/* Genome-wide Efficient Mixed Model Association (GEMMA) Copyright (C) 2011 Xiang Zhou This program 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, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. */ #include <iostream> #include <fstream> #include <sstream> #include <iomanip> #include <cmath> #include <iostream> #include <stdio.h> #include <stdlib.h> #include <ctime> #include <cstring> #include <algorithm> #include "gsl/gsl_vector.h" #include "gsl/gsl_matrix.h" #include "gsl/gsl_linalg.h" #include "gsl/gsl_blas.h" #include "gsl/gsl_eigen.h" #include "gsl/gsl_randist.h" #include "gsl/gsl_cdf.h" #include "gsl/gsl_roots.h" #include "lapack.h" #ifdef FORCE_FLOAT #include "param_float.h" #include "bslmm_float.h" #include "lmm_float.h" //for class FUNC_PARAM and MatrixCalcLR #include "lm_float.h" #include "mathfunc_float.h" //for function CenterVector #else #include "param.h" #include "bslmm.h" #include "lmm.h" #include "lm.h" #include "mathfunc.h" #endif using namespace std; void BSLMM::CopyFromParam (PARAM &cPar) { a_mode=cPar.a_mode; d_pace=cPar.d_pace; file_bfile=cPar.file_bfile; file_geno=cPar.file_geno; file_out=cPar.file_out; path_out=cPar.path_out; l_min=cPar.h_min; l_max=cPar.h_max; n_region=cPar.n_region; pve_null=cPar.pve_null; pheno_mean=cPar.pheno_mean; time_UtZ=0.0; time_Omega=0.0; n_accept=0; h_min=cPar.h_min; h_max=cPar.h_max; h_scale=cPar.h_scale; rho_min=cPar.rho_min; rho_max=cPar.rho_max; rho_scale=cPar.rho_scale; logp_min=cPar.logp_min; logp_max=cPar.logp_max; logp_scale=cPar.logp_scale; s_min=cPar.s_min; s_max=cPar.s_max; w_step=cPar.w_step; s_step=cPar.s_step; r_pace=cPar.r_pace; w_pace=cPar.w_pace; n_mh=cPar.n_mh; geo_mean=cPar.geo_mean; randseed=cPar.randseed; trace_G=cPar.trace_G; ni_total=cPar.ni_total; ns_total=cPar.ns_total; ni_test=cPar.ni_test; ns_test=cPar.ns_test; n_cvt=cPar.n_cvt; indicator_idv=cPar.indicator_idv; indicator_snp=cPar.indicator_snp; snpInfo=cPar.snpInfo; return; } void BSLMM::CopyToParam (PARAM &cPar) { cPar.time_UtZ=time_UtZ; cPar.time_Omega=time_Omega; cPar.time_Proposal=time_Proposal; cPar.cHyp_initial=cHyp_initial; cPar.n_accept=n_accept; cPar.pheno_mean=pheno_mean; cPar.randseed=randseed; return; } void BSLMM::WriteBV (const gsl_vector *bv) { string file_str; file_str=path_out+"/"+file_out; file_str+=".bv.txt"; ofstream outfile (file_str.c_str(), ofstream::out); if (!outfile) {cout<<"error writing file: "<<file_str.c_str()<<endl; return;} size_t t=0; for (size_t i=0; i<ni_total; ++i) { if (indicator_idv[i]==0) { outfile<<"NA"<<endl; } else { outfile<<scientific<<setprecision(6)<<gsl_vector_get(bv, t)<<endl; t++; } } outfile.clear(); outfile.close(); return; } void BSLMM::WriteParam (vector<pair<double, double> > &beta_g, const gsl_vector *alpha, const size_t w) { string file_str; file_str=path_out+"/"+file_out; file_str+=".param.txt"; ofstream outfile (file_str.c_str(), ofstream::out); if (!outfile) {cout<<"error writing file: "<<file_str.c_str()<<endl; return;} outfile<<"chr"<<"\t"<<"rs"<<"\t" <<"ps"<<"\t"<<"n_miss"<<"\t"<<"alpha"<<"\t" <<"beta"<<"\t"<<"gamma"<<endl; size_t t=0; for (size_t i=0; i<ns_total; ++i) { if (indicator_snp[i]==0) {continue;} outfile<<snpInfo[i].chr<<"\t"<<snpInfo[i].rs_number<<"\t" <<snpInfo[i].base_position<<"\t"<<snpInfo[i].n_miss<<"\t"; outfile<<scientific<<setprecision(6)<<gsl_vector_get(alpha, t)<<"\t"; if (beta_g[t].second!=0) { outfile<<beta_g[t].first/beta_g[t].second<<"\t"<<beta_g[t].second/(double)w<<endl; } else { outfile<<0.0<<"\t"<<0.0<<endl; } t++; } outfile.clear(); outfile.close(); return; } void BSLMM::WriteParam (const gsl_vector *alpha) { string file_str; file_str=path_out+"/"+file_out; file_str+=".param.txt"; ofstream outfile (file_str.c_str(), ofstream::out); if (!outfile) {cout<<"error writing file: "<<file_str.c_str()<<endl; return;} outfile<<"chr"<<"\t"<<"rs"<<"\t" <<"ps"<<"\t"<<"n_miss"<<"\t"<<"alpha"<<"\t" <<"beta"<<"\t"<<"gamma"<<endl; size_t t=0; for (size_t i=0; i<ns_total; ++i) { if (indicator_snp[i]==0) {continue;} outfile<<snpInfo[i].chr<<"\t"<<snpInfo[i].rs_number<<"\t" <<snpInfo[i].base_position<<"\t"<<snpInfo[i].n_miss<<"\t"; outfile<<scientific<<setprecision(6)<<gsl_vector_get(alpha, t)<<"\t"; outfile<<0.0<<"\t"<<0.0<<endl; t++; } outfile.clear(); outfile.close(); return; } void BSLMM::WriteResult (const int flag, const gsl_matrix *Result_hyp, const gsl_matrix *Result_gamma, const size_t w_col) { string file_gamma, file_hyp; file_gamma=path_out+"/"+file_out; file_gamma+=".gamma.txt"; file_hyp=path_out+"/"+file_out; file_hyp+=".hyp.txt"; ofstream outfile_gamma, outfile_hyp; if (flag==0) { outfile_gamma.open (file_gamma.c_str(), ofstream::out); outfile_hyp.open (file_hyp.c_str(), ofstream::out); if (!outfile_gamma) {cout<<"error writing file: "<<file_gamma<<endl; return;} if (!outfile_hyp) {cout<<"error writing file: "<<file_hyp<<endl; return;} outfile_hyp<<"h \t pve \t rho \t pge \t pi \t n_gamma"<<endl; for (size_t i=0; i<s_max; ++i) { outfile_gamma<<"s"<<i<<"\t"; } outfile_gamma<<endl; } else { outfile_gamma.open (file_gamma.c_str(), ofstream::app); outfile_hyp.open (file_hyp.c_str(), ofstream::app); if (!outfile_gamma) {cout<<"error writing file: "<<file_gamma<<endl; return;} if (!outfile_hyp) {cout<<"error writing file: "<<file_hyp<<endl; return;} size_t w; if (w_col==0) {w=w_pace;} else {w=w_col;} for (size_t i=0; i<w; ++i) { outfile_hyp<<scientific; for (size_t j=0; j<4; ++j) { outfile_hyp<<setprecision(6)<<gsl_matrix_get (Result_hyp, i, j)<<"\t"; } outfile_hyp<<setprecision(6)<<exp(gsl_matrix_get (Result_hyp, i, 4))<<"\t"; outfile_hyp<<(int)gsl_matrix_get (Result_hyp, i, 5)<<"\t"; outfile_hyp<<endl; } for (size_t i=0; i<w; ++i) { for (size_t j=0; j<s_max; ++j) { outfile_gamma<<(int)gsl_matrix_get (Result_gamma, i, j)<<"\t"; } outfile_gamma<<endl; } } outfile_hyp.close(); outfile_hyp.clear(); outfile_gamma.close(); outfile_gamma.clear(); return; } void BSLMM::CalcPgamma (double *p_gamma) { double p, s=0.0; for (size_t i=0; i<ns_test; ++i) { p=0.7*gsl_ran_geometric_pdf (i+1, 1.0/geo_mean)+0.3/(double)ns_test; p_gamma[i]=p; s+=p; } for (size_t i=0; i<ns_test; ++i) { p=p_gamma[i]; p_gamma[i]=p/s; } return; } void BSLMM::SetXgamma (gsl_matrix *Xgamma, const gsl_matrix *X, vector<size_t> &rank) { size_t pos; for (size_t i=0; i<rank.size(); ++i) { pos=mapRank2pos[rank[i]]; gsl_vector_view Xgamma_col=gsl_matrix_column (Xgamma, i); gsl_vector_const_view X_col=gsl_matrix_const_column (X, pos); gsl_vector_memcpy (&Xgamma_col.vector, &X_col.vector); } return; } double BSLMM::CalcPveLM (const gsl_matrix *UtXgamma, const gsl_vector *Uty, const double sigma_a2) { double pve, var_y; gsl_matrix *Omega=gsl_matrix_alloc (UtXgamma->size2, UtXgamma->size2); gsl_vector *Xty=gsl_vector_alloc (UtXgamma->size2); gsl_vector *OiXty=gsl_vector_alloc (UtXgamma->size2); gsl_matrix_set_identity (Omega); gsl_matrix_scale (Omega, 1.0/sigma_a2); #ifdef WITH_LAPACK lapack_dgemm ((char *)"T", (char *)"N", 1.0, UtXgamma, UtXgamma, 1.0, Omega); #else gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, UtXgamma, UtXgamma, 1.0, Omega); #endif gsl_blas_dgemv (CblasTrans, 1.0, UtXgamma, Uty, 0.0, Xty); CholeskySolve(Omega, Xty, OiXty); gsl_blas_ddot (Xty, OiXty, &pve); gsl_blas_ddot (Uty, Uty, &var_y); pve/=var_y; gsl_matrix_free (Omega); gsl_vector_free (Xty); gsl_vector_free (OiXty); return pve; } void BSLMM::InitialMCMC (const gsl_matrix *UtX, const gsl_vector *Uty, vector<size_t> &rank, class HYPBSLMM &cHyp, vector<pair<size_t, double> > &pos_loglr) { double q_genome=gsl_cdf_chisq_Qinv(0.05/(double)ns_test, 1); cHyp.n_gamma=0; for (size_t i=0; i<pos_loglr.size(); ++i) { if (2.0*pos_loglr[i].second>q_genome) {cHyp.n_gamma++;} } if (cHyp.n_gamma<10) {cHyp.n_gamma=10;} if (cHyp.n_gamma>s_max) {cHyp.n_gamma=s_max;} if (cHyp.n_gamma<s_min) {cHyp.n_gamma=s_min;} rank.clear(); for (size_t i=0; i<cHyp.n_gamma; ++i) { rank.push_back(i); } cHyp.logp=log((double)cHyp.n_gamma/(double)ns_test); cHyp.h=pve_null; if (cHyp.logp==0) {cHyp.logp=-0.000001;} if (cHyp.h==0) {cHyp.h=0.1;} gsl_matrix *UtXgamma=gsl_matrix_alloc (ni_test, cHyp.n_gamma); SetXgamma (UtXgamma, UtX, rank); double sigma_a2; if (trace_G!=0) { sigma_a2=cHyp.h*1.0/(trace_G*(1-cHyp.h)*exp(cHyp.logp)*(double)ns_test); } else { sigma_a2=cHyp.h*1.0/( (1-cHyp.h)*exp(cHyp.logp)*(double)ns_test); } if (sigma_a2==0) {sigma_a2=0.025;} cHyp.rho=CalcPveLM (UtXgamma, Uty, sigma_a2)/cHyp.h; gsl_matrix_free (UtXgamma); if (cHyp.rho>1.0) {cHyp.rho=1.0;} if (cHyp.h<h_min) {cHyp.h=h_min;} if (cHyp.h>h_max) {cHyp.h=h_max;} if (cHyp.rho<rho_min) {cHyp.rho=rho_min;} if (cHyp.rho>rho_max) {cHyp.rho=rho_max;} if (cHyp.logp<logp_min) {cHyp.logp=logp_min;} if (cHyp.logp>logp_max) {cHyp.logp=logp_max;} // if (fix_sigma>=0) { // fix_sigma=cHyp.h; // rho_max=1-cHyp.h; // cHyp.rho=rho_max/2.0; // } //Initial for grid sampling: // cHyp.h=0.225; // cHyp.rho=1.0; // cHyp.logp=-4.835429; cout<<"initial value of h = "<<cHyp.h<<endl; cout<<"initial value of rho = "<<cHyp.rho<<endl; cout<<"initial value of pi = "<<exp(cHyp.logp)<<endl; cout<<"initial value of |gamma| = "<<cHyp.n_gamma<<endl; return; } double BSLMM::CalcPosterior (const gsl_vector *Uty, const gsl_vector *K_eval, gsl_vector *Utu, gsl_vector *alpha_prime, class HYPBSLMM &cHyp) { double sigma_b2=cHyp.h*(1.0-cHyp.rho)/(trace_G*(1-cHyp.h)); gsl_vector *Utu_rand=gsl_vector_alloc (Uty->size); gsl_vector *weight_Hi=gsl_vector_alloc (Uty->size); double logpost=0.0; double d, ds, uy, Hi_yy=0, logdet_H=0.0; for (size_t i=0; i<ni_test; ++i) { d=gsl_vector_get (K_eval, i)*sigma_b2; ds=d/(d+1.0); d=1.0/(d+1.0); gsl_vector_set (weight_Hi, i, d); logdet_H-=log(d); uy=gsl_vector_get (Uty, i); Hi_yy+=d*uy*uy; gsl_vector_set (Utu_rand, i, gsl_ran_gaussian(gsl_r, 1)*sqrt(ds)); } //sample tau double tau=1.0; if (a_mode==11) {tau = gsl_ran_gamma (gsl_r, (double)ni_test/2.0, 2.0/Hi_yy); } //sample alpha gsl_vector_memcpy (alpha_prime, Uty); gsl_vector_mul (alpha_prime, weight_Hi); gsl_vector_scale (alpha_prime, sigma_b2); //sample u gsl_vector_memcpy (Utu, alpha_prime); gsl_vector_mul (Utu, K_eval); if (a_mode==11) {gsl_vector_scale (Utu_rand, sqrt(1.0/tau));} gsl_vector_add (Utu, Utu_rand); //for quantitative traits, calculate pve and ppe if (a_mode==11) { gsl_blas_ddot (Utu, Utu, &d); cHyp.pve=d/(double)ni_test; cHyp.pve/=cHyp.pve+1.0/tau; cHyp.pge=0.0; } //calculate likelihood logpost=-0.5*logdet_H; if (a_mode==11) {logpost-=0.5*(double)ni_test*log(Hi_yy);} else {logpost-=0.5*Hi_yy;} logpost+=((double)cHyp.n_gamma-1.0)*cHyp.logp+((double)ns_test-(double)cHyp.n_gamma)*log(1-exp(cHyp.logp)); gsl_vector_free (Utu_rand); gsl_vector_free (weight_Hi); return logpost; } double BSLMM::CalcPosterior (const gsl_matrix *UtXgamma, const gsl_vector *Uty, const gsl_vector *K_eval, gsl_vector *UtXb, gsl_vector *Utu, gsl_vector *alpha_prime, gsl_vector *beta, class HYPBSLMM &cHyp) { clock_t time_start; double sigma_a2=cHyp.h*cHyp.rho/(trace_G*(1-cHyp.h)*exp(cHyp.logp)*(double)ns_test); double sigma_b2=cHyp.h*(1.0-cHyp.rho)/(trace_G*(1-cHyp.h)); double logpost=0.0; double d, ds, uy, P_yy=0, logdet_O=0.0, logdet_H=0.0; gsl_matrix *UtXgamma_eval=gsl_matrix_alloc (UtXgamma->size1, UtXgamma->size2); gsl_matrix *Omega=gsl_matrix_alloc (UtXgamma->size2, UtXgamma->size2); gsl_vector *XtHiy=gsl_vector_alloc (UtXgamma->size2); gsl_vector *beta_hat=gsl_vector_alloc (UtXgamma->size2); gsl_vector *Utu_rand=gsl_vector_alloc (UtXgamma->size1); gsl_vector *weight_Hi=gsl_vector_alloc (UtXgamma->size1); gsl_matrix_memcpy (UtXgamma_eval, UtXgamma); logdet_H=0.0; P_yy=0.0; for (size_t i=0; i<ni_test; ++i) { gsl_vector_view UtXgamma_row=gsl_matrix_row (UtXgamma_eval, i); d=gsl_vector_get (K_eval, i)*sigma_b2; ds=d/(d+1.0); d=1.0/(d+1.0); gsl_vector_set (weight_Hi, i, d); logdet_H-=log(d); uy=gsl_vector_get (Uty, i); P_yy+=d*uy*uy; gsl_vector_scale (&UtXgamma_row.vector, d); gsl_vector_set (Utu_rand, i, gsl_ran_gaussian(gsl_r, 1)*sqrt(ds)); } //calculate Omega gsl_matrix_set_identity (Omega); time_start=clock(); #ifdef WITH_LAPACK lapack_dgemm ((char *)"T", (char *)"N", sigma_a2, UtXgamma_eval, UtXgamma, 1.0, Omega); #else gsl_blas_dgemm (CblasTrans, CblasNoTrans, sigma_a2, UtXgamma_eval, UtXgamma, 1.0, Omega); #endif time_Omega+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); //calculate beta_hat gsl_blas_dgemv (CblasTrans, 1.0, UtXgamma_eval, Uty, 0.0, XtHiy); logdet_O=CholeskySolve(Omega, XtHiy, beta_hat); gsl_vector_scale (beta_hat, sigma_a2); gsl_blas_ddot (XtHiy, beta_hat, &d); P_yy-=d; //sample tau double tau=1.0; if (a_mode==11) {tau =gsl_ran_gamma (gsl_r, (double)ni_test/2.0, 2.0/P_yy); } //sample beta for (size_t i=0; i<beta->size; i++) { d=gsl_ran_gaussian(gsl_r, 1); gsl_vector_set(beta, i, d); } gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, Omega, beta); //it compuates inv(L^T(Omega)) %*% beta; gsl_vector_scale(beta, sqrt(sigma_a2/tau)); gsl_vector_add(beta, beta_hat); gsl_blas_dgemv (CblasNoTrans, 1.0, UtXgamma, beta, 0.0, UtXb); //sample alpha gsl_vector_memcpy (alpha_prime, Uty); gsl_vector_sub (alpha_prime, UtXb); gsl_vector_mul (alpha_prime, weight_Hi); gsl_vector_scale (alpha_prime, sigma_b2); //sample u gsl_vector_memcpy (Utu, alpha_prime); gsl_vector_mul (Utu, K_eval); if (a_mode==11) {gsl_vector_scale (Utu_rand, sqrt(1.0/tau));} gsl_vector_add (Utu, Utu_rand); //for quantitative traits, calculate pve and pge if (a_mode==11) { gsl_blas_ddot (UtXb, UtXb, &d); cHyp.pge=d/(double)ni_test; gsl_blas_ddot (Utu, Utu, &d); cHyp.pve=cHyp.pge+d/(double)ni_test; if (cHyp.pve==0) {cHyp.pge=0.0;} else {cHyp.pge/=cHyp.pve;} cHyp.pve/=cHyp.pve+1.0/tau; } gsl_matrix_free (UtXgamma_eval); gsl_matrix_free (Omega); gsl_vector_free (XtHiy); gsl_vector_free (beta_hat); gsl_vector_free (Utu_rand); gsl_vector_free (weight_Hi); logpost=-0.5*logdet_H-0.5*logdet_O; if (a_mode==11) {logpost-=0.5*(double)ni_test*log(P_yy);} else {logpost-=0.5*P_yy;} // else {logpost+=-0.5*P_yy*tau+0.5*(double)ni_test*log(tau);} logpost+=((double)cHyp.n_gamma-1.0)*cHyp.logp+((double)ns_test-(double)cHyp.n_gamma)*log(1.0-exp(cHyp.logp)); return logpost; } //calculate pve and pge, and calculate z_hat for case-control data void BSLMM::CalcCC_PVEnZ (const gsl_matrix *U, const gsl_vector *Utu, gsl_vector *z_hat, class HYPBSLMM &cHyp) { double d; gsl_blas_ddot (Utu, Utu, &d); cHyp.pve=d/(double)ni_test; gsl_blas_dgemv (CblasNoTrans, 1.0, U, Utu, 0.0, z_hat); cHyp.pve/=cHyp.pve+1.0; cHyp.pge=0.0; return; } //calculate pve and pge, and calculate z_hat for case-control data void BSLMM::CalcCC_PVEnZ (const gsl_matrix *U, const gsl_vector *UtXb, const gsl_vector *Utu, gsl_vector *z_hat, class HYPBSLMM &cHyp) { double d; gsl_vector *UtXbU=gsl_vector_alloc (Utu->size); gsl_blas_ddot (UtXb, UtXb, &d); cHyp.pge=d/(double)ni_test; gsl_blas_ddot (Utu, Utu, &d); cHyp.pve=cHyp.pge+d/(double)ni_test; gsl_vector_memcpy (UtXbU, Utu); gsl_vector_add (UtXbU, UtXb); gsl_blas_dgemv (CblasNoTrans, 1.0, U, UtXbU, 0.0, z_hat); if (cHyp.pve==0) {cHyp.pge=0.0;} else {cHyp.pge/=cHyp.pve;} cHyp.pve/=cHyp.pve+1.0; gsl_vector_free(UtXbU); return; } void BSLMM::SampleZ (const gsl_vector *y, const gsl_vector *z_hat, gsl_vector *z) { double d1, d2, z_rand=0.0; for (size_t i=0; i<z->size; ++i) { d1=gsl_vector_get (y, i); d2=gsl_vector_get (z_hat, i); //y is centerred for case control studies if (d1<=0.0) { //control, right truncated do { z_rand=d2+gsl_ran_gaussian(gsl_r, 1.0); } while (z_rand>0.0); } else { do { z_rand=d2+gsl_ran_gaussian(gsl_r, 1.0); } while (z_rand<0.0); } gsl_vector_set (z, i, z_rand); } return; } double BSLMM::ProposeHnRho (const class HYPBSLMM &cHyp_old, class HYPBSLMM &cHyp_new, const size_t &repeat) { double h=cHyp_old.h, rho=cHyp_old.rho; double d_h=(h_max-h_min)*h_scale, d_rho=(rho_max-rho_min)*rho_scale; for (size_t i=0; i<repeat; ++i) { h=h+(gsl_rng_uniform(gsl_r)-0.5)*d_h; if (h<h_min) {h=2*h_min-h;} if (h>h_max) {h=2*h_max-h;} rho=rho+(gsl_rng_uniform(gsl_r)-0.5)*d_rho; if (rho<rho_min) {rho=2*rho_min-rho;} if (rho>rho_max) {rho=2*rho_max-rho;} } /* //Grid Sampling for (size_t i=0; i<repeat; ++i) { if (gsl_rng_uniform(gsl_r)<0.66) {continue;} h=h+(gsl_rng_uniform_int(gsl_r, 2)-0.5)*0.1; if (h<h_min) {h=h_max;} if (h>h_max) {h=h_min;} } for (size_t i=0; i<repeat; ++i) { if (gsl_rng_uniform(gsl_r)<0.66) {continue;} rho=rho+(gsl_rng_uniform_int(gsl_r, 2)-0.5)*0.1; if (rho<rho_min) {rho=rho_max;} if (rho>rho_max) {rho=rho_min;} } */ cHyp_new.h=h; cHyp_new.rho=rho; return 0.0; } double BSLMM::ProposePi (const class HYPBSLMM &cHyp_old, class HYPBSLMM &cHyp_new, const size_t &repeat) { double logp_old=cHyp_old.logp, logp_new=cHyp_old.logp; double log_ratio=0.0; double d_logp=min(0.1, (logp_max-logp_min)*logp_scale); for (size_t i=0; i<repeat; ++i) { logp_new=logp_old+(gsl_rng_uniform(gsl_r)-0.5)*d_logp; if (logp_new<logp_min) {logp_new=2*logp_min-logp_new;} if (logp_new>logp_max) {logp_new=2*logp_max-logp_new;} log_ratio+=logp_new-logp_old; logp_old=logp_new; } /* //Grid Sampling for (size_t i=0; i<repeat; ++i) { if (gsl_rng_uniform(gsl_r)<0.66) {continue;} logp_new=logp_old+(gsl_rng_uniform_int(gsl_r, 2)-0.5)*0.5*log(10.0); if (logp_new<logp_min) {logp_new=logp_max;} if (logp_new>logp_max) {logp_new=logp_min;} log_ratio+=logp_new-logp_old; logp_old=logp_new; } */ cHyp_new.logp=logp_new; return log_ratio; } bool comp_vec (size_t a, size_t b) { return (a < b); } double BSLMM::ProposeGamma (const vector<size_t> &rank_old, vector<size_t> &rank_new, const double *p_gamma, const class HYPBSLMM &cHyp_old, class HYPBSLMM &cHyp_new, const size_t &repeat) { map<size_t, int> mapRank2in; size_t r; double unif, logp=0.0; int flag_gamma; size_t r_add, r_remove, col_id; rank_new.clear(); if (cHyp_old.n_gamma!=rank_old.size()) {cout<<"size wrong"<<endl;} if (cHyp_old.n_gamma!=0) { for (size_t i=0; i<rank_old.size(); ++i) { r=rank_old[i]; rank_new.push_back(r); mapRank2in[r]=1; } } cHyp_new.n_gamma=cHyp_old.n_gamma; for (size_t i=0; i<repeat; ++i) { unif=gsl_rng_uniform(gsl_r); if (unif < 0.40 && cHyp_new.n_gamma<s_max) {flag_gamma=1;} else if (unif>=0.40 && unif < 0.80 && cHyp_new.n_gamma>s_min) {flag_gamma=2;} else if (unif>=0.80 && cHyp_new.n_gamma>0 && cHyp_new.n_gamma<ns_test) {flag_gamma=3;} else {flag_gamma=4;} if(flag_gamma==1) {//add a snp; do { r_add=gsl_ran_discrete (gsl_r, gsl_t); } while (mapRank2in.count(r_add)!=0); double prob_total=1.0; for (size_t i=0; i<cHyp_new.n_gamma; ++i) { r=rank_new[i]; prob_total-=p_gamma[r]; } mapRank2in[r_add]=1; rank_new.push_back(r_add); cHyp_new.n_gamma++; logp+=-log(p_gamma[r_add]/prob_total)-log((double)cHyp_new.n_gamma); } else if (flag_gamma==2) {//delete a snp; col_id=gsl_rng_uniform_int(gsl_r, cHyp_new.n_gamma); r_remove=rank_new[col_id]; double prob_total=1.0; for (size_t i=0; i<cHyp_new.n_gamma; ++i) { r=rank_new[i]; prob_total-=p_gamma[r]; } prob_total+=p_gamma[r_remove]; mapRank2in.erase(r_remove); rank_new.erase(rank_new.begin()+col_id); logp+=log(p_gamma[r_remove]/prob_total)+log((double)cHyp_new.n_gamma); cHyp_new.n_gamma--; } else if (flag_gamma==3) {//switch a snp; col_id=gsl_rng_uniform_int(gsl_r, cHyp_new.n_gamma); r_remove=rank_new[col_id]; //careful with the proposal do { r_add=gsl_ran_discrete (gsl_r, gsl_t); } while (mapRank2in.count(r_add)!=0); double prob_total=1.0; for (size_t i=0; i<cHyp_new.n_gamma; ++i) { r=rank_new[i]; prob_total-=p_gamma[r]; } logp+=log(p_gamma[r_remove]/(prob_total+p_gamma[r_remove]-p_gamma[r_add]) ); logp-=log(p_gamma[r_add]/prob_total); mapRank2in.erase(r_remove); mapRank2in[r_add]=1; rank_new.erase(rank_new.begin()+col_id); rank_new.push_back(r_add); } else {logp+=0;}//do not change } stable_sort (rank_new.begin(), rank_new.end(), comp_vec); mapRank2in.clear(); return logp; } bool comp_lr (pair<size_t, double> a, pair<size_t, double> b) { return (a.second > b.second); } //if a_mode==13 then Uty==y void BSLMM::MCMC (const gsl_matrix *U, const gsl_matrix *UtX, const gsl_vector *Uty, const gsl_vector *K_eval, const gsl_vector *y) { clock_t time_start; class HYPBSLMM cHyp_old, cHyp_new; gsl_matrix *Result_hyp=gsl_matrix_alloc (w_pace, 6); gsl_matrix *Result_gamma=gsl_matrix_alloc (w_pace, s_max); gsl_vector *alpha_prime=gsl_vector_alloc (ni_test); gsl_vector *alpha_new=gsl_vector_alloc (ni_test); gsl_vector *alpha_old=gsl_vector_alloc (ni_test); gsl_vector *Utu=gsl_vector_alloc (ni_test); gsl_vector *Utu_new=gsl_vector_alloc (ni_test); gsl_vector *Utu_old=gsl_vector_alloc (ni_test); gsl_vector *UtXb_new=gsl_vector_alloc (ni_test); gsl_vector *UtXb_old=gsl_vector_alloc (ni_test); gsl_vector *z_hat=gsl_vector_alloc (ni_test); gsl_vector *z=gsl_vector_alloc (ni_test); gsl_vector *Utz=gsl_vector_alloc (ni_test); gsl_vector_memcpy (Utz, Uty); double logPost_new, logPost_old; double logMHratio; double mean_z=0.0; gsl_matrix_set_zero (Result_gamma); gsl_vector_set_zero (Utu); gsl_vector_set_zero (alpha_prime); if (a_mode==13) { pheno_mean=0.0; } vector<pair<double, double> > beta_g; for (size_t i=0; i<ns_test; i++) { beta_g.push_back(make_pair(0.0, 0.0)); } vector<size_t> rank_new, rank_old; vector<double> beta_new, beta_old; vector<pair<size_t, double> > pos_loglr; time_start=clock(); MatrixCalcLR (U, UtX, Utz, K_eval, l_min, l_max, n_region, pos_loglr); time_Proposal=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); stable_sort (pos_loglr.begin(), pos_loglr.end(), comp_lr); for (size_t i=0; i<ns_test; ++i) { mapRank2pos[i]=pos_loglr[i].first; } //calculate proposal distribution for gamma (unnormalized), and set up gsl_r and gsl_t gsl_rng_env_setup(); const gsl_rng_type * gslType; gslType = gsl_rng_default; if (randseed<0) { time_t rawtime; time (&rawtime); tm * ptm = gmtime (&rawtime); randseed = (unsigned) (ptm->tm_hour%24*3600+ptm->tm_min*60+ptm->tm_sec); } gsl_r = gsl_rng_alloc(gslType); gsl_rng_set(gsl_r, randseed); double *p_gamma = new double[ns_test]; CalcPgamma (p_gamma); gsl_t=gsl_ran_discrete_preproc (ns_test, p_gamma); //initial parameters InitialMCMC (UtX, Utz, rank_old, cHyp_old, pos_loglr); // if (fix_sigma>=0) { // rho_max=1-fix_sigma; // cHyp_old.h=fix_sigma/(1-cHyp_old.rho); // } cHyp_initial=cHyp_old; if (cHyp_old.n_gamma==0 || cHyp_old.rho==0) { logPost_old=CalcPosterior(Utz, K_eval, Utu_old, alpha_old, cHyp_old); beta_old.clear(); for (size_t i=0; i<cHyp_old.n_gamma; ++i) { beta_old.push_back(0); } } else { gsl_matrix *UtXgamma=gsl_matrix_alloc (ni_test, cHyp_old.n_gamma); gsl_vector *beta=gsl_vector_alloc (cHyp_old.n_gamma); SetXgamma (UtXgamma, UtX, rank_old); logPost_old=CalcPosterior(UtXgamma, Utz, K_eval, UtXb_old, Utu_old, alpha_old, beta, cHyp_old); beta_old.clear(); for (size_t i=0; i<beta->size; ++i) { beta_old.push_back(gsl_vector_get(beta, i)); } gsl_matrix_free (UtXgamma); gsl_vector_free (beta); } //calculate centered z_hat, and pve if (a_mode==13) { time_start=clock(); if (cHyp_old.n_gamma==0 || cHyp_old.rho==0) { CalcCC_PVEnZ (U, Utu_old, z_hat, cHyp_old); } else { CalcCC_PVEnZ (U, UtXb_old, Utu_old, z_hat, cHyp_old); } time_UtZ+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); } //start MCMC int accept; size_t total_step=w_step+s_step; size_t w=0, w_col, pos; size_t repeat=0; for (size_t t=0; t<total_step; ++t) { if (t%d_pace==0 || t==total_step-1) {ProgressBar ("Running MCMC ", t, total_step-1, (double)n_accept/(double)(t*n_mh+1));} // if (t>10) {break;} if (a_mode==13) { SampleZ (y, z_hat, z); mean_z=CenterVector (z); time_start=clock(); gsl_blas_dgemv (CblasTrans, 1.0, U, z, 0.0, Utz); time_UtZ+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); //First proposal if (cHyp_old.n_gamma==0 || cHyp_old.rho==0) { logPost_old=CalcPosterior(Utz, K_eval, Utu_old, alpha_old, cHyp_old); beta_old.clear(); for (size_t i=0; i<cHyp_old.n_gamma; ++i) { beta_old.push_back(0); } } else { gsl_matrix *UtXgamma=gsl_matrix_alloc (ni_test, cHyp_old.n_gamma); gsl_vector *beta=gsl_vector_alloc (cHyp_old.n_gamma); SetXgamma (UtXgamma, UtX, rank_old); logPost_old=CalcPosterior(UtXgamma, Utz, K_eval, UtXb_old, Utu_old, alpha_old, beta, cHyp_old); beta_old.clear(); for (size_t i=0; i<beta->size; ++i) { beta_old.push_back(gsl_vector_get(beta, i)); } gsl_matrix_free (UtXgamma); gsl_vector_free (beta); } } //MH steps for (size_t i=0; i<n_mh; ++i) { if (gsl_rng_uniform(gsl_r)<0.33) {repeat = 1+gsl_rng_uniform_int(gsl_r, 20);} else {repeat=1;} logMHratio=0.0; logMHratio+=ProposeHnRho(cHyp_old, cHyp_new, repeat); logMHratio+=ProposeGamma (rank_old, rank_new, p_gamma, cHyp_old, cHyp_new, repeat); logMHratio+=ProposePi(cHyp_old, cHyp_new, repeat); // if (fix_sigma>=0) { // cHyp_new.h=fix_sigma/(1-cHyp_new.rho); // } if (cHyp_new.n_gamma==0 || cHyp_new.rho==0) { logPost_new=CalcPosterior(Utz, K_eval, Utu_new, alpha_new, cHyp_new); beta_new.clear(); for (size_t i=0; i<cHyp_new.n_gamma; ++i) { beta_new.push_back(0); } } else { gsl_matrix *UtXgamma=gsl_matrix_alloc (ni_test, cHyp_new.n_gamma); gsl_vector *beta=gsl_vector_alloc (cHyp_new.n_gamma); SetXgamma (UtXgamma, UtX, rank_new); logPost_new=CalcPosterior(UtXgamma, Utz, K_eval, UtXb_new, Utu_new, alpha_new, beta, cHyp_new); beta_new.clear(); for (size_t i=0; i<beta->size; ++i) { beta_new.push_back(gsl_vector_get(beta, i)); } gsl_matrix_free (UtXgamma); gsl_vector_free (beta); } logMHratio+=logPost_new-logPost_old; if (logMHratio>0 || log(gsl_rng_uniform(gsl_r))<logMHratio) {accept=1; n_accept++;} else {accept=0;} if (accept==1) { logPost_old=logPost_new; rank_old.clear(); beta_old.clear(); if (rank_new.size()!=0) { for (size_t i=0; i<rank_new.size(); ++i) { rank_old.push_back(rank_new[i]); beta_old.push_back(beta_new[i]); } } cHyp_old=cHyp_new; gsl_vector_memcpy (alpha_old, alpha_new); gsl_vector_memcpy (UtXb_old, UtXb_new); gsl_vector_memcpy (Utu_old, Utu_new); } else {cHyp_new=cHyp_old;} } //calculate z_hat, and pve if (a_mode==13) { time_start=clock(); if (cHyp_old.n_gamma==0 || cHyp_old.rho==0) { CalcCC_PVEnZ (U, Utu_old, z_hat, cHyp_old); } else { CalcCC_PVEnZ (U, UtXb_old, Utu_old, z_hat, cHyp_old); } //sample mu and update z hat gsl_vector_sub (z, z_hat); mean_z+=CenterVector(z); mean_z+=gsl_ran_gaussian(gsl_r, sqrt(1.0/(double) ni_test) ); gsl_vector_add_constant (z_hat, mean_z); time_UtZ+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); } //Save data if (t<w_step) {continue;} else { if (t%r_pace==0) { w_col=w%w_pace; if (w_col==0) { if (w==0) {WriteResult (0, Result_hyp, Result_gamma, w_col);} else { WriteResult (1, Result_hyp, Result_gamma, w_col); gsl_matrix_set_zero (Result_hyp); gsl_matrix_set_zero (Result_gamma); } } gsl_matrix_set (Result_hyp, w_col, 0, cHyp_old.h); gsl_matrix_set (Result_hyp, w_col, 1, cHyp_old.pve); gsl_matrix_set (Result_hyp, w_col, 2, cHyp_old.rho); gsl_matrix_set (Result_hyp, w_col, 3, cHyp_old.pge); gsl_matrix_set (Result_hyp, w_col, 4, cHyp_old.logp); gsl_matrix_set (Result_hyp, w_col, 5, cHyp_old.n_gamma); for (size_t i=0; i<cHyp_old.n_gamma; ++i) { pos=mapRank2pos[rank_old[i]]+1; gsl_matrix_set (Result_gamma, w_col, i, pos); beta_g[pos-1].first+=beta_old[i]; beta_g[pos-1].second+=1.0; } gsl_vector_add (alpha_prime, alpha_old); gsl_vector_add (Utu, Utu_old); if (a_mode==13) { pheno_mean+=mean_z; } w++; } } } cout<<endl; w_col=w%w_pace; WriteResult (1, Result_hyp, Result_gamma, w_col); gsl_matrix_free(Result_hyp); gsl_matrix_free(Result_gamma); gsl_vector_free(z_hat); gsl_vector_free(z); gsl_vector_free(Utz); gsl_vector_free(UtXb_new); gsl_vector_free(UtXb_old); gsl_vector_free(alpha_new); gsl_vector_free(alpha_old); gsl_vector_free(Utu_new); gsl_vector_free(Utu_old); gsl_vector_scale (alpha_prime, 1.0/(double)w); gsl_vector_scale (Utu, 1.0/(double)w); if (a_mode==13) { pheno_mean/=(double)w; } gsl_vector *alpha=gsl_vector_alloc (ns_test); gsl_blas_dgemv (CblasTrans, 1.0/(double)ns_test, UtX, alpha_prime, 0.0, alpha); WriteParam (beta_g, alpha, w); gsl_vector_free(alpha); gsl_blas_dgemv (CblasNoTrans, 1.0, U, Utu, 0.0, alpha_prime); WriteBV(alpha_prime); gsl_vector_free(alpha_prime); gsl_vector_free(Utu); delete [] p_gamma; beta_g.clear(); return; } void BSLMM::RidgeR(const gsl_matrix *U, const gsl_matrix *UtX, const gsl_vector *Uty, const gsl_vector *eval, const double lambda) { gsl_vector *beta=gsl_vector_alloc (UtX->size2); gsl_vector *H_eval=gsl_vector_alloc (Uty->size); gsl_vector *bv=gsl_vector_alloc (Uty->size); gsl_vector_memcpy (H_eval, eval); gsl_vector_scale (H_eval, lambda); gsl_vector_add_constant (H_eval, 1.0); gsl_vector_memcpy (bv, Uty); gsl_vector_div (bv, H_eval); gsl_blas_dgemv (CblasTrans, lambda/(double)UtX->size2, UtX, bv, 0.0, beta); gsl_vector_add_constant (H_eval, -1.0); gsl_vector_mul (H_eval, bv); gsl_blas_dgemv (CblasNoTrans, 1.0, U, H_eval, 0.0, bv); WriteParam (beta); WriteBV(bv); gsl_vector_free (H_eval); gsl_vector_free (beta); gsl_vector_free (bv); return; } //below fits MCMC for rho=1 void BSLMM::CalcXtX (const gsl_matrix *X, const gsl_vector *y, const size_t s_size, gsl_matrix *XtX, gsl_vector *Xty) { time_t time_start=clock(); gsl_matrix_const_view X_sub=gsl_matrix_const_submatrix(X, 0, 0, X->size1, s_size); gsl_matrix_view XtX_sub=gsl_matrix_submatrix(XtX, 0, 0, s_size, s_size); gsl_vector_view Xty_sub=gsl_vector_subvector(Xty, 0, s_size); #ifdef WITH_LAPACK lapack_dgemm ((char *)"T", (char *)"N", 1.0, &X_sub.matrix, &X_sub.matrix, 0.0, &XtX_sub.matrix); #else gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, &X_sub.matrix, &X_sub.matrix, 0.0, &XtX_sub.matrix); #endif gsl_blas_dgemv(CblasTrans, 1.0, &X_sub.matrix, y, 0.0, &Xty_sub.vector); time_Omega+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); return; } void BSLMM::SetXgamma (const gsl_matrix *X, const gsl_matrix *X_old, const gsl_matrix *XtX_old, const gsl_vector *Xty_old, const gsl_vector *y, const vector<size_t> &rank_old, const vector<size_t> &rank_new, gsl_matrix *X_new, gsl_matrix *XtX_new, gsl_vector *Xty_new) { double d; //rank_old and rank_new are sorted already inside PorposeGamma //calculate vectors rank_remove and rank_add // size_t v_size=max(rank_old.size(), rank_new.size()); //make sure that v_size is larger than repeat size_t v_size=20; vector<size_t> rank_remove(v_size), rank_add(v_size), rank_union(s_max+v_size); vector<size_t>::iterator it; it=set_difference (rank_old.begin(), rank_old.end(), rank_new.begin(), rank_new.end(), rank_remove.begin()); rank_remove.resize(it-rank_remove.begin()); it=set_difference (rank_new.begin(), rank_new.end(), rank_old.begin(), rank_old.end(), rank_add.begin()); rank_add.resize(it-rank_add.begin()); it=set_union (rank_new.begin(), rank_new.end(), rank_old.begin(), rank_old.end(), rank_union.begin()); rank_union.resize(it-rank_union.begin()); //map rank_remove and rank_add map<size_t, int> mapRank2in_remove, mapRank2in_add; for (size_t i=0; i<rank_remove.size(); i++) { mapRank2in_remove[rank_remove[i]]=1; } for (size_t i=0; i<rank_add.size(); i++) { mapRank2in_add[rank_add[i]]=1; } //obtain the subset of matrix/vector gsl_matrix_const_view Xold_sub=gsl_matrix_const_submatrix(X_old, 0, 0, X_old->size1, rank_old.size()); gsl_matrix_const_view XtXold_sub=gsl_matrix_const_submatrix(XtX_old, 0, 0, rank_old.size(), rank_old.size()); gsl_vector_const_view Xtyold_sub=gsl_vector_const_subvector(Xty_old, 0, rank_old.size()); gsl_matrix_view Xnew_sub=gsl_matrix_submatrix(X_new, 0, 0, X_new->size1, rank_new.size()); gsl_matrix_view XtXnew_sub=gsl_matrix_submatrix(XtX_new, 0, 0, rank_new.size(), rank_new.size()); gsl_vector_view Xtynew_sub=gsl_vector_subvector(Xty_new, 0, rank_new.size()); //get X_new and calculate XtX_new /* if (rank_remove.size()==0 && rank_add.size()==0) { gsl_matrix_memcpy(&Xnew_sub.matrix, &Xold_sub.matrix); gsl_matrix_memcpy(&XtXnew_sub.matrix, &XtXold_sub.matrix); gsl_vector_memcpy(&Xtynew_sub.vector, &Xtyold_sub.vector); } else { gsl_matrix *X_temp=gsl_matrix_alloc(X_old->size1, rank_old.size()-rank_remove.size() ); gsl_matrix *XtX_temp=gsl_matrix_alloc(X_temp->size2, X_temp->size2); gsl_vector *Xty_temp=gsl_vector_alloc(X_temp->size2); if (rank_remove.size()==0) { gsl_matrix_memcpy (X_temp, &Xold_sub.matrix); gsl_matrix_memcpy (XtX_temp, &XtXold_sub.matrix); gsl_vector_memcpy (Xty_temp, &Xtyold_sub.vector); } else { size_t i_temp=0, j_temp; for (size_t i=0; i<rank_old.size(); i++) { if (mapRank2in_remove.count(rank_old[i])!=0) {continue;} gsl_vector_const_view Xold_col=gsl_matrix_const_column(X_old, i); gsl_vector_view Xtemp_col=gsl_matrix_column(X_temp, i_temp); gsl_vector_memcpy (&Xtemp_col.vector, &Xold_col.vector); d=gsl_vector_get (Xty_old, i); gsl_vector_set (Xty_temp, i_temp, d); j_temp=i_temp; for (size_t j=i; j<rank_old.size(); j++) { if (mapRank2in_remove.count(rank_old[j])!=0) {continue;} d=gsl_matrix_get (XtX_old, i, j); gsl_matrix_set (XtX_temp, i_temp, j_temp, d); if (i_temp!=j_temp) {gsl_matrix_set (XtX_temp, j_temp, i_temp, d);} j_temp++; } i_temp++; } } if (rank_add.size()==0) { gsl_matrix_memcpy (&Xnew_sub.matrix, X_temp); gsl_matrix_memcpy (&XtXnew_sub.matrix, XtX_temp); gsl_vector_memcpy (&Xtynew_sub.vector, Xty_temp); } else { gsl_matrix *X_add=gsl_matrix_alloc(X_old->size1, rank_add.size() ); gsl_matrix *XtX_aa=gsl_matrix_alloc(X_add->size2, X_add->size2); gsl_matrix *XtX_at=gsl_matrix_alloc(X_add->size2, X_temp->size2); gsl_vector *Xty_add=gsl_vector_alloc(X_add->size2); //get X_add SetXgamma (X_add, X, rank_add); //get t(X_add)X_add and t(X_add)X_temp clock_t time_start=clock(); //somehow the lapack_dgemm does not work here //#ifdef WITH_LAPACK //lapack_dgemm ((char *)"T", (char *)"N", 1.0, X_add, X_add, 0.0, XtX_aa); //lapack_dgemm ((char *)"T", (char *)"N", 1.0, X_add, X_temp, 0.0, XtX_at); //#else gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, X_add, X_add, 0.0, XtX_aa); gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, X_add, X_temp, 0.0, XtX_at); //#endif gsl_blas_dgemv(CblasTrans, 1.0, X_add, y, 0.0, Xty_add); time_Omega+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); //save to X_new, XtX_new and Xty_new size_t i_temp=0, j_temp, i_flag=0, j_flag=0; for (size_t i=0; i<rank_new.size(); i++) { if (mapRank2in_add.count(rank_new[i])!=0) {i_flag=1;} else {i_flag=0;} gsl_vector_view Xnew_col=gsl_matrix_column(X_new, i); if (i_flag==1) { gsl_vector_view Xcopy_col=gsl_matrix_column(X_add, i-i_temp); gsl_vector_memcpy (&Xnew_col.vector, &Xcopy_col.vector); } else { gsl_vector_view Xcopy_col=gsl_matrix_column(X_temp, i_temp); gsl_vector_memcpy (&Xnew_col.vector, &Xcopy_col.vector); } if (i_flag==1) { d=gsl_vector_get (Xty_add, i-i_temp); } else { d=gsl_vector_get (Xty_temp, i_temp); } gsl_vector_set (Xty_new, i, d); j_temp=i_temp; for (size_t j=i; j<rank_new.size(); j++) { if (mapRank2in_add.count(rank_new[j])!=0) {j_flag=1;} else {j_flag=0;} if (i_flag==1 && j_flag==1) { d=gsl_matrix_get(XtX_aa, i-i_temp, j-j_temp); } else if (i_flag==1) { d=gsl_matrix_get(XtX_at, i-i_temp, j_temp); } else if (j_flag==1) { d=gsl_matrix_get(XtX_at, j-j_temp, i_temp); } else { d=gsl_matrix_get(XtX_temp, i_temp, j_temp); } gsl_matrix_set (XtX_new, i, j, d); if (i!=j) {gsl_matrix_set (XtX_new, j, i, d);} if (j_flag==0) {j_temp++;} } if (i_flag==0) {i_temp++;} } gsl_matrix_free(X_add); gsl_matrix_free(XtX_aa); gsl_matrix_free(XtX_at); gsl_vector_free(Xty_add); } gsl_matrix_free(X_temp); gsl_matrix_free(XtX_temp); gsl_vector_free(Xty_temp); } */ if (rank_remove.size()==0 && rank_add.size()==0) { gsl_matrix_memcpy(&Xnew_sub.matrix, &Xold_sub.matrix); gsl_matrix_memcpy(&XtXnew_sub.matrix, &XtXold_sub.matrix); gsl_vector_memcpy(&Xtynew_sub.vector, &Xtyold_sub.vector); } else { size_t i_old, j_old, i_new, j_new, i_add, j_add, i_flag, j_flag; if (rank_add.size()==0) { i_old=0; i_new=0; for (size_t i=0; i<rank_union.size(); i++) { if (mapRank2in_remove.count(rank_old[i_old])!=0) {i_old++; continue;} gsl_vector_view Xnew_col=gsl_matrix_column(X_new, i_new); gsl_vector_const_view Xcopy_col=gsl_matrix_const_column(X_old, i_old); gsl_vector_memcpy (&Xnew_col.vector, &Xcopy_col.vector); d=gsl_vector_get (Xty_old, i_old); gsl_vector_set (Xty_new, i_new, d); j_old=i_old; j_new=i_new; for (size_t j=i; j<rank_union.size(); j++) { if (mapRank2in_remove.count(rank_old[j_old])!=0) {j_old++; continue;} d=gsl_matrix_get(XtX_old, i_old, j_old); gsl_matrix_set (XtX_new, i_new, j_new, d); if (i_new!=j_new) {gsl_matrix_set (XtX_new, j_new, i_new, d);} j_old++; j_new++; } i_old++; i_new++; } } else { gsl_matrix *X_add=gsl_matrix_alloc(X_old->size1, rank_add.size() ); gsl_matrix *XtX_aa=gsl_matrix_alloc(X_add->size2, X_add->size2); gsl_matrix *XtX_ao=gsl_matrix_alloc(X_add->size2, X_old->size2); gsl_vector *Xty_add=gsl_vector_alloc(X_add->size2); //get X_add SetXgamma (X_add, X, rank_add); //get t(X_add)X_add and t(X_add)X_temp clock_t time_start=clock(); //somehow the lapack_dgemm does not work here //#ifdef WITH_LAPACK //lapack_dgemm ((char *)"T", (char *)"N", 1.0, X_add, X_add, 0.0, XtX_aa); //lapack_dgemm ((char *)"T", (char *)"N", 1.0, X_add, X_temp, 0.0, XtX_at); //#else gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, X_add, X_add, 0.0, XtX_aa); gsl_blas_dgemm (CblasTrans, CblasNoTrans, 1.0, X_add, X_old, 0.0, XtX_ao); //#endif gsl_blas_dgemv(CblasTrans, 1.0, X_add, y, 0.0, Xty_add); time_Omega+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); //save to X_new, XtX_new and Xty_new i_old=0; i_new=0; i_add=0; for (size_t i=0; i<rank_union.size(); i++) { if (mapRank2in_remove.count(rank_old[i_old])!=0) {i_old++; continue;} if (mapRank2in_add.count(rank_new[i_new])!=0) {i_flag=1;} else {i_flag=0;} gsl_vector_view Xnew_col=gsl_matrix_column(X_new, i_new); if (i_flag==1) { gsl_vector_view Xcopy_col=gsl_matrix_column(X_add, i_add); gsl_vector_memcpy (&Xnew_col.vector, &Xcopy_col.vector); } else { gsl_vector_const_view Xcopy_col=gsl_matrix_const_column(X_old, i_old); gsl_vector_memcpy (&Xnew_col.vector, &Xcopy_col.vector); } if (i_flag==1) { d=gsl_vector_get (Xty_add, i_add); } else { d=gsl_vector_get (Xty_old, i_old); } gsl_vector_set (Xty_new, i_new, d); j_old=i_old; j_new=i_new; j_add=i_add; for (size_t j=i; j<rank_union.size(); j++) { if (mapRank2in_remove.count(rank_old[j_old])!=0) {j_old++; continue;} if (mapRank2in_add.count(rank_new[j_new])!=0) {j_flag=1;} else {j_flag=0;} if (i_flag==1 && j_flag==1) { d=gsl_matrix_get(XtX_aa, i_add, j_add); } else if (i_flag==1) { d=gsl_matrix_get(XtX_ao, i_add, j_old); } else if (j_flag==1) { d=gsl_matrix_get(XtX_ao, j_add, i_old); } else { d=gsl_matrix_get(XtX_old, i_old, j_old); } gsl_matrix_set (XtX_new, i_new, j_new, d); if (i_new!=j_new) {gsl_matrix_set (XtX_new, j_new, i_new, d);} j_new++; if (j_flag==1) {j_add++;} else {j_old++;} } i_new++; if (i_flag==1) {i_add++;} else {i_old++;} } gsl_matrix_free(X_add); gsl_matrix_free(XtX_aa); gsl_matrix_free(XtX_ao); gsl_vector_free(Xty_add); } } rank_remove.clear(); rank_add.clear(); rank_union.clear(); mapRank2in_remove.clear(); mapRank2in_add.clear(); return; } double BSLMM::CalcPosterior (const double yty, class HYPBSLMM &cHyp) { double logpost=0.0; //for quantitative traits, calculate pve and pge //pve and pge for case/control data are calculted in CalcCC_PVEnZ if (a_mode==11) { cHyp.pve=0.0; cHyp.pge=1.0; } //calculate likelihood if (a_mode==11) {logpost-=0.5*(double)ni_test*log(yty);} else {logpost-=0.5*yty;} logpost+=((double)cHyp.n_gamma-1.0)*cHyp.logp+((double)ns_test-(double)cHyp.n_gamma)*log(1-exp(cHyp.logp)); return logpost; } double BSLMM::CalcPosterior (const gsl_matrix *Xgamma, const gsl_matrix *XtX, const gsl_vector *Xty, const double yty, const size_t s_size, gsl_vector *Xb, gsl_vector *beta, class HYPBSLMM &cHyp) { double sigma_a2=cHyp.h/( (1-cHyp.h)*exp(cHyp.logp)*(double)ns_test); double logpost=0.0; double d, P_yy=yty, logdet_O=0.0; gsl_matrix_const_view Xgamma_sub=gsl_matrix_const_submatrix (Xgamma, 0, 0, Xgamma->size1, s_size); gsl_matrix_const_view XtX_sub=gsl_matrix_const_submatrix (XtX, 0, 0, s_size, s_size); gsl_vector_const_view Xty_sub=gsl_vector_const_subvector (Xty, 0, s_size); gsl_matrix *Omega=gsl_matrix_alloc (s_size, s_size); gsl_matrix *M_temp=gsl_matrix_alloc (s_size, s_size); gsl_vector *beta_hat=gsl_vector_alloc (s_size); gsl_vector *Xty_temp=gsl_vector_alloc (s_size); gsl_vector_memcpy (Xty_temp, &Xty_sub.vector); //calculate Omega gsl_matrix_memcpy (Omega, &XtX_sub.matrix); gsl_matrix_scale (Omega, sigma_a2); gsl_matrix_set_identity (M_temp); gsl_matrix_add (Omega, M_temp); //calculate beta_hat logdet_O=CholeskySolve(Omega, Xty_temp, beta_hat); gsl_vector_scale (beta_hat, sigma_a2); gsl_blas_ddot (Xty_temp, beta_hat, &d); P_yy-=d; //sample tau double tau=1.0; if (a_mode==11) {tau =gsl_ran_gamma (gsl_r, (double)ni_test/2.0, 2.0/P_yy); } //sample beta for (size_t i=0; i<s_size; i++) { d=gsl_ran_gaussian(gsl_r, 1); gsl_vector_set(beta, i, d); } gsl_vector_view beta_sub=gsl_vector_subvector(beta, 0, s_size); gsl_blas_dtrsv(CblasUpper, CblasNoTrans, CblasNonUnit, Omega, &beta_sub.vector); //it compuates inv(L^T(Omega)) %*% beta; gsl_vector_scale(&beta_sub.vector, sqrt(sigma_a2/tau)); gsl_vector_add(&beta_sub.vector, beta_hat); gsl_blas_dgemv (CblasNoTrans, 1.0, &Xgamma_sub.matrix, &beta_sub.vector, 0.0, Xb); //for quantitative traits, calculate pve and pge if (a_mode==11) { gsl_blas_ddot (Xb, Xb, &d); cHyp.pve=d/(double)ni_test; cHyp.pve/=cHyp.pve+1.0/tau; cHyp.pge=1.0; } logpost=-0.5*logdet_O; if (a_mode==11) {logpost-=0.5*(double)ni_test*log(P_yy);} else {logpost-=0.5*P_yy;} logpost+=((double)cHyp.n_gamma-1.0)*cHyp.logp+((double)ns_test-(double)cHyp.n_gamma)*log(1.0-exp(cHyp.logp)); gsl_matrix_free (Omega); gsl_matrix_free (M_temp); gsl_vector_free (beta_hat); gsl_vector_free (Xty_temp); return logpost; } //calculate pve and pge, and calculate z_hat for case-control data void BSLMM::CalcCC_PVEnZ (gsl_vector *z_hat, class HYPBSLMM &cHyp) { gsl_vector_set_zero(z_hat); cHyp.pve=0.0; cHyp.pge=1.0; return; } //calculate pve and pge, and calculate z_hat for case-control data void BSLMM::CalcCC_PVEnZ (const gsl_vector *Xb, gsl_vector *z_hat, class HYPBSLMM &cHyp) { double d; gsl_blas_ddot (Xb, Xb, &d); cHyp.pve=d/(double)ni_test; cHyp.pve/=cHyp.pve+1.0; cHyp.pge=1.0; gsl_vector_memcpy (z_hat, Xb); return; } //if a_mode==13, then run probit model void BSLMM::MCMC (const gsl_matrix *X, const gsl_vector *y) { clock_t time_start; double time_set=0, time_post=0; class HYPBSLMM cHyp_old, cHyp_new; gsl_matrix *Result_hyp=gsl_matrix_alloc (w_pace, 6); gsl_matrix *Result_gamma=gsl_matrix_alloc (w_pace, s_max); gsl_vector *Xb_new=gsl_vector_alloc (ni_test); gsl_vector *Xb_old=gsl_vector_alloc (ni_test); gsl_vector *z_hat=gsl_vector_alloc (ni_test); gsl_vector *z=gsl_vector_alloc (ni_test); gsl_matrix *Xgamma_old=gsl_matrix_alloc (ni_test, s_max); gsl_matrix *XtX_old=gsl_matrix_alloc (s_max, s_max); gsl_vector *Xtz_old=gsl_vector_alloc (s_max); gsl_vector *beta_old=gsl_vector_alloc (s_max); gsl_matrix *Xgamma_new=gsl_matrix_alloc (ni_test, s_max); gsl_matrix *XtX_new=gsl_matrix_alloc (s_max, s_max); gsl_vector *Xtz_new=gsl_vector_alloc (s_max); gsl_vector *beta_new=gsl_vector_alloc (s_max); double ztz=0.0; gsl_vector_memcpy (z, y); //for quantitative traits, y is centered already in gemma.cpp, but just in case double mean_z=CenterVector (z); gsl_blas_ddot(z, z, &ztz); double logPost_new, logPost_old; double logMHratio; gsl_matrix_set_zero (Result_gamma); if (a_mode==13) { pheno_mean=0.0; } vector<pair<double, double> > beta_g; for (size_t i=0; i<ns_test; i++) { beta_g.push_back(make_pair(0.0, 0.0)); } vector<size_t> rank_new, rank_old; vector<pair<size_t, double> > pos_loglr; time_start=clock(); MatrixCalcLmLR (X, z, pos_loglr); time_Proposal=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); stable_sort (pos_loglr.begin(), pos_loglr.end(), comp_lr); for (size_t i=0; i<ns_test; ++i) { mapRank2pos[i]=pos_loglr[i].first; } //calculate proposal distribution for gamma (unnormalized), and set up gsl_r and gsl_t gsl_rng_env_setup(); const gsl_rng_type * gslType; gslType = gsl_rng_default; if (randseed<0) { time_t rawtime; time (&rawtime); tm * ptm = gmtime (&rawtime); randseed = (unsigned) (ptm->tm_hour%24*3600+ptm->tm_min*60+ptm->tm_sec); } gsl_r = gsl_rng_alloc(gslType); gsl_rng_set(gsl_r, randseed); double *p_gamma = new double[ns_test]; CalcPgamma (p_gamma); gsl_t=gsl_ran_discrete_preproc (ns_test, p_gamma); //initial parameters InitialMCMC (X, z, rank_old, cHyp_old, pos_loglr); cHyp_initial=cHyp_old; if (cHyp_old.n_gamma==0) { logPost_old=CalcPosterior (ztz, cHyp_old); } else { SetXgamma (Xgamma_old, X, rank_old); CalcXtX (Xgamma_old, z, rank_old.size(), XtX_old, Xtz_old); logPost_old=CalcPosterior (Xgamma_old, XtX_old, Xtz_old, ztz, rank_old.size(), Xb_old, beta_old, cHyp_old); } //calculate centered z_hat, and pve if (a_mode==13) { if (cHyp_old.n_gamma==0) { CalcCC_PVEnZ (z_hat, cHyp_old); } else { CalcCC_PVEnZ (Xb_old, z_hat, cHyp_old); } } //start MCMC int accept; size_t total_step=w_step+s_step; size_t w=0, w_col, pos; size_t repeat=0; for (size_t t=0; t<total_step; ++t) { if (t%d_pace==0 || t==total_step-1) {ProgressBar ("Running MCMC ", t, total_step-1, (double)n_accept/(double)(t*n_mh+1));} // if (t>10) {break;} if (a_mode==13) { SampleZ (y, z_hat, z); mean_z=CenterVector (z); gsl_blas_ddot(z,z,&ztz); //First proposal if (cHyp_old.n_gamma==0) { logPost_old=CalcPosterior (ztz, cHyp_old); } else { gsl_matrix_view Xold_sub=gsl_matrix_submatrix(Xgamma_old, 0, 0, ni_test, rank_old.size()); gsl_vector_view Xtz_sub=gsl_vector_subvector(Xtz_old, 0, rank_old.size()); gsl_blas_dgemv (CblasTrans, 1.0, &Xold_sub.matrix, z, 0.0, &Xtz_sub.vector); logPost_old=CalcPosterior (Xgamma_old, XtX_old, Xtz_old, ztz, rank_old.size(), Xb_old, beta_old, cHyp_old); } } //MH steps for (size_t i=0; i<n_mh; ++i) { if (gsl_rng_uniform(gsl_r)<0.33) {repeat = 1+gsl_rng_uniform_int(gsl_r, 20);} else {repeat=1;} logMHratio=0.0; logMHratio+=ProposeHnRho(cHyp_old, cHyp_new, repeat); logMHratio+=ProposeGamma (rank_old, rank_new, p_gamma, cHyp_old, cHyp_new, repeat); logMHratio+=ProposePi(cHyp_old, cHyp_new, repeat); if (cHyp_new.n_gamma==0) { logPost_new=CalcPosterior (ztz, cHyp_new); } else { //this if makes sure that rank_old.size()==rank_remove.size() does not happen if (cHyp_new.n_gamma<=20 || cHyp_old.n_gamma<=20) { time_start=clock(); SetXgamma (Xgamma_new, X, rank_new); CalcXtX (Xgamma_new, z, rank_new.size(), XtX_new, Xtz_new); time_set+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); } else { time_start=clock(); SetXgamma (X, Xgamma_old, XtX_old, Xtz_old, z, rank_old, rank_new, Xgamma_new, XtX_new, Xtz_new); time_set+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); } time_start=clock(); logPost_new=CalcPosterior (Xgamma_new, XtX_new, Xtz_new, ztz, rank_new.size(), Xb_new, beta_new, cHyp_new); time_post+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); } logMHratio+=logPost_new-logPost_old; if (logMHratio>0 || log(gsl_rng_uniform(gsl_r))<logMHratio) {accept=1; n_accept++;} else {accept=0;} //cout<<rank_new.size()<<"\t"<<rank_old.size()<<"\t"<<logPost_new<<"\t"<<logPost_old<<endl; if (accept==1) { logPost_old=logPost_new; cHyp_old=cHyp_new; gsl_vector_memcpy (Xb_old, Xb_new); rank_old.clear(); if (rank_new.size()!=0) { for (size_t i=0; i<rank_new.size(); ++i) { rank_old.push_back(rank_new[i]); } gsl_matrix_view Xold_sub=gsl_matrix_submatrix(Xgamma_old, 0, 0, ni_test, rank_new.size()); gsl_matrix_view XtXold_sub=gsl_matrix_submatrix(XtX_old, 0, 0, rank_new.size(), rank_new.size()); gsl_vector_view Xtzold_sub=gsl_vector_subvector(Xtz_old, 0, rank_new.size()); gsl_vector_view betaold_sub=gsl_vector_subvector(beta_old, 0, rank_new.size()); gsl_matrix_view Xnew_sub=gsl_matrix_submatrix(Xgamma_new, 0, 0, ni_test, rank_new.size()); gsl_matrix_view XtXnew_sub=gsl_matrix_submatrix(XtX_new, 0, 0, rank_new.size(), rank_new.size()); gsl_vector_view Xtznew_sub=gsl_vector_subvector(Xtz_new, 0, rank_new.size()); gsl_vector_view betanew_sub=gsl_vector_subvector(beta_new, 0, rank_new.size()); gsl_matrix_memcpy(&Xold_sub.matrix, &Xnew_sub.matrix); gsl_matrix_memcpy(&XtXold_sub.matrix, &XtXnew_sub.matrix); gsl_vector_memcpy(&Xtzold_sub.vector, &Xtznew_sub.vector); gsl_vector_memcpy(&betaold_sub.vector, &betanew_sub.vector); } } else { cHyp_new=cHyp_old; } } //calculate z_hat, and pve if (a_mode==13) { if (cHyp_old.n_gamma==0) { CalcCC_PVEnZ (z_hat, cHyp_old); } else { CalcCC_PVEnZ (Xb_old, z_hat, cHyp_old); } //sample mu and update z hat gsl_vector_sub (z, z_hat); mean_z+=CenterVector(z); mean_z+=gsl_ran_gaussian(gsl_r, sqrt(1.0/(double) ni_test) ); gsl_vector_add_constant (z_hat, mean_z); } //Save data if (t<w_step) {continue;} else { if (t%r_pace==0) { w_col=w%w_pace; if (w_col==0) { if (w==0) {WriteResult (0, Result_hyp, Result_gamma, w_col);} else { WriteResult (1, Result_hyp, Result_gamma, w_col); gsl_matrix_set_zero (Result_hyp); gsl_matrix_set_zero (Result_gamma); } } gsl_matrix_set (Result_hyp, w_col, 0, cHyp_old.h); gsl_matrix_set (Result_hyp, w_col, 1, cHyp_old.pve); gsl_matrix_set (Result_hyp, w_col, 2, cHyp_old.rho); gsl_matrix_set (Result_hyp, w_col, 3, cHyp_old.pge); gsl_matrix_set (Result_hyp, w_col, 4, cHyp_old.logp); gsl_matrix_set (Result_hyp, w_col, 5, cHyp_old.n_gamma); for (size_t i=0; i<cHyp_old.n_gamma; ++i) { pos=mapRank2pos[rank_old[i]]+1; gsl_matrix_set (Result_gamma, w_col, i, pos); beta_g[pos-1].first+=gsl_vector_get(beta_old, i); beta_g[pos-1].second+=1.0; } if (a_mode==13) { pheno_mean+=mean_z; } w++; } } } cout<<endl; cout<<"time on selecting Xgamma: "<<time_set<<endl; cout<<"time on calculating posterior: "<<time_post<<endl; w_col=w%w_pace; WriteResult (1, Result_hyp, Result_gamma, w_col); gsl_vector *alpha=gsl_vector_alloc (ns_test); gsl_vector_set_zero (alpha); WriteParam (beta_g, alpha, w); gsl_vector_free(alpha); gsl_matrix_free(Result_hyp); gsl_matrix_free(Result_gamma); gsl_vector_free(z_hat); gsl_vector_free(z); gsl_vector_free(Xb_new); gsl_vector_free(Xb_old); gsl_matrix_free(Xgamma_old); gsl_matrix_free(XtX_old); gsl_vector_free(Xtz_old); gsl_vector_free(beta_old); gsl_matrix_free(Xgamma_new); gsl_matrix_free(XtX_new); gsl_vector_free(Xtz_new); gsl_vector_free(beta_new); delete [] p_gamma; beta_g.clear(); return; }