/* Genome-wide Efficient Mixed Model Association (GEMMA) Copyright (C) 2011-2017, 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 "logistic.h" #include "lapack.h" #include "io.h" #include "param.h" #include "bslmmdap.h" #include "lmm.h" #include "lm.h" #include "mathfunc.h" using namespace std; void BSLMMDAP::CopyFromParam (PARAM &cPar) { file_out=cPar.file_out; path_out=cPar.path_out; time_UtZ=0.0; time_Omega=0.0; h_min=cPar.h_min; h_max=cPar.h_max; h_ngrid=cPar.h_ngrid; rho_min=cPar.rho_min; rho_max=cPar.rho_max; rho_ngrid=cPar.rho_ngrid; if (h_min<=0) {h_min=0.01;} if (h_max>=1) {h_max=0.99;} if (rho_min<=0) {rho_min=0.01;} if (rho_max>=1) {rho_max=0.99;} 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; indicator_idv=cPar.indicator_idv; indicator_snp=cPar.indicator_snp; snpInfo=cPar.snpInfo; return; } void BSLMMDAP::CopyToParam (PARAM &cPar) { cPar.time_UtZ=time_UtZ; cPar.time_Omega=time_Omega; return; } // Read hyp file. void ReadFile_hyb (const string &file_hyp, vector<double> &vec_sa2, vector<double> &vec_sb2, vector<double> &vec_wab) { vec_sa2.clear(); vec_sb2.clear(); vec_wab.clear(); igzstream infile (file_hyp.c_str(), igzstream::in); if (!infile) { cout<<"error! fail to open hyp file: "<<file_hyp<<endl; return; } string line; char *ch_ptr; getline(infile, line); while (!safeGetline(infile, line).eof()) { ch_ptr=strtok ((char *)line.c_str(), " , \t"); ch_ptr=strtok (NULL, " , \t"); ch_ptr=strtok (NULL, " , \t"); vec_sa2.push_back(atof(ch_ptr)); ch_ptr=strtok (NULL, " , \t"); vec_sb2.push_back(atof(ch_ptr)); ch_ptr=strtok (NULL, " , \t"); vec_wab.push_back(atof(ch_ptr)); } infile.close(); infile.clear(); return; } // Read bf file. void ReadFile_bf (const string &file_bf, vector<string> &vec_rs, vector<vector<vector<double> > > &BF) { BF.clear(); vec_rs.clear(); igzstream infile (file_bf.c_str(), igzstream::in); if (!infile) {cout<<"error! fail to open bf file: "<<file_bf<<endl; return;} string line, rs, block; vector<double> vec_bf; vector<vector<double> > mat_bf; char *ch_ptr; size_t bf_size, flag_block; getline(infile, line); size_t t=0; while (!safeGetline(infile, line).eof()) { flag_block=0; ch_ptr=strtok ((char *)line.c_str(), " , \t"); rs=ch_ptr; vec_rs.push_back(rs); ch_ptr=strtok (NULL, " , \t"); if (t==0) { block=ch_ptr; } else { if (strcmp(ch_ptr, block.c_str() )!=0) { flag_block=1; block=ch_ptr; } } ch_ptr=strtok (NULL, " , \t"); while (ch_ptr!=NULL) { vec_bf.push_back(atof(ch_ptr)); ch_ptr=strtok (NULL, " , \t"); } if (t==0) { bf_size=vec_bf.size(); } else { if (bf_size!=vec_bf.size()) { cout<<"error! unequal row size in bf file."<<endl; } } if (flag_block==0) { mat_bf.push_back(vec_bf); } else { BF.push_back(mat_bf); mat_bf.clear(); } vec_bf.clear(); t++; } infile.close(); infile.clear(); return; } // Read category files. // Read both continuous and discrete category file, record mapRS2catc. void ReadFile_cat (const string &file_cat, const vector<string> &vec_rs, gsl_matrix *Ac, gsl_matrix_int *Ad, gsl_vector_int *dlevel, size_t &kc, size_t &kd) { igzstream infile (file_cat.c_str(), igzstream::in); if (!infile) { cout<<"error! fail to open category file: "<<file_cat<<endl; return; } string line; char *ch_ptr; string rs, chr, a1, a0, pos, cm; // Read header. HEADER header; !safeGetline(infile, line).eof(); ReadHeader_io (line, header); // Use the header to determine the number of categories. kc=header.catc_col.size(); kd=header.catd_col.size(); //set up storage and mapper map<string, vector<double> > mapRS2catc; map<string, vector<int> > mapRS2catd; vector<double> catc; vector<int> catd; // Read the following lines to record mapRS2cat. while (!safeGetline(infile, line).eof()) { ch_ptr=strtok ((char *)line.c_str(), " , \t"); if (header.rs_col==0) { rs=chr+":"+pos; } catc.clear(); catd.clear(); for (size_t i=0; i<header.coln; i++) { if (header.rs_col!=0 && header.rs_col==i+1) { rs=ch_ptr; } else if (header.chr_col!=0 && header.chr_col==i+1) { chr=ch_ptr; } else if (header.pos_col!=0 && header.pos_col==i+1) { pos=ch_ptr; } else if (header.cm_col!=0 && header.cm_col==i+1) { cm=ch_ptr; } else if (header.a1_col!=0 && header.a1_col==i+1) { a1=ch_ptr; } else if (header.a0_col!=0 && header.a0_col==i+1) { a0=ch_ptr; } else if (header.catc_col.size()!=0 && header.catc_col.count(i+1)!=0 ) { catc.push_back(atof(ch_ptr)); } else if (header.catd_col.size()!=0 && header.catd_col.count(i+1)!=0 ) { catd.push_back(atoi(ch_ptr)); } else {} ch_ptr=strtok (NULL, " , \t"); } if (mapRS2catc.count(rs)==0 && kc>0) {mapRS2catc[rs]=catc;} if (mapRS2catd.count(rs)==0 && kd>0) {mapRS2catd[rs]=catd;} } // Load into Ad and Ac. if (kc>0) { Ac=gsl_matrix_alloc(vec_rs.size(), kc); for (size_t i=0; i<vec_rs.size(); i++) { if (mapRS2catc.count(vec_rs[i])!=0) { for (size_t j=0; j<kc; j++) { gsl_matrix_set(Ac, i, j, mapRS2catc[vec_rs[i]][j]); } } else { for (size_t j=0; j<kc; j++) { gsl_matrix_set(Ac, i, j, 0); } } } } if (kd>0) { Ad=gsl_matrix_int_alloc(vec_rs.size(), kd); for (size_t i=0; i<vec_rs.size(); i++) { if (mapRS2catd.count(vec_rs[i])!=0) { for (size_t j=0; j<kd; j++) { gsl_matrix_int_set(Ad, i, j, mapRS2catd[vec_rs[i]][j]); } } else { for (size_t j=0; j<kd; j++) { gsl_matrix_int_set(Ad, i, j, 0); } } } dlevel=gsl_vector_int_alloc(kd); map<int, int> rcd; int val; for (size_t j=0; j<kd; j++) { rcd.clear(); for (size_t i=0; i<Ad->size1; i++) { val = gsl_matrix_int_get(Ad, i, j); rcd[val] = 1; } gsl_vector_int_set (dlevel, j, rcd.size()); } } infile.clear(); infile.close(); return; } void BSLMMDAP::WriteResult (const gsl_matrix *Hyper, const gsl_matrix *BF) { string file_bf, file_hyp; file_bf=path_out+"/"+file_out; file_bf+=".bf.txt"; file_hyp=path_out+"/"+file_out; file_hyp+=".hyp.txt"; ofstream outfile_bf, outfile_hyp; outfile_bf.open (file_bf.c_str(), ofstream::out); outfile_hyp.open (file_hyp.c_str(), ofstream::out); if (!outfile_bf) { cout<<"error writing file: "<<file_bf<<endl; return; } if (!outfile_hyp) { cout<<"error writing file: "<<file_hyp<<endl; return; } outfile_hyp<<"h"<<"\t"<<"rho"<<"\t"<<"sa2"<<"\t"<<"sb2"<<"\t"<< "weight"<<endl; outfile_hyp<<scientific; for (size_t i=0; i<Hyper->size1; i++) { for (size_t j=0; j<Hyper->size2; j++) { outfile_hyp<<setprecision(6)<<gsl_matrix_get (Hyper, i, j)<<"\t"; } outfile_hyp<<endl; } outfile_bf<<"chr"<<"\t"<<"rs"<<"\t"<<"ps"<<"\t"<<"n_miss"; for (size_t i=0; i<BF->size2; i++) { outfile_bf<<"\t"<<"BF"<<i+1; } outfile_bf<<endl; size_t t=0; for (size_t i=0; i<ns_total; ++i) { if (indicator_snp[i]==0) {continue;} outfile_bf<<snpInfo[i].chr<<"\t"<<snpInfo[i].rs_number<<"\t" <<snpInfo[i].base_position<<"\t"<<snpInfo[i].n_miss; outfile_bf<<scientific; for (size_t j=0; j<BF->size2; j++) { outfile_bf<<"\t"<<setprecision(6)<<gsl_matrix_get (BF, t, j); } outfile_bf<<endl; t++; } outfile_hyp.close(); outfile_hyp.clear(); outfile_bf.close(); outfile_bf.clear(); return; } void BSLMMDAP::WriteResult (const vector<string> &vec_rs, const gsl_matrix *Hyper, const gsl_vector *pip, const gsl_vector *coef) { string file_gamma, file_hyp, file_coef; file_gamma=path_out+"/"+file_out; file_gamma+=".gamma.txt"; file_hyp=path_out+"/"+file_out; file_hyp+=".hyp.txt"; file_coef=path_out+"/"+file_out; file_coef+=".coef.txt"; ofstream outfile_gamma, outfile_hyp, outfile_coef; outfile_gamma.open (file_gamma.c_str(), ofstream::out); outfile_hyp.open (file_hyp.c_str(), ofstream::out); outfile_coef.open (file_coef.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; } if (!outfile_coef) { cout<<"error writing file: "<<file_coef<<endl; return; } outfile_hyp<<"h"<<"\t"<<"rho"<<"\t"<<"sa2"<<"\t"<<"sb2"<<"\t"<< "weight"<<endl; outfile_hyp<<scientific; for (size_t i=0; i<Hyper->size1; i++) { for (size_t j=0; j<Hyper->size2; j++) { outfile_hyp<<setprecision(6)<<gsl_matrix_get (Hyper, i, j)<<"\t"; } outfile_hyp<<endl; } outfile_gamma<<"rs"<<"\t"<<"gamma"<<endl; for (size_t i=0; i<vec_rs.size(); ++i) { outfile_gamma<<vec_rs[i]<<"\t"<<scientific<<setprecision(6)<< gsl_vector_get(pip, i)<<endl; } outfile_coef<<"coef"<<endl; outfile_coef<<scientific; for (size_t i=0; i<coef->size; i++) { outfile_coef<<setprecision(6)<<gsl_vector_get (coef, i)<<endl; } outfile_coef.close(); outfile_coef.clear(); outfile_hyp.close(); outfile_hyp.clear(); outfile_gamma.close(); outfile_gamma.clear(); return; } double BSLMMDAP::CalcMarginal (const gsl_vector *Uty, const gsl_vector *K_eval, const double sigma_b2, const double tau) { gsl_vector *weight_Hi=gsl_vector_alloc (Uty->size); double logm=0.0; double d, 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; 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; } // Calculate likelihood. logm=-0.5*logdet_H-0.5*tau*Hi_yy+0.5*log(tau)*(double)ni_test; gsl_vector_free (weight_Hi); return logm; } double BSLMMDAP::CalcMarginal (const gsl_matrix *UtXgamma, const gsl_vector *Uty, const gsl_vector *K_eval, const double sigma_a2, const double sigma_b2, const double tau) { clock_t time_start; double logm=0.0; double d, 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 *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; 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); } // Calculate Omega. gsl_matrix_set_identity (Omega); time_start=clock(); lapack_dgemm ((char *)"T", (char *)"N", sigma_a2, UtXgamma_eval, UtXgamma, 1.0, Omega); 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; gsl_matrix_free (UtXgamma_eval); gsl_matrix_free (Omega); gsl_vector_free (XtHiy); gsl_vector_free (beta_hat); gsl_vector_free (weight_Hi); logm=-0.5*logdet_H-0.5*logdet_O-0.5*tau*P_yy+0.5*log(tau)* (double)ni_test; return logm; } double BSLMMDAP::CalcPrior (class HYPBSLMM &cHyp) { double logprior=0; logprior=((double)cHyp.n_gamma-1.0)*cHyp.logp+ ((double)ns_test-(double)cHyp.n_gamma)*log(1.0-exp(cHyp.logp)); return logprior; } // Where A is the ni_test by n_cat matrix of annotations. void BSLMMDAP::DAP_CalcBF (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; // Set up BF. double tau, h, rho, sigma_a2, sigma_b2, d; size_t ns_causal=10; size_t n_grid=h_ngrid*rho_ngrid; vector<double> vec_sa2, vec_sb2, logm_null; gsl_matrix *BF=gsl_matrix_alloc(ns_test, n_grid); gsl_matrix *Xgamma=gsl_matrix_alloc(ni_test, 1); gsl_matrix *Hyper=gsl_matrix_alloc(n_grid, 5); // Compute tau by using yty. gsl_blas_ddot (Uty, Uty, &tau); tau=(double)ni_test/tau; // Set up grid values for sigma_a2 and sigma_b2 based on an // approximately even grid for h and rho, and a fixed number // of causals. size_t ij=0; for (size_t i=0; i<h_ngrid; i++) { h=h_min+(h_max-h_min)*(double)i/((double)h_ngrid-1); for (size_t j=0; j<rho_ngrid; j++) { rho=rho_min+(rho_max-rho_min)*(double)j/((double)rho_ngrid-1); sigma_a2=h*rho/((1-h)*(double)ns_causal); sigma_b2=h*(1.0-rho)/(trace_G*(1-h)); vec_sa2.push_back(sigma_a2); vec_sb2.push_back(sigma_b2); logm_null.push_back(CalcMarginal (Uty, K_eval, 0.0, tau)); gsl_matrix_set (Hyper, ij, 0, h); gsl_matrix_set (Hyper, ij, 1, rho); gsl_matrix_set (Hyper, ij, 2, sigma_a2); gsl_matrix_set (Hyper, ij, 3, sigma_b2); gsl_matrix_set (Hyper, ij, 4, 1/(double)n_grid); ij++; } } // Compute BF factors. time_start=clock(); cout<<"Calculating BF..."<<endl; for (size_t t=0; t<ns_test; t++) { gsl_vector_view Xgamma_col=gsl_matrix_column (Xgamma, 0); gsl_vector_const_view X_col=gsl_matrix_const_column (UtX, t); gsl_vector_memcpy (&Xgamma_col.vector, &X_col.vector); for (size_t ij=0; ij<n_grid; ij++) { sigma_a2=vec_sa2[ij]; sigma_b2=vec_sb2[ij]; d=CalcMarginal (Xgamma, Uty, K_eval, sigma_a2, sigma_b2, tau); d-=logm_null[ij]; d=exp(d); gsl_matrix_set(BF, t, ij, d); } } time_Proposal=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); // Save results. WriteResult (Hyper, BF); // Free matrices and vectors. gsl_matrix_free(BF); gsl_matrix_free(Xgamma); gsl_matrix_free(Hyper); return; } void single_ct_regression(const gsl_matrix_int *Xd, const gsl_vector_int *dlevel, const gsl_vector *pip_vec, gsl_vector *coef, gsl_vector *prior_vec) { map<int,double> sum_pip; map<int,double> sum; int levels = gsl_vector_int_get(dlevel,0); for(int i=0;i<levels;i++){ sum_pip[i] = sum[i] = 0; } for(int i=0;i<Xd->size1;i++){ int cat = gsl_matrix_int_get(Xd,i,0); sum_pip[cat] += gsl_vector_get(pip_vec,i); sum[cat] += 1; } for(int i=0;i<Xd->size1;i++){ int cat = gsl_matrix_int_get(Xd,i,0); gsl_vector_set(prior_vec,i,sum_pip[cat]/sum[cat]); } for(int i=0;i<levels;i++){ double new_prior = sum_pip[i]/sum[i]; gsl_vector_set(coef, i, log(new_prior/(1-new_prior)) ); } return; } // Where A is the ni_test by n_cat matrix of annotations. void BSLMMDAP::DAP_EstimateHyper (const size_t kc, const size_t kd, const vector<string> &vec_rs, const vector<double> &vec_sa2, const vector<double> &vec_sb2, const vector<double> &wab, const vector<vector<vector<double> > > &BF, gsl_matrix *Ac, gsl_matrix_int *Ad, gsl_vector_int *dlevel) { clock_t time_start; // Set up BF. double h, rho, sigma_a2, sigma_b2, d, s, logm, logm_save; size_t t1, t2; size_t n_grid=wab.size(), ns_test=vec_rs.size(); gsl_vector *prior_vec=gsl_vector_alloc(ns_test); gsl_matrix *Hyper=gsl_matrix_alloc(n_grid, 5); gsl_vector *pip=gsl_vector_alloc(ns_test); gsl_vector *coef=gsl_vector_alloc(kc+kd+1); // Perform the EM algorithm. vector<double> vec_wab, vec_wab_new; // Initial values. for (size_t t=0; t<ns_test; t++) { gsl_vector_set (prior_vec, t, (double)BF.size()/(double)ns_test); } for (size_t ij=0; ij<n_grid; ij++) { vec_wab.push_back(wab[ij]); vec_wab_new.push_back(wab[ij]); } // EM iteration. size_t it=0; double dif=1; while (it<100 && dif>1e-3) { // Update E_gamma. t1=0, t2=0; for (size_t b=0; b<BF.size(); b++) { s=1; for (size_t m=0; m<BF[b].size(); m++) { d=0; for (size_t ij=0; ij<n_grid; ij++) { d+=vec_wab_new[ij]*BF[b][m][ij]; } d*=gsl_vector_get(prior_vec,t1)/(1-gsl_vector_get(prior_vec,t1)); gsl_vector_set(pip, t1, d); s+=d; t1++; } for (size_t m=0; m<BF[b].size(); m++) { d=gsl_vector_get(pip, t2)/s; gsl_vector_set(pip, t2, d); t2++; } } // Update E_wab. s=0; for (size_t ij=0; ij<n_grid; ij++) { vec_wab_new[ij]=0; t1=0; for (size_t b=0; b<BF.size(); b++) { d=1; for (size_t m=0; m<BF[b].size(); m++) { d+=gsl_vector_get(prior_vec, t1)/ (1-gsl_vector_get(prior_vec, t1))*vec_wab[ij]*BF[b][m][ij]; t1++; } vec_wab_new[ij]+=log(d); } s=max(s, vec_wab_new[ij]); } d=0; for (size_t ij=0; ij<n_grid; ij++) { vec_wab_new[ij]=exp(vec_wab_new[ij]-s); d+=vec_wab_new[ij]; } for (size_t ij=0; ij<n_grid; ij++) { vec_wab_new[ij]/=d; } // Update coef, and pi. if(kc==0 && kd==0){ // No annotation. s=0; for (size_t t=0; t<pip->size; t++) { s+=gsl_vector_get(pip, t); } s=s/(double)pip->size; for (size_t t=0; t<pip->size; t++) { gsl_vector_set(prior_vec, t, s); } gsl_vector_set (coef, 0, log(s/(1-s))); } else if(kc==0 && kd!=0){ // Only discrete annotations. if(kd == 1){ single_ct_regression(Ad, dlevel, pip, coef, prior_vec); }else{ logistic_cat_fit(coef, Ad, dlevel, pip, 0, 0); logistic_cat_pred(coef, Ad, dlevel, prior_vec); } } else if (kc!=0 && kd==0) { // Only continuous annotations. logistic_cont_fit(coef, Ac, pip, 0, 0); logistic_cont_pred(coef, Ac, prior_vec); } else if (kc!=0 && kd!=0) { // Both continuous and categorical annotations. logistic_mixed_fit(coef, Ad, dlevel, Ac, pip, 0, 0); logistic_mixed_pred(coef, Ad, dlevel, Ac, prior_vec); } // Compute marginal likelihood. logm=0; t1=0; for (size_t b=0; b<BF.size(); b++) { d=1; s=0; for (size_t m=0; m<BF[b].size(); m++) { s+=log(1-gsl_vector_get(prior_vec, t1)); for (size_t ij=0; ij<n_grid; ij++) { d+=gsl_vector_get(prior_vec, t1)/ (1-gsl_vector_get(prior_vec, t1))*vec_wab[ij]*BF[b][m][ij]; } } logm+=log(d)+s; t1++; } if (it>0) { dif=logm-logm_save; } logm_save=logm; it++; cout<<"iteration = "<<it<<"; marginal likelihood = "<<logm<<endl; } // Update h and rho that correspond to w_ab. for (size_t ij=0; ij<n_grid; ij++) { sigma_a2=vec_sa2[ij]; sigma_b2=vec_sb2[ij]; d=exp(gsl_vector_get(coef, coef->size-1))/ (1+exp(gsl_vector_get(coef, coef->size-1))); h=(d*(double)ns_test*sigma_a2+1*sigma_b2)/ (1+d*(double)ns_test*sigma_a2+1*sigma_b2); rho=d*(double)ns_test*sigma_a2/ (d*(double)ns_test*sigma_a2+1*sigma_b2); gsl_matrix_set (Hyper, ij, 0, h); gsl_matrix_set (Hyper, ij, 1, rho); gsl_matrix_set (Hyper, ij, 2, sigma_a2); gsl_matrix_set (Hyper, ij, 3, sigma_b2); gsl_matrix_set (Hyper, ij, 4, vec_wab_new[ij]); } // Obtain beta and alpha parameters. // Save results. WriteResult (vec_rs, Hyper, pip, coef); // Free matrices and vectors. gsl_vector_free(prior_vec); gsl_matrix_free(Hyper); gsl_vector_free(pip); gsl_vector_free(coef); return; }