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Diffstat (limited to 'mvlmm.cpp')
| -rw-r--r-- | mvlmm.cpp | 3749 |
1 files changed, 0 insertions, 3749 deletions
diff --git a/mvlmm.cpp b/mvlmm.cpp deleted file mode 100644 index 4b910ee..0000000 --- a/mvlmm.cpp +++ /dev/null @@ -1,3749 +0,0 @@ -/* - 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 <bitset> -#include <cstring> - -#include "gsl/gsl_vector.h" -#include "gsl/gsl_matrix.h" -#include "gsl/gsl_linalg.h" -#include "gsl/gsl_blas.h" - -#include "gsl/gsl_cdf.h" -#include "gsl/gsl_roots.h" -#include "gsl/gsl_min.h" -#include "gsl/gsl_integration.h" - -#include "io.h" -#include "lapack.h" -#include "gzstream.h" - -#ifdef FORCE_FLOAT -#include "lmm_float.h" -#include "mvlmm_float.h" -#else -#include "lmm.h" -#include "mvlmm.h" -#endif - - - -using namespace std; - - -//in this file, X, Y are already transformed (i.e. UtX and UtY) - - -void MVLMM::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.l_min; - l_max=cPar.l_max; - n_region=cPar.n_region; - p_nr=cPar.p_nr; - em_iter=cPar.em_iter; - nr_iter=cPar.nr_iter; - em_prec=cPar.em_prec; - nr_prec=cPar.nr_prec; - crt=cPar.crt; - - Vg_remle_null=cPar.Vg_remle_null; - Ve_remle_null=cPar.Ve_remle_null; - Vg_mle_null=cPar.Vg_mle_null; - Ve_mle_null=cPar.Ve_mle_null; - - time_UtX=0.0; - time_opt=0.0; - - 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; - - n_ph=cPar.n_ph; - - indicator_idv=cPar.indicator_idv; - indicator_snp=cPar.indicator_snp; - snpInfo=cPar.snpInfo; - - return; -} - - -void MVLMM::CopyToParam (PARAM &cPar) -{ - cPar.time_UtX=time_UtX; - cPar.time_opt=time_opt; - - cPar.Vg_remle_null=Vg_remle_null; - cPar.Ve_remle_null=Ve_remle_null; - cPar.Vg_mle_null=Vg_mle_null; - cPar.Ve_mle_null=Ve_mle_null; - - cPar.VVg_remle_null=VVg_remle_null; - cPar.VVe_remle_null=VVe_remle_null; - cPar.VVg_mle_null=VVg_mle_null; - cPar.VVe_mle_null=VVe_mle_null; - - cPar.beta_remle_null=beta_remle_null; - cPar.se_beta_remle_null=se_beta_remle_null; - cPar.beta_mle_null=beta_mle_null; - cPar.se_beta_mle_null=se_beta_mle_null; - - cPar.logl_remle_H0=logl_remle_H0; - cPar.logl_mle_H0=logl_mle_H0; - return; -} - - -void MVLMM::WriteFiles () -{ - string file_str; - file_str=path_out+"/"+file_out; - file_str+=".assoc.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"<<"allele1"<<"\t"<<"allele0"<<"\t"<<"af"<<"\t"; - - for (size_t i=0; i<n_ph; i++) { - outfile<<"beta_"<<i+1<<"\t"; - } - for (size_t i=0; i<n_ph; i++) { - for (size_t j=i; j<n_ph; j++) { - outfile<<"Vbeta_"<<i+1<<"_"<<j+1<<"\t"; - } - } - - if (a_mode==1) { - outfile<<"p_wald"<<endl; - } else if (a_mode==2) { - outfile<<"p_lrt"<<endl; - } else if (a_mode==3) { - outfile<<"p_score"<<endl; - } else if (a_mode==4) { - outfile<<"p_wald"<<"\t"<<"p_lrt"<<"\t"<<"p_score"<<endl; - } else {} - - - size_t t=0, c=0; - for (size_t i=0; i<snpInfo.size(); ++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"<<snpInfo[i].a_minor<<"\t"<<snpInfo[i].a_major<<"\t"<<fixed<<setprecision(3)<<snpInfo[i].maf<<"\t"; - - outfile<<scientific<<setprecision(6); - - for (size_t i=0; i<n_ph; i++) { - outfile<<sumStat[t].v_beta[i]<<"\t"; - } - - c=0; - for (size_t i=0; i<n_ph; i++) { - for (size_t j=i; j<n_ph; j++) { - outfile<<sumStat[t].v_Vbeta[c]<<"\t"; - c++; - } - } - - if (a_mode==1) { - outfile<<sumStat[t].p_wald <<endl; - } else if (a_mode==2) { - outfile<<sumStat[t].p_lrt<<endl; - } else if (a_mode==3) { - outfile<<sumStat[t].p_score<<endl; - } else if (a_mode==4) { - outfile<<sumStat[t].p_wald <<"\t"<<sumStat[t].p_lrt<<"\t"<<sumStat[t].p_score<<endl; - } else {} - - t++; - } - - - outfile.close(); - outfile.clear(); - return; -} - - - - -//below are functions for EM algorithm - - - - - - -double EigenProc (const gsl_matrix *V_g, const gsl_matrix *V_e, gsl_vector *D_l, gsl_matrix *UltVeh, gsl_matrix *UltVehi) -{ - size_t d_size=V_g->size1; - double d, logdet_Ve=0.0; - - //eigen decomposition of V_e - gsl_matrix *Lambda=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e_temp=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e_h=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e_hi=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *VgVehi=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *U_l=gsl_matrix_alloc (d_size, d_size); - - gsl_matrix_memcpy(V_e_temp, V_e); - EigenDecomp(V_e_temp, U_l, D_l, 0); - - //calculate V_e_h and V_e_hi - gsl_matrix_set_zero(V_e_h); - gsl_matrix_set_zero(V_e_hi); - for (size_t i=0; i<d_size; i++) { - d=gsl_vector_get (D_l, i); - if (d<=0) {continue;} - logdet_Ve+=log(d); - - gsl_vector_view U_col=gsl_matrix_column(U_l, i); - d=sqrt(d); - gsl_blas_dsyr (CblasUpper, d, &U_col.vector, V_e_h); - d=1.0/d; - gsl_blas_dsyr (CblasUpper, d, &U_col.vector, V_e_hi); - } - - //copy the upper part to lower part - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<i; j++) { - gsl_matrix_set (V_e_h, i, j, gsl_matrix_get(V_e_h, j, i)); - gsl_matrix_set (V_e_hi, i, j, gsl_matrix_get(V_e_hi, j, i)); - } - } - - //calculate Lambda=V_ehi V_g V_ehi - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, V_g, V_e_hi, 0.0, VgVehi); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, V_e_hi, VgVehi, 0.0, Lambda); - - //eigen decomposition of Lambda - EigenDecomp(Lambda, U_l, D_l, 0); - - for (size_t i=0; i<d_size; i++) { - d=gsl_vector_get (D_l, i); - if (d<0) {gsl_vector_set (D_l, i, 0);} - } - - //calculate UltVeh and UltVehi - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, U_l, V_e_h, 0.0, UltVeh); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, U_l, V_e_hi, 0.0, UltVehi); - /* - cout<<"Vg: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get (V_g, i, j)<<" "; - } - cout<<endl; - } - cout<<"Ve: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get (V_e, i, j)<<" "; - } - cout<<endl; - } - - cout<<"Dl: "<<endl; - for (size_t i=0; i<d_size; i++) { - cout<<gsl_vector_get (D_l, i)<<endl; - } - cout<<"UltVeh: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get (UltVeh, i, j)<<" "; - } - cout<<endl; - } - */ - - //free memory - gsl_matrix_free (Lambda); - gsl_matrix_free (V_e_temp); - gsl_matrix_free (V_e_h); - gsl_matrix_free (V_e_hi); - gsl_matrix_free (VgVehi); - gsl_matrix_free (U_l); - - return logdet_Ve; -} - -//Qi=(\sum_{k=1}^n x_kx_k^T\otimes(delta_k*Dl+I)^{-1} )^{-1} -double CalcQi (const gsl_vector *eval, const gsl_vector *D_l, const gsl_matrix *X, gsl_matrix *Qi) -{ - size_t n_size=eval->size, d_size=D_l->size, dc_size=Qi->size1; - size_t c_size=dc_size/d_size; - - double delta, dl, d1, d2, d, logdet_Q; - - gsl_matrix *Q=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix_set_zero (Q); - - for (size_t i=0; i<c_size; i++) { - for (size_t j=0; j<c_size; j++) { - for (size_t l=0; l<d_size; l++) { - dl=gsl_vector_get(D_l, l); - - if (j<i) { - d=gsl_matrix_get (Q, j*d_size+l, i*d_size+l); - } else { - d=0.0; - for (size_t k=0; k<n_size; k++) { - d1=gsl_matrix_get(X, i, k); - d2=gsl_matrix_get(X, j, k); - delta=gsl_vector_get(eval, k); - d+=d1*d2/(dl*delta+1.0); - } - } - - gsl_matrix_set (Q, i*d_size+l, j*d_size+l, d); - } - } - } - - //calculate LU decomposition of Q, and invert Q and calculate |Q| - int sig; - gsl_permutation * pmt=gsl_permutation_alloc (dc_size); - LUDecomp (Q, pmt, &sig); - LUInvert (Q, pmt, Qi); - - logdet_Q=LULndet (Q); - - gsl_matrix_free (Q); - gsl_permutation_free (pmt); - - return logdet_Q; -} - -//xHiy=\sum_{k=1}^n x_k\otimes ((delta_k*Dl+I)^{-1}Ul^TVe^{-1/2}y -void CalcXHiY(const gsl_vector *eval, const gsl_vector *D_l, const gsl_matrix *X, const gsl_matrix *UltVehiY, gsl_vector *xHiy) -{ - size_t n_size=eval->size, c_size=X->size1, d_size=D_l->size; - - gsl_vector_set_zero (xHiy); - - double x, delta, dl, y, d; - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - for (size_t j=0; j<c_size; j++) { - d=0.0; - for (size_t k=0; k<n_size; k++) { - x=gsl_matrix_get(X, j, k); - y=gsl_matrix_get(UltVehiY, i, k); - delta=gsl_vector_get(eval, k); - d+=x*y/(delta*dl+1.0); - } - gsl_vector_set(xHiy, j*d_size+i, d); - } - } - /* - cout<<"xHiy: "<<endl; - for (size_t i=0; i<(d_size*c_size); i++) { - cout<<gsl_vector_get(xHiy, i)<<endl; - } - */ - return; -} - - -//OmegaU=D_l/(delta Dl+I)^{-1} -//OmegaE=delta D_l/(delta Dl+I)^{-1} -void CalcOmega (const gsl_vector *eval, const gsl_vector *D_l, gsl_matrix *OmegaU, gsl_matrix *OmegaE) -{ - size_t n_size=eval->size, d_size=D_l->size; - double delta, dl, d_u, d_e; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - - d_u=dl/(delta*dl+1.0); - d_e=delta*d_u; - - gsl_matrix_set(OmegaU, i, k, d_u); - gsl_matrix_set(OmegaE, i, k, d_e); - } - } - - return; -} - - -void UpdateU (const gsl_matrix *OmegaE, const gsl_matrix *UltVehiY, const gsl_matrix *UltVehiBX, gsl_matrix *UltVehiU) -{ - gsl_matrix_memcpy (UltVehiU, UltVehiY); - gsl_matrix_sub (UltVehiU, UltVehiBX); - - gsl_matrix_mul_elements (UltVehiU, OmegaE); - return; -} - - -void UpdateE (const gsl_matrix *UltVehiY, const gsl_matrix *UltVehiBX, const gsl_matrix *UltVehiU, gsl_matrix *UltVehiE) -{ - gsl_matrix_memcpy (UltVehiE, UltVehiY); - gsl_matrix_sub (UltVehiE, UltVehiBX); - gsl_matrix_sub (UltVehiE, UltVehiU); - - return; -} - - - -void UpdateL_B (const gsl_matrix *X, const gsl_matrix *XXti, const gsl_matrix *UltVehiY, const gsl_matrix *UltVehiU, gsl_matrix *UltVehiBX, gsl_matrix *UltVehiB) -{ - size_t c_size=X->size1, d_size=UltVehiY->size1; - - gsl_matrix *YUX=gsl_matrix_alloc (d_size, c_size); - - gsl_matrix_memcpy (UltVehiBX, UltVehiY); - gsl_matrix_sub (UltVehiBX, UltVehiU); - - gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, UltVehiBX, X, 0.0, YUX); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, YUX, XXti, 0.0, UltVehiB); - - gsl_matrix_free(YUX); - - return; -} - -void UpdateRL_B (const gsl_vector *xHiy, const gsl_matrix *Qi, gsl_matrix *UltVehiB) -{ - size_t d_size=UltVehiB->size1, c_size=UltVehiB->size2, dc_size=Qi->size1; - - gsl_vector *b=gsl_vector_alloc (dc_size); - - //calculate b=Qiv - gsl_blas_dgemv(CblasNoTrans, 1.0, Qi, xHiy, 0.0, b); - - //copy b to UltVehiB - for (size_t i=0; i<c_size; i++) { - gsl_vector_view UltVehiB_col=gsl_matrix_column (UltVehiB, i); - gsl_vector_const_view b_subcol=gsl_vector_const_subvector (b, i*d_size, d_size); - gsl_vector_memcpy (&UltVehiB_col.vector, &b_subcol.vector); - } - - gsl_vector_free(b); - - return; -} - - - -void UpdateV (const gsl_vector *eval, const gsl_matrix *U, const gsl_matrix *E, const gsl_matrix *Sigma_uu, const gsl_matrix *Sigma_ee, gsl_matrix *V_g, gsl_matrix *V_e) -{ - size_t n_size=eval->size, d_size=U->size1; - - gsl_matrix_set_zero (V_g); - gsl_matrix_set_zero (V_e); - - double delta; - - //calculate the first part: UD^{-1}U^T and EE^T - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - if (delta==0) {continue;} - - gsl_vector_const_view U_col=gsl_matrix_const_column (U, k); - gsl_blas_dsyr (CblasUpper, 1.0/delta, &U_col.vector, V_g); - } - - gsl_blas_dsyrk(CblasUpper, CblasNoTrans, 1.0, E, 0.0, V_e); - - //copy the upper part to lower part - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<i; j++) { - gsl_matrix_set (V_g, i, j, gsl_matrix_get(V_g, j, i)); - gsl_matrix_set (V_e, i, j, gsl_matrix_get(V_e, j, i)); - } - } - - //add Sigma - gsl_matrix_add (V_g, Sigma_uu); - gsl_matrix_add (V_e, Sigma_ee); - - //scale by 1/n - gsl_matrix_scale (V_g, 1.0/(double)n_size); - gsl_matrix_scale (V_e, 1.0/(double)n_size); - - return; -} - - -void CalcSigma (const char func_name, const gsl_vector *eval, const gsl_vector *D_l, const gsl_matrix *X, const gsl_matrix *OmegaU, const gsl_matrix *OmegaE, const gsl_matrix *UltVeh, const gsl_matrix *Qi, gsl_matrix *Sigma_uu, gsl_matrix *Sigma_ee) -{ - if (func_name!='R' && func_name!='L' && func_name!='r' && func_name!='l') {cout<<"func_name only takes 'R' or 'L': 'R' for log-restricted likelihood, 'L' for log-likelihood."<<endl; return;} - - size_t n_size=eval->size, c_size=X->size1, d_size=D_l->size, dc_size=Qi->size1; - - gsl_matrix_set_zero(Sigma_uu); - gsl_matrix_set_zero(Sigma_ee); - - double delta, dl, x, d; - - //calculate the first diagonal term - gsl_vector_view Suu_diag=gsl_matrix_diagonal (Sigma_uu); - gsl_vector_view See_diag=gsl_matrix_diagonal (Sigma_ee); - - for (size_t k=0; k<n_size; k++) { - gsl_vector_const_view OmegaU_col=gsl_matrix_const_column (OmegaU, k); - gsl_vector_const_view OmegaE_col=gsl_matrix_const_column (OmegaE, k); - - gsl_vector_add (&Suu_diag.vector, &OmegaU_col.vector); - gsl_vector_add (&See_diag.vector, &OmegaE_col.vector); - } - - //calculate the second term for reml - if (func_name=='R' || func_name=='r') { - gsl_matrix *M_u=gsl_matrix_alloc(dc_size, d_size); - gsl_matrix *M_e=gsl_matrix_alloc(dc_size, d_size); - gsl_matrix *QiM=gsl_matrix_alloc(dc_size, d_size); - - gsl_matrix_set_zero(M_u); - gsl_matrix_set_zero(M_e); - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - //if (delta==0) {continue;} - - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - for (size_t j=0; j<c_size; j++) { - x=gsl_matrix_get(X, j, k); - d=x/(delta*dl+1.0); - gsl_matrix_set(M_e, j*d_size+i, i, d); - gsl_matrix_set(M_u, j*d_size+i, i, d*dl); - } - } - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Qi, M_u, 0.0, QiM); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, delta, M_u, QiM, 1.0, Sigma_uu); - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Qi, M_e, 0.0, QiM); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, M_e, QiM, 1.0, Sigma_ee); - } - - gsl_matrix_free(M_u); - gsl_matrix_free(M_e); - gsl_matrix_free(QiM); - } - - //multiply both sides by VehUl - gsl_matrix *M=gsl_matrix_alloc (d_size, d_size); - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Sigma_uu, UltVeh, 0.0, M); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, M, 0.0, Sigma_uu); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Sigma_ee, UltVeh, 0.0, M); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, M, 0.0, Sigma_ee); - - gsl_matrix_free(M); - return; -} - - -//'R' for restricted likelihood and 'L' for likelihood -//'R' update B and 'L' don't -//only calculate -0.5*\sum_{k=1}^n|H_k|-0.5yPxy -double MphCalcLogL (const gsl_vector *eval, const gsl_vector *xHiy, const gsl_vector *D_l, const gsl_matrix *UltVehiY, const gsl_matrix *Qi) -{ - size_t n_size=eval->size, d_size=D_l->size, dc_size=Qi->size1; - double logl=0.0, delta, dl, y, d; - - //calculate yHiy+log|H_k| - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - for (size_t i=0; i<d_size; i++) { - y=gsl_matrix_get(UltVehiY, i, k); - dl=gsl_vector_get(D_l, i); - d=delta*dl+1.0; - - logl+=y*y/d+log(d); - } - } - - //calculate the rest of yPxy - gsl_vector *Qiv=gsl_vector_alloc(dc_size); - - gsl_blas_dgemv(CblasNoTrans, 1.0, Qi, xHiy, 0.0, Qiv); - gsl_blas_ddot(xHiy, Qiv, &d); - - logl-=d; - - gsl_vector_free(Qiv); - - return -0.5*logl; -} - - - - - -//Y is a dxn matrix, X is a cxn matrix, B is a dxc matrix, V_g is a dxd matrix, V_e is a dxd matrix, eval is a size n vector -//'R' for restricted likelihood and 'L' for likelihood -double MphEM (const char func_name, const size_t max_iter, const double max_prec, const gsl_vector *eval, const gsl_matrix *X, const gsl_matrix *Y, gsl_matrix *U_hat, gsl_matrix *E_hat, gsl_matrix *OmegaU, gsl_matrix *OmegaE, gsl_matrix *UltVehiY, gsl_matrix *UltVehiBX, gsl_matrix *UltVehiU, gsl_matrix *UltVehiE, gsl_matrix *V_g, gsl_matrix *V_e, gsl_matrix *B) -{ - if (func_name!='R' && func_name!='L' && func_name!='r' && func_name!='l') {cout<<"func_name only takes 'R' or 'L': 'R' for log-restricted likelihood, 'L' for log-likelihood."<<endl; return 0.0;} - - size_t n_size=eval->size, c_size=X->size1, d_size=Y->size1; - size_t dc_size=d_size*c_size; - - gsl_matrix *XXt=gsl_matrix_alloc (c_size, c_size); - gsl_matrix *XXti=gsl_matrix_alloc (c_size, c_size); - gsl_vector *D_l=gsl_vector_alloc (d_size); - gsl_matrix *UltVeh=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVehi=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVehiB=gsl_matrix_alloc (d_size, c_size); - gsl_matrix *Qi=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *Sigma_uu=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *Sigma_ee=gsl_matrix_alloc (d_size, d_size); - gsl_vector *xHiy=gsl_vector_alloc (dc_size); - gsl_permutation * pmt=gsl_permutation_alloc (c_size); - - double logl_const=0.0, logl_old=0.0, logl_new=0.0, logdet_Q, logdet_Ve; - int sig; - - //calculate |XXt| and (XXt)^{-1} - gsl_blas_dsyrk (CblasUpper, CblasNoTrans, 1.0, X, 0.0, XXt); - for (size_t i=0; i<c_size; ++i) { - for (size_t j=0; j<i; ++j) { - gsl_matrix_set (XXt, i, j, gsl_matrix_get (XXt, j, i)); - } - } - - LUDecomp (XXt, pmt, &sig); - LUInvert (XXt, pmt, XXti); - - //calculate the constant for logl - if (func_name=='R' || func_name=='r') { - logl_const=-0.5*(double)(n_size-c_size)*(double)d_size*log(2.0*M_PI)+0.5*(double)d_size*LULndet (XXt); - } else { - logl_const=-0.5*(double)n_size*(double)d_size*log(2.0*M_PI); - } - - //start EM - for (size_t t=0; t<max_iter; t++) { - logdet_Ve=EigenProc (V_g, V_e, D_l, UltVeh, UltVehi); - - logdet_Q=CalcQi (eval, D_l, X, Qi); - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehi, Y, 0.0, UltVehiY); - CalcXHiY(eval, D_l, X, UltVehiY, xHiy); - - //calculate log likelihood/restricted likelihood value, and terminate if change is small - logl_new=logl_const+MphCalcLogL (eval, xHiy, D_l, UltVehiY, Qi)-0.5*(double)n_size*logdet_Ve; - if (func_name=='R' || func_name=='r') { - logl_new+=-0.5*(logdet_Q-(double)c_size*logdet_Ve); - } - if (t!=0 && abs(logl_new-logl_old)<max_prec) {break;} - logl_old=logl_new; - - /* - cout<<"iteration = "<<t<<" log-likelihood = "<<logl_old<<"\t"<<logl_new<<endl; - - cout<<"Vg: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get(V_g, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"Ve: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get(V_e, i, j)<<"\t"; - } - cout<<endl; - } - */ - - CalcOmega (eval, D_l, OmegaU, OmegaE); - - //Update UltVehiB, UltVehiU - if (func_name=='R' || func_name=='r') { - UpdateRL_B(xHiy, Qi, UltVehiB); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehiB, X, 0.0, UltVehiBX); - } else if (t==0) { - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehi, B, 0.0, UltVehiB); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehiB, X, 0.0, UltVehiBX); - } - - UpdateU(OmegaE, UltVehiY, UltVehiBX, UltVehiU); - - if (func_name=='L' || func_name=='l') { - //UltVehiBX is destroyed here - UpdateL_B(X, XXti, UltVehiY, UltVehiU, UltVehiBX, UltVehiB); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehiB, X, 0.0, UltVehiBX); - } - - UpdateE(UltVehiY, UltVehiBX, UltVehiU, UltVehiE); - - //calculate U_hat, E_hat and B - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, UltVehiU, 0.0, U_hat); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, UltVehiE, 0.0, E_hat); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, UltVehiB, 0.0, B); - - //calculate Sigma_uu and Sigma_ee - CalcSigma (func_name, eval, D_l, X, OmegaU, OmegaE, UltVeh, Qi, Sigma_uu, Sigma_ee); - - //update V_g and V_e - UpdateV (eval, U_hat, E_hat, Sigma_uu, Sigma_ee, V_g, V_e); - } - - gsl_matrix_free(XXt); - gsl_matrix_free(XXti); - gsl_vector_free(D_l); - gsl_matrix_free(UltVeh); - gsl_matrix_free(UltVehi); - gsl_matrix_free(UltVehiB); - gsl_matrix_free(Qi); - gsl_matrix_free(Sigma_uu); - gsl_matrix_free(Sigma_ee); - gsl_vector_free(xHiy); - gsl_permutation_free(pmt); - - return logl_new; -} - - - - - - - -//calculate p-value, beta (d by 1 vector) and V(beta) -double MphCalcP (const gsl_vector *eval, const gsl_vector *x_vec, const gsl_matrix *W, const gsl_matrix *Y, const gsl_matrix *V_g, const gsl_matrix *V_e, gsl_matrix *UltVehiY, gsl_vector *beta, gsl_matrix *Vbeta) -{ - size_t n_size=eval->size, c_size=W->size1, d_size=V_g->size1; - size_t dc_size=d_size*c_size; - double delta, dl, d, d1, d2, dy, dx, dw, logdet_Ve, logdet_Q, p_value; - - gsl_vector *D_l=gsl_vector_alloc (d_size); - gsl_matrix *UltVeh=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVehi=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *Qi=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *WHix=gsl_matrix_alloc (dc_size, d_size); - gsl_matrix *QiWHix=gsl_matrix_alloc(dc_size, d_size); - - gsl_matrix *xPx=gsl_matrix_alloc (d_size, d_size); - gsl_vector *xPy=gsl_vector_alloc (d_size); - //gsl_vector *UltVehiy=gsl_vector_alloc (d_size); - gsl_vector *WHiy=gsl_vector_alloc (dc_size); - - gsl_matrix_set_zero (xPx); - gsl_matrix_set_zero (WHix); - gsl_vector_set_zero (xPy); - gsl_vector_set_zero (WHiy); - - //eigen decomposition and calculate log|Ve| - logdet_Ve=EigenProc (V_g, V_e, D_l, UltVeh, UltVehi); - - //calculate Qi and log|Q| - logdet_Q=CalcQi (eval, D_l, W, Qi); - - //calculate UltVehiY - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehi, Y, 0.0, UltVehiY); - - //calculate WHix, WHiy, xHiy, xHix - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - - d1=0.0; d2=0.0; - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - dx=gsl_vector_get(x_vec, k); - dy=gsl_matrix_get(UltVehiY, i, k); - - d1+=dx*dy/(delta*dl+1.0); - d2+=dx*dx/(delta*dl+1.0); - } - gsl_vector_set (xPy, i, d1); - gsl_matrix_set (xPx, i, i, d2); - - for (size_t j=0; j<c_size; j++) { - d1=0.0; d2=0.0; - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - dx=gsl_vector_get(x_vec, k); - dw=gsl_matrix_get(W, j, k); - dy=gsl_matrix_get(UltVehiY, i, k); - - //if (delta==0) {continue;} - d1+=dx*dw/(delta*dl+1.0); - d2+=dy*dw/(delta*dl+1.0); - } - gsl_matrix_set(WHix, j*d_size+i, i, d1); - gsl_vector_set(WHiy, j*d_size+i, d2); - } - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Qi, WHix, 0.0, QiWHix); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, -1.0, WHix, QiWHix, 1.0, xPx); - gsl_blas_dgemv(CblasTrans, -1.0, QiWHix, WHiy, 1.0, xPy); - - //calculate V(beta) and beta - int sig; - gsl_permutation * pmt=gsl_permutation_alloc (d_size); - LUDecomp (xPx, pmt, &sig); - LUSolve (xPx, pmt, xPy, D_l); - LUInvert (xPx, pmt, Vbeta); - - //need to multiply UltVehi on both sides or one side - gsl_blas_dgemv(CblasTrans, 1.0, UltVeh, D_l, 0.0, beta); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Vbeta, UltVeh, 0.0, xPx); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, xPx, 0.0, Vbeta); - - //calculate test statistic and p value - gsl_blas_ddot(D_l, xPy, &d); - - p_value=gsl_cdf_chisq_Q (d, (double)d_size); - //d*=(double)(n_size-c_size-d_size)/((double)d_size*(double)(n_size-c_size-1)); - //p_value=gsl_cdf_fdist_Q (d, (double)d_size, (double)(n_size-c_size-d_size)); - - gsl_vector_free(D_l); - gsl_matrix_free(UltVeh); - gsl_matrix_free(UltVehi); - gsl_matrix_free(Qi); - gsl_matrix_free(WHix); - gsl_matrix_free(QiWHix); - - gsl_matrix_free(xPx); - gsl_vector_free(xPy); - gsl_vector_free(WHiy); - - gsl_permutation_free(pmt); - - return p_value; -} - - - -//calculate B and its standard error (which is a matrix of the same dimension as B) -void MphCalcBeta (const gsl_vector *eval, const gsl_matrix *W, const gsl_matrix *Y, const gsl_matrix *V_g, const gsl_matrix *V_e, gsl_matrix *UltVehiY, gsl_matrix *B, gsl_matrix *se_B) -{ - size_t n_size=eval->size, c_size=W->size1, d_size=V_g->size1; - size_t dc_size=d_size*c_size; - double delta, dl, d, dy, dw, logdet_Ve, logdet_Q; - - gsl_vector *D_l=gsl_vector_alloc (d_size); - gsl_matrix *UltVeh=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVehi=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *Qi=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *Qi_temp=gsl_matrix_alloc (dc_size, dc_size); - //gsl_vector *UltVehiy=gsl_vector_alloc (d_size); - gsl_vector *WHiy=gsl_vector_alloc (dc_size); - gsl_vector *QiWHiy=gsl_vector_alloc (dc_size); - gsl_vector *beta=gsl_vector_alloc (dc_size); - gsl_matrix *Vbeta=gsl_matrix_alloc (dc_size, dc_size); - - gsl_vector_set_zero (WHiy); - - //eigen decomposition and calculate log|Ve| - logdet_Ve=EigenProc (V_g, V_e, D_l, UltVeh, UltVehi); - - //calculate Qi and log|Q| - logdet_Q=CalcQi (eval, D_l, W, Qi); - - //calculate UltVehiY - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehi, Y, 0.0, UltVehiY); - - //calculate WHiy - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - - for (size_t j=0; j<c_size; j++) { - d=0.0; - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - dw=gsl_matrix_get(W, j, k); - dy=gsl_matrix_get(UltVehiY, i, k); - - //if (delta==0) {continue;} - d+=dy*dw/(delta*dl+1.0); - } - gsl_vector_set(WHiy, j*d_size+i, d); - } - } - - gsl_blas_dgemv(CblasNoTrans, 1.0, Qi, WHiy, 0.0, QiWHiy); - - //need to multiply I_c\otimes UltVehi on both sides or one side - for (size_t i=0; i<c_size; i++) { - gsl_vector_view QiWHiy_sub=gsl_vector_subvector(QiWHiy, i*d_size, d_size); - gsl_vector_view beta_sub=gsl_vector_subvector(beta, i*d_size, d_size); - gsl_blas_dgemv(CblasTrans, 1.0, UltVeh, &QiWHiy_sub.vector, 0.0, &beta_sub.vector); - - for (size_t j=0; j<c_size; j++) { - gsl_matrix_view Qi_sub=gsl_matrix_submatrix (Qi, i*d_size, j*d_size, d_size, d_size); - gsl_matrix_view Qitemp_sub=gsl_matrix_submatrix (Qi_temp, i*d_size, j*d_size, d_size, d_size); - gsl_matrix_view Vbeta_sub=gsl_matrix_submatrix (Vbeta, i*d_size, j*d_size, d_size, d_size); - - if (j<i) { - gsl_matrix_view Vbeta_sym=gsl_matrix_submatrix (Vbeta, j*d_size, i*d_size, d_size, d_size); - gsl_matrix_transpose_memcpy (&Vbeta_sub.matrix, &Vbeta_sym.matrix); - } else { - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &Qi_sub.matrix, UltVeh, 0.0, &Qitemp_sub.matrix); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, &Qitemp_sub.matrix, 0.0, &Vbeta_sub.matrix); - } - } - } - - //copy beta to B, and Vbeta to se_B - for (size_t j=0; j<B->size2; j++) { - for (size_t i=0; i<B->size1; i++) { - gsl_matrix_set(B, i, j, gsl_vector_get(beta, j*d_size+i)); - gsl_matrix_set(se_B, i, j, sqrt(gsl_matrix_get(Vbeta, j*d_size+i, j*d_size+i))); - } - } - - //free matrices - gsl_vector_free(D_l); - gsl_matrix_free(UltVeh); - gsl_matrix_free(UltVehi); - gsl_matrix_free(Qi); - gsl_matrix_free(Qi_temp); - gsl_vector_free(WHiy); - gsl_vector_free(QiWHiy); - gsl_vector_free(beta); - gsl_matrix_free(Vbeta); - - return; -} - - - -//below are functions for Newton-Raphson's algorithm - - - - - -//calculate all Hi and return logdet_H=\sum_{k=1}^{n}log|H_k| -//and calculate Qi and return logdet_Q -//and calculate yPy -void CalcHiQi (const gsl_vector *eval, const gsl_matrix *X, const gsl_matrix *V_g, const gsl_matrix *V_e, gsl_matrix *Hi_all, gsl_matrix *Qi, double &logdet_H, double &logdet_Q) -{ - gsl_matrix_set_zero (Hi_all); - gsl_matrix_set_zero (Qi); - logdet_H=0.0; logdet_Q=0.0; - - size_t n_size=eval->size, c_size=X->size1, d_size=V_g->size1; - double logdet_Ve=0.0, delta, dl, d; - - gsl_matrix *mat_dd=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVeh=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVehi=gsl_matrix_alloc (d_size, d_size); - gsl_vector *D_l=gsl_vector_alloc (d_size); - - //calculate D_l, UltVeh and UltVehi - logdet_Ve=EigenProc (V_g, V_e, D_l, UltVeh, UltVehi); - - //calculate each Hi and log|H_k| - logdet_H=(double)n_size*logdet_Ve; - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - gsl_matrix_memcpy (mat_dd, UltVehi); - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - d=delta*dl+1.0; - - gsl_vector_view mat_row=gsl_matrix_row (mat_dd, i); - gsl_vector_scale (&mat_row.vector, 1.0/d); - - logdet_H+=log(d); - } - - gsl_matrix_view Hi_k=gsl_matrix_submatrix(Hi_all, 0, k*d_size, d_size, d_size); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVehi, mat_dd, 0.0, &Hi_k.matrix); - } - - //calculate Qi, and multiply I\otimes UtVeh on both side - //and calculate logdet_Q, don't forget to substract c_size*logdet_Ve - logdet_Q=CalcQi (eval, D_l, X, Qi)-(double)c_size*logdet_Ve; - - for (size_t i=0; i<c_size; i++) { - for (size_t j=0; j<c_size; j++) { - gsl_matrix_view Qi_sub=gsl_matrix_submatrix (Qi, i*d_size, j*d_size, d_size, d_size); - if (j<i) { - gsl_matrix_view Qi_sym=gsl_matrix_submatrix (Qi, j*d_size, i*d_size, d_size, d_size); - gsl_matrix_transpose_memcpy (&Qi_sub.matrix, &Qi_sym.matrix); - } else { - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &Qi_sub.matrix, UltVeh, 0.0, mat_dd); - gsl_blas_dgemm(CblasTrans, CblasNoTrans, 1.0, UltVeh, mat_dd, 0.0, &Qi_sub.matrix); - } - } - } - - //free memory - gsl_matrix_free(mat_dd); - gsl_matrix_free(UltVeh); - gsl_matrix_free(UltVehi); - gsl_vector_free(D_l); - - return; -} - - - - -//calculate all Hiy -void Calc_Hiy_all (const gsl_matrix *Y, const gsl_matrix *Hi_all, gsl_matrix *Hiy_all) -{ - gsl_matrix_set_zero (Hiy_all); - - size_t n_size=Y->size2, d_size=Y->size1; - - for (size_t k=0; k<n_size; k++) { - gsl_matrix_const_view Hi_k=gsl_matrix_const_submatrix(Hi_all, 0, k*d_size, d_size, d_size); - gsl_vector_const_view y_k=gsl_matrix_const_column(Y, k); - gsl_vector_view Hiy_k=gsl_matrix_column(Hiy_all, k); - - gsl_blas_dgemv (CblasNoTrans, 1.0, &Hi_k.matrix, &y_k.vector, 0.0, &Hiy_k.vector); - } - - return; -} - - -//calculate all xHi -void Calc_xHi_all (const gsl_matrix *X, const gsl_matrix *Hi_all, gsl_matrix *xHi_all) -{ - gsl_matrix_set_zero (xHi_all); - - size_t n_size=X->size2, c_size=X->size1, d_size=Hi_all->size1; - - double d; - - for (size_t k=0; k<n_size; k++) { - gsl_matrix_const_view Hi_k=gsl_matrix_const_submatrix(Hi_all, 0, k*d_size, d_size, d_size); - - for (size_t i=0; i<c_size; i++) { - d=gsl_matrix_get (X, i, k); - gsl_matrix_view xHi_sub=gsl_matrix_submatrix(xHi_all, i*d_size, k*d_size, d_size, d_size); - gsl_matrix_memcpy(&xHi_sub.matrix, &Hi_k.matrix); - gsl_matrix_scale(&xHi_sub.matrix, d); - } - } - - return; -} - - -//calculate scalar yHiy -double Calc_yHiy (const gsl_matrix *Y, const gsl_matrix *Hiy_all) -{ - double yHiy=0.0, d; - size_t n_size=Y->size2; - - for (size_t k=0; k<n_size; k++) { - gsl_vector_const_view y_k=gsl_matrix_const_column(Y, k); - gsl_vector_const_view Hiy_k=gsl_matrix_const_column(Hiy_all, k); - - gsl_blas_ddot (&Hiy_k.vector, &y_k.vector, &d); - yHiy+=d; - } - - return yHiy; -} - - -//calculate the vector xHiy -void Calc_xHiy (const gsl_matrix *Y, const gsl_matrix *xHi, gsl_vector *xHiy) -{ - gsl_vector_set_zero (xHiy); - - size_t n_size=Y->size2, d_size=Y->size1, dc_size=xHi->size1; - - for (size_t k=0; k<n_size; k++) { - gsl_matrix_const_view xHi_k=gsl_matrix_const_submatrix(xHi, 0, k*d_size, dc_size, d_size); - gsl_vector_const_view y_k=gsl_matrix_const_column(Y, k); - - gsl_blas_dgemv (CblasNoTrans, 1.0, &xHi_k.matrix, &y_k.vector, 1.0, xHiy); - } - - return; -} - - - - -//0<=i,j<d_size -size_t GetIndex (const size_t i, const size_t j, const size_t d_size) -{ - if (i>=d_size || j>=d_size) {cout<<"error in GetIndex."<<endl; return 0;} - - size_t s, l; - if (j<i) {s=j; l=i;} else {s=i; l=j;} - - return (2*d_size-s+1)*s/2+l-s; -} - - - -void Calc_yHiDHiy (const gsl_vector *eval, const gsl_matrix *Hiy, const size_t i, const size_t j, double &yHiDHiy_g, double &yHiDHiy_e) -{ - yHiDHiy_g=0.0; - yHiDHiy_e=0.0; - - size_t n_size=eval->size; - - double delta, d1, d2; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - d1=gsl_matrix_get (Hiy, i, k); - d2=gsl_matrix_get (Hiy, j, k); - - if (i==j) { - yHiDHiy_g+=delta*d1*d2; - yHiDHiy_e+=d1*d2; - } else { - yHiDHiy_g+=delta*d1*d2*2.0; - yHiDHiy_e+=d1*d2*2.0; - } - } - - return; -} - - - -void Calc_xHiDHiy (const gsl_vector *eval, const gsl_matrix *xHi, const gsl_matrix *Hiy, const size_t i, const size_t j, gsl_vector *xHiDHiy_g, gsl_vector *xHiDHiy_e) -{ - gsl_vector_set_zero(xHiDHiy_g); - gsl_vector_set_zero(xHiDHiy_e); - - size_t n_size=eval->size, d_size=Hiy->size1; - - double delta, d; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - gsl_vector_const_view xHi_col_i=gsl_matrix_const_column (xHi, k*d_size+i); - d=gsl_matrix_get (Hiy, j, k); - - gsl_blas_daxpy (d*delta, &xHi_col_i.vector, xHiDHiy_g); - gsl_blas_daxpy (d, &xHi_col_i.vector, xHiDHiy_e); - - if (i!=j) { - gsl_vector_const_view xHi_col_j=gsl_matrix_const_column (xHi, k*d_size+j); - d=gsl_matrix_get (Hiy, i, k); - - gsl_blas_daxpy (d*delta, &xHi_col_j.vector, xHiDHiy_g); - gsl_blas_daxpy (d, &xHi_col_j.vector, xHiDHiy_e); - } - } - - return; -} - - -void Calc_xHiDHix (const gsl_vector *eval, const gsl_matrix *xHi, const size_t i, const size_t j, gsl_matrix *xHiDHix_g, gsl_matrix *xHiDHix_e) -{ - gsl_matrix_set_zero(xHiDHix_g); - gsl_matrix_set_zero(xHiDHix_e); - - size_t n_size=eval->size, dc_size=xHi->size1; - size_t d_size=xHi->size2/n_size; - - double delta; - - gsl_matrix *mat_dcdc=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *mat_dcdc_t=gsl_matrix_alloc (dc_size, dc_size); - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - gsl_vector_const_view xHi_col_i=gsl_matrix_const_column (xHi, k*d_size+i); - gsl_vector_const_view xHi_col_j=gsl_matrix_const_column (xHi, k*d_size+j); - - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (1.0, &xHi_col_i.vector, &xHi_col_j.vector, mat_dcdc); - - gsl_matrix_transpose_memcpy (mat_dcdc_t, mat_dcdc); - - gsl_matrix_add (xHiDHix_e, mat_dcdc); - - gsl_matrix_scale (mat_dcdc, delta); - gsl_matrix_add (xHiDHix_g, mat_dcdc); - - if (i!=j) { - gsl_matrix_add (xHiDHix_e, mat_dcdc_t); - - gsl_matrix_scale (mat_dcdc_t, delta); - gsl_matrix_add (xHiDHix_g, mat_dcdc_t); - } - } - - gsl_matrix_free(mat_dcdc); - gsl_matrix_free(mat_dcdc_t); - - return; -} - - - -void Calc_yHiDHiDHiy (const gsl_vector *eval, const gsl_matrix *Hi, const gsl_matrix *Hiy, const size_t i1, const size_t j1, const size_t i2, const size_t j2, double &yHiDHiDHiy_gg, double &yHiDHiDHiy_ee, double &yHiDHiDHiy_ge) -{ - yHiDHiDHiy_gg=0.0; - yHiDHiDHiy_ee=0.0; - yHiDHiDHiy_ge=0.0; - - size_t n_size=eval->size, d_size=Hiy->size1; - - double delta, d_Hiy_i1, d_Hiy_j1, d_Hiy_i2, d_Hiy_j2, d_Hi_i1i2, d_Hi_i1j2, d_Hi_j1i2, d_Hi_j1j2; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - d_Hiy_i1=gsl_matrix_get (Hiy, i1, k); - d_Hiy_j1=gsl_matrix_get (Hiy, j1, k); - d_Hiy_i2=gsl_matrix_get (Hiy, i2, k); - d_Hiy_j2=gsl_matrix_get (Hiy, j2, k); - - d_Hi_i1i2=gsl_matrix_get (Hi, i1, k*d_size+i2); - d_Hi_i1j2=gsl_matrix_get (Hi, i1, k*d_size+j2); - d_Hi_j1i2=gsl_matrix_get (Hi, j1, k*d_size+i2); - d_Hi_j1j2=gsl_matrix_get (Hi, j1, k*d_size+j2); - - if (i1==j1) { - yHiDHiDHiy_gg+=delta*delta*(d_Hiy_i1*d_Hi_j1i2*d_Hiy_j2); - yHiDHiDHiy_ee+=(d_Hiy_i1*d_Hi_j1i2*d_Hiy_j2); - yHiDHiDHiy_ge+=delta*(d_Hiy_i1*d_Hi_j1i2*d_Hiy_j2); - - if (i2!=j2) { - yHiDHiDHiy_gg+=delta*delta*(d_Hiy_i1*d_Hi_j1j2*d_Hiy_i2); - yHiDHiDHiy_ee+=(d_Hiy_i1*d_Hi_j1j2*d_Hiy_i2); - yHiDHiDHiy_ge+=delta*(d_Hiy_i1*d_Hi_j1j2*d_Hiy_i2); - } - } else { - yHiDHiDHiy_gg+=delta*delta*(d_Hiy_i1*d_Hi_j1i2*d_Hiy_j2+d_Hiy_j1*d_Hi_i1i2*d_Hiy_j2); - yHiDHiDHiy_ee+=(d_Hiy_i1*d_Hi_j1i2*d_Hiy_j2+d_Hiy_j1*d_Hi_i1i2*d_Hiy_j2); - yHiDHiDHiy_ge+=delta*(d_Hiy_i1*d_Hi_j1i2*d_Hiy_j2+d_Hiy_j1*d_Hi_i1i2*d_Hiy_j2); - - if (i2!=j2) { - yHiDHiDHiy_gg+=delta*delta*(d_Hiy_i1*d_Hi_j1j2*d_Hiy_i2+d_Hiy_j1*d_Hi_i1j2*d_Hiy_i2); - yHiDHiDHiy_ee+=(d_Hiy_i1*d_Hi_j1j2*d_Hiy_i2+d_Hiy_j1*d_Hi_i1j2*d_Hiy_i2); - yHiDHiDHiy_ge+=delta*(d_Hiy_i1*d_Hi_j1j2*d_Hiy_i2+d_Hiy_j1*d_Hi_i1j2*d_Hiy_i2); - } - } - } - - return; -} - - -void Calc_xHiDHiDHiy (const gsl_vector *eval, const gsl_matrix *Hi, const gsl_matrix *xHi, const gsl_matrix *Hiy, const size_t i1, const size_t j1, const size_t i2, const size_t j2, gsl_vector *xHiDHiDHiy_gg, gsl_vector *xHiDHiDHiy_ee, gsl_vector *xHiDHiDHiy_ge) -{ - gsl_vector_set_zero(xHiDHiDHiy_gg); - gsl_vector_set_zero(xHiDHiDHiy_ee); - gsl_vector_set_zero(xHiDHiDHiy_ge); - - size_t n_size=eval->size, d_size=Hiy->size1; - - double delta, d_Hiy_i, d_Hiy_j, d_Hi_i1i2, d_Hi_i1j2, d_Hi_j1i2, d_Hi_j1j2; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - gsl_vector_const_view xHi_col_i=gsl_matrix_const_column (xHi, k*d_size+i1); - gsl_vector_const_view xHi_col_j=gsl_matrix_const_column (xHi, k*d_size+j1); - - d_Hiy_i=gsl_matrix_get (Hiy, i2, k); - d_Hiy_j=gsl_matrix_get (Hiy, j2, k); - - d_Hi_i1i2=gsl_matrix_get (Hi, i1, k*d_size+i2); - d_Hi_i1j2=gsl_matrix_get (Hi, i1, k*d_size+j2); - d_Hi_j1i2=gsl_matrix_get (Hi, j1, k*d_size+i2); - d_Hi_j1j2=gsl_matrix_get (Hi, j1, k*d_size+j2); - - if (i1==j1) { - gsl_blas_daxpy (delta*delta*d_Hi_j1i2*d_Hiy_j, &xHi_col_i.vector, xHiDHiDHiy_gg); - gsl_blas_daxpy (d_Hi_j1i2*d_Hiy_j, &xHi_col_i.vector, xHiDHiDHiy_ee); - gsl_blas_daxpy (delta*d_Hi_j1i2*d_Hiy_j, &xHi_col_i.vector, xHiDHiDHiy_ge); - - if (i2!=j2) { - gsl_blas_daxpy (delta*delta*d_Hi_j1j2*d_Hiy_i, &xHi_col_i.vector, xHiDHiDHiy_gg); - gsl_blas_daxpy (d_Hi_j1j2*d_Hiy_i, &xHi_col_i.vector, xHiDHiDHiy_ee); - gsl_blas_daxpy (delta*d_Hi_j1j2*d_Hiy_i, &xHi_col_i.vector, xHiDHiDHiy_ge); - } - } else { - gsl_blas_daxpy (delta*delta*d_Hi_j1i2*d_Hiy_j, &xHi_col_i.vector, xHiDHiDHiy_gg); - gsl_blas_daxpy (d_Hi_j1i2*d_Hiy_j, &xHi_col_i.vector, xHiDHiDHiy_ee); - gsl_blas_daxpy (delta*d_Hi_j1i2*d_Hiy_j, &xHi_col_i.vector, xHiDHiDHiy_ge); - - gsl_blas_daxpy (delta*delta*d_Hi_i1i2*d_Hiy_j, &xHi_col_j.vector, xHiDHiDHiy_gg); - gsl_blas_daxpy (d_Hi_i1i2*d_Hiy_j, &xHi_col_j.vector, xHiDHiDHiy_ee); - gsl_blas_daxpy (delta*d_Hi_i1i2*d_Hiy_j, &xHi_col_j.vector, xHiDHiDHiy_ge); - - if (i2!=j2) { - gsl_blas_daxpy (delta*delta*d_Hi_j1j2*d_Hiy_i, &xHi_col_i.vector, xHiDHiDHiy_gg); - gsl_blas_daxpy (d_Hi_j1j2*d_Hiy_i, &xHi_col_i.vector, xHiDHiDHiy_ee); - gsl_blas_daxpy (delta*d_Hi_j1j2*d_Hiy_i, &xHi_col_i.vector, xHiDHiDHiy_ge); - - gsl_blas_daxpy (delta*delta*d_Hi_i1j2*d_Hiy_i, &xHi_col_j.vector, xHiDHiDHiy_gg); - gsl_blas_daxpy (d_Hi_i1j2*d_Hiy_i, &xHi_col_j.vector, xHiDHiDHiy_ee); - gsl_blas_daxpy (delta*d_Hi_i1j2*d_Hiy_i, &xHi_col_j.vector, xHiDHiDHiy_ge); - } - } - } - - return; -} - - -void Calc_xHiDHiDHix (const gsl_vector *eval, const gsl_matrix *Hi, const gsl_matrix *xHi, const size_t i1, const size_t j1, const size_t i2, const size_t j2, gsl_matrix *xHiDHiDHix_gg, gsl_matrix *xHiDHiDHix_ee, gsl_matrix *xHiDHiDHix_ge) -{ - gsl_matrix_set_zero(xHiDHiDHix_gg); - gsl_matrix_set_zero(xHiDHiDHix_ee); - gsl_matrix_set_zero(xHiDHiDHix_ge); - - size_t n_size=eval->size, d_size=Hi->size1, dc_size=xHi->size1; - - double delta, d_Hi_i1i2, d_Hi_i1j2, d_Hi_j1i2, d_Hi_j1j2; - - gsl_matrix *mat_dcdc=gsl_matrix_alloc (dc_size, dc_size); - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - gsl_vector_const_view xHi_col_i1=gsl_matrix_const_column (xHi, k*d_size+i1); - gsl_vector_const_view xHi_col_j1=gsl_matrix_const_column (xHi, k*d_size+j1); - gsl_vector_const_view xHi_col_i2=gsl_matrix_const_column (xHi, k*d_size+i2); - gsl_vector_const_view xHi_col_j2=gsl_matrix_const_column (xHi, k*d_size+j2); - - d_Hi_i1i2=gsl_matrix_get (Hi, i1, k*d_size+i2); - d_Hi_i1j2=gsl_matrix_get (Hi, i1, k*d_size+j2); - d_Hi_j1i2=gsl_matrix_get (Hi, j1, k*d_size+i2); - d_Hi_j1j2=gsl_matrix_get (Hi, j1, k*d_size+j2); - - if (i1==j1) { - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (d_Hi_j1i2, &xHi_col_i1.vector, &xHi_col_j2.vector, mat_dcdc); - - gsl_matrix_add(xHiDHiDHix_ee, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_ge, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_gg, mat_dcdc); - - if (i2!=j2) { - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (d_Hi_j1j2, &xHi_col_i1.vector, &xHi_col_i2.vector, mat_dcdc); - - gsl_matrix_add(xHiDHiDHix_ee, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_ge, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_gg, mat_dcdc); - } - } else { - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (d_Hi_j1i2, &xHi_col_i1.vector, &xHi_col_j2.vector, mat_dcdc); - - gsl_matrix_add(xHiDHiDHix_ee, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_ge, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_gg, mat_dcdc); - - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (d_Hi_i1i2, &xHi_col_j1.vector, &xHi_col_j2.vector, mat_dcdc); - - gsl_matrix_add(xHiDHiDHix_ee, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_ge, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_gg, mat_dcdc); - - if (i2!=j2) { - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (d_Hi_j1j2, &xHi_col_i1.vector, &xHi_col_i2.vector, mat_dcdc); - - gsl_matrix_add(xHiDHiDHix_ee, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_ge, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_gg, mat_dcdc); - - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (d_Hi_i1j2, &xHi_col_j1.vector, &xHi_col_i2.vector, mat_dcdc); - - gsl_matrix_add(xHiDHiDHix_ee, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_ge, mat_dcdc); - gsl_matrix_scale(mat_dcdc, delta); - gsl_matrix_add(xHiDHiDHix_gg, mat_dcdc); - } - } - } - - gsl_matrix_free(mat_dcdc); - - return; -} - - - -void Calc_traceHiD (const gsl_vector *eval, const gsl_matrix *Hi, const size_t i, const size_t j, double &tHiD_g, double &tHiD_e) -{ - tHiD_g=0.0; - tHiD_e=0.0; - - size_t n_size=eval->size, d_size=Hi->size1; - double delta, d; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - d=gsl_matrix_get (Hi, j, k*d_size+i); - - if (i==j) { - tHiD_g+=delta*d; - tHiD_e+=d; - } else { - tHiD_g+=delta*d*2.0; - tHiD_e+=d*2.0; - } - } - - return; -} - - -void Calc_traceHiDHiD (const gsl_vector *eval, const gsl_matrix *Hi, const size_t i1, const size_t j1, const size_t i2, const size_t j2, double &tHiDHiD_gg, double &tHiDHiD_ee, double &tHiDHiD_ge) -{ - tHiDHiD_gg=0.0; - tHiDHiD_ee=0.0; - tHiDHiD_ge=0.0; - - size_t n_size=eval->size, d_size=Hi->size1; - double delta, d_Hi_i1i2, d_Hi_i1j2, d_Hi_j1i2, d_Hi_j1j2; - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - d_Hi_i1i2=gsl_matrix_get (Hi, i1, k*d_size+i2); - d_Hi_i1j2=gsl_matrix_get (Hi, i1, k*d_size+j2); - d_Hi_j1i2=gsl_matrix_get (Hi, j1, k*d_size+i2); - d_Hi_j1j2=gsl_matrix_get (Hi, j1, k*d_size+j2); - - if (i1==j1) { - tHiDHiD_gg+=delta*delta*d_Hi_i1j2*d_Hi_j1i2; - tHiDHiD_ee+=d_Hi_i1j2*d_Hi_j1i2; - tHiDHiD_ge+=delta*d_Hi_i1j2*d_Hi_j1i2; - - if (i2!=j2) { - tHiDHiD_gg+=delta*delta*d_Hi_i1i2*d_Hi_j1j2; - tHiDHiD_ee+=d_Hi_i1i2*d_Hi_j1j2; - tHiDHiD_ge+=delta*d_Hi_i1i2*d_Hi_j1j2; - } - } else { - tHiDHiD_gg+=delta*delta*(d_Hi_i1j2*d_Hi_j1i2+d_Hi_j1j2*d_Hi_i1i2); - tHiDHiD_ee+=(d_Hi_i1j2*d_Hi_j1i2+d_Hi_j1j2*d_Hi_i1i2); - tHiDHiD_ge+=delta*(d_Hi_i1j2*d_Hi_j1i2+d_Hi_j1j2*d_Hi_i1i2); - - if (i2!=j2) { - tHiDHiD_gg+=delta*delta*(d_Hi_i1i2*d_Hi_j1j2+d_Hi_j1i2*d_Hi_i1j2); - tHiDHiD_ee+=(d_Hi_i1i2*d_Hi_j1j2+d_Hi_j1i2*d_Hi_i1j2); - tHiDHiD_ge+=delta*(d_Hi_i1i2*d_Hi_j1j2+d_Hi_j1i2*d_Hi_i1j2); - } - } - } - - return; -} - - -//trace(PD)=trace((Hi-HixQixHi)D)=trace(HiD)-trace(HixQixHiD) -void Calc_tracePD (const gsl_vector *eval, const gsl_matrix *Qi, const gsl_matrix *Hi, const gsl_matrix *xHiDHix_all_g, const gsl_matrix *xHiDHix_all_e, const size_t i, const size_t j, double &tPD_g, double &tPD_e) -{ - size_t dc_size=Qi->size1, d_size=Hi->size1; - size_t v=GetIndex(i, j, d_size); - - double d; - - //calculate the first part: trace(HiD) - Calc_traceHiD (eval, Hi, i, j, tPD_g, tPD_e); - - //calculate the second part: -trace(HixQixHiD) - for (size_t k=0; k<dc_size; k++) { - gsl_vector_const_view Qi_row=gsl_matrix_const_row (Qi, k); - gsl_vector_const_view xHiDHix_g_col=gsl_matrix_const_column (xHiDHix_all_g, v*dc_size+k); - gsl_vector_const_view xHiDHix_e_col=gsl_matrix_const_column (xHiDHix_all_e, v*dc_size+k); - - gsl_blas_ddot(&Qi_row.vector, &xHiDHix_g_col.vector, &d); - tPD_g-=d; - gsl_blas_ddot(&Qi_row.vector, &xHiDHix_e_col.vector, &d); - tPD_e-=d; - } - - return; -} - - - -//trace(PDPD)=trace((Hi-HixQixHi)D(Hi-HixQixHi)D) -//=trace(HiDHiD)-trace(HixQixHiDHiD)-trace(HiDHixQixHiD)+trace(HixQixHiDHixQixHiD) -void Calc_tracePDPD (const gsl_vector *eval, const gsl_matrix *Qi, const gsl_matrix *Hi, const gsl_matrix *xHi, const gsl_matrix *QixHiDHix_all_g, const gsl_matrix *QixHiDHix_all_e, const gsl_matrix *xHiDHiDHix_all_gg, const gsl_matrix *xHiDHiDHix_all_ee, const gsl_matrix *xHiDHiDHix_all_ge, const size_t i1, const size_t j1, const size_t i2, const size_t j2, double &tPDPD_gg, double &tPDPD_ee, double &tPDPD_ge) -{ - size_t dc_size=Qi->size1, d_size=Hi->size1; - size_t v_size=d_size*(d_size+1)/2; - size_t v1=GetIndex(i1, j1, d_size), v2=GetIndex(i2, j2, d_size); - - double d; - - //calculate the first part: trace(HiDHiD) - Calc_traceHiDHiD (eval, Hi, i1, j1, i2, j2, tPDPD_gg, tPDPD_ee, tPDPD_ge); - - //calculate the second and third parts: -trace(HixQixHiDHiD)-trace(HiDHixQixHiD) - for (size_t i=0; i<dc_size; i++) { - gsl_vector_const_view Qi_row=gsl_matrix_const_row (Qi, i); - gsl_vector_const_view xHiDHiDHix_gg_col=gsl_matrix_const_column (xHiDHiDHix_all_gg, (v1*v_size+v2)*dc_size+i); - gsl_vector_const_view xHiDHiDHix_ee_col=gsl_matrix_const_column (xHiDHiDHix_all_ee, (v1*v_size+v2)*dc_size+i); - gsl_vector_const_view xHiDHiDHix_ge_col=gsl_matrix_const_column (xHiDHiDHix_all_ge, (v1*v_size+v2)*dc_size+i); - - gsl_blas_ddot(&Qi_row.vector, &xHiDHiDHix_gg_col.vector, &d); - tPDPD_gg-=d*2.0; - gsl_blas_ddot(&Qi_row.vector, &xHiDHiDHix_ee_col.vector, &d); - tPDPD_ee-=d*2.0; - gsl_blas_ddot(&Qi_row.vector, &xHiDHiDHix_ge_col.vector, &d); - tPDPD_ge-=d*2.0; - /* - gsl_vector_const_view xHiDHiDHix_gg_row=gsl_matrix_const_row (xHiDHiDHix_gg, i); - gsl_vector_const_view xHiDHiDHix_ee_row=gsl_matrix_const_row (xHiDHiDHix_ee, i); - gsl_vector_const_view xHiDHiDHix_ge_row=gsl_matrix_const_row (xHiDHiDHix_ge, i); - - gsl_blas_ddot(&Qi_row.vector, &xHiDHiDHix_gg_row.vector, &d); - tPDPD_gg-=d; - gsl_blas_ddot(&Qi_row.vector, &xHiDHiDHix_ee_row.vector, &d); - tPDPD_ee-=d; - gsl_blas_ddot(&Qi_row.vector, &xHiDHiDHix_ge_row.vector, &d); - tPDPD_ge-=d; - */ - } - - //calculate the fourth part: trace(HixQixHiDHixQixHiD) - for (size_t i=0; i<dc_size; i++) { - //gsl_vector_const_view QixHiDHix_g_row1=gsl_matrix_const_subrow (QixHiDHix_all_g, i, v1*dc_size, dc_size); - //gsl_vector_const_view QixHiDHix_e_row1=gsl_matrix_const_subrow (QixHiDHix_all_e, i, v1*dc_size, dc_size); - - gsl_vector_const_view QixHiDHix_g_fullrow1=gsl_matrix_const_row (QixHiDHix_all_g, i); - gsl_vector_const_view QixHiDHix_e_fullrow1=gsl_matrix_const_row (QixHiDHix_all_e, i); - gsl_vector_const_view QixHiDHix_g_row1=gsl_vector_const_subvector (&QixHiDHix_g_fullrow1.vector, v1*dc_size, dc_size); - gsl_vector_const_view QixHiDHix_e_row1=gsl_vector_const_subvector (&QixHiDHix_e_fullrow1.vector, v1*dc_size, dc_size); - - gsl_vector_const_view QixHiDHix_g_col2=gsl_matrix_const_column (QixHiDHix_all_g, v2*dc_size+i); - gsl_vector_const_view QixHiDHix_e_col2=gsl_matrix_const_column (QixHiDHix_all_e, v2*dc_size+i); - - gsl_blas_ddot(&QixHiDHix_g_row1.vector, &QixHiDHix_g_col2.vector, &d); - tPDPD_gg+=d; - gsl_blas_ddot(&QixHiDHix_e_row1.vector, &QixHiDHix_e_col2.vector, &d); - tPDPD_ee+=d; - gsl_blas_ddot(&QixHiDHix_g_row1.vector, &QixHiDHix_e_col2.vector, &d); - tPDPD_ge+=d; - } - - return; -} - - - -//calculate (xHiDHiy) for every pair of i j -void Calc_xHiDHiy_all (const gsl_vector *eval, const gsl_matrix *xHi, const gsl_matrix *Hiy, gsl_matrix *xHiDHiy_all_g, gsl_matrix *xHiDHiy_all_e) -{ - gsl_matrix_set_zero(xHiDHiy_all_g); - gsl_matrix_set_zero(xHiDHiy_all_e); - - size_t d_size=Hiy->size1; - size_t v; - - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - if (j<i) {continue;} - v=GetIndex(i, j, d_size); - - gsl_vector_view xHiDHiy_g=gsl_matrix_column (xHiDHiy_all_g, v); - gsl_vector_view xHiDHiy_e=gsl_matrix_column (xHiDHiy_all_e, v); - - Calc_xHiDHiy (eval, xHi, Hiy, i, j, &xHiDHiy_g.vector, &xHiDHiy_e.vector); - } - } - return; -} - - -//calculate (xHiDHix) for every pair of i j -void Calc_xHiDHix_all (const gsl_vector *eval, const gsl_matrix *xHi, gsl_matrix *xHiDHix_all_g, gsl_matrix *xHiDHix_all_e) -{ - gsl_matrix_set_zero(xHiDHix_all_g); - gsl_matrix_set_zero(xHiDHix_all_e); - - size_t d_size=xHi->size2/eval->size, dc_size=xHi->size1; - size_t v; - - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - if (j<i) {continue;} - v=GetIndex(i, j, d_size); - - gsl_matrix_view xHiDHix_g=gsl_matrix_submatrix (xHiDHix_all_g, 0, v*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHix_e=gsl_matrix_submatrix (xHiDHix_all_e, 0, v*dc_size, dc_size, dc_size); - - Calc_xHiDHix (eval, xHi, i, j, &xHiDHix_g.matrix, &xHiDHix_e.matrix); - } - } - return; -} - - - -//calculate (xHiDHiy) for every pair of i j -void Calc_xHiDHiDHiy_all (const size_t v_size, const gsl_vector *eval, const gsl_matrix *Hi, const gsl_matrix *xHi, const gsl_matrix *Hiy, gsl_matrix *xHiDHiDHiy_all_gg, gsl_matrix *xHiDHiDHiy_all_ee, gsl_matrix *xHiDHiDHiy_all_ge) -{ - gsl_matrix_set_zero(xHiDHiDHiy_all_gg); - gsl_matrix_set_zero(xHiDHiDHiy_all_ee); - gsl_matrix_set_zero(xHiDHiDHiy_all_ge); - - size_t d_size=Hiy->size1; - size_t v1, v2; - - for (size_t i1=0; i1<d_size; i1++) { - for (size_t j1=0; j1<d_size; j1++) { - if (j1<i1) {continue;} - v1=GetIndex(i1, j1, d_size); - - for (size_t i2=0; i2<d_size; i2++) { - for (size_t j2=0; j2<d_size; j2++) { - if (j2<i2) {continue;} - v2=GetIndex(i2, j2, d_size); - - gsl_vector_view xHiDHiDHiy_gg=gsl_matrix_column (xHiDHiDHiy_all_gg, v1*v_size+v2); - gsl_vector_view xHiDHiDHiy_ee=gsl_matrix_column (xHiDHiDHiy_all_ee, v1*v_size+v2); - gsl_vector_view xHiDHiDHiy_ge=gsl_matrix_column (xHiDHiDHiy_all_ge, v1*v_size+v2); - - Calc_xHiDHiDHiy (eval, Hi, xHi, Hiy, i1, j1, i2, j2, &xHiDHiDHiy_gg.vector, &xHiDHiDHiy_ee.vector, &xHiDHiDHiy_ge.vector); - } - } - } - } - return; -} - - -//calculate (xHiDHix) for every pair of i j -void Calc_xHiDHiDHix_all (const size_t v_size, const gsl_vector *eval, const gsl_matrix *Hi, const gsl_matrix *xHi, gsl_matrix *xHiDHiDHix_all_gg, gsl_matrix *xHiDHiDHix_all_ee, gsl_matrix *xHiDHiDHix_all_ge) -{ - gsl_matrix_set_zero(xHiDHiDHix_all_gg); - gsl_matrix_set_zero(xHiDHiDHix_all_ee); - gsl_matrix_set_zero(xHiDHiDHix_all_ge); - - size_t d_size=xHi->size2/eval->size, dc_size=xHi->size1; - size_t v1, v2; - - for (size_t i1=0; i1<d_size; i1++) { - for (size_t j1=0; j1<d_size; j1++) { - if (j1<i1) {continue;} - v1=GetIndex(i1, j1, d_size); - - for (size_t i2=0; i2<d_size; i2++) { - for (size_t j2=0; j2<d_size; j2++) { - if (j2<i2) {continue;} - v2=GetIndex(i2, j2, d_size); - - if (v2<v1) {continue;} - - gsl_matrix_view xHiDHiDHix_gg1=gsl_matrix_submatrix (xHiDHiDHix_all_gg, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ee1=gsl_matrix_submatrix (xHiDHiDHix_all_ee, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ge1=gsl_matrix_submatrix (xHiDHiDHix_all_ge, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - - Calc_xHiDHiDHix (eval, Hi, xHi, i1, j1, i2, j2, &xHiDHiDHix_gg1.matrix, &xHiDHiDHix_ee1.matrix, &xHiDHiDHix_ge1.matrix); - - if (v2!=v1) { - gsl_matrix_view xHiDHiDHix_gg2=gsl_matrix_submatrix (xHiDHiDHix_all_gg, 0, (v2*v_size+v1)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ee2=gsl_matrix_submatrix (xHiDHiDHix_all_ee, 0, (v2*v_size+v1)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ge2=gsl_matrix_submatrix (xHiDHiDHix_all_ge, 0, (v2*v_size+v1)*dc_size, dc_size, dc_size); - - gsl_matrix_memcpy (&xHiDHiDHix_gg2.matrix, &xHiDHiDHix_gg1.matrix); - gsl_matrix_memcpy (&xHiDHiDHix_ee2.matrix, &xHiDHiDHix_ee1.matrix); - gsl_matrix_memcpy (&xHiDHiDHix_ge2.matrix, &xHiDHiDHix_ge1.matrix); - } - } - } - } - } - - - /* - size_t n_size=eval->size; - double delta, d_Hi_ij; - - gsl_matrix *mat_dcdc=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *mat_dcdc_temp=gsl_matrix_alloc (dc_size, dc_size); - - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get (eval, k); - - for (size_t i1=0; i1<d_size; i1++) { - for (size_t j2=0; j2<d_size; j2++) { - gsl_vector_const_view xHi_col_i=gsl_matrix_const_column (xHi, k*d_size+i1); - gsl_vector_const_view xHi_col_j=gsl_matrix_const_column (xHi, k*d_size+j2); - - gsl_matrix_set_zero (mat_dcdc); - gsl_blas_dger (1.0, &xHi_col_i.vector, &xHi_col_j.vector, mat_dcdc); - - for (size_t j1=0; j1<d_size; j1++) { - for (size_t i2=0; i2<d_size; i2++) { - d_Hi_ij=gsl_matrix_get (Hi, j1, k*d_size+i2); - - v1=GetIndex(i1, j1, d_size); - v2=GetIndex(i2, j2, d_size); - - gsl_matrix_view xHiDHiDHix_gg=gsl_matrix_submatrix (xHiDHiDHix_all_gg, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ee=gsl_matrix_submatrix (xHiDHiDHix_all_ee, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ge=gsl_matrix_submatrix (xHiDHiDHix_all_ge, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - - gsl_matrix_memcpy (mat_dcdc_temp, mat_dcdc); - - gsl_matrix_scale (mat_dcdc_temp, d_Hi_ij); - gsl_matrix_add(&xHiDHiDHix_ee.matrix, mat_dcdc_temp); - gsl_matrix_scale(mat_dcdc_temp, delta); - gsl_matrix_add(&xHiDHiDHix_ge.matrix, mat_dcdc_temp); - gsl_matrix_scale(mat_dcdc_temp, delta); - gsl_matrix_add(&xHiDHiDHix_gg.matrix, mat_dcdc_temp); - } - } - } - } - } - - for (size_t i1=0; i1<d_size; i1++) { - for (size_t j1=0; j1<d_size; j1++) { - v1=GetIndex(i1, j1, d_size); - - for (size_t i2=0; i2<d_size; i2++) { - for (size_t j2=0; j2<d_size; j2++) { - v2=GetIndex(i2, j2, d_size); - - if (i1!=j1 && i2!=j2) {continue;} - - gsl_matrix_view xHiDHiDHix_gg=gsl_matrix_submatrix (xHiDHiDHix_all_gg, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ee=gsl_matrix_submatrix (xHiDHiDHix_all_ee, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_view xHiDHiDHix_ge=gsl_matrix_submatrix (xHiDHiDHix_all_ge, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - - if ( (i1==j1 && i2!=j2) || (i1!=j1 && i2==j2) ) { - gsl_matrix_scale (&xHiDHiDHix_gg.matrix, 0.5); - gsl_matrix_scale (&xHiDHiDHix_ee.matrix, 0.5); - gsl_matrix_scale (&xHiDHiDHix_ge.matrix, 0.5); - } else { - gsl_matrix_scale (&xHiDHiDHix_gg.matrix, 0.25); - gsl_matrix_scale (&xHiDHiDHix_ee.matrix, 0.25); - gsl_matrix_scale (&xHiDHiDHix_ge.matrix, 0.25); - } - } - } - } - } - - gsl_matrix_free (mat_dcdc); - gsl_matrix_free (mat_dcdc_temp); - */ - - return; -} - - - -//calculate (xHiDHix)Qi(xHiy) for every pair of i, j -void Calc_xHiDHixQixHiy_all (const gsl_matrix *xHiDHix_all_g, const gsl_matrix *xHiDHix_all_e, const gsl_vector *QixHiy, gsl_matrix *xHiDHixQixHiy_all_g, gsl_matrix *xHiDHixQixHiy_all_e) -{ - size_t dc_size=xHiDHix_all_g->size1; - size_t v_size=xHiDHix_all_g->size2/dc_size; - - for (size_t i=0; i<v_size; i++) { - gsl_matrix_const_view xHiDHix_g=gsl_matrix_const_submatrix (xHiDHix_all_g, 0, i*dc_size, dc_size, dc_size); - gsl_matrix_const_view xHiDHix_e=gsl_matrix_const_submatrix (xHiDHix_all_e, 0, i*dc_size, dc_size, dc_size); - - gsl_vector_view xHiDHixQixHiy_g=gsl_matrix_column (xHiDHixQixHiy_all_g, i); - gsl_vector_view xHiDHixQixHiy_e=gsl_matrix_column (xHiDHixQixHiy_all_e, i); - - gsl_blas_dgemv (CblasNoTrans, 1.0, &xHiDHix_g.matrix, QixHiy, 0.0, &xHiDHixQixHiy_g.vector); - gsl_blas_dgemv (CblasNoTrans, 1.0, &xHiDHix_e.matrix, QixHiy, 0.0, &xHiDHixQixHiy_e.vector); - } - - return; -} - -//calculate Qi(xHiDHiy) and Qi(xHiDHix)Qi(xHiy) for each pair of i j (i<=j) -void Calc_QiVec_all (const gsl_matrix *Qi, const gsl_matrix *vec_all_g, const gsl_matrix *vec_all_e, gsl_matrix *Qivec_all_g, gsl_matrix *Qivec_all_e) -{ - for (size_t i=0; i<vec_all_g->size2; i++) { - gsl_vector_const_view vec_g=gsl_matrix_const_column (vec_all_g, i); - gsl_vector_const_view vec_e=gsl_matrix_const_column (vec_all_e, i); - - gsl_vector_view Qivec_g=gsl_matrix_column (Qivec_all_g, i); - gsl_vector_view Qivec_e=gsl_matrix_column (Qivec_all_e, i); - - gsl_blas_dgemv (CblasNoTrans, 1.0, Qi, &vec_g.vector, 0.0, &Qivec_g.vector); - gsl_blas_dgemv (CblasNoTrans, 1.0, Qi, &vec_e.vector, 0.0, &Qivec_e.vector); - } - - return; -} - - -//calculate Qi(xHiDHix) for each pair of i j (i<=j) -void Calc_QiMat_all (const gsl_matrix *Qi, const gsl_matrix *mat_all_g, const gsl_matrix *mat_all_e, gsl_matrix *Qimat_all_g, gsl_matrix *Qimat_all_e) -{ - size_t dc_size=Qi->size1; - size_t v_size=mat_all_g->size2/mat_all_g->size1; - - for (size_t i=0; i<v_size; i++) { - gsl_matrix_const_view mat_g=gsl_matrix_const_submatrix (mat_all_g, 0, i*dc_size, dc_size, dc_size); - gsl_matrix_const_view mat_e=gsl_matrix_const_submatrix (mat_all_e, 0, i*dc_size, dc_size, dc_size); - - gsl_matrix_view Qimat_g=gsl_matrix_submatrix (Qimat_all_g, 0, i*dc_size, dc_size, dc_size); - gsl_matrix_view Qimat_e=gsl_matrix_submatrix (Qimat_all_e, 0, i*dc_size, dc_size, dc_size); - - gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, Qi, &mat_g.matrix, 0.0, &Qimat_g.matrix); - gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, Qi, &mat_e.matrix, 0.0, &Qimat_e.matrix); - } - - return; -} - - - -//calculate yPDPy -//yPDPy=y(Hi-HixQixHi)D(Hi-HixQixHi)y -//=ytHiDHiy -//-(yHix)Qi(xHiDHiy)-(yHiDHix)Qi(xHiy) -//+(yHix)Qi(xHiDHix)Qi(xtHiy) -void Calc_yPDPy (const gsl_vector *eval, const gsl_matrix *Hiy, const gsl_vector *QixHiy, const gsl_matrix *xHiDHiy_all_g, const gsl_matrix *xHiDHiy_all_e, const gsl_matrix *xHiDHixQixHiy_all_g, const gsl_matrix *xHiDHixQixHiy_all_e, const size_t i, const size_t j, double &yPDPy_g, double &yPDPy_e) -{ - size_t d_size=Hiy->size1; - size_t v=GetIndex(i, j, d_size); - - double d; - - //first part: ytHiDHiy - Calc_yHiDHiy (eval, Hiy, i, j, yPDPy_g, yPDPy_e); - - //second and third parts: -(yHix)Qi(xHiDHiy)-(yHiDHix)Qi(xHiy) - gsl_vector_const_view xHiDHiy_g=gsl_matrix_const_column (xHiDHiy_all_g, v); - gsl_vector_const_view xHiDHiy_e=gsl_matrix_const_column (xHiDHiy_all_e, v); - - gsl_blas_ddot(QixHiy, &xHiDHiy_g.vector, &d); - yPDPy_g-=d*2.0; - gsl_blas_ddot(QixHiy, &xHiDHiy_e.vector, &d); - yPDPy_e-=d*2.0; - - //fourth part: +(yHix)Qi(xHiDHix)Qi(xHiy) - gsl_vector_const_view xHiDHixQixHiy_g=gsl_matrix_const_column (xHiDHixQixHiy_all_g, v); - gsl_vector_const_view xHiDHixQixHiy_e=gsl_matrix_const_column (xHiDHixQixHiy_all_e, v); - - gsl_blas_ddot(QixHiy, &xHiDHixQixHiy_g.vector, &d); - yPDPy_g+=d; - gsl_blas_ddot(QixHiy, &xHiDHixQixHiy_e.vector, &d); - yPDPy_e+=d; - - return; -} - -//calculate yPDPDPy=y(Hi-HixQixHi)D(Hi-HixQixHi)D(Hi-HixQixHi)y -//yPDPDPy=yHiDHiDHiy -//-(yHix)Qi(xHiDHiDHiy)-(yHiDHiDHix)Qi(xHiy) -//-(yHiDHix)Qi(xHiDHiy) -//+(yHix)Qi(xHiDHix)Qi(xHiDHiy)+(yHiDHix)Qi(xHiDHix)Qi(xHiy) -//+(yHix)Qi(xHiDHiDHix)Qi(xHiy) -//-(yHix)Qi(xHiDHix)Qi(xHiDHix)Qi(xHiy) -void Calc_yPDPDPy (const gsl_vector *eval, const gsl_matrix *Hi, const gsl_matrix *xHi, const gsl_matrix *Hiy, const gsl_vector *QixHiy, const gsl_matrix *xHiDHiy_all_g, const gsl_matrix *xHiDHiy_all_e, const gsl_matrix *QixHiDHiy_all_g, const gsl_matrix *QixHiDHiy_all_e, const gsl_matrix *xHiDHixQixHiy_all_g, const gsl_matrix *xHiDHixQixHiy_all_e, const gsl_matrix *QixHiDHixQixHiy_all_g, const gsl_matrix *QixHiDHixQixHiy_all_e, const gsl_matrix *xHiDHiDHiy_all_gg, const gsl_matrix *xHiDHiDHiy_all_ee, const gsl_matrix *xHiDHiDHiy_all_ge, const gsl_matrix *xHiDHiDHix_all_gg, const gsl_matrix *xHiDHiDHix_all_ee, const gsl_matrix *xHiDHiDHix_all_ge, const size_t i1, const size_t j1, const size_t i2, const size_t j2, double &yPDPDPy_gg, double &yPDPDPy_ee, double &yPDPDPy_ge) -{ - size_t d_size=Hi->size1, dc_size=xHi->size1; - size_t v1=GetIndex(i1, j1, d_size), v2=GetIndex(i2, j2, d_size); - size_t v_size=d_size*(d_size+1)/2; - - double d; - - gsl_vector *xHiDHiDHixQixHiy=gsl_vector_alloc (dc_size); - - //first part: yHiDHiDHiy - Calc_yHiDHiDHiy (eval, Hi, Hiy, i1, j1, i2, j2, yPDPDPy_gg, yPDPDPy_ee, yPDPDPy_ge); - - //second and third parts: -(yHix)Qi(xHiDHiDHiy)-(yHiDHiDHix)Qi(xHiy) - gsl_vector_const_view xHiDHiDHiy_gg1=gsl_matrix_const_column (xHiDHiDHiy_all_gg, v1*v_size+v2); - gsl_vector_const_view xHiDHiDHiy_ee1=gsl_matrix_const_column (xHiDHiDHiy_all_ee, v1*v_size+v2); - gsl_vector_const_view xHiDHiDHiy_ge1=gsl_matrix_const_column (xHiDHiDHiy_all_ge, v1*v_size+v2); - - gsl_vector_const_view xHiDHiDHiy_gg2=gsl_matrix_const_column (xHiDHiDHiy_all_gg, v2*v_size+v1); - gsl_vector_const_view xHiDHiDHiy_ee2=gsl_matrix_const_column (xHiDHiDHiy_all_ee, v2*v_size+v1); - gsl_vector_const_view xHiDHiDHiy_ge2=gsl_matrix_const_column (xHiDHiDHiy_all_ge, v2*v_size+v1); - - gsl_blas_ddot(QixHiy, &xHiDHiDHiy_gg1.vector, &d); - yPDPDPy_gg-=d; - gsl_blas_ddot(QixHiy, &xHiDHiDHiy_ee1.vector, &d); - yPDPDPy_ee-=d; - gsl_blas_ddot(QixHiy, &xHiDHiDHiy_ge1.vector, &d); - yPDPDPy_ge-=d; - - gsl_blas_ddot(QixHiy, &xHiDHiDHiy_gg2.vector, &d); - yPDPDPy_gg-=d; - gsl_blas_ddot(QixHiy, &xHiDHiDHiy_ee2.vector, &d); - yPDPDPy_ee-=d; - gsl_blas_ddot(QixHiy, &xHiDHiDHiy_ge2.vector, &d); - yPDPDPy_ge-=d; - - //fourth part: -(yHiDHix)Qi(xHiDHiy) - gsl_vector_const_view xHiDHiy_g1=gsl_matrix_const_column (xHiDHiy_all_g, v1); - gsl_vector_const_view xHiDHiy_e1=gsl_matrix_const_column (xHiDHiy_all_e, v1); - gsl_vector_const_view QixHiDHiy_g2=gsl_matrix_const_column (QixHiDHiy_all_g, v2); - gsl_vector_const_view QixHiDHiy_e2=gsl_matrix_const_column (QixHiDHiy_all_e, v2); - - gsl_blas_ddot(&xHiDHiy_g1.vector, &QixHiDHiy_g2.vector, &d); - yPDPDPy_gg-=d; - gsl_blas_ddot(&xHiDHiy_e1.vector, &QixHiDHiy_e2.vector, &d); - yPDPDPy_ee-=d; - gsl_blas_ddot(&xHiDHiy_g1.vector, &QixHiDHiy_e2.vector, &d); - yPDPDPy_ge-=d; - - //fifth and sixth parts: +(yHix)Qi(xHiDHix)Qi(xHiDHiy)+(yHiDHix)Qi(xHiDHix)Qi(xHiy) - gsl_vector_const_view QixHiDHiy_g1=gsl_matrix_const_column (QixHiDHiy_all_g, v1); - gsl_vector_const_view QixHiDHiy_e1=gsl_matrix_const_column (QixHiDHiy_all_e, v1); - - gsl_vector_const_view xHiDHixQixHiy_g1=gsl_matrix_const_column (xHiDHixQixHiy_all_g, v1); - gsl_vector_const_view xHiDHixQixHiy_e1=gsl_matrix_const_column (xHiDHixQixHiy_all_e, v1); - gsl_vector_const_view xHiDHixQixHiy_g2=gsl_matrix_const_column (xHiDHixQixHiy_all_g, v2); - gsl_vector_const_view xHiDHixQixHiy_e2=gsl_matrix_const_column (xHiDHixQixHiy_all_e, v2); - - gsl_blas_ddot(&xHiDHixQixHiy_g1.vector, &QixHiDHiy_g2.vector, &d); - yPDPDPy_gg+=d; - gsl_blas_ddot(&xHiDHixQixHiy_g2.vector, &QixHiDHiy_g1.vector, &d); - yPDPDPy_gg+=d; - - gsl_blas_ddot(&xHiDHixQixHiy_e1.vector, &QixHiDHiy_e2.vector, &d); - yPDPDPy_ee+=d; - gsl_blas_ddot(&xHiDHixQixHiy_e2.vector, &QixHiDHiy_e1.vector, &d); - yPDPDPy_ee+=d; - - gsl_blas_ddot(&xHiDHixQixHiy_g1.vector, &QixHiDHiy_e2.vector, &d); - yPDPDPy_ge+=d; - gsl_blas_ddot(&xHiDHixQixHiy_e2.vector, &QixHiDHiy_g1.vector, &d); - yPDPDPy_ge+=d; - - //seventh part: +(yHix)Qi(xHiDHiDHix)Qi(xHiy) - gsl_matrix_const_view xHiDHiDHix_gg=gsl_matrix_const_submatrix (xHiDHiDHix_all_gg, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_const_view xHiDHiDHix_ee=gsl_matrix_const_submatrix (xHiDHiDHix_all_ee, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_const_view xHiDHiDHix_ge=gsl_matrix_const_submatrix (xHiDHiDHix_all_ge, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - - gsl_blas_dgemv (CblasNoTrans, 1.0, &xHiDHiDHix_gg.matrix, QixHiy, 0.0, xHiDHiDHixQixHiy); - gsl_blas_ddot(xHiDHiDHixQixHiy, QixHiy, &d); - yPDPDPy_gg+=d; - gsl_blas_dgemv (CblasNoTrans, 1.0, &xHiDHiDHix_ee.matrix, QixHiy, 0.0, xHiDHiDHixQixHiy); - gsl_blas_ddot(xHiDHiDHixQixHiy, QixHiy, &d); - yPDPDPy_ee+=d; - gsl_blas_dgemv (CblasNoTrans, 1.0, &xHiDHiDHix_ge.matrix, QixHiy, 0.0, xHiDHiDHixQixHiy); - gsl_blas_ddot(xHiDHiDHixQixHiy, QixHiy, &d); - yPDPDPy_ge+=d; - - //eighth part: -(yHix)Qi(xHiDHix)Qi(xHiDHix)Qi(xHiy) - gsl_vector_const_view QixHiDHixQixHiy_g1=gsl_matrix_const_column (QixHiDHixQixHiy_all_g, v1); - gsl_vector_const_view QixHiDHixQixHiy_e1=gsl_matrix_const_column (QixHiDHixQixHiy_all_e, v1); - - gsl_blas_ddot(&QixHiDHixQixHiy_g1.vector, &xHiDHixQixHiy_g2.vector, &d); - yPDPDPy_gg-=d; - gsl_blas_ddot(&QixHiDHixQixHiy_e1.vector, &xHiDHixQixHiy_e2.vector, &d); - yPDPDPy_ee-=d; - gsl_blas_ddot(&QixHiDHixQixHiy_g1.vector, &xHiDHixQixHiy_e2.vector, &d); - yPDPDPy_ge-=d; - - //free memory - gsl_vector_free(xHiDHiDHixQixHiy); - - return; -} - - -//calculate Edgeworth correctation factors for small samples -//notation and method follows Thomas J. Rothenberg, Econometirca 1984; 52 (4) -//M=xHiDHix -void CalcCRT (const gsl_matrix *Hessian_inv, const gsl_matrix *Qi, const gsl_matrix *QixHiDHix_all_g, const gsl_matrix *QixHiDHix_all_e, const gsl_matrix *xHiDHiDHix_all_gg, const gsl_matrix *xHiDHiDHix_all_ee, const gsl_matrix *xHiDHiDHix_all_ge, const size_t d_size, double &crt_a, double &crt_b, double &crt_c) -{ - crt_a=0.0; crt_b=0.0; crt_c=0.0; - - size_t dc_size=Qi->size1, v_size=Hessian_inv->size1/2; - size_t c_size=dc_size/d_size; - double h_gg, h_ge, h_ee, d, B=0.0, C=0.0, D=0.0; - double trCg1, trCe1, trCg2, trCe2, trB_gg, trB_ge, trB_ee, trCC_gg, trCC_ge, trCC_ee, trD_gg=0.0, trD_ge=0.0, trD_ee=0.0; - - gsl_matrix *QiMQi_g1=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMQi_e1=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMQi_g2=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMQi_e2=gsl_matrix_alloc (dc_size, dc_size); - - gsl_matrix *QiMQisQisi_g1=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *QiMQisQisi_e1=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *QiMQisQisi_g2=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *QiMQisQisi_e2=gsl_matrix_alloc (d_size, d_size); - - gsl_matrix *QiMQiMQi_gg=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMQiMQi_ge=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMQiMQi_ee=gsl_matrix_alloc (dc_size, dc_size); - - gsl_matrix *QiMMQi_gg=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMMQi_ge=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *QiMMQi_ee=gsl_matrix_alloc (dc_size, dc_size); - - gsl_matrix *Qi_si=gsl_matrix_alloc (d_size, d_size); - - gsl_matrix *M_dd=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *M_dcdc=gsl_matrix_alloc (dc_size, dc_size); - - //invert Qi_sub to Qi_si - gsl_matrix *Qi_sub=gsl_matrix_alloc (d_size, d_size); - - gsl_matrix_const_view Qi_s=gsl_matrix_const_submatrix (Qi, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - - int sig; - gsl_permutation * pmt=gsl_permutation_alloc (d_size); - - gsl_matrix_memcpy (Qi_sub, &Qi_s.matrix); - LUDecomp (Qi_sub, pmt, &sig); - LUInvert (Qi_sub, pmt, Qi_si); - - gsl_permutation_free(pmt); - gsl_matrix_free(Qi_sub); - - //calculate correctation factors - for (size_t v1=0; v1<v_size; v1++) { - //calculate Qi(xHiDHix)Qi, and subpart of it - gsl_matrix_const_view QiM_g1=gsl_matrix_const_submatrix (QixHiDHix_all_g, 0, v1*dc_size, dc_size, dc_size); - gsl_matrix_const_view QiM_e1=gsl_matrix_const_submatrix (QixHiDHix_all_e, 0, v1*dc_size, dc_size, dc_size); - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_g1.matrix, Qi, 0.0, QiMQi_g1); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_e1.matrix, Qi, 0.0, QiMQi_e1); - - gsl_matrix_view QiMQi_g1_s=gsl_matrix_submatrix (QiMQi_g1, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - gsl_matrix_view QiMQi_e1_s=gsl_matrix_submatrix (QiMQi_e1, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - - /* - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<setprecision(6)<<gsl_matrix_get(&QiMQi_g1_s.matrix, i, j)<<"\t"; - } - cout<<endl; - } -*/ - //calculate trCg1 and trCe1 - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQi_g1_s.matrix, Qi_si, 0.0, QiMQisQisi_g1); - trCg1=0.0; - for (size_t k=0; k<d_size; k++) { - trCg1-=gsl_matrix_get (QiMQisQisi_g1, k, k); - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQi_e1_s.matrix, Qi_si, 0.0, QiMQisQisi_e1); - trCe1=0.0; - for (size_t k=0; k<d_size; k++) { - trCe1-=gsl_matrix_get (QiMQisQisi_e1, k, k); - } - /* - cout<<v1<<endl; - cout<<"trCg1 = "<<trCg1<<", trCe1 = "<<trCe1<<endl; - */ - for (size_t v2=0; v2<v_size; v2++) { - if (v2<v1) {continue;} - - //calculate Qi(xHiDHix)Qi, and subpart of it - gsl_matrix_const_view QiM_g2=gsl_matrix_const_submatrix (QixHiDHix_all_g, 0, v2*dc_size, dc_size, dc_size); - gsl_matrix_const_view QiM_e2=gsl_matrix_const_submatrix (QixHiDHix_all_e, 0, v2*dc_size, dc_size, dc_size); - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_g2.matrix, Qi, 0.0, QiMQi_g2); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_e2.matrix, Qi, 0.0, QiMQi_e2); - - gsl_matrix_view QiMQi_g2_s=gsl_matrix_submatrix (QiMQi_g2, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - gsl_matrix_view QiMQi_e2_s=gsl_matrix_submatrix (QiMQi_e2, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - - //calculate trCg2 and trCe2 - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQi_g2_s.matrix, Qi_si, 0.0, QiMQisQisi_g2); - trCg2=0.0; - for (size_t k=0; k<d_size; k++) { - trCg2-=gsl_matrix_get (QiMQisQisi_g2, k, k); - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQi_e2_s.matrix, Qi_si, 0.0, QiMQisQisi_e2); - trCe2=0.0; - for (size_t k=0; k<d_size; k++) { - trCe2-=gsl_matrix_get (QiMQisQisi_e2, k, k); - } - - //calculate trCC_gg, trCC_ge, trCC_ee - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, QiMQisQisi_g1, QiMQisQisi_g2, 0.0, M_dd); - trCC_gg=0.0; - for (size_t k=0; k<d_size; k++) { - trCC_gg+=gsl_matrix_get (M_dd, k, k); - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, QiMQisQisi_g1, QiMQisQisi_e2, 0.0, M_dd); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, QiMQisQisi_e1, QiMQisQisi_g2, 1.0, M_dd); - trCC_ge=0.0; - for (size_t k=0; k<d_size; k++) { - trCC_ge+=gsl_matrix_get (M_dd, k, k); - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, QiMQisQisi_e1, QiMQisQisi_e2, 0.0, M_dd); - trCC_ee=0.0; - for (size_t k=0; k<d_size; k++) { - trCC_ee+=gsl_matrix_get (M_dd, k, k); - } - - //calculate Qi(xHiDHix)Qi(xHiDHix)Qi, and subpart of it - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_g1.matrix, QiMQi_g2, 0.0, QiMQiMQi_gg); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_g1.matrix, QiMQi_e2, 0.0, QiMQiMQi_ge); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_e1.matrix, QiMQi_g2, 1.0, QiMQiMQi_ge); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiM_e1.matrix, QiMQi_e2, 0.0, QiMQiMQi_ee); - - gsl_matrix_view QiMQiMQi_gg_s=gsl_matrix_submatrix (QiMQiMQi_gg, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - gsl_matrix_view QiMQiMQi_ge_s=gsl_matrix_submatrix (QiMQiMQi_ge, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - gsl_matrix_view QiMQiMQi_ee_s=gsl_matrix_submatrix (QiMQiMQi_ee, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - - //and part of trB_gg, trB_ge, trB_ee - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQiMQi_gg_s.matrix, Qi_si, 0.0, M_dd); - trB_gg=0.0; - for (size_t k=0; k<d_size; k++) { - d=gsl_matrix_get (M_dd, k, k); - trB_gg-=d; - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQiMQi_ge_s.matrix, Qi_si, 0.0, M_dd); - trB_ge=0.0; - for (size_t k=0; k<d_size; k++) { - d=gsl_matrix_get (M_dd, k, k); - trB_ge-=d; - } - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMQiMQi_ee_s.matrix, Qi_si, 0.0, M_dd); - trB_ee=0.0; - for (size_t k=0; k<d_size; k++) { - d=gsl_matrix_get (M_dd, k, k); - trB_ee-=d; - } - - //calculate Qi(xHiDHiDHix)Qi, and subpart of it - gsl_matrix_const_view MM_gg=gsl_matrix_const_submatrix (xHiDHiDHix_all_gg, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_const_view MM_ge=gsl_matrix_const_submatrix (xHiDHiDHix_all_ge, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - gsl_matrix_const_view MM_ee=gsl_matrix_const_submatrix (xHiDHiDHix_all_ee, 0, (v1*v_size+v2)*dc_size, dc_size, dc_size); - - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Qi, &MM_gg.matrix, 0.0, M_dcdc); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, M_dcdc, Qi, 0.0, QiMMQi_gg); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Qi, &MM_ge.matrix, 0.0, M_dcdc); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, M_dcdc, Qi, 0.0, QiMMQi_ge); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Qi, &MM_ee.matrix, 0.0, M_dcdc); - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, M_dcdc, Qi, 0.0, QiMMQi_ee); - - gsl_matrix_view QiMMQi_gg_s=gsl_matrix_submatrix (QiMMQi_gg, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - gsl_matrix_view QiMMQi_ge_s=gsl_matrix_submatrix (QiMMQi_ge, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - gsl_matrix_view QiMMQi_ee_s=gsl_matrix_submatrix (QiMMQi_ee, (c_size-1)*d_size, (c_size-1)*d_size, d_size, d_size); - - //calculate the other part of trB_gg, trB_ge, trB_ee - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMMQi_gg_s.matrix, Qi_si, 0.0, M_dd); - for (size_t k=0; k<d_size; k++) { - trB_gg+=gsl_matrix_get (M_dd, k, k); - } - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMMQi_ge_s.matrix, Qi_si, 0.0, M_dd); - for (size_t k=0; k<d_size; k++) { - trB_ge+=2.0*gsl_matrix_get (M_dd, k, k); - } - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &QiMMQi_ee_s.matrix, Qi_si, 0.0, M_dd); - for (size_t k=0; k<d_size; k++) { - trB_ee+=gsl_matrix_get (M_dd, k, k); - } - - - //calculate trD_gg, trD_ge, trD_ee - trD_gg=2.0*trB_gg; - trD_ge=2.0*trB_ge; - trD_ee=2.0*trB_ee; - - //calculate B, C and D - h_gg=-1.0*gsl_matrix_get (Hessian_inv, v1, v2); - h_ge=-1.0*gsl_matrix_get (Hessian_inv, v1, v2+v_size); - h_ee=-1.0*gsl_matrix_get (Hessian_inv, v1+v_size, v2+v_size); - - B+=h_gg*trB_gg+h_ge*trB_ge+h_ee*trB_ee; - C+=h_gg*(trCC_gg+0.5*trCg1*trCg2)+h_ge*(trCC_ge+0.5*trCg1*trCe2+0.5*trCe1*trCg2)+h_ee*(trCC_ee+0.5*trCe1*trCe2); - D+=h_gg*(trCC_gg+0.5*trD_gg)+h_ge*(trCC_ge+0.5*trD_ge)+h_ee*(trCC_ee+0.5*trD_ee); - - if (v1!=v2) { - B+=h_gg*trB_gg+h_ge*trB_ge+h_ee*trB_ee; - C+=h_gg*(trCC_gg+0.5*trCg1*trCg2)+h_ge*(trCC_ge+0.5*trCg1*trCe2+0.5*trCe1*trCg2)+h_ee*(trCC_ee+0.5*trCe1*trCe2); - D+=h_gg*(trCC_gg+0.5*trD_gg)+h_ge*(trCC_ge+0.5*trD_ge)+h_ee*(trCC_ee+0.5*trD_ee); - } - - /* - cout<<v1<<"\t"<<v2<<endl; - cout<<h_gg<<"\t"<<h_ge<<"\t"<<h_ee<<endl; - cout<<trB_gg<<"\t"<<trB_ge<<"\t"<<trB_ee<<endl; - cout<<trCg1<<"\t"<<trCe1<<"\t"<<trCg2<<"\t"<<trCe2<<endl; - cout<<trCC_gg<<"\t"<<trCC_ge<<"\t"<<trCC_ee<<endl; - cout<<trD_gg<<"\t"<<trD_ge<<"\t"<<trD_ee<<endl; - */ - } - } - - //calculate a, b, c from B C D - crt_a=2.0*D-C; - crt_b=2.0*B; - crt_c=C; - /* - cout<<B<<"\t"<<C<<"\t"<<D<<endl; - cout<<setprecision(6)<<crt_a<<"\t"<<crt_b<<"\t"<<crt_c<<endl; - */ - //free matrix memory - gsl_matrix_free(QiMQi_g1); - gsl_matrix_free(QiMQi_e1); - gsl_matrix_free(QiMQi_g2); - gsl_matrix_free(QiMQi_e2); - - gsl_matrix_free(QiMQisQisi_g1); - gsl_matrix_free(QiMQisQisi_e1); - gsl_matrix_free(QiMQisQisi_g2); - gsl_matrix_free(QiMQisQisi_e2); - - gsl_matrix_free(QiMQiMQi_gg); - gsl_matrix_free(QiMQiMQi_ge); - gsl_matrix_free(QiMQiMQi_ee); - - gsl_matrix_free(QiMMQi_gg); - gsl_matrix_free(QiMMQi_ge); - gsl_matrix_free(QiMMQi_ee); - - gsl_matrix_free(Qi_si); - - gsl_matrix_free(M_dd); - gsl_matrix_free(M_dcdc); - - return; -} - - - - - -//calculate first-order and second-order derivatives -void CalcDev (const char func_name, const gsl_vector *eval, const gsl_matrix *Qi, const gsl_matrix *Hi, const gsl_matrix *xHi, const gsl_matrix *Hiy, const gsl_vector *QixHiy, gsl_vector *gradient, gsl_matrix *Hessian_inv, double &crt_a, double &crt_b, double &crt_c) -{ - if (func_name!='R' && func_name!='L' && func_name!='r' && func_name!='l') {cout<<"func_name only takes 'R' or 'L': 'R' for log-restricted likelihood, 'L' for log-likelihood."<<endl; return;} - - size_t dc_size=Qi->size1, d_size=Hi->size1; - size_t c_size=dc_size/d_size; - size_t v_size=d_size*(d_size+1)/2; - size_t v1, v2; - double dev1_g, dev1_e, dev2_gg, dev2_ee, dev2_ge; - - gsl_matrix *Hessian=gsl_matrix_alloc (v_size*2, v_size*2); - - gsl_matrix *xHiDHiy_all_g=gsl_matrix_alloc (dc_size, v_size); - gsl_matrix *xHiDHiy_all_e=gsl_matrix_alloc (dc_size, v_size); - gsl_matrix *xHiDHix_all_g=gsl_matrix_alloc (dc_size, v_size*dc_size); - gsl_matrix *xHiDHix_all_e=gsl_matrix_alloc (dc_size, v_size*dc_size); - gsl_matrix *xHiDHixQixHiy_all_g=gsl_matrix_alloc (dc_size, v_size); - gsl_matrix *xHiDHixQixHiy_all_e=gsl_matrix_alloc (dc_size, v_size); - - gsl_matrix *QixHiDHiy_all_g=gsl_matrix_alloc (dc_size, v_size); - gsl_matrix *QixHiDHiy_all_e=gsl_matrix_alloc (dc_size, v_size); - gsl_matrix *QixHiDHix_all_g=gsl_matrix_alloc (dc_size, v_size*dc_size); - gsl_matrix *QixHiDHix_all_e=gsl_matrix_alloc (dc_size, v_size*dc_size); - gsl_matrix *QixHiDHixQixHiy_all_g=gsl_matrix_alloc (dc_size, v_size); - gsl_matrix *QixHiDHixQixHiy_all_e=gsl_matrix_alloc (dc_size, v_size); - - gsl_matrix *xHiDHiDHiy_all_gg=gsl_matrix_alloc (dc_size, v_size*v_size); - gsl_matrix *xHiDHiDHiy_all_ee=gsl_matrix_alloc (dc_size, v_size*v_size); - gsl_matrix *xHiDHiDHiy_all_ge=gsl_matrix_alloc (dc_size, v_size*v_size); - gsl_matrix *xHiDHiDHix_all_gg=gsl_matrix_alloc (dc_size, v_size*v_size*dc_size); - gsl_matrix *xHiDHiDHix_all_ee=gsl_matrix_alloc (dc_size, v_size*v_size*dc_size); - gsl_matrix *xHiDHiDHix_all_ge=gsl_matrix_alloc (dc_size, v_size*v_size*dc_size); - - //calculate xHiDHiy_all, xHiDHix_all and xHiDHixQixHiy_all - Calc_xHiDHiy_all (eval, xHi, Hiy, xHiDHiy_all_g, xHiDHiy_all_e); - Calc_xHiDHix_all (eval, xHi, xHiDHix_all_g, xHiDHix_all_e); - Calc_xHiDHixQixHiy_all (xHiDHix_all_g, xHiDHix_all_e, QixHiy, xHiDHixQixHiy_all_g, xHiDHixQixHiy_all_e); - - Calc_xHiDHiDHiy_all (v_size, eval, Hi, xHi, Hiy, xHiDHiDHiy_all_gg, xHiDHiDHiy_all_ee, xHiDHiDHiy_all_ge); - Calc_xHiDHiDHix_all (v_size, eval, Hi, xHi, xHiDHiDHix_all_gg, xHiDHiDHix_all_ee, xHiDHiDHix_all_ge); - - //calculate QixHiDHiy_all, QixHiDHix_all and QixHiDHixQixHiy_all - Calc_QiVec_all (Qi, xHiDHiy_all_g, xHiDHiy_all_e, QixHiDHiy_all_g, QixHiDHiy_all_e); - Calc_QiVec_all (Qi, xHiDHixQixHiy_all_g, xHiDHixQixHiy_all_e, QixHiDHixQixHiy_all_g, QixHiDHixQixHiy_all_e); - Calc_QiMat_all (Qi, xHiDHix_all_g, xHiDHix_all_e, QixHiDHix_all_g, QixHiDHix_all_e); - - double tHiD_g, tHiD_e, tPD_g, tPD_e, tHiDHiD_gg, tHiDHiD_ee, tHiDHiD_ge, tPDPD_gg, tPDPD_ee, tPDPD_ge; - double yPDPy_g, yPDPy_e, yPDPDPy_gg, yPDPDPy_ee, yPDPDPy_ge; - - //calculate gradient and Hessian for Vg - for (size_t i1=0; i1<d_size; i1++) { - for (size_t j1=0; j1<d_size; j1++) { - if (j1<i1) {continue;} - v1=GetIndex (i1, j1, d_size); - - Calc_yPDPy (eval, Hiy, QixHiy, xHiDHiy_all_g, xHiDHiy_all_e, xHiDHixQixHiy_all_g, xHiDHixQixHiy_all_e, i1, j1, yPDPy_g, yPDPy_e); - - if (func_name=='R' || func_name=='r') { - Calc_tracePD (eval, Qi, Hi, xHiDHix_all_g, xHiDHix_all_e, i1, j1, tPD_g, tPD_e); - //cout<<i1<<" "<<j1<<" "<<yPDPy_g<<" "<<yPDPy_e<<" "<<tPD_g<<" "<<tPD_e<<endl; - - dev1_g=-0.5*tPD_g+0.5*yPDPy_g; - dev1_e=-0.5*tPD_e+0.5*yPDPy_e; - } else { - Calc_traceHiD (eval, Hi, i1, j1, tHiD_g, tHiD_e); - - dev1_g=-0.5*tHiD_g+0.5*yPDPy_g; - dev1_e=-0.5*tHiD_e+0.5*yPDPy_e; - } - - gsl_vector_set (gradient, v1, dev1_g); - gsl_vector_set (gradient, v1+v_size, dev1_e); - - for (size_t i2=0; i2<d_size; i2++) { - for (size_t j2=0; j2<d_size; j2++) { - if (j2<i2) {continue;} - v2=GetIndex (i2, j2, d_size); - - if (v2<v1) {continue;} - - Calc_yPDPDPy (eval, Hi, xHi, Hiy, QixHiy, xHiDHiy_all_g, xHiDHiy_all_e, QixHiDHiy_all_g, QixHiDHiy_all_e, xHiDHixQixHiy_all_g, xHiDHixQixHiy_all_e, QixHiDHixQixHiy_all_g, QixHiDHixQixHiy_all_e, xHiDHiDHiy_all_gg, xHiDHiDHiy_all_ee, xHiDHiDHiy_all_ge, xHiDHiDHix_all_gg, xHiDHiDHix_all_ee, xHiDHiDHix_all_ge, i1, j1, i2, j2, yPDPDPy_gg, yPDPDPy_ee, yPDPDPy_ge); - - //cout<<i1<<" "<<j1<<" "<<i2<<" "<<j2<<" "<<yPDPDPy_gg<<" "<<yPDPDPy_ee<<" "<<yPDPDPy_ge<<endl; - //AI for reml - if (func_name=='R' || func_name=='r') { - Calc_tracePDPD (eval, Qi, Hi, xHi, QixHiDHix_all_g, QixHiDHix_all_e, xHiDHiDHix_all_gg, xHiDHiDHix_all_ee, xHiDHiDHix_all_ge, i1, j1, i2, j2, tPDPD_gg, tPDPD_ee, tPDPD_ge); - - dev2_gg=0.5*tPDPD_gg-yPDPDPy_gg; - dev2_ee=0.5*tPDPD_ee-yPDPDPy_ee; - dev2_ge=0.5*tPDPD_ge-yPDPDPy_ge; - /* - dev2_gg=-0.5*yPDPDPy_gg; - dev2_ee=-0.5*yPDPDPy_ee; - dev2_ge=-0.5*yPDPDPy_ge; - */ - } else { - Calc_traceHiDHiD (eval, Hi, i1, j1, i2, j2, tHiDHiD_gg, tHiDHiD_ee, tHiDHiD_ge); - - dev2_gg=0.5*tHiDHiD_gg-yPDPDPy_gg; - dev2_ee=0.5*tHiDHiD_ee-yPDPDPy_ee; - dev2_ge=0.5*tHiDHiD_ge-yPDPDPy_ge; - } - - //set up Hessian - gsl_matrix_set (Hessian, v1, v2, dev2_gg); - gsl_matrix_set (Hessian, v1+v_size, v2+v_size, dev2_ee); - gsl_matrix_set (Hessian, v1, v2+v_size, dev2_ge); - gsl_matrix_set (Hessian, v2+v_size, v1, dev2_ge); - - if (v1!=v2) { - gsl_matrix_set (Hessian, v2, v1, dev2_gg); - gsl_matrix_set (Hessian, v2+v_size, v1+v_size, dev2_ee); - gsl_matrix_set (Hessian, v2, v1+v_size, dev2_ge); - gsl_matrix_set (Hessian, v1+v_size, v2, dev2_ge); - } - } - } - } - } - - /* - cout<<"Hessian: "<<endl; - for (size_t i=0; i<2*v_size; i++) { - for (size_t j=0; j<2*v_size; j++) { - cout<<gsl_matrix_get(Hessian, i, j)<<"\t"; - } - cout<<endl; - } - */ - - - //Invert Hessian - int sig; - gsl_permutation * pmt=gsl_permutation_alloc (v_size*2); - - LUDecomp (Hessian, pmt, &sig); - LUInvert (Hessian, pmt, Hessian_inv); - /* - cout<<"Hessian Inverse: "<<endl; - for (size_t i=0; i<2*v_size; i++) { - for (size_t j=0; j<2*v_size; j++) { - cout<<gsl_matrix_get(Hessian_inv, i, j)<<"\t"; - } - cout<<endl; - } - */ - gsl_permutation_free(pmt); - gsl_matrix_free(Hessian); - - //calculate Edgeworth correction factors - //after inverting Hessian - if (c_size>1) { - CalcCRT (Hessian_inv, Qi, QixHiDHix_all_g, QixHiDHix_all_e, xHiDHiDHix_all_gg, xHiDHiDHix_all_ee, xHiDHiDHix_all_ge, d_size, crt_a, crt_b, crt_c); - } else { - crt_a=0.0; crt_b=0.0; crt_c=0.0; - } - - gsl_matrix_free(xHiDHiy_all_g); - gsl_matrix_free(xHiDHiy_all_e); - gsl_matrix_free(xHiDHix_all_g); - gsl_matrix_free(xHiDHix_all_e); - gsl_matrix_free(xHiDHixQixHiy_all_g); - gsl_matrix_free(xHiDHixQixHiy_all_e); - - gsl_matrix_free(QixHiDHiy_all_g); - gsl_matrix_free(QixHiDHiy_all_e); - gsl_matrix_free(QixHiDHix_all_g); - gsl_matrix_free(QixHiDHix_all_e); - gsl_matrix_free(QixHiDHixQixHiy_all_g); - gsl_matrix_free(QixHiDHixQixHiy_all_e); - - gsl_matrix_free(xHiDHiDHiy_all_gg); - gsl_matrix_free(xHiDHiDHiy_all_ee); - gsl_matrix_free(xHiDHiDHiy_all_ge); - gsl_matrix_free(xHiDHiDHix_all_gg); - gsl_matrix_free(xHiDHiDHix_all_ee); - gsl_matrix_free(xHiDHiDHix_all_ge); - - return; -} - - -//update Vg, Ve -void UpdateVgVe (const gsl_matrix *Hessian_inv, const gsl_vector *gradient, const double step_scale, gsl_matrix *V_g, gsl_matrix *V_e) -{ - size_t v_size=gradient->size/2, d_size=V_g->size1; - size_t v; - - gsl_vector *vec_v=gsl_vector_alloc (v_size*2); - - double d; - - //vectorize Vg and Ve - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - if (j<i) {continue;} - v=GetIndex(i, j, d_size); - - d=gsl_matrix_get (V_g, i, j); - gsl_vector_set (vec_v, v, d); - - d=gsl_matrix_get (V_e, i, j); - gsl_vector_set (vec_v, v+v_size, d); - } - } - - gsl_blas_dgemv (CblasNoTrans, -1.0*step_scale, Hessian_inv, gradient, 1.0, vec_v); - - //save Vg and Ve - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - if (j<i) {continue;} - v=GetIndex(i, j, d_size); - - d=gsl_vector_get (vec_v, v); - gsl_matrix_set (V_g, i, j, d); - gsl_matrix_set (V_g, j, i, d); - - d=gsl_vector_get (vec_v, v+v_size); - gsl_matrix_set (V_e, i, j, d); - gsl_matrix_set (V_e, j, i, d); - } - } - - gsl_vector_free(vec_v); - - return; -} - - - - - - -double MphNR (const char func_name, const size_t max_iter, const double max_prec, const gsl_vector *eval, const gsl_matrix *X, const gsl_matrix *Y, gsl_matrix *Hi_all, gsl_matrix *xHi_all, gsl_matrix *Hiy_all, gsl_matrix *V_g, gsl_matrix *V_e, gsl_matrix *Hessian_inv, double &crt_a, double &crt_b, double &crt_c) -{ - if (func_name!='R' && func_name!='L' && func_name!='r' && func_name!='l') {cout<<"func_name only takes 'R' or 'L': 'R' for log-restricted likelihood, 'L' for log-likelihood."<<endl; return 0.0;} - size_t n_size=eval->size, c_size=X->size1, d_size=Y->size1; - size_t dc_size=d_size*c_size; - size_t v_size=d_size*(d_size+1)/2; - - double logdet_H, logdet_Q, yPy, logl_const, logl_old=0.0, logl_new=0.0, step_scale; - int sig; - size_t step_iter, flag_pd; - - gsl_matrix *Vg_save=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *Ve_save=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_temp=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *U_temp=gsl_matrix_alloc (d_size, d_size); - gsl_vector *D_temp=gsl_vector_alloc (d_size); - gsl_vector *xHiy=gsl_vector_alloc (dc_size); - gsl_vector *QixHiy=gsl_vector_alloc (dc_size); - gsl_matrix *Qi=gsl_matrix_alloc (dc_size, dc_size); - gsl_matrix *XXt=gsl_matrix_alloc (c_size, c_size); - - gsl_vector *gradient=gsl_vector_alloc (v_size*2); - - //calculate |XXt| and (XXt)^{-1} - gsl_blas_dsyrk (CblasUpper, CblasNoTrans, 1.0, X, 0.0, XXt); - for (size_t i=0; i<c_size; ++i) { - for (size_t j=0; j<i; ++j) { - gsl_matrix_set (XXt, i, j, gsl_matrix_get (XXt, j, i)); - } - } - - gsl_permutation * pmt=gsl_permutation_alloc (c_size); - LUDecomp (XXt, pmt, &sig); - gsl_permutation_free (pmt); -// LUInvert (XXt, pmt, XXti); - - //calculate the constant for logl - if (func_name=='R' || func_name=='r') { - logl_const=-0.5*(double)(n_size-c_size)*(double)d_size*log(2.0*M_PI)+0.5*(double)d_size*LULndet (XXt); - } else { - logl_const=-0.5*(double)n_size*(double)d_size*log(2.0*M_PI); - } - //optimization iterations - - for (size_t t=0; t<max_iter; t++) { - gsl_matrix_memcpy (Vg_save, V_g); - gsl_matrix_memcpy (Ve_save, V_e); - - step_scale=1.0; step_iter=0; - do { - gsl_matrix_memcpy (V_g, Vg_save); - gsl_matrix_memcpy (V_e, Ve_save); - - //update Vg, Ve, and invert Hessian - if (t!=0) {UpdateVgVe (Hessian_inv, gradient, step_scale, V_g, V_e);} - - //check if both Vg and Ve are positive definite - flag_pd=1; - gsl_matrix_memcpy (V_temp, V_e); - EigenDecomp(V_temp, U_temp, D_temp, 0); - for (size_t i=0; i<d_size; i++) { - if (gsl_vector_get (D_temp, i)<=0) {flag_pd=0;} - } - gsl_matrix_memcpy (V_temp, V_g); - EigenDecomp(V_temp, U_temp, D_temp, 0); - for (size_t i=0; i<d_size; i++) { - if (gsl_vector_get (D_temp, i)<=0) {flag_pd=0;} - } - - //if flag_pd==1 continue to calculate quantities and logl - if (flag_pd==1) { - CalcHiQi (eval, X, V_g, V_e, Hi_all, Qi, logdet_H, logdet_Q); - Calc_Hiy_all (Y, Hi_all, Hiy_all); - Calc_xHi_all (X, Hi_all, xHi_all); - - //calculate QixHiy and yPy - Calc_xHiy (Y, xHi_all, xHiy); - gsl_blas_dgemv (CblasNoTrans, 1.0, Qi, xHiy, 0.0, QixHiy); - - gsl_blas_ddot (QixHiy, xHiy, &yPy); - yPy=Calc_yHiy (Y, Hiy_all)-yPy; - - //calculate log likelihood/restricted likelihood value - if (func_name=='R' || func_name=='r') { - logl_new=logl_const-0.5*logdet_H-0.5*logdet_Q-0.5*yPy; - } else { - logl_new=logl_const-0.5*logdet_H-0.5*yPy; - } - } - - step_scale/=2.0; - step_iter++; - - //cout<<t<<"\t"<<step_iter<<"\t"<<logl_old<<"\t"<<logl_new<<"\t"<<flag_pd<<endl; - } while ( (flag_pd==0 || logl_new<logl_old || logl_new-logl_old>10 ) && step_iter<10 && t!=0); - - //terminate if change is small - if (t!=0) { - if (logl_new<logl_old || flag_pd==0) { - gsl_matrix_memcpy (V_g, Vg_save); - gsl_matrix_memcpy (V_e, Ve_save); - break; - } - - if (logl_new-logl_old<max_prec) { - break; - } - } - - logl_old=logl_new; - - CalcDev (func_name, eval, Qi, Hi_all, xHi_all, Hiy_all, QixHiy, gradient, Hessian_inv, crt_a, crt_b, crt_c); - - - //output estimates in each iteration - /* - cout<<func_name<<" iteration = "<<t<<" log-likelihood = "<<logl_old<<"\t"<<logl_new<<endl; - - cout<<"Vg: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get(V_g, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"Ve: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<d_size; j++) { - cout<<gsl_matrix_get(V_e, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"Hessian: "<<endl; - for (size_t i=0; i<Hessian_inv->size1; i++) { - for (size_t j=0; j<Hessian_inv->size2; j++) { - cout<<gsl_matrix_get(Hessian_inv, i, j)<<"\t"; - } - cout<<endl; - } - */ - } - - //mutiply Hessian_inv with -1.0 - //now Hessian_inv is the variance matrix - gsl_matrix_scale (Hessian_inv, -1.0); - - gsl_matrix_free(Vg_save); - gsl_matrix_free(Ve_save); - gsl_matrix_free(V_temp); - gsl_matrix_free(U_temp); - gsl_vector_free(D_temp); - gsl_vector_free(xHiy); - gsl_vector_free(QixHiy); - - gsl_matrix_free(Qi); - gsl_matrix_free(XXt); - - gsl_vector_free(gradient); - - return logl_new; -} - - - - - -//initialize Vg, Ve and B -void MphInitial(const size_t em_iter, const double em_prec, const size_t nr_iter, const double nr_prec, const gsl_vector *eval, const gsl_matrix *X, const gsl_matrix *Y, const double l_min, const double l_max, const size_t n_region, gsl_matrix *V_g, gsl_matrix *V_e, gsl_matrix *B) -{ - gsl_matrix_set_zero (V_g); - gsl_matrix_set_zero (V_e); - gsl_matrix_set_zero (B); - - size_t n_size=eval->size, c_size=X->size1, d_size=Y->size1; - double a, b, c; - double lambda, logl, vg, ve; - - //Initial the diagonal elements of Vg and Ve using univariate LMM and REML estimates - gsl_matrix *Xt=gsl_matrix_alloc (n_size, c_size); - gsl_vector *beta_temp=gsl_vector_alloc(c_size); - gsl_vector *se_beta_temp=gsl_vector_alloc(c_size); - - gsl_matrix_transpose_memcpy (Xt, X); - - for (size_t i=0; i<d_size; i++) { - gsl_vector_const_view Y_row=gsl_matrix_const_row (Y, i); - CalcLambda ('R', eval, Xt, &Y_row.vector, l_min, l_max, n_region, lambda, logl); - CalcLmmVgVeBeta (eval, Xt, &Y_row.vector, lambda, vg, ve, beta_temp, se_beta_temp); - - gsl_matrix_set(V_g, i, i, vg); - gsl_matrix_set(V_e, i, i, ve); - } - - gsl_matrix_free (Xt); - gsl_vector_free (beta_temp); - gsl_vector_free (se_beta_temp); - - //if number of phenotypes is above four, then obtain the off diagonal elements with two trait models - if (d_size>4) { - //first obtain good initial values - //large matrices for EM - gsl_matrix *U_hat=gsl_matrix_alloc (2, n_size); - gsl_matrix *E_hat=gsl_matrix_alloc (2, n_size); - gsl_matrix *OmegaU=gsl_matrix_alloc (2, n_size); - gsl_matrix *OmegaE=gsl_matrix_alloc (2, n_size); - gsl_matrix *UltVehiY=gsl_matrix_alloc (2, n_size); - gsl_matrix *UltVehiBX=gsl_matrix_alloc (2, n_size); - gsl_matrix *UltVehiU=gsl_matrix_alloc (2, n_size); - gsl_matrix *UltVehiE=gsl_matrix_alloc (2, n_size); - - //large matrices for NR - gsl_matrix *Hi_all=gsl_matrix_alloc (2, 2*n_size); //each dxd block is H_k^{-1} - gsl_matrix *Hiy_all=gsl_matrix_alloc (2, n_size); //each column is H_k^{-1}y_k - gsl_matrix *xHi_all=gsl_matrix_alloc (2*c_size, 2*n_size); //each dcxdc block is x_k\otimes H_k^{-1} - gsl_matrix *Hessian=gsl_matrix_alloc (6, 6); - - //2 by n matrix of Y - gsl_matrix *Y_sub=gsl_matrix_alloc (2, n_size); - gsl_matrix *Vg_sub=gsl_matrix_alloc (2, 2); - gsl_matrix *Ve_sub=gsl_matrix_alloc (2, 2); - gsl_matrix *B_sub=gsl_matrix_alloc (2, c_size); - - for (size_t i=0; i<d_size; i++) { - gsl_vector_view Y_sub1=gsl_matrix_row (Y_sub, 0); - gsl_vector_const_view Y_1=gsl_matrix_const_row (Y, i); - gsl_vector_memcpy (&Y_sub1.vector, &Y_1.vector); - - for (size_t j=i+1; j<d_size; j++) { - gsl_vector_view Y_sub2=gsl_matrix_row (Y_sub, 1); - gsl_vector_const_view Y_2=gsl_matrix_const_row (Y, j); - gsl_vector_memcpy (&Y_sub2.vector, &Y_2.vector); - - gsl_matrix_set_zero (Vg_sub); - gsl_matrix_set_zero (Ve_sub); - gsl_matrix_set (Vg_sub, 0, 0, gsl_matrix_get (V_g, i, i)); - gsl_matrix_set (Ve_sub, 0, 0, gsl_matrix_get (V_e, i, i)); - gsl_matrix_set (Vg_sub, 1, 1, gsl_matrix_get (V_g, j, j)); - gsl_matrix_set (Ve_sub, 1, 1, gsl_matrix_get (V_e, j, j)); - - logl=MphEM ('R', em_iter, em_prec, eval, X, Y_sub, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, Vg_sub, Ve_sub, B_sub); - logl=MphNR ('R', nr_iter, nr_prec, eval, X, Y_sub, Hi_all, xHi_all, Hiy_all, Vg_sub, Ve_sub, Hessian, a, b, c); - - gsl_matrix_set(V_g, i, j, gsl_matrix_get (Vg_sub, 0, 1)); - gsl_matrix_set(V_g, j, i, gsl_matrix_get (Vg_sub, 0, 1)); - - gsl_matrix_set(V_e, i, j, ve=gsl_matrix_get (Ve_sub, 0, 1)); - gsl_matrix_set(V_e, j, i, ve=gsl_matrix_get (Ve_sub, 0, 1)); - } - } - - //free matrices - gsl_matrix_free(U_hat); - gsl_matrix_free(E_hat); - gsl_matrix_free(OmegaU); - gsl_matrix_free(OmegaE); - gsl_matrix_free(UltVehiY); - gsl_matrix_free(UltVehiBX); - gsl_matrix_free(UltVehiU); - gsl_matrix_free(UltVehiE); - - gsl_matrix_free(Hi_all); - gsl_matrix_free(Hiy_all); - gsl_matrix_free(xHi_all); - gsl_matrix_free(Hessian); - - gsl_matrix_free(Y_sub); - gsl_matrix_free(Vg_sub); - gsl_matrix_free(Ve_sub); - gsl_matrix_free(B_sub); - - /* - //second, maximize a increasingly large matrix - for (size_t i=1; i<d_size; i++) { - //large matrices for EM - gsl_matrix *U_hat=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *E_hat=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *OmegaU=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *OmegaE=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *UltVehiY=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *UltVehiBX=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *UltVehiU=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *UltVehiE=gsl_matrix_alloc (i+1, n_size); - - //large matrices for NR - gsl_matrix *Hi_all=gsl_matrix_alloc (i+1, (i+1)*n_size); //each dxd block is H_k^{-1} - gsl_matrix *Hiy_all=gsl_matrix_alloc (i+1, n_size); //each column is H_k^{-1}y_k - gsl_matrix *xHi_all=gsl_matrix_alloc ((i+1)*c_size, (i+1)*n_size); //each dcxdc block is x_k\otimes H_k^{-1} - gsl_matrix *Hessian=gsl_matrix_alloc ((i+1)*(i+2), (i+1)*(i+2)); - - //(i+1) by n matrix of Y - gsl_matrix *Y_sub=gsl_matrix_alloc (i+1, n_size); - gsl_matrix *Vg_sub=gsl_matrix_alloc (i+1, i+1); - gsl_matrix *Ve_sub=gsl_matrix_alloc (i+1, i+1); - gsl_matrix *B_sub=gsl_matrix_alloc (i+1, c_size); - - gsl_matrix_const_view Y_sub_view=gsl_matrix_const_submatrix (Y, 0, 0, i+1, n_size); - gsl_matrix_view Vg_sub_view=gsl_matrix_submatrix (V_g, 0, 0, i+1, i+1); - gsl_matrix_view Ve_sub_view=gsl_matrix_submatrix (V_e, 0, 0, i+1, i+1); - - gsl_matrix_memcpy (Y_sub, &Y_sub_view.matrix); - gsl_matrix_memcpy (Vg_sub, &Vg_sub_view.matrix); - gsl_matrix_memcpy (Ve_sub, &Ve_sub_view.matrix); - - logl=MphEM ('R', em_iter, em_prec, eval, X, Y_sub, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, Vg_sub, Ve_sub, B_sub); - logl=MphNR ('R', nr_iter, nr_prec, eval, X, Y_sub, Hi_all, xHi_all, Hiy_all, Vg_sub, Ve_sub, Hessian, crt_a, crt_b, crt_c); - - gsl_matrix_memcpy (&Vg_sub_view.matrix, Vg_sub); - gsl_matrix_memcpy (&Ve_sub_view.matrix, Ve_sub); - - //free matrices - gsl_matrix_free(U_hat); - gsl_matrix_free(E_hat); - gsl_matrix_free(OmegaU); - gsl_matrix_free(OmegaE); - gsl_matrix_free(UltVehiY); - gsl_matrix_free(UltVehiBX); - gsl_matrix_free(UltVehiU); - gsl_matrix_free(UltVehiE); - - gsl_matrix_free(Hi_all); - gsl_matrix_free(Hiy_all); - gsl_matrix_free(xHi_all); - gsl_matrix_free(Hessian); - - gsl_matrix_free(Y_sub); - gsl_matrix_free(Vg_sub); - gsl_matrix_free(Ve_sub); - gsl_matrix_free(B_sub); - } - */ - } - - //calculate B hat using GSL estimate - gsl_matrix *UltVehiY=gsl_matrix_alloc (d_size, n_size); - - gsl_vector *D_l=gsl_vector_alloc (d_size); - gsl_matrix *UltVeh=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *UltVehi=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *Qi=gsl_matrix_alloc (d_size*c_size, d_size*c_size); - gsl_vector *XHiy=gsl_vector_alloc (d_size*c_size); - gsl_vector *beta=gsl_vector_alloc (d_size*c_size); - - gsl_vector_set_zero (XHiy); - - double logdet_Ve, logdet_Q, dl, d, delta, dx, dy; - - //eigen decomposition and calculate log|Ve| - logdet_Ve=EigenProc (V_g, V_e, D_l, UltVeh, UltVehi); - - //calculate Qi and log|Q| - logdet_Q=CalcQi (eval, D_l, X, Qi); - - //calculate UltVehiY - gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, UltVehi, Y, 0.0, UltVehiY); - - //calculate XHiy - for (size_t i=0; i<d_size; i++) { - dl=gsl_vector_get(D_l, i); - - for (size_t j=0; j<c_size; j++) { - d=0.0; - for (size_t k=0; k<n_size; k++) { - delta=gsl_vector_get(eval, k); - dx=gsl_matrix_get(X, j, k); - dy=gsl_matrix_get(UltVehiY, i, k); - - //if (delta==0) {continue;} - d+=dy*dx/(delta*dl+1.0); - } - gsl_vector_set(XHiy, j*d_size+i, d); - } - } - - gsl_blas_dgemv(CblasNoTrans, 1.0, Qi, XHiy, 0.0, beta); - - //multiply beta by UltVeh and save to B - for (size_t i=0; i<c_size; i++) { - gsl_vector_view B_col=gsl_matrix_column (B, i); - gsl_vector_view beta_sub=gsl_vector_subvector (beta, i*d_size, d_size); - gsl_blas_dgemv(CblasTrans, 1.0, UltVeh, &beta_sub.vector, 0.0, &B_col.vector); - } - - //free memory - gsl_matrix_free(UltVehiY); - - gsl_vector_free(D_l); - gsl_matrix_free(UltVeh); - gsl_matrix_free(UltVehi); - gsl_matrix_free(Qi); - gsl_vector_free(XHiy); - gsl_vector_free(beta); - - return; -} - - - -//p value correction -//mode=1 Wald; mode=2 LRT; mode=3 SCORE; -double PCRT (const size_t mode, const size_t d_size, const double p_value, const double crt_a, const double crt_b, const double crt_c) -{ - double p_crt=0.0, chisq_crt=0.0, q=(double)d_size; - double chisq=gsl_cdf_chisq_Qinv(p_value, (double)d_size ); - - if (mode==1) { - double a=crt_c/(2.0*q*(q+2.0)); - double b=1.0+(crt_a+crt_b)/(2.0*q); - chisq_crt=(-1.0*b+sqrt(b*b+4.0*a*chisq))/(2.0*a); - } else if (mode==2) { - chisq_crt=chisq/(1.0+crt_a/(2.0*q) ); - } else { - /* - double a=-1.0*crt_c/(2.0*q*(q+2.0)); - double b=1.0+(crt_a-crt_b)/(2.0*q); - chisq_crt=(-1.0*b+sqrt(b*b+4.0*a*chisq))/(2.0*a); - */ - chisq_crt=chisq; - } - - p_crt=gsl_cdf_chisq_Q (chisq_crt, (double)d_size ); - - //cout<<crt_a<<"\t"<<crt_b<<"\t"<<crt_c<<endl; - //cout<<setprecision(10)<<p_value<<"\t"<<p_crt<<endl; - - return p_crt; -} - - - -void MVLMM::AnalyzeBimbam (const gsl_matrix *U, const gsl_vector *eval, const gsl_matrix *UtW, const gsl_matrix *UtY) -{ - igzstream infile (file_geno.c_str(), igzstream::in); -// ifstream infile (file_geno.c_str(), ifstream::in); - if (!infile) {cout<<"error reading genotype file:"<<file_geno<<endl; return;} - - clock_t time_start=clock(); - time_UtX=0; time_opt=0; - - string line; - char *ch_ptr; - - // double lambda_mle=0, lambda_remle=0, beta=0, se=0, ; - double logl_H0=0.0, logl_H1=0.0, p_wald=0, p_lrt=0, p_score=0; - double crt_a, crt_b, crt_c; - int n_miss, c_phen; - double geno, x_mean; - size_t c=0; - // double s=0.0; - size_t n_size=UtY->size1, d_size=UtY->size2, c_size=UtW->size2; - - size_t dc_size=d_size*(c_size+1), v_size=d_size*(d_size+1)/2; - - //large matrices for EM - gsl_matrix *U_hat=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *E_hat=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *OmegaU=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *OmegaE=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiY=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiBX=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiU=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiE=gsl_matrix_alloc (d_size, n_size); - - //large matrices for NR - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); //each dxd block is H_k^{-1} - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); //each column is H_k^{-1}y_k - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); //each dcxdc block is x_k\otimes H_k^{-1} - gsl_matrix *Hessian=gsl_matrix_alloc (v_size*2, v_size*2); - - gsl_vector *x=gsl_vector_alloc (n_size); - gsl_vector *x_miss=gsl_vector_alloc (n_size); - - gsl_matrix *Y=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *X=gsl_matrix_alloc (c_size+1, n_size); - gsl_matrix *V_g=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *B=gsl_matrix_alloc (d_size, c_size+1); - gsl_vector *beta=gsl_vector_alloc (d_size); - gsl_matrix *Vbeta=gsl_matrix_alloc (d_size, d_size); - - //null estimates for initial values - gsl_matrix *V_g_null=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e_null=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *B_null=gsl_matrix_alloc (d_size, c_size+1); - gsl_matrix *se_B_null=gsl_matrix_alloc (d_size, c_size); - - gsl_matrix_view X_sub=gsl_matrix_submatrix (X, 0, 0, c_size, n_size); - gsl_matrix_view B_sub=gsl_matrix_submatrix (B, 0, 0, d_size, c_size); - gsl_matrix_view xHi_all_sub=gsl_matrix_submatrix (xHi_all, 0, 0, d_size*c_size, d_size*n_size); - - gsl_matrix_transpose_memcpy (Y, UtY); - - gsl_matrix_transpose_memcpy (&X_sub.matrix, UtW); - - gsl_vector_view X_row=gsl_matrix_row(X, c_size); - gsl_vector_set_zero(&X_row.vector); - gsl_vector_view B_col=gsl_matrix_column(B, c_size); - gsl_vector_set_zero(&B_col.vector); - - MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, &X_sub.matrix, Y, l_min, l_max, n_region, V_g, V_e, &B_sub.matrix); - logl_H0=MphEM ('R', em_iter, em_prec, eval, &X_sub.matrix, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, &B_sub.matrix); - logl_H0=MphNR ('R', nr_iter, nr_prec, eval, &X_sub.matrix, Y, Hi_all, &xHi_all_sub.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub.matrix, Y, V_g, V_e, UltVehiY, &B_sub.matrix, se_B_null); - - c=0; - Vg_remle_null.clear(); - Ve_remle_null.clear(); - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - Vg_remle_null.push_back(gsl_matrix_get (V_g, i, j) ); - Ve_remle_null.push_back(gsl_matrix_get (V_e, i, j) ); - VVg_remle_null.push_back(gsl_matrix_get (Hessian, c, c) ); - VVe_remle_null.push_back(gsl_matrix_get (Hessian, c+v_size, c+v_size) ); - c++; - } - } - beta_remle_null.clear(); - se_beta_remle_null.clear(); - for (size_t i=0; i<se_B_null->size1; i++) { - for (size_t j=0; j<se_B_null->size2; j++) { - beta_remle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_remle_null.push_back(gsl_matrix_get(se_B_null, i, j) ); - } - } - logl_remle_H0=logl_H0; - - cout.setf(std::ios_base::fixed, std::ios_base::floatfield); - cout.precision(4); - - cout<<"REMLE estimate for Vg in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_g, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Vg): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c, c))<<"\t"; - } - cout<<endl; - } - cout<<"REMLE estimate for Ve in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_e, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Ve): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c+v_size, c+v_size))<<"\t"; - } - cout<<endl; - } - cout<<"REMLE likelihood = "<<logl_H0<<endl; - - - logl_H0=MphEM ('L', em_iter, em_prec, eval, &X_sub.matrix, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, &B_sub.matrix); - logl_H0=MphNR ('L', nr_iter, nr_prec, eval, &X_sub.matrix, Y, Hi_all, &xHi_all_sub.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub.matrix, Y, V_g, V_e, UltVehiY, &B_sub.matrix, se_B_null); - - c=0; - Vg_mle_null.clear(); - Ve_mle_null.clear(); - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - Vg_mle_null.push_back(gsl_matrix_get (V_g, i, j) ); - Ve_mle_null.push_back(gsl_matrix_get (V_e, i, j) ); - VVg_mle_null.push_back(gsl_matrix_get (Hessian, c, c) ); - VVe_mle_null.push_back(gsl_matrix_get (Hessian, c+v_size, c+v_size) ); - c++; - } - } - beta_mle_null.clear(); - se_beta_mle_null.clear(); - for (size_t i=0; i<se_B_null->size1; i++) { - for (size_t j=0; j<se_B_null->size2; j++) { - beta_mle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_mle_null.push_back(gsl_matrix_get(se_B_null, i, j) ); - } - } - logl_mle_H0=logl_H0; - - cout<<"MLE estimate for Vg in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_g, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Vg): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c, c))<<"\t"; - } - cout<<endl; - } - cout<<"MLE estimate for Ve in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_e, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Ve): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c+v_size, c+v_size))<<"\t"; - } - cout<<endl; - } - cout<<"MLE likelihood = "<<logl_H0<<endl; - - - vector<double> v_beta, v_Vg, v_Ve, v_Vbeta; - for (size_t i=0; i<d_size; i++) { - v_beta.push_back(0.0); - } - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - v_Vg.push_back(0.0); - v_Ve.push_back(0.0); - v_Vbeta.push_back(0.0); - } - } - - gsl_matrix_memcpy (V_g_null, V_g); - gsl_matrix_memcpy (V_e_null, V_e); - gsl_matrix_memcpy (B_null, B); - - //start reading genotypes and analyze - for (size_t t=0; t<indicator_snp.size(); ++t) { - //if (t>=1) {break;} - !safeGetline(infile, line).eof(); - if (t%d_pace==0 || t==(ns_total-1)) {ProgressBar ("Reading SNPs ", t, ns_total-1);} - if (indicator_snp[t]==0) {continue;} - - ch_ptr=strtok ((char *)line.c_str(), " , \t"); - ch_ptr=strtok (NULL, " , \t"); - ch_ptr=strtok (NULL, " , \t"); - - x_mean=0.0; c_phen=0; n_miss=0; - gsl_vector_set_zero(x_miss); - for (size_t i=0; i<ni_total; ++i) { - ch_ptr=strtok (NULL, " , \t"); - if (indicator_idv[i]==0) {continue;} - - if (strcmp(ch_ptr, "NA")==0) {gsl_vector_set(x_miss, c_phen, 0.0); n_miss++;} - else { - geno=atof(ch_ptr); - - gsl_vector_set(x, c_phen, geno); - gsl_vector_set(x_miss, c_phen, 1.0); - x_mean+=geno; - } - c_phen++; - } - - x_mean/=(double)(ni_test-n_miss); - - for (size_t i=0; i<ni_test; ++i) { - if (gsl_vector_get (x_miss, i)==0) {gsl_vector_set(x, i, x_mean);} - geno=gsl_vector_get(x, i); - if (x_mean>1) { - gsl_vector_set(x, i, 2-geno); - } - } - - //calculate statistics - time_start=clock(); - gsl_blas_dgemv (CblasTrans, 1.0, U, x, 0.0, &X_row.vector); - time_UtX+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - //initial values - gsl_matrix_memcpy (V_g, V_g_null); - gsl_matrix_memcpy (V_e, V_e_null); - gsl_matrix_memcpy (B, B_null); - - time_start=clock(); - - //3 is before 1 - if (a_mode==3 || a_mode==4) { - p_score=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g_null, V_e_null, UltVehiY, beta, Vbeta); - if (p_score<p_nr && crt==1) { - logl_H1=MphNR ('R', 1, nr_prec*10, eval, X, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - p_score=PCRT (3, d_size, p_score, crt_a, crt_b, crt_c); - } - } - - if (a_mode==2 || a_mode==4) { - logl_H1=MphEM ('L', em_iter/10, em_prec*10, eval, X, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, B); - //calculate beta and Vbeta - p_lrt=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - p_lrt=gsl_cdf_chisq_Q (2.0*(logl_H1-logl_H0), (double)d_size ); - - if (p_lrt<p_nr) { - logl_H1=MphNR ('L', nr_iter/10, nr_prec*10, eval, X, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - //calculate beta and Vbeta - p_lrt=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - p_lrt=gsl_cdf_chisq_Q (2.0*(logl_H1-logl_H0), (double)d_size ); - - if (crt==1) { - p_lrt=PCRT (2, d_size, p_lrt, crt_a, crt_b, crt_c); - } - } - } - - if (a_mode==1 || a_mode==4) { - logl_H1=MphEM ('R', em_iter/10, em_prec*10, eval, X, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, B); - p_wald=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - - if (p_wald<p_nr) { - logl_H1=MphNR ('R', nr_iter/10, nr_prec*10, eval, X, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - p_wald=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - - if (crt==1) { - p_wald=PCRT (1, d_size, p_wald, crt_a, crt_b, crt_c); - } - } - } - - if (x_mean>1) {gsl_vector_scale(beta, -1.0);} - - time_opt+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - //store summary data - //SUMSTAT SNPs={snpInfo[t].get_chr(), snpInfo[t].get_rs(), snpInfo[t].get_pos(), n_miss, beta, se, lambda_remle, lambda_mle, p_wald, p_lrt, p_score}; - for (size_t i=0; i<d_size; i++) { - v_beta[i]=gsl_vector_get (beta, i); - } - - c=0; - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - v_Vg[c]=gsl_matrix_get (V_g, i, j); - v_Ve[c]=gsl_matrix_get (V_e, i, j); - v_Vbeta[c]=gsl_matrix_get (Vbeta, i, j); - c++; - } - } - - MPHSUMSTAT SNPs={v_beta, p_wald, p_lrt, p_score, v_Vg, v_Ve, v_Vbeta}; - sumStat.push_back(SNPs); - } - cout<<endl; - - - infile.close(); - infile.clear(); - - gsl_matrix_free(U_hat); - gsl_matrix_free(E_hat); - gsl_matrix_free(OmegaU); - gsl_matrix_free(OmegaE); - gsl_matrix_free(UltVehiY); - gsl_matrix_free(UltVehiBX); - gsl_matrix_free(UltVehiU); - gsl_matrix_free(UltVehiE); - - gsl_matrix_free(Hi_all); - gsl_matrix_free(Hiy_all); - gsl_matrix_free(xHi_all); - gsl_matrix_free(Hessian); - - gsl_vector_free(x); - gsl_vector_free(x_miss); - - gsl_matrix_free(Y); - gsl_matrix_free(X); - gsl_matrix_free(V_g); - gsl_matrix_free(V_e); - gsl_matrix_free(B); - gsl_vector_free(beta); - gsl_matrix_free(Vbeta); - - gsl_matrix_free(V_g_null); - gsl_matrix_free(V_e_null); - gsl_matrix_free(B_null); - gsl_matrix_free(se_B_null); - - return; -} - - - - - - - -void MVLMM::AnalyzePlink (const gsl_matrix *U, const gsl_vector *eval, const gsl_matrix *UtW, const gsl_matrix *UtY) -{ - string file_bed=file_bfile+".bed"; - ifstream infile (file_bed.c_str(), ios::binary); - if (!infile) {cout<<"error reading bed file:"<<file_bed<<endl; return;} - - clock_t time_start=clock(); - time_UtX=0; time_opt=0; - - char ch[1]; - bitset<8> b; - - // double lambda_mle=0, lambda_remle=0, beta=0, se=0, ; - double logl_H0=0.0, logl_H1=0.0, p_wald=0, p_lrt=0, p_score=0; - double crt_a, crt_b, crt_c; - int n_bit, n_miss, ci_total, ci_test; - double geno, x_mean; - size_t c=0; - // double s=0.0; - size_t n_size=UtY->size1, d_size=UtY->size2, c_size=UtW->size2; - size_t dc_size=d_size*(c_size+1), v_size=d_size*(d_size+1)/2; - - //large matrices for EM - gsl_matrix *U_hat=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *E_hat=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *OmegaU=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *OmegaE=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiY=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiBX=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiU=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiE=gsl_matrix_alloc (d_size, n_size); - - //large matrices for NR - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); //each dxd block is H_k^{-1} - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); //each column is H_k^{-1}y_k - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); //each dcxdc block is x_k\otimes H_k^{-1} - gsl_matrix *Hessian=gsl_matrix_alloc (v_size*2, v_size*2); - - gsl_vector *x=gsl_vector_alloc (n_size); - - gsl_matrix *Y=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *X=gsl_matrix_alloc (c_size+1, n_size); - gsl_matrix *V_g=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *B=gsl_matrix_alloc (d_size, c_size+1); - gsl_vector *beta=gsl_vector_alloc (d_size); - gsl_matrix *Vbeta=gsl_matrix_alloc (d_size, d_size); - - //null estimates for initial values - gsl_matrix *V_g_null=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *V_e_null=gsl_matrix_alloc (d_size, d_size); - gsl_matrix *B_null=gsl_matrix_alloc (d_size, c_size+1); - gsl_matrix *se_B_null=gsl_matrix_alloc (d_size, c_size); - - gsl_matrix_view X_sub=gsl_matrix_submatrix (X, 0, 0, c_size, n_size); - gsl_matrix_view B_sub=gsl_matrix_submatrix (B, 0, 0, d_size, c_size); - gsl_matrix_view xHi_all_sub=gsl_matrix_submatrix (xHi_all, 0, 0, d_size*c_size, d_size*n_size); - - gsl_matrix_transpose_memcpy (Y, UtY); - gsl_matrix_transpose_memcpy (&X_sub.matrix, UtW); - - gsl_vector_view X_row=gsl_matrix_row(X, c_size); - gsl_vector_set_zero(&X_row.vector); - gsl_vector_view B_col=gsl_matrix_column(B, c_size); - gsl_vector_set_zero(&B_col.vector); - - //time_start=clock(); - MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, &X_sub.matrix, Y, l_min, l_max, n_region, V_g, V_e, &B_sub.matrix); - - logl_H0=MphEM ('R', em_iter, em_prec, eval, &X_sub.matrix, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, &B_sub.matrix); - logl_H0=MphNR ('R', nr_iter, nr_prec, eval, &X_sub.matrix, Y, Hi_all, &xHi_all_sub.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub.matrix, Y, V_g, V_e, UltVehiY, &B_sub.matrix, se_B_null); - //cout<<"time for REML in the null = "<<(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0)<<endl; - - c=0; - Vg_remle_null.clear(); - Ve_remle_null.clear(); - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - Vg_remle_null.push_back(gsl_matrix_get (V_g, i, j) ); - Ve_remle_null.push_back(gsl_matrix_get (V_e, i, j) ); - VVg_remle_null.push_back(gsl_matrix_get (Hessian, c, c) ); - VVe_remle_null.push_back(gsl_matrix_get (Hessian, c+v_size, c+v_size) ); - c++; - } - } - beta_remle_null.clear(); - se_beta_remle_null.clear(); - for (size_t i=0; i<se_B_null->size1; i++) { - for (size_t j=0; j<se_B_null->size2; j++) { - beta_remle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_remle_null.push_back(gsl_matrix_get(se_B_null, i, j) ); - } - } - logl_remle_H0=logl_H0; - - cout.setf(std::ios_base::fixed, std::ios_base::floatfield); - cout.precision(4); - cout<<"REMLE estimate for Vg in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_g, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Vg): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c, c))<<"\t"; - } - cout<<endl; - } - cout<<"REMLE estimate for Ve in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_e, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Ve): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c+v_size, c+v_size))<<"\t"; - } - cout<<endl; - } - cout<<"REMLE likelihood = "<<logl_H0<<endl; - - //time_start=clock(); - logl_H0=MphEM ('L', em_iter, em_prec, eval, &X_sub.matrix, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, &B_sub.matrix); - logl_H0=MphNR ('L', nr_iter, nr_prec, eval, &X_sub.matrix, Y, Hi_all, &xHi_all_sub.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub.matrix, Y, V_g, V_e, UltVehiY, &B_sub.matrix, se_B_null); - //cout<<"time for MLE in the null = "<<(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0)<<endl; - - c=0; - Vg_mle_null.clear(); - Ve_mle_null.clear(); - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - Vg_mle_null.push_back(gsl_matrix_get (V_g, i, j) ); - Ve_mle_null.push_back(gsl_matrix_get (V_e, i, j) ); - VVg_mle_null.push_back(gsl_matrix_get (Hessian, c, c) ); - VVe_mle_null.push_back(gsl_matrix_get (Hessian, c+v_size, c+v_size) ); - c++; - } - } - beta_mle_null.clear(); - se_beta_mle_null.clear(); - for (size_t i=0; i<se_B_null->size1; i++) { - for (size_t j=0; j<se_B_null->size2; j++) { - beta_mle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_mle_null.push_back(gsl_matrix_get(se_B_null, i, j) ); - } - } - logl_mle_H0=logl_H0; - - cout<<"MLE estimate for Vg in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_g, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Vg): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c, c))<<"\t"; - } - cout<<endl; - } - cout<<"MLE estimate for Ve in the null model: "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - cout<<gsl_matrix_get(V_e, i, j)<<"\t"; - } - cout<<endl; - } - cout<<"se(Ve): "<<endl; - for (size_t i=0; i<d_size; i++) { - for (size_t j=0; j<=i; j++) { - c=GetIndex(i, j, d_size); - cout<<sqrt(gsl_matrix_get(Hessian, c+v_size, c+v_size))<<"\t"; - } - cout<<endl; - } - cout<<"MLE likelihood = "<<logl_H0<<endl; - - vector<double> v_beta, v_Vg, v_Ve, v_Vbeta; - for (size_t i=0; i<d_size; i++) { - v_beta.push_back(0.0); - } - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - v_Vg.push_back(0.0); - v_Ve.push_back(0.0); - v_Vbeta.push_back(0.0); - } - } - - gsl_matrix_memcpy (V_g_null, V_g); - gsl_matrix_memcpy (V_e_null, V_e); - gsl_matrix_memcpy (B_null, B); - - - //start reading genotypes and analyze - - //calculate n_bit and c, the number of bit for each snp - if (ni_total%4==0) {n_bit=ni_total/4;} - else {n_bit=ni_total/4+1; } - - //print the first three majic numbers - for (int i=0; i<3; ++i) { - infile.read(ch,1); - b=ch[0]; - } - - for (vector<SNPINFO>::size_type t=0; t<snpInfo.size(); ++t) { - if (t%d_pace==0 || t==snpInfo.size()-1) {ProgressBar ("Reading SNPs ", t, snpInfo.size()-1);} - if (indicator_snp[t]==0) {continue;} - - //if (t>=0) {break;} - //if (snpInfo[t].rs_number!="MAG18140902") {continue;} - //cout<<t<<endl; - - infile.seekg(t*n_bit+3); //n_bit, and 3 is the number of magic numbers - - //read genotypes - x_mean=0.0; n_miss=0; ci_total=0; ci_test=0; - for (int i=0; i<n_bit; ++i) { - infile.read(ch,1); - b=ch[0]; - for (size_t j=0; j<4; ++j) { //minor allele homozygous: 2.0; major: 0.0; - if ((i==(n_bit-1)) && ci_total==(int)ni_total) {break;} - if (indicator_idv[ci_total]==0) {ci_total++; continue;} - - if (b[2*j]==0) { - if (b[2*j+1]==0) {gsl_vector_set(x, ci_test, 2); x_mean+=2.0; } - else {gsl_vector_set(x, ci_test, 1); x_mean+=1.0; } - } - else { - if (b[2*j+1]==1) {gsl_vector_set(x, ci_test, 0); } - else {gsl_vector_set(x, ci_test, -9); n_miss++; } - } - - ci_total++; - ci_test++; - } - } - - x_mean/=(double)(ni_test-n_miss); - - for (size_t i=0; i<ni_test; ++i) { - geno=gsl_vector_get(x,i); - if (geno==-9) {gsl_vector_set(x, i, x_mean); geno=x_mean;} - if (x_mean>1) { - gsl_vector_set(x, i, 2-geno); - } - } - - /* - if (t==0) { - ofstream outfile ("./snp1.txt", ofstream::out); - if (!outfile) {cout<<"error writing file: "<<endl; return;} - for (size_t i=0; i<x->size; i++) { - outfile<<gsl_vector_get(x, i)<<endl; - } - outfile.clear(); - outfile.close(); - } - */ - - //calculate statistics - time_start=clock(); - gsl_blas_dgemv (CblasTrans, 1.0, U, x, 0.0, &X_row.vector); - time_UtX+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - //initial values - gsl_matrix_memcpy (V_g, V_g_null); - gsl_matrix_memcpy (V_e, V_e_null); - gsl_matrix_memcpy (B, B_null); - - time_start=clock(); - - //3 is before 1 - if (a_mode==3 || a_mode==4) { - p_score=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g_null, V_e_null, UltVehiY, beta, Vbeta); - - if (p_score<p_nr && crt==1) { - logl_H1=MphNR ('R', 1, nr_prec*10, eval, X, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - p_score=PCRT (3, d_size, p_score, crt_a, crt_b, crt_c); - } - } - - if (a_mode==2 || a_mode==4) { - logl_H1=MphEM ('L', em_iter/10, em_prec*10, eval, X, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, B); - //calculate beta and Vbeta - p_lrt=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - p_lrt=gsl_cdf_chisq_Q (2.0*(logl_H1-logl_H0), (double)d_size ); - - if (p_lrt<p_nr) { - logl_H1=MphNR ('L', nr_iter/10, nr_prec*10, eval, X, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - - //calculate beta and Vbeta - p_lrt=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - p_lrt=gsl_cdf_chisq_Q (2.0*(logl_H1-logl_H0), (double)d_size ); - if (crt==1) { - p_lrt=PCRT (2, d_size, p_lrt, crt_a, crt_b, crt_c); - } - } - } - - if (a_mode==1 || a_mode==4) { - logl_H1=MphEM ('R', em_iter/10, em_prec*10, eval, X, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, B); - p_wald=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - - if (p_wald<p_nr) { - logl_H1=MphNR ('R', nr_iter/10, nr_prec*10, eval, X, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - p_wald=MphCalcP (eval, &X_row.vector, &X_sub.matrix, Y, V_g, V_e, UltVehiY, beta, Vbeta); - - if (crt==1) { - p_wald=PCRT (1, d_size, p_wald, crt_a, crt_b, crt_c); - } - } - } - - //cout<<setprecision(10)<<p_wald<<"\t"<<p_lrt<<"\t"<<p_score<<endl; - - if (x_mean>1) {gsl_vector_scale(beta, -1.0);} - - time_opt+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - //store summary data - //SUMSTAT SNPs={snpInfo[t].get_chr(), snpInfo[t].get_rs(), snpInfo[t].get_pos(), n_miss, beta, se, lambda_remle, lambda_mle, p_wald, p_lrt, p_score}; - for (size_t i=0; i<d_size; i++) { - v_beta[i]=gsl_vector_get (beta, i); - } - - c=0; - for (size_t i=0; i<d_size; i++) { - for (size_t j=i; j<d_size; j++) { - v_Vg[c]=gsl_matrix_get (V_g, i, j); - v_Ve[c]=gsl_matrix_get (V_e, i, j); - v_Vbeta[c]=gsl_matrix_get (Vbeta, i, j); - c++; - } - } - - MPHSUMSTAT SNPs={v_beta, p_wald, p_lrt, p_score, v_Vg, v_Ve, v_Vbeta}; - sumStat.push_back(SNPs); - } - cout<<endl; - - //cout<<"time_opt = "<<time_opt<<endl; - - infile.close(); - infile.clear(); - - gsl_matrix_free(U_hat); - gsl_matrix_free(E_hat); - gsl_matrix_free(OmegaU); - gsl_matrix_free(OmegaE); - gsl_matrix_free(UltVehiY); - gsl_matrix_free(UltVehiBX); - gsl_matrix_free(UltVehiU); - gsl_matrix_free(UltVehiE); - - gsl_matrix_free(Hi_all); - gsl_matrix_free(Hiy_all); - gsl_matrix_free(xHi_all); - gsl_matrix_free(Hessian); - - gsl_vector_free(x); - - gsl_matrix_free(Y); - gsl_matrix_free(X); - gsl_matrix_free(V_g); - gsl_matrix_free(V_e); - gsl_matrix_free(B); - gsl_vector_free(beta); - gsl_matrix_free(Vbeta); - - gsl_matrix_free(V_g_null); - gsl_matrix_free(V_e_null); - gsl_matrix_free(B_null); - gsl_matrix_free(se_B_null); - - return; -} - - - - -//calculate Vg, Ve, B, se(B) in the null mvLMM model -//both B and se_B are d by c matrices -void CalcMvLmmVgVeBeta (const gsl_vector *eval, const gsl_matrix *UtW, const gsl_matrix *UtY, const size_t em_iter, const size_t nr_iter, const double em_prec, const double nr_prec, const double l_min, const double l_max, const size_t n_region, gsl_matrix *V_g, gsl_matrix *V_e, gsl_matrix *B, gsl_matrix *se_B) -{ - size_t n_size=UtY->size1, d_size=UtY->size2, c_size=UtW->size2; - size_t dc_size=d_size*c_size, v_size=d_size*(d_size+1)/2; - - double logl, crt_a, crt_b, crt_c; - - //large matrices for EM - gsl_matrix *U_hat=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *E_hat=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *OmegaU=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *OmegaE=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiY=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiBX=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiU=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *UltVehiE=gsl_matrix_alloc (d_size, n_size); - - //large matrices for NR - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); //each dxd block is H_k^{-1} - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); //each column is H_k^{-1}y_k - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); //each dcxdc block is x_k\otimes H_k^{-1} - gsl_matrix *Hessian=gsl_matrix_alloc (v_size*2, v_size*2); - - //transpose matrices - gsl_matrix *Y=gsl_matrix_alloc (d_size, n_size); - gsl_matrix *W=gsl_matrix_alloc (c_size, n_size); - gsl_matrix_transpose_memcpy (Y, UtY); - gsl_matrix_transpose_memcpy (W, UtW); - - //initial, EM, NR, and calculate B - MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, W, Y, l_min, l_max, n_region, V_g, V_e, B); - logl=MphEM ('R', em_iter, em_prec, eval, W, Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, V_e, B); - logl=MphNR ('R', nr_iter, nr_prec, eval, W, Y, Hi_all, xHi_all, Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, W, Y, V_g, V_e, UltVehiY, B, se_B); - - //free matrices - gsl_matrix_free(U_hat); - gsl_matrix_free(E_hat); - gsl_matrix_free(OmegaU); - gsl_matrix_free(OmegaE); - gsl_matrix_free(UltVehiY); - gsl_matrix_free(UltVehiBX); - gsl_matrix_free(UltVehiU); - gsl_matrix_free(UltVehiE); - - gsl_matrix_free(Hi_all); - gsl_matrix_free(Hiy_all); - gsl_matrix_free(xHi_all); - gsl_matrix_free(Hessian); - - gsl_matrix_free(Y); - gsl_matrix_free(W); - - return; -} - |