log_Ef_T = log(log_Ef_T);
double sum_lgamma_bnu = 0;
for (int i=0; i<p; i++) sum_lgamma_bnu += lgamma((b + nu[i])/(double)2);
double sum_bnu_log_diag_Ti = 0;
vector<double> colsums(p,0);
for (int j=0; j<p; j++) for (int i=0; i<=j; i++) colsums[j] += G[i*p + j];
for (int i=0; i<p; i++) sum_bnu_log_diag_Ti += (b + nu[i] + colsums[i])*log(Ti[i*(p+1)]);
double result = ( (double)size_graph / 2 ) * log( M_PI ) + ( (double)p * b / 2 + size_graph ) * log( 2 ) +
sum_lgamma_bnu + sum_bnu_log_diag_Ti;
result += log_Ef_T;
}
return(result);
}
int update_b(int b_old, int G[], double K[], double D[], int p, int L, int ns[])
{
double lambda = 1 ; //What is lambda
double q_ratio; // to be used in prior
int b_new;
if (b_old == 3)
{
b_new = 4;
q_ratio = 0.5;
}
else
{
if ((double)rand()/RAND_MAX > 0.5) b_new = b_old + 1;
else b_new = b_old - 1;
if(b_old == 4 && b_new == 3) q_ratio = 2; // the case if b goes from 4 to 3.
else q_ratio = 1;
}
//prior
double logr = log(lambda)*(b_new - b_old) + log((double)factorial(b_old-3)/factorial(b_new-3)) + log(q_ratio);
for (int l=0; l<L; l++)
{
logr += ns[l]*(gnorm(&G[l*p*p], b_old, D, p, 100)-gnorm(&G[l*p*p], b_new, D, p, 100)+log(determinant(&K[l*p*p], p))*(b_new - b_old));
}
if (logr > log((double)rand()/RAND_MAX)) return(b_new);
else return(b_old);
}
void update_D(double D[], int G[], double K[], int b, int p, int L, int ns[])
{
double alpha = 2.0, beta = 2.0;
double c = 5;
vector<double> D_new(p*p);
memcpy(&D_new[0], D, p*p*sizeof(double));
default_random_engine generator;
vector<double> gnorm_old(L);
vector<double> gnorm_new(L);
//Calculate the first gnorm.
for (int l=0; l<L; l++) gnorm_old[l] = gnorm(&G[l*p*p], b, D, p, 100);
//Begin update.
for (int j=0; j<p; j++)
{
double d_old = D[j*(p+1)];
gamma_distribution<double> rgamma( c*d_old, 1/c );
double d_new = rgamma(generator); D_new[j*(p+1)] = d_new;
// Get q ratio first
double logr = c*log(c)*(d_new - d_old) - lgamma(c*d_new) + lgamma(c*d_old) + (c*d_new-1)*log(d_old) - (c*d_old-1)*log(d_new) +c*(d_new-d_old)
// Then prior.
+ (alpha-1)*log(d_new / d_old) - beta*(d_new - d_old);
for (int l=0; l<L; l++)
{
gnorm_new[l] = gnorm(&G[l*p*p], b, &D_new[0], p, 100);
logr += ns[l]*(gnorm_old[l] - gnorm_new[l]) +log(K[l*p*p + j*(p+1)]*(d_new-d_old)) ;
}
if (logr > log((double)rand()/RAND_MAX))
{
D[j*(p+1)] = d_new;
memcpy(&gnorm_old[0], &gnorm_new[0], L*sizeof(double));
}
else
{
D_new[j*(p+1)] = d_old; //if the last proposal is not accepted, we reload the original value from D.
}
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Takes symmatric matrix A (p x p) and
// retrieves A12(1x(p-1)) and A22((p-1)x(p-1))
// Like A12=A[j, -j], and A22=A[-j, -j] in R
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void sub_matrices1( double A[], double A12[], double A22[], int psub, int pdim )
{
int i, ixpdim, ixp1, p1 = pdim - 1, subxp = psub * pdim, mpsub = pdim - psub - 1;
int size_psub = sizeof( double ) * psub;
int size_mpsub = sizeof( double ) * mpsub;
memcpy( A12, A + subxp, size_psub );
memcpy( A12 + psub, A + subxp + psub + 1, size_mpsub );
for( i = 0; i < psub; i++ )
{
ixpdim = i * pdim;
ixp1 = i * p1;
memcpy( A22 + ixp1 , A + ixpdim , size_psub );
memcpy( A22 + ixp1 + psub, A + ixpdim + psub + 1, size_mpsub );
}
for( i = psub + 1; i < pdim; i++ )
{
ixpdim = i * pdim;
ixp1 = ( i - 1 ) * p1;
memcpy( A22 + ixp1 , A + ixpdim , size_psub );
memcpy( A22 + ixp1 + psub, A + ixpdim + psub + 1, size_mpsub );
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Takes symmetric matrix A (p x p) and
// retrieves upper part of sub_matrix B (p_sub x p_sub), dictated by vector sub
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void sub_matrix_upper( double A[], double sub_A[], int sub[], int psub, int pdim )
{
int i, j, ixp, subixp;
for( i = 0; i < psub; i++ )
{
ixp = i * psub;
subixp = sub[ i ] * pdim;
for( j = 0; j <= i; j++ )
sub_A[ ixp + j ] = A[ subixp + sub[ j ] ];
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Takes square matrix A (p x p) and
// retrieves vector sub_A which is 'sub' th row of matrix A, minus 'sub' element
// Likes A[j, -j] in R
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void sub_row_mins( double A[], double sub_A[], int subj, int pdim )
{
int subxp = subj * pdim;
memcpy( sub_A , A + subxp , sizeof( double ) * subj );
memcpy( sub_A + subj, A + subxp + subj + 1, sizeof( double ) * ( pdim - subj - 1 ) );
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Takes square matrix A (p x p) and
// retrieves sub_matrix sub_A(p-2 x 2) which is sub cols of matrix A, minus two elements
// Likes A[-(i,j), (i,j)] in R
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void sub_cols_mins( double A[], double sub_A[], int subi, int subj, int pdim )
{
int p2 = pdim - 2, subixp = subi * pdim, subjxp = subj * pdim;
memcpy( sub_A , A + subixp , sizeof( double ) * subi );
memcpy( sub_A + subi , A + subixp + subi + 1, sizeof( double ) * ( subj - subi - 1 ) );
memcpy( sub_A + subj - 1, A + subixp + subj + 1, sizeof( double ) * ( pdim - subj - 1 ) );
memcpy( sub_A + p2 , A + subjxp , sizeof( double ) * subi );
memcpy( sub_A + p2 + subi , A + subjxp + subi + 1, sizeof( double ) * ( subj - subi - 1 ) );
memcpy( sub_A + p2 + subj - 1, A + subjxp + subj + 1, sizeof( double ) * ( pdim - subj - 1 ) );
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Takes square matrix A (p x p) and
// retrieves A11_inv ( 2 x 2 ), A21 ( ( p - 2 ) x 2 ), and A22 ( ( p - 2 ) x ( p - 2 ) )
// Like A11_inv=inv ( A[ e, e ] ), A21 = A[ -e, e ], and A22 = A[ -e, -e ] in R
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void sub_matrices_inv( double A[], double A11_inv[], double A21[], double A22[], int sub0, int sub1, int pdim )
{
int i, ixp, ixp2, p2 = pdim - 2;
int sub0xp = sub0 * pdim, sub1xp = sub1 * pdim, sub0_plus = sub0 + 1, sub1_plus = sub1 + 1;
double a11 = A[ sub0 * pdim + sub0 ];
double a12 = A[ sub0 * pdim + sub1 ];
double a22 = A[ sub1 * pdim + sub1 ];
double det_A11 = a11 * a22 - a12 * a12;
A11_inv[ 0 ] = a22 / det_A11;
A11_inv[ 1 ] = - a12 / det_A11;
A11_inv[ 2 ] = A11_inv[ 1 ];
A11_inv[ 3 ] = a11 / det_A11;
int size_sub0 = sizeof( double ) * sub0;
int size_sub1_sub0 = sizeof( double ) * ( sub1 - sub0_plus );
int size_pdim_sub0 = sizeof( double ) * ( pdim - sub1_plus );
memcpy( A21 , A + sub0xp , size_sub0 );
memcpy( A21 + sub0 , A + sub0xp + sub0_plus, size_sub1_sub0 );
memcpy( A21 + sub1 - 1, A + sub0xp + sub1_plus, size_pdim_sub0 );
memcpy( A21 + p2 , A + sub1xp , size_sub0 );
memcpy( A21 + p2 + sub0 , A + sub1xp + sub0_plus, size_sub1_sub0 );
memcpy( A21 + p2 + sub1 - 1, A + sub1xp + sub1_plus, size_pdim_sub0 );
for( i = 0; i < sub0; i++ )
{
ixp = i * pdim;
ixp2 = i * p2;
memcpy( A22 + ixp2 , A + ixp , size_sub0 );
memcpy( A22 + ixp2 + sub0 , A + ixp + sub0_plus, size_sub1_sub0 );
memcpy( A22 + ixp2 + sub1 - 1, A + ixp + sub1_plus, size_pdim_sub0 );
}
for( i = sub0_plus; i < sub1; i++ )
{
ixp = i * pdim;
ixp2 = ( i - 1 ) * p2;
memcpy( A22 + ixp2 , A + ixp , size_sub0 );
memcpy( A22 + ixp2 + sub0 , A + ixp + sub0_plus, size_sub1_sub0 );
memcpy( A22 + ixp2 + sub1 - 1, A + ixp + sub1_plus, size_pdim_sub0 );
}
for( i = sub1_plus; i < pdim; i++ )
{
ixp = i * pdim;
ixp2 = ( i - 2 ) * p2;
memcpy( A22 + ixp2 , A + ixp , size_sub0 );
memcpy( A22 + ixp2 + sub0 , A + ixp + sub0_plus, size_sub1_sub0 );
memcpy( A22 + ixp2 + sub1 - 1, A + ixp + sub1_plus, size_pdim_sub0 );
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// computing birth/death rate or alpha for element (i,j)
// it is for double Metropolis-Hasting algorihtms
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void log_H_ij( double K[], double sigma[], double *log_Hij, int selected_edge_i, int selected_edge_j,
double Kj12[], double Kj12xK22_inv[], double K12[], double K12xK22_inv[], double K121[],
double sigmaj12[], double sigmaj22[], double sigma12[], double sigma22[], double sigma11_inv[], double sigma21xsigma11_inv[],
int dim, int p1, int p2, int jj,
double Dsijj, double Dsij, double Dsjj )
{
int one = 1, two = 2;
double alpha = 1.0, beta = 0.0, alpha1 = -1.0, beta1 = 1.0;
char transT = 'T', transN = 'N', sideL = 'L';
//double sigmaj11 = sigma[*jj]; // sigma[j, j]
sub_matrices1( sigma, sigmaj12, sigmaj22, 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[ selected_edge_j * ( dim + 1 ) ];
//F77_NAME(dsyr)( &sideL, p1, &sigmajj_inv, sigmaj12, &one, sigmaj22, p1 FCONE );
dsyr_( &sideL, &p1, &sigmajj_inv, sigmaj12, &one, sigmaj22, &p1 );
// For (i,j) = 0 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
sub_row_mins( K, Kj12, selected_edge_j, dim ); // K12 = K[j, -j]
Kj12[ selected_edge_i ] = 0.0; // K12[1,i] = 0
// Kj12xK22_inv = Kj12 %*% Kj22_inv here sigmaj22 instead of Kj22_inv
//F77_NAME(dsymv)( &sideL, p1, &alpha, &sigmaj22[0], p1, Kj12, &one, &beta, Kj12xK22_inv, &one FCONE );
dsymv_( &sideL, &p1, &alpha, &sigmaj22[0], &p1, Kj12, &one, &beta, Kj12xK22_inv, &one );
// K022 = Kj12xK22_inv %*% t(Kj12)
//double K022 = F77_NAME(ddot)( p1, Kj12xK22_inv, &one, Kj12, &one );
double K022 = ddot_( &p1, Kj12xK22_inv, &one, Kj12, &one );
// For (i,j) = 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
sub_cols_mins( K, K12, selected_edge_i, selected_edge_j, dim ); // K21 = K[-e, e]
sub_matrices_inv( sigma, sigma11_inv, sigma12, sigma22, selected_edge_i, selected_edge_j, dim );
// sigma21xsigma11_inv = sigma21 %*% sigma11_inv
//F77_NAME(dgemm)( &transN, &transN, p2, &two, &two, &alpha, sigma12, p2, sigma11_inv, &two, &beta, sigma21xsigma11_inv, p2 FCONE FCONE );
dgemm_( &transN, &transN, &p2, &two, &two, &alpha, sigma12, &p2, sigma11_inv, &two, &beta, sigma21xsigma11_inv, &p2 );
// sigma22 = sigma22 - sigma21xsigma11_inv %*% t( sigma21 )
//F77_NAME(dgemm)( &transN, &transT, p2, p2, &two, &alpha1, sigma21xsigma11_inv, p2, sigma12, p2, &beta1, sigma22, p2 FCONE FCONE );
dgemm_( &transN, &transT, &p2, &p2, &two, &alpha1, sigma21xsigma11_inv, &p2, sigma12, &p2, &beta1, sigma22, &p2 );
// K12xK22_inv = t( K21 ) %*% K22_inv here sigam12 = K22_inv
//F77_NAME(dgemm)( &transT, &transN, &two, p2, p2, &alpha, K12, p2, sigma22, p2, &beta, K12xK22_inv, &two FCONE FCONE );
dgemm_( &transT, &transN, &two, &p2, &p2, &alpha, K12, &p2, sigma22, &p2, &beta, K12xK22_inv, &two );
// K121 = K12xK22_inv %*% K21
//F77_NAME(dgemm)( &transN, &transN, &two, &two, p2, &alpha, K12xK22_inv, &two, K12, p2, &beta, K121, &two FCONE FCONE );
dgemm_( &transN, &transN, &two, &two, &p2, &alpha, K12xK22_inv, &two, K12, &p2, &beta, K121, &two );
// Finished (i,j) = 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
double a11 = K[selected_edge_i *dim + selected_edge_i] - K121[0];
double sum_diag = Dsjj * ( K022 - K121[3] ) - Dsij * ( K121[1] + K121[2] );
// Dsijj = Dsii - Dsij * Dsij / Dsjj;
//*log_Hij = ( log( static_cast<double>(*Dsjj) ) - log( static_cast<double>(a11) ) + *Dsijj * a11 - sum_diag ) / 2;
*log_Hij = 0.5 * ( log( Dsjj / a11 ) + Dsijj * a11 - sum_diag );
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// rgwish ONLY for inside of MCMC algorithm
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void rgwish_sigma( int G[], int size_node[], double Ts[], double K[], double sigma[], int b_star,
int dim, double threshold,
double sigma_start[], double inv_C[], double beta_star[], double sigma_i[],
double sigma_start_N_i[], double sigma_N_i[], int N_i[] )
{
int i, i1, j, ij, ip, l, size_node_i, info, one = 1, pxp = dim * dim, dim1 = dim + 1, bKdim = b_star + dim - 1;
double alpha = 1.0, beta = 0.0;
char transT = 'T', transN = 'N', side = 'R', upper = 'U';
// - - STEP 1: sampling from wishart distributions - - - - - - - - - - - - - - - - - - - - - -|
// - - Sample values in Psi matrix
//GetRNGstate();
default_random_engine generator;
normal_distribution<double> distribution_2(0.0,1.0);
#pragma omp parallel for
for( i = 0; i < dim; i++ )
{
//sigma_start[ i * dim1 ] = sqrt( Rf_rgamma( ( bKdim - i ) * 0.5, 2.0 ) ); // i * dim1 = i * dim + i
gamma_distribution<double> distribution(( bKdim - i ) * 0.5, 2.0 ); //Rf_rgamma uses scale while C++ uses beta.
sigma_start[ i * dim1 ] = sqrt( distribution(generator) ); // i * dim1 = i * dim + i
//sigma_start[i * dim1] = sqrt( rchisq( bKdim - i ) ); // i * dim1 = i * dim + i
}
#pragma omp parallel for
for( j = 1; j < dim; j++ )
for( int i = 0; i < j; i++ )
{
sigma_start[ j * dim + i ] = distribution_2(generator);
sigma_start[ i * dim + j ] = 0.0;
}
//PutRNGstate();
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// C = psi %*% Ts I used psi = psi %*% Ts Now is sigma_start = sigma_start %*% Ts
//F77_NAME(dtrmm)( &side, &upper, &transN, &transN, &dim, &dim, &alpha, Ts, &dim, &sigma_start[0], &dim FCONE FCONE FCONE FCONE );
dtrmm_(&side, &upper, &transN, &transN, &dim, &dim, &alpha, Ts, &dim, &sigma_start[0], &dim);
side = 'L';
// creating an identity matrix
#pragma omp parallel for
for( i = 0; i < dim; i++ )
for( int j = 0; j < dim; j++ )
inv_C[ j * dim + i ] = ( i == j );
// op( A )*X = alpha*B, or X*op( A ) = alpha*B,
//F77_NAME(dtrsm)( &side, &upper, &transN, &transN, &dim, &dim, &alpha, &sigma_start[0], &dim, &inv_C[0], &dim FCONE FCONE FCONE FCONE );
dtrsm_(&side, &upper, &transN, &transN, &dim, &dim, &alpha, &sigma_start[0], &dim, &inv_C[0], &dim);
// sigma_start = inv_C %*% t( inv_C )
//F77_NAME(dgemm)( &transN, &transT, &dim, &dim, &dim, &alpha, &inv_C[0], &dim, &inv_C[0], &dim, &beta, &sigma_start[0], &dim FCONE FCONE );
dgemm_(&transN, &transT, &dim, &dim, &dim, &alpha, &inv_C[0], &dim, &inv_C[0], &dim, &beta, &sigma_start[0], &dim);
memcpy( sigma, &sigma_start[0], sizeof( double ) * pxp );
// double temp, max_diff = 1.0, threshold_c = *threshold;
double mean_diff = 1.0;
int counter = 0;
while( ( mean_diff > threshold ) and ( counter < 5000 ) )
{
counter++;
mean_diff = 0.0;
for( i = 0; i < dim; i++ )
{
ip = i * dim;
size_node_i = size_node[ i ];
if( size_node_i > 0 )
{
l = 0;
for( j = 0; j < dim; j++ )
{
ij = ip + j;
if( G[ ij ] )
{
sigma_start_N_i[ l ] = sigma_start[ ij ];
N_i[ l++ ] = j;
}
else
beta_star[ j ] = 0.0;
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
sub_matrix_upper( sigma, &sigma_N_i[0], &N_i[0], size_node_i, dim );
// A * X = B for sigma_start_N_i := (sigma_N_i)^{-1} * sigma_start_N_i
//F77_NAME(dposv)( &upper, &size_node_i, &one, &sigma_N_i[0], &size_node_i, &sigma_start_N_i[0], &size_node_i, &info FCONE );
dposv_(&upper, &size_node_i, &one, &sigma_N_i[0], &size_node_i, &sigma_start_N_i[0], &size_node_i, &info);
for( j = 0; j < size_node_i; j++ ) beta_star[ N_i[ j ] ] = sigma_start_N_i[ j ];
// sigma_i = sigma %*% beta_star
//F77_NAME(dsymv)( &side, &dim, &alpha, sigma, &dim, &beta_star[0], &one, &beta, &sigma_i[0], &one FCONE );
dsymv_(&side, &dim, &alpha, sigma, &dim, &beta_star[0], &one, &beta, &sigma_i[0], &one);
memcpy( sigma + ip, sigma_i, sizeof( double ) * i );
for( j = 0; j < i; j++ )
{
ij = j * dim + i;
mean_diff += fabs( static_cast<double>( sigma[ ij ] - sigma_i[ j ] ) );
// temp = fabs( static_cast<double>( sigma[ ij ] - sigma_i[ j ] ) );
// max_diff = ( temp > max_diff ) ? temp : max_diff;
sigma[ ij ] = sigma_i[ j ];
}
i1 = i + 1;
memcpy( sigma + ip + i1, sigma_i + i1, sizeof( double ) * ( dim - i1 ) );
for( j = i1; j < dim; j++ )
{
ij = j * dim + i;
mean_diff += fabs( static_cast<double>( sigma[ ij ] - sigma_i[ j ] ) );
// temp = fabs( static_cast<double>( sigma[ ij ] - sigma_i[ j ] ) );
// max_diff = ( temp > max_diff ) ? temp : max_diff;
sigma[ ij ] = sigma_i[ j ];
}
}else{
for( j = 0; j < i; j++ )
{
ij = j * dim + i;
mean_diff += fabs( static_cast<double>( sigma[ ij ] ) );
// temp = fabs( static_cast<double>( sigma[ ij ] ) );
// max_diff = ( temp > max_diff ) ? temp : max_diff;
sigma[ ij ] = 0.0;
sigma[ ip + j ] = 0.0;
}
for( j = i + 1; j < dim; j++ )
{
ij = j * dim + i;
mean_diff += fabs( static_cast<double>( sigma[ ij ] ) );
// temp = fabs( static_cast<double>( sigma[ ij ] ) );
// max_diff = ( temp > max_diff ) ? temp : max_diff;
sigma[ ij ] = 0.0;
sigma[ ip + j ] = 0.0;
}
}
}
mean_diff /= pxp;
}
memcpy( &sigma_start[0], sigma, sizeof( double ) * pxp );
inverse( &sigma_start[0], K, dim );
// creating an identity matrix
//#pragma omp parallel for
//for( i = 0; i < dim; i++ )
// for( int j = 0; j < dim; j++ )
// K[ j * dim + i ] = ( i == j );
// LAPACK function: computes solution to A * X = B, where A is symmetric positive definite matrix
//F77_NAME(dposv)( &upper, &dim, &dim, &sigma_start[0], &dim, K, &dim, &info );
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// Parallel Computation for birth-death rates for double BD-MCMC algorithm
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void rates_bdmcmc_dmh_parallel( double rates[], double log_ratio_g_prior[], int G[], int index_row[], int index_col[], int *sub_qp, double Ds[], double D[],
double sigma[], double K[], double sigma_dmh[],
double K_dmh[], int L, int dim )
{
int p1 = dim - 1, p2 = dim - 2, p2x2 = ( dim - 2 ) * 2;
#pragma omp parallel
{
int pxp = dim*dim;
int index_rate_j, i, j, ij, jj;
double Dsjj, Dsij, Dsijj, Dij, Dijj, Djj, log_rate;
double *K121 = new double[ 4 ];
double *Kj12 = new double[ p1 ];
double *sigmaj12 = new double[ p1 ];
double *sigmaj22 = new double[ p1 * p1 ];
double *Kj12xK22_inv = new double[ p1 ];
double *K21 = new double[ p2x2 ];
double *sigma12 = new double[ p2x2 ];
double *sigma22 = new double[ p2 * p2 ];
double *sigma11_inv = new double[ 4 ];
double *sigma21xsigma11_inv = new double[ p2x2 ];
double *K12xK22_inv = new double[ p2x2 ];
double *K12 = new double[ p2x2 ];
for (int l=0; l<L; l++)
{
#pragma omp for
for( j = 1; j < dim; j++ )
{
index_rate_j = l*dim*(dim - 1)/2 + ( j * ( j - 1 ) ) / 2;
jj = j * dim + j;
Dsjj = Ds[ l*dim*dim + jj ];
Djj = D[ jj ];
for( i = 0; i < j; i++ )
{
ij = j * dim + i;
int lij = ij + l*dim*dim;
Dsij = Ds[ lij ];
Dsijj = - Dsij * Dsij / Dsjj;
Dij = D[ ij ];
Dijj = - Dij * Dij / Djj;
double logH_ij, logI_p;
log_H_ij( &K[l*pxp], &sigma[l*pxp], &logH_ij, i, j,
&Kj12[0], &Kj12xK22_inv[0], &K12[0], &K12xK22_inv[0], &K121[0],
&sigmaj12[0], &sigmaj22[0], &sigma12[0], &sigma22[0], &sigma11_inv[0], &sigma21xsigma11_inv[0],
dim, p1, p2, jj,
Dsijj, Dsij, Dsjj );
log_H_ij( &K_dmh[l*pxp], &sigma_dmh[l*pxp], &logI_p, i, j,
&Kj12[0], &Kj12xK22_inv[0], &K12[0], &K12xK22_inv[0], &K121[0],
&sigmaj12[0], &sigmaj22[0], &sigma12[0], &sigma22[0], &sigma11_inv[0], &sigma21xsigma11_inv[0],
dim, p1, p2, jj,
Dijj, Dij, Djj );
//log_rate = ( G[ ij ] ) ? ( logH_ij - logI_p ) : ( logI_p - logH_ij );
log_rate = ( G[ lij ] ) ? ( logH_ij - logI_p ) - log_ratio_g_prior[ lij ] : ( logI_p - logH_ij ) + log_ratio_g_prior[ lij ];
rates[ index_rate_j + i ] = ( log_rate < 0.0 ) ? exp( log_rate ) : 1.0;
}
}
}
delete[] K121;
delete[] Kj12;
delete[] sigmaj12;
delete[] sigmaj22;
delete[] Kj12xK22_inv;
delete[] K21;
delete[] sigma12;
delete[] sigma22;
delete[] sigma11_inv;
delete[] sigma21xsigma11_inv;
delete[] K12xK22_inv;
delete[] K12;
}
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// To select an edge for BDMCMC algorithm
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void select_edge( double rates[], int *index_selected_edge, double *sum_rates, int qp_star )
{
// rates = sum_sort_rates
vector<double>cumulative_rates( qp_star, 0.0 );
cumulative_rates[ 0 ] = rates[ 0 ];
for( int i = 1; i < qp_star; i++ )
cumulative_rates[ i ] = cumulative_rates[ i - 1 ] + rates[ i ];
*sum_rates = cumulative_rates[ qp_star - 1 ];
// GetRNGstate();
//double random_value = *sum_rates * unif_rand(); // Rf_runif( 0.0, *sum_rates );
double random_value = *sum_rates * (double)rand()/RAND_MAX; // Rf_runif( 0.0, *sum_rates );
// PutRNGstate();
//int counter = 0;
//while( random_value > cumulative_rates[ counter ] ) ++counter;
//*index_selected_edge = counter;
// To start, find the subscript of the middle position.
int lower_bound = 0;
int upper_bound = qp_star - 1;
int position = upper_bound / 2; // ( lower_bound + upper_bound ) / 2;
while( upper_bound - lower_bound > 1 )
{
//if ( rates[position] > random_value ) { upper_bound = position; } else { lower_bound = position; }
( cumulative_rates[ position ] > random_value ) ? upper_bound = position : lower_bound = position;
position = ( lower_bound + upper_bound ) / 2;
}
*index_selected_edge = ( cumulative_rates[ position ] < random_value ) ? ++position : position;
}
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
// birth-death MCMC for Gaussian Graphical models
// Based on Double Metropolis-Hastings
// it is for Bayesian model averaging
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
void ggm_DMH_bdmcmc_ma( int iteration, int burn_in, int G[], double g_prior[],
double K[], int dim, double threshold, double K_hat[], double p_links[],
int b1, int ns[], double S[], double D[], int L, int print_c,
double beta0[], double beta1[], double X[])
{
int index_selected_edge, selected_edge_l, selected_edge_i, selected_edge_j, selected_edge_ij;
int ip, i, j, ij, pxp = dim * dim, Lxpxp = L * pxp, one = 1;
int qp = L * dim * ( dim - 1 ) / 2;
double sum_weights = 0.0, weight_C, sum_rates;
vector<double> sigma( Lxpxp );
for(int l=0; l<L; l++)
inverse( &K[l*pxp], &sigma[l*pxp], dim );
vector<double> p_links_Cpp( Lxpxp, 0.0 );
vector<double> K_hat_Cpp( Lxpxp, 0.0 );
// - - for rgwish_sigma
vector<double> sigma_start( Lxpxp );
vector<double> inv_C( Lxpxp );
vector<double> beta_star( L*dim );
vector<double> sigma_i( L*dim );
vector<double> sigma_start_N_i( L*dim ); // For dynamic memory used
vector<double> sigma_N_i( Lxpxp ); // For dynamic memory used
vector<int> N_i( L*dim ); // For dynamic memory used
// - - - - - - - - - - - - - - - - - - - -
vector<double> sigma_dmh( Lxpxp ); // for double Metropolis-Hastings
vector<double> K_dmh( Lxpxp ); // for double Metropolis-Hastings
vector<double> Ds(Lxpxp); //Newly introduced to update with every D.
vector<double> Ts(Lxpxp); //Newly introduced to update with every D.
vector<double> Ti(pxp); //Newly introduced to update with every D.
// Counting size of notes
vector<int> size_node( L*dim, 0 );
for( i = 0; i < L*dim; i++ )
{
ip = i * dim;
for( j = 0; j < dim; j++ ) size_node[ i ] += G[ ip + j ];
}
// For finding the index of rates
vector<int> index_L( qp ); // newly added to record group
vector<int> index_row( qp ); // already multiplied by L above.
vector<int> index_col( qp );
int counter = 0 ;
for( int l=0; l<L; l++)
for( j = 1; j < dim; j++ )
for( i = 0; i < j; i++ )
{
ij = g_prior[ (l*dim + j) * dim + i ];
if( ( ij != 0.0 ) or ( ij != 1.0 ) )
{
index_L[ counter ] = l;
index_row[ counter ] = i;
index_col[ counter ] = j;
counter++;
}
}
int sub_qp = counter;
//cout << "sub_qp is " << sub_qp << endl;
vector<double> rates( sub_qp );
vector<double> log_ratio_g_prior( L * pxp );
vector<int> b_star(L);
// - - - Main loop for birth-death MCMC - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -|
//GetRNGstate();
cout << "Begin MCMC.\n";
int print_conter = 0;
for( int i_mcmc = 0; i_mcmc < iteration; i_mcmc++ )
{
if( ( i_mcmc + 1 ) % print_c == 0 ){
++print_conter;
//( print_conter != 20 ) ? Rprintf( "%i%%->", print_conter * 5 ) : Rprintf( " done" );
( print_conter != 20 ) ? cout<< print_conter * 5 << "%->" : cout << " done\n" ;
}
// Calculate b_star
for (int l=0; l<L; l++) b_star[l] = ns[l] + b1;
//Update Ds after D is updated.
for (int l=0; l<L; l++)
for (int i=0; i<dim; i++)
for (int j=0; j<dim; j++)
{
int pos = i*dim + j;
Ds[l*pxp + pos] = D[pos] + S[l*pxp + pos];
}
// Subsequently update Ts.
char uplo = 'U';
int info;
for (int l=0; l<L; l++)
{
inverse(&Ds[l*pxp], &Ts[l*pxp], dim); //Cycle Ts to save memory.
dpotrf_( &uplo, &dim, &Ts[l*pxp], &dim, &info );
}