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Diffstat (limited to 'src/mvlmm.cpp')
| -rw-r--r-- | src/mvlmm.cpp | 10159 |
1 files changed, 5101 insertions, 5058 deletions
diff --git a/src/mvlmm.cpp b/src/mvlmm.cpp index 78cd926..eb591ca 100644 --- a/src/mvlmm.cpp +++ b/src/mvlmm.cpp @@ -16,895 +16,914 @@ along with this program. If not, see <http://www.gnu.org/licenses/>. */ -#include <iostream> #include <fstream> +#include <iostream> #include <sstream> -#include <iomanip> +#include <assert.h> +#include <bitset> #include <cmath> +#include <cstring> +#include <iomanip> #include <iostream> #include <stdio.h> #include <stdlib.h> -#include <bitset> -#include <cstring> -#include <assert.h> -#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 "gsl/gsl_linalg.h" +#include "gsl/gsl_matrix.h" +#include "gsl/gsl_min.h" +#include "gsl/gsl_roots.h" +#include "gsl/gsl_vector.h" -#include "io.h" -#include "lapack.h" #include "eigenlib.h" #include "gzstream.h" +#include "io.h" +#include "lapack.h" #include "lmm.h" #include "mvlmm.h" 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_oxford=cPar.file_oxford; - 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::CopyFromParam(PARAM &cPar) { + a_mode = cPar.a_mode; + d_pace = cPar.d_pace; + + file_bfile = cPar.file_bfile; + file_geno = cPar.file_geno; + file_oxford = cPar.file_oxford; + 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; +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.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.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.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; + 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; +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); - - //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; +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); + + // 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; +// 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); - } - } - - return; -} +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); + } + } + 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; +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); + 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; + 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); - } - } + gsl_matrix_set(OmegaU, i, k, d_u); + gsl_matrix_set(OmegaE, i, k, d_e); + } + } - return; + 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); +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; + 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); +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; + 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; +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 *YUX = gsl_matrix_alloc(d_size, c_size); - gsl_matrix_memcpy (UltVehiBX, UltVehiY); - gsl_matrix_sub (UltVehiBX, UltVehiU); + 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_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); + gsl_matrix_free(YUX); - return; + 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; +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); + gsl_vector *b = gsl_vector_alloc(dc_size); - // Calculate b=Qiv. - gsl_blas_dgemv(CblasNoTrans, 1.0, Qi, xHiy, 0.0, b); + // 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); - } + // 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); + gsl_vector_free(b); - return; + 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; +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); + gsl_matrix_set_zero(V_g); + gsl_matrix_set_zero(V_e); - double delta; + 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;} + // 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_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); + 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)); - } - } + // 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); + // 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); + // 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; + 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; - size_t 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); - - 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; +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; + size_t 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); + + 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); - } - } +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); + // 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); + gsl_blas_dgemv(CblasNoTrans, 1.0, Qi, xHiy, 0.0, Qiv); + gsl_blas_ddot(xHiy, Qiv, &d); - logl-=d; + logl -= d; - gsl_vector_free(Qiv); + gsl_vector_free(Qiv); - return -0.5*logl; + 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; - double 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; - - 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; +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; + double 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; + + 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 *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); - - 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); - - 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; +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 *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); + + 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); + + 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 *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); - - 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; +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 *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); + + 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. @@ -912,996 +931,962 @@ void MphCalcBeta (const gsl_vector *eval, const gsl_matrix *W, // 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\o times 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; +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\o times 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); +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; + 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); + 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); - } + gsl_blas_dgemv(CblasNoTrans, 1.0, &Hi_k.matrix, &y_k.vector, 0.0, + &Hiy_k.vector); + } - return; + 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); +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; + size_t n_size = X->size2, c_size = X->size1, d_size = Hi_all->size1; - double d; + 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 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); - } - } + 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; + 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; +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); + 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; - } + gsl_blas_ddot(&Hiy_k.vector, &y_k.vector, &d); + yHiy += d; + } - return yHiy; + 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); +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; + 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); + 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); - } + gsl_blas_dgemv(CblasNoTrans, 1.0, &xHi_k.matrix, &y_k.vector, 1.0, xHiy); + } - return; + 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; +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; +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; + size_t n_size = eval->size; - double delta, d1, d2; + 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); + 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; - } - } + 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; + 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); +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; - size_t n_size=eval->size, d_size=Hiy->size1; + double delta, d; - double delta, d; + for (size_t k = 0; k < n_size; k++) { + delta = gsl_vector_get(eval, k); - 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_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); - 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); - 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); - } - } + gsl_blas_daxpy(d * delta, &xHi_col_j.vector, xHiDHiy_g); + gsl_blas_daxpy(d, &xHi_col_j.vector, xHiDHiy_e); + } + } - return; + 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); +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; + size_t n_size = eval->size, dc_size = xHi->size1; + size_t d_size = xHi->size2 / n_size; - double delta; + 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); + 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); + 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_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_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_transpose_memcpy(mat_dcdc_t, mat_dcdc); - gsl_matrix_add (xHiDHix_e, mat_dcdc); + gsl_matrix_add(xHiDHix_e, mat_dcdc); - gsl_matrix_scale (mat_dcdc, delta); - gsl_matrix_add (xHiDHix_g, 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); + 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_scale(mat_dcdc_t, delta); + gsl_matrix_add(xHiDHix_g, mat_dcdc_t); + } + } - gsl_matrix_free(mat_dcdc); - gsl_matrix_free(mat_dcdc_t); + gsl_matrix_free(mat_dcdc); + gsl_matrix_free(mat_dcdc_t); - return; + 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; - double 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_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; + double 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; - double 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_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; + double 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); -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; + 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_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; +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; +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; - } - - // Calculate the fourth part: trace(HixQixHiDHixQixHiD). - for (size_t i=0; i<dc_size; i++) { - - 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; +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; + } + + // Calculate the fourth part: trace(HixQixHiDHixQixHiD). + for (size_t i = 0; i < dc_size; i++) { + + 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 (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; +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 (i,j). -void Calc_xHiDHix_all (const gsl_vector *eval, const gsl_matrix *xHi, - gsl_matrix *xHiDHix_all_g, gsl_matrix *xHiDHix_all_e) { +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 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); - + + 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_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); + 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 (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; +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 (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); - } - } - } - } - } - - return; +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); + } + } + } + } + } + + return; } // Calculate (xHiDHix)Qi(xHiy) for every pair (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; +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; +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; +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; +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 @@ -1912,3445 +1897,3503 @@ void Calc_yPDPy (const gsl_vector *eval, const gsl_matrix *Hiy, // + (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; +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; - double 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 correction 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); - - // 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); - } - - 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); - } - } - } - - // Calculate a, b, c from B C D. - crt_a=2.0*D-C; - crt_b=2.0*B; - crt_c=C; - - // 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; +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; + double 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 correction 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); + + // 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); + } + + 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); + } + } + } + + // Calculate a, b, c from B C D. + crt_a = 2.0 * D - C; + crt_b = 2.0 * B; + crt_c = C; + + // 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; - double 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); - - 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); - - // 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; - } 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); - } - } - } - } - } - - // Invert Hessian. - int sig; - gsl_permutation * pmt=gsl_permutation_alloc (v_size*2); - - LUDecomp (Hessian, pmt, &sig); - LUInvert (Hessian, pmt, Hessian_inv); - - 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; +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; + double 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); + + 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); + + // 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; + } 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); + } + } + } + } + } + + // Invert Hessian. + int sig; + gsl_permutation *pmt = gsl_permutation_alloc(v_size * 2); + + LUDecomp(Hessian, pmt, &sig); + LUInvert(Hessian, pmt, Hessian_inv); + + 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; +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); + gsl_vector *vec_v = gsl_vector_alloc(v_size * 2); - double d; + 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); + // 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_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); - } - } + 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); + 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); + // 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); + 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); - } - } + 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); + gsl_vector_free(vec_v); - return; + 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; - double 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); - - // 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++; - - } 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); - } - - // 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; +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; + double 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); + + // 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++; + + } 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); + } + + // 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; - - // Initialize 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. Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (2, 2*n_size); - - // Each column is H_k^{-1}y_k. - gsl_matrix *Hiy_all=gsl_matrix_alloc (2, n_size); - - // Each dcxdc block is x_k\otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (2*c_size, 2*n_size); - 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); - } - - // 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); - 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; + 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; + + // Initialize 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. Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(2, 2 * n_size); + + // Each column is H_k^{-1}y_k. + gsl_matrix *Hiy_all = gsl_matrix_alloc(2, n_size); + + // Each dcxdc block is x_k\otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(2 * c_size, 2 * n_size); + 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); + } + + // 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); + 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 { - chisq_crt=chisq; - } - - p_crt=gsl_cdf_chisq_Q (chisq_crt, (double)d_size ); - - return p_crt; +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 { + chisq_crt = chisq; + } + + p_crt = gsl_cdf_chisq_Q(chisq_crt, (double)d_size); + + return p_crt; } // WJA added. -void MVLMM::Analyzebgen (const gsl_matrix *U, const gsl_vector *eval, - const gsl_matrix *UtW, const gsl_matrix *UtY) { - string file_bgen=file_oxford+".bgen"; - ifstream infile (file_bgen.c_str(), ios::binary); - if (!infile) { - cout<<"error reading bgen file:"<<file_bgen<<endl; - return; - } - - clock_t time_start=clock(); - time_UtX=0; time_opt=0; - - string line; - - // Create a large matrix. - size_t msize=10000; - gsl_matrix *Xlarge=gsl_matrix_alloc (U->size1, msize); - gsl_matrix *UtXlarge=gsl_matrix_alloc (U->size1, msize); - gsl_matrix_set_zero(Xlarge); - - 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; - 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. Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); - - // Each column is H_k^{-1}y_k. - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); - - // Each dcxdc block is x_k\otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); - 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); - - // Read in header. - uint32_t bgen_snp_block_offset; - uint32_t bgen_header_length; - uint32_t bgen_nsamples; - uint32_t bgen_nsnps; - uint32_t bgen_flags; - infile.read(reinterpret_cast<char*>(&bgen_snp_block_offset),4); - infile.read(reinterpret_cast<char*>(&bgen_header_length),4); - bgen_snp_block_offset-=4; - infile.read(reinterpret_cast<char*>(&bgen_nsnps),4); - bgen_snp_block_offset-=4; - infile.read(reinterpret_cast<char*>(&bgen_nsamples),4); - bgen_snp_block_offset-=4; - infile.ignore(4+bgen_header_length-20); - bgen_snp_block_offset-=4+bgen_header_length-20; - infile.read(reinterpret_cast<char*>(&bgen_flags),4); - bgen_snp_block_offset-=4; - bool CompressedSNPBlocks=bgen_flags&0x1; - - infile.ignore(bgen_snp_block_offset); - - double bgen_geno_prob_AA, bgen_geno_prob_AB, bgen_geno_prob_BB; - double bgen_geno_prob_non_miss; - - uint32_t bgen_N; - uint16_t bgen_LS; - uint16_t bgen_LR; - uint16_t bgen_LC; - uint32_t bgen_SNP_pos; - uint32_t bgen_LA; - std::string bgen_A_allele; - uint32_t bgen_LB; - std::string bgen_B_allele; - uint32_t bgen_P; - size_t unzipped_data_size; - string id; - string rs; - string chr; - std::cout<<"Warning: WJA hard coded SNP missingness threshold "<< - "of 10%"<<std::endl; - - // Start reading genotypes and analyze. - size_t csnp=0, t_last=0; - for (size_t t=0; t<indicator_snp.size(); ++t) { - if (indicator_snp[t]==0) {continue;} - t_last++; - } - for (size_t t=0; t<indicator_snp.size(); ++t) { - if (t%d_pace==0 || t==(ns_total-1)) { - ProgressBar ("Reading SNPs ", t, ns_total-1); - } - if (indicator_snp[t]==0) {continue;} - - // Read SNP header. - id.clear(); - rs.clear(); - chr.clear(); - bgen_A_allele.clear(); - bgen_B_allele.clear(); - - infile.read(reinterpret_cast<char*>(&bgen_N),4); - infile.read(reinterpret_cast<char*>(&bgen_LS),2); - - id.resize(bgen_LS); - infile.read(&id[0], bgen_LS); - - infile.read(reinterpret_cast<char*>(&bgen_LR),2); - rs.resize(bgen_LR); - infile.read(&rs[0], bgen_LR); - - infile.read(reinterpret_cast<char*>(&bgen_LC),2); - chr.resize(bgen_LC); - infile.read(&chr[0], bgen_LC); - - infile.read(reinterpret_cast<char*>(&bgen_SNP_pos),4); - - infile.read(reinterpret_cast<char*>(&bgen_LA),4); - bgen_A_allele.resize(bgen_LA); - infile.read(&bgen_A_allele[0], bgen_LA); - - infile.read(reinterpret_cast<char*>(&bgen_LB),4); - bgen_B_allele.resize(bgen_LB); - infile.read(&bgen_B_allele[0], bgen_LB); - - uint16_t unzipped_data[3*bgen_N]; - - if (indicator_snp[t]==0) { - if(CompressedSNPBlocks) - infile.read(reinterpret_cast<char*>(&bgen_P),4); - else - bgen_P=6*bgen_N; - - infile.ignore(static_cast<size_t>(bgen_P)); - - continue; - } - - if(CompressedSNPBlocks) { - - infile.read(reinterpret_cast<char*>(&bgen_P),4); - uint8_t zipped_data[bgen_P]; - - unzipped_data_size=6*bgen_N; - - infile.read(reinterpret_cast<char*>(zipped_data),bgen_P); - - int result=uncompress(reinterpret_cast<Bytef*>(unzipped_data), - reinterpret_cast<uLongf*>(&unzipped_data_size), - reinterpret_cast<Bytef*>(zipped_data), - static_cast<uLong> (bgen_P)); - assert(result == Z_OK); - - } else { - - bgen_P=6*bgen_N; - infile.read(reinterpret_cast<char*>(unzipped_data),bgen_P); - } - - x_mean=0.0; c_phen=0; n_miss=0; - gsl_vector_set_zero(x_miss); - for (size_t i=0; i<bgen_N; ++i) { - if (indicator_idv[i]==0) {continue;} - - bgen_geno_prob_AA = - static_cast<double>(unzipped_data[i*3])/32768.0; - bgen_geno_prob_AB = - static_cast<double>(unzipped_data[i*3+1])/32768.0; - bgen_geno_prob_BB = - static_cast<double>(unzipped_data[i*3+2])/32768.0; - - // WJA. - bgen_geno_prob_non_miss=bgen_geno_prob_AA + - bgen_geno_prob_AB+bgen_geno_prob_BB; - if (bgen_geno_prob_non_miss<0.9) { - gsl_vector_set(x_miss, c_phen, 0.0); - n_miss++; - } - else { - - bgen_geno_prob_AA/=bgen_geno_prob_non_miss; - bgen_geno_prob_AB/=bgen_geno_prob_non_miss; - bgen_geno_prob_BB/=bgen_geno_prob_non_miss; - - geno=2.0*bgen_geno_prob_BB+bgen_geno_prob_AB; - - gsl_vector_set(x, c_phen, geno); - gsl_vector_set(x_miss, c_phen, 1.0); - x_mean+=geno; - } - c_phen++; - } - - x_mean/=static_cast<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);} - } - - gsl_vector_view Xlarge_col=gsl_matrix_column (Xlarge, csnp%msize); - gsl_vector_memcpy (&Xlarge_col.vector, x); - csnp++; - - if (csnp%msize==0 || csnp==t_last ) { - size_t l=0; - if (csnp%msize==0) {l=msize;} else {l=csnp%msize;} - - gsl_matrix_view Xlarge_sub = - gsl_matrix_submatrix(Xlarge, 0, 0, Xlarge->size1, l); - gsl_matrix_view UtXlarge_sub = - gsl_matrix_submatrix(UtXlarge, 0, 0, UtXlarge->size1, l); - - time_start=clock(); - eigenlib_dgemm ("T", "N", 1.0, U, &Xlarge_sub.matrix, 0.0, - &UtXlarge_sub.matrix); - time_UtX+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - gsl_matrix_set_zero (Xlarge); - - for (size_t i=0; i<l; i++) { - gsl_vector_view UtXlarge_col=gsl_matrix_column (UtXlarge, i); - gsl_vector_memcpy (&X_row.vector, &UtXlarge_col.vector); - - // 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); - } - } - } - - time_opt+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - // Store summary data. - 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); - - gsl_matrix_free(Xlarge); - gsl_matrix_free(UtXlarge); - - return; +void MVLMM::Analyzebgen(const gsl_matrix *U, const gsl_vector *eval, + const gsl_matrix *UtW, const gsl_matrix *UtY) { + string file_bgen = file_oxford + ".bgen"; + ifstream infile(file_bgen.c_str(), ios::binary); + if (!infile) { + cout << "error reading bgen file:" << file_bgen << endl; + return; + } + + clock_t time_start = clock(); + time_UtX = 0; + time_opt = 0; + + string line; + + // Create a large matrix. + size_t msize = LMM_BATCH_SIZE; + gsl_matrix *Xlarge = gsl_matrix_alloc(U->size1, msize); + gsl_matrix *UtXlarge = gsl_matrix_alloc(U->size1, msize); + gsl_matrix_set_zero(Xlarge); + + 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; + 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. Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(d_size, d_size * n_size); + + // Each column is H_k^{-1}y_k. + gsl_matrix *Hiy_all = gsl_matrix_alloc(d_size, n_size); + + // Each dcxdc block is x_k\otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(dc_size, d_size * n_size); + 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); + + // Read in header. + uint32_t bgen_snp_block_offset; + uint32_t bgen_header_length; + uint32_t bgen_nsamples; + uint32_t bgen_nsnps; + uint32_t bgen_flags; + infile.read(reinterpret_cast<char *>(&bgen_snp_block_offset), 4); + infile.read(reinterpret_cast<char *>(&bgen_header_length), 4); + bgen_snp_block_offset -= 4; + infile.read(reinterpret_cast<char *>(&bgen_nsnps), 4); + bgen_snp_block_offset -= 4; + infile.read(reinterpret_cast<char *>(&bgen_nsamples), 4); + bgen_snp_block_offset -= 4; + infile.ignore(4 + bgen_header_length - 20); + bgen_snp_block_offset -= 4 + bgen_header_length - 20; + infile.read(reinterpret_cast<char *>(&bgen_flags), 4); + bgen_snp_block_offset -= 4; + bool CompressedSNPBlocks = bgen_flags & 0x1; + + infile.ignore(bgen_snp_block_offset); + + double bgen_geno_prob_AA, bgen_geno_prob_AB, bgen_geno_prob_BB; + double bgen_geno_prob_non_miss; + + uint32_t bgen_N; + uint16_t bgen_LS; + uint16_t bgen_LR; + uint16_t bgen_LC; + uint32_t bgen_SNP_pos; + uint32_t bgen_LA; + std::string bgen_A_allele; + uint32_t bgen_LB; + std::string bgen_B_allele; + uint32_t bgen_P; + size_t unzipped_data_size; + string id; + string rs; + string chr; + std::cout << "Warning: WJA hard coded SNP missingness threshold " + << "of 10%" << std::endl; + + // Start reading genotypes and analyze. + size_t csnp = 0, t_last = 0; + for (size_t t = 0; t < indicator_snp.size(); ++t) { + if (indicator_snp[t] == 0) { + continue; + } + t_last++; + } + for (size_t t = 0; t < indicator_snp.size(); ++t) { + if (t % d_pace == 0 || t == (ns_total - 1)) { + ProgressBar("Reading SNPs ", t, ns_total - 1); + } + if (indicator_snp[t] == 0) { + continue; + } + + // Read SNP header. + id.clear(); + rs.clear(); + chr.clear(); + bgen_A_allele.clear(); + bgen_B_allele.clear(); + + infile.read(reinterpret_cast<char *>(&bgen_N), 4); + infile.read(reinterpret_cast<char *>(&bgen_LS), 2); + + id.resize(bgen_LS); + infile.read(&id[0], bgen_LS); + + infile.read(reinterpret_cast<char *>(&bgen_LR), 2); + rs.resize(bgen_LR); + infile.read(&rs[0], bgen_LR); + + infile.read(reinterpret_cast<char *>(&bgen_LC), 2); + chr.resize(bgen_LC); + infile.read(&chr[0], bgen_LC); + + infile.read(reinterpret_cast<char *>(&bgen_SNP_pos), 4); + + infile.read(reinterpret_cast<char *>(&bgen_LA), 4); + bgen_A_allele.resize(bgen_LA); + infile.read(&bgen_A_allele[0], bgen_LA); + + infile.read(reinterpret_cast<char *>(&bgen_LB), 4); + bgen_B_allele.resize(bgen_LB); + infile.read(&bgen_B_allele[0], bgen_LB); + + uint16_t unzipped_data[3 * bgen_N]; + + if (indicator_snp[t] == 0) { + if (CompressedSNPBlocks) + infile.read(reinterpret_cast<char *>(&bgen_P), 4); + else + bgen_P = 6 * bgen_N; + + infile.ignore(static_cast<size_t>(bgen_P)); + + continue; + } + + if (CompressedSNPBlocks) { + + infile.read(reinterpret_cast<char *>(&bgen_P), 4); + uint8_t zipped_data[bgen_P]; + + unzipped_data_size = 6 * bgen_N; + + infile.read(reinterpret_cast<char *>(zipped_data), bgen_P); + + int result = uncompress(reinterpret_cast<Bytef *>(unzipped_data), + reinterpret_cast<uLongf *>(&unzipped_data_size), + reinterpret_cast<Bytef *>(zipped_data), + static_cast<uLong>(bgen_P)); + assert(result == Z_OK); + + } else { + + bgen_P = 6 * bgen_N; + infile.read(reinterpret_cast<char *>(unzipped_data), bgen_P); + } + + x_mean = 0.0; + c_phen = 0; + n_miss = 0; + gsl_vector_set_zero(x_miss); + for (size_t i = 0; i < bgen_N; ++i) { + if (indicator_idv[i] == 0) { + continue; + } + + bgen_geno_prob_AA = static_cast<double>(unzipped_data[i * 3]) / 32768.0; + bgen_geno_prob_AB = + static_cast<double>(unzipped_data[i * 3 + 1]) / 32768.0; + bgen_geno_prob_BB = + static_cast<double>(unzipped_data[i * 3 + 2]) / 32768.0; + + // WJA. + bgen_geno_prob_non_miss = + bgen_geno_prob_AA + bgen_geno_prob_AB + bgen_geno_prob_BB; + if (bgen_geno_prob_non_miss < 0.9) { + gsl_vector_set(x_miss, c_phen, 0.0); + n_miss++; + } else { + + bgen_geno_prob_AA /= bgen_geno_prob_non_miss; + bgen_geno_prob_AB /= bgen_geno_prob_non_miss; + bgen_geno_prob_BB /= bgen_geno_prob_non_miss; + + geno = 2.0 * bgen_geno_prob_BB + bgen_geno_prob_AB; + + gsl_vector_set(x, c_phen, geno); + gsl_vector_set(x_miss, c_phen, 1.0); + x_mean += geno; + } + c_phen++; + } + + x_mean /= static_cast<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); + } + } + + gsl_vector_view Xlarge_col = gsl_matrix_column(Xlarge, csnp % msize); + gsl_vector_memcpy(&Xlarge_col.vector, x); + csnp++; + + if (csnp % msize == 0 || csnp == t_last) { + size_t l = 0; + if (csnp % msize == 0) { + l = msize; + } else { + l = csnp % msize; + } + + gsl_matrix_view Xlarge_sub = + gsl_matrix_submatrix(Xlarge, 0, 0, Xlarge->size1, l); + gsl_matrix_view UtXlarge_sub = + gsl_matrix_submatrix(UtXlarge, 0, 0, UtXlarge->size1, l); + + time_start = clock(); + eigenlib_dgemm("T", "N", 1.0, U, &Xlarge_sub.matrix, 0.0, + &UtXlarge_sub.matrix); + time_UtX += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0); + + gsl_matrix_set_zero(Xlarge); + + for (size_t i = 0; i < l; i++) { + gsl_vector_view UtXlarge_col = gsl_matrix_column(UtXlarge, i); + gsl_vector_memcpy(&X_row.vector, &UtXlarge_col.vector); + + // 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); + } + } + } + + time_opt += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0); + + // Store summary data. + 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); + + gsl_matrix_free(Xlarge); + gsl_matrix_free(UtXlarge); + + return; } -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); - 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 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; - 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; - - // Create a large matrix. - size_t msize=10000; - gsl_matrix *Xlarge=gsl_matrix_alloc (U->size1, msize); - gsl_matrix *UtXlarge=gsl_matrix_alloc (U->size1, msize); - gsl_matrix_set_zero(Xlarge); - - // 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. - // Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); - - // Each column is H_k^{-1}y_k. - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); - - // Each dcxdc block is x_k \otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); - 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. - size_t csnp=0, t_last=0; - for (size_t t=0; t<indicator_snp.size(); ++t) { - if (indicator_snp[t]==0) {continue;} - t_last++; - } - for (size_t t=0; t<indicator_snp.size(); ++t) { - !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); - } - - gsl_vector_view Xlarge_col=gsl_matrix_column (Xlarge, csnp%msize); - gsl_vector_memcpy (&Xlarge_col.vector, x); - csnp++; - - if (csnp%msize==0 || csnp==t_last ) { - size_t l=0; - if (csnp%msize==0) {l=msize;} else {l=csnp%msize;} - - gsl_matrix_view Xlarge_sub = - gsl_matrix_submatrix(Xlarge, 0, 0, Xlarge->size1, l); - gsl_matrix_view UtXlarge_sub = - gsl_matrix_submatrix(UtXlarge, 0, 0, UtXlarge->size1, l); - - time_start=clock(); - eigenlib_dgemm ("T", "N", 1.0, U, &Xlarge_sub.matrix, 0.0, - &UtXlarge_sub.matrix); - time_UtX+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - gsl_matrix_set_zero (Xlarge); - - for (size_t i=0; i<l; i++) { - gsl_vector_view UtXlarge_col=gsl_matrix_column (UtXlarge, i); - gsl_vector_memcpy (&X_row.vector, &UtXlarge_col.vector); - - // 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); - } - } - } - - time_opt+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - // Store summary data. - 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); - - gsl_matrix_free(Xlarge); - gsl_matrix_free(UtXlarge); - - return; +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); + 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 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; + 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; + + // Create a large matrix. + size_t msize = LMM_BATCH_SIZE; + gsl_matrix *Xlarge = gsl_matrix_alloc(U->size1, msize); + gsl_matrix *UtXlarge = gsl_matrix_alloc(U->size1, msize); + gsl_matrix_set_zero(Xlarge); + + // 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. + // Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(d_size, d_size * n_size); + + // Each column is H_k^{-1}y_k. + gsl_matrix *Hiy_all = gsl_matrix_alloc(d_size, n_size); + + // Each dcxdc block is x_k \otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(dc_size, d_size * n_size); + 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. + size_t csnp = 0, t_last = 0; + for (size_t t = 0; t < indicator_snp.size(); ++t) { + if (indicator_snp[t] == 0) { + continue; + } + t_last++; + } + for (size_t t = 0; t < indicator_snp.size(); ++t) { + !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); + } + + gsl_vector_view Xlarge_col = gsl_matrix_column(Xlarge, csnp % msize); + gsl_vector_memcpy(&Xlarge_col.vector, x); + csnp++; + + if (csnp % msize == 0 || csnp == t_last) { + size_t l = 0; + if (csnp % msize == 0) { + l = msize; + } else { + l = csnp % msize; + } + + gsl_matrix_view Xlarge_sub = + gsl_matrix_submatrix(Xlarge, 0, 0, Xlarge->size1, l); + gsl_matrix_view UtXlarge_sub = + gsl_matrix_submatrix(UtXlarge, 0, 0, UtXlarge->size1, l); + + time_start = clock(); + eigenlib_dgemm("T", "N", 1.0, U, &Xlarge_sub.matrix, 0.0, + &UtXlarge_sub.matrix); + time_UtX += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0); + + gsl_matrix_set_zero(Xlarge); + + for (size_t i = 0; i < l; i++) { + gsl_vector_view UtXlarge_col = gsl_matrix_column(UtXlarge, i); + gsl_vector_memcpy(&X_row.vector, &UtXlarge_col.vector); + + // 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); + } + } + } + + time_opt += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0); + + // Store summary data. + 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); + + gsl_matrix_free(Xlarge); + gsl_matrix_free(UtXlarge); + + 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 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; - 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; - - // Create a large matrix. - size_t msize=10000; - gsl_matrix *Xlarge=gsl_matrix_alloc (U->size1, msize); - gsl_matrix *UtXlarge=gsl_matrix_alloc (U->size1, msize); - gsl_matrix_set_zero(Xlarge); - - // 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. - // Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); - - // Each column is H_k^{-1}y_k. - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); - - // Each dcxdc block is x_k\otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); - - 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); - - 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. - // 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 magic numbers. - for (int i=0; i<3; ++i) { - infile.read(ch,1); - b=ch[0]; - } - - size_t csnp=0, t_last=0; - for (size_t t=0; t<indicator_snp.size(); ++t) { - if (indicator_snp[t]==0) {continue;} - t_last++; - } - 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;} - - // n_bit, and 3 is the number of magic numbers. - infile.seekg(t*n_bit+3); - - //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]; - - // Minor allele homozygous: 2.0; major: 0.0; - for (size_t j=0; j<4; ++j) { - 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;} - } - - gsl_vector_view Xlarge_col=gsl_matrix_column (Xlarge, csnp%msize); - gsl_vector_memcpy (&Xlarge_col.vector, x); - csnp++; - - if (csnp%msize==0 || csnp==t_last ) { - size_t l=0; - if (csnp%msize==0) {l=msize;} else {l=csnp%msize;} - - gsl_matrix_view Xlarge_sub = - gsl_matrix_submatrix(Xlarge, 0, 0, Xlarge->size1, l); - gsl_matrix_view UtXlarge_sub = - gsl_matrix_submatrix(UtXlarge, 0, 0, UtXlarge->size1, l); - - time_start=clock(); - eigenlib_dgemm ("T", "N", 1.0, U, &Xlarge_sub.matrix, 0.0, - &UtXlarge_sub.matrix); - time_UtX+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - gsl_matrix_set_zero (Xlarge); - - for (size_t i=0; i<l; i++) { - gsl_vector_view UtXlarge_col=gsl_matrix_column (UtXlarge, i); - gsl_vector_memcpy (&X_row.vector, &UtXlarge_col.vector); - - // 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); - } - } - } - - time_opt+=(clock()-time_start)/(double(CLOCKS_PER_SEC)*60.0); - - // Store summary data. - 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_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); - - gsl_matrix_free(Xlarge); - gsl_matrix_free(UtXlarge); - - 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 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; + 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; + + // Create a large matrix. + size_t msize = LMM_BATCH_SIZE; + gsl_matrix *Xlarge = gsl_matrix_alloc(U->size1, msize); + gsl_matrix *UtXlarge = gsl_matrix_alloc(U->size1, msize); + gsl_matrix_set_zero(Xlarge); + + // 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. + // Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(d_size, d_size * n_size); + + // Each column is H_k^{-1}y_k. + gsl_matrix *Hiy_all = gsl_matrix_alloc(d_size, n_size); + + // Each dcxdc block is x_k\otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(dc_size, d_size * n_size); + + 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); + + 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. + // 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 magic numbers. + for (int i = 0; i < 3; ++i) { + infile.read(ch, 1); + b = ch[0]; + } + + size_t csnp = 0, t_last = 0; + for (size_t t = 0; t < indicator_snp.size(); ++t) { + if (indicator_snp[t] == 0) { + continue; + } + t_last++; + } + 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; + } + + // n_bit, and 3 is the number of magic numbers. + infile.seekg(t * n_bit + 3); + + // 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]; + + // Minor allele homozygous: 2.0; major: 0.0; + for (size_t j = 0; j < 4; ++j) { + 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; + } + } + + gsl_vector_view Xlarge_col = gsl_matrix_column(Xlarge, csnp % msize); + gsl_vector_memcpy(&Xlarge_col.vector, x); + csnp++; + + if (csnp % msize == 0 || csnp == t_last) { + size_t l = 0; + if (csnp % msize == 0) { + l = msize; + } else { + l = csnp % msize; + } + + gsl_matrix_view Xlarge_sub = + gsl_matrix_submatrix(Xlarge, 0, 0, Xlarge->size1, l); + gsl_matrix_view UtXlarge_sub = + gsl_matrix_submatrix(UtXlarge, 0, 0, UtXlarge->size1, l); + + time_start = clock(); + eigenlib_dgemm("T", "N", 1.0, U, &Xlarge_sub.matrix, 0.0, + &UtXlarge_sub.matrix); + time_UtX += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0); + + gsl_matrix_set_zero(Xlarge); + + for (size_t i = 0; i < l; i++) { + gsl_vector_view UtXlarge_col = gsl_matrix_column(UtXlarge, i); + gsl_vector_memcpy(&X_row.vector, &UtXlarge_col.vector); + + // 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); + } + } + } + + time_opt += (clock() - time_start) / (double(CLOCKS_PER_SEC) * 60.0); + + // Store summary data. + 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_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); + + gsl_matrix_free(Xlarge); + gsl_matrix_free(UtXlarge); + + 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. - // Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); - - // Each column is H_k^{-1}y_k. - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); - - // Each dcxdc block is x_k\otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); - 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; +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. + // Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(d_size, d_size * n_size); + + // Each column is H_k^{-1}y_k. + gsl_matrix *Hiy_all = gsl_matrix_alloc(d_size, n_size); + + // Each dcxdc block is x_k\otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(dc_size, d_size * n_size); + 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; } -void MVLMM::AnalyzeBimbamGXE (const gsl_matrix *U, const gsl_vector *eval, - const gsl_matrix *UtW, const gsl_matrix *UtY, - const gsl_vector *env) { - igzstream infile (file_geno.c_str(), igzstream::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 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; - size_t n_size=UtY->size1, d_size=UtY->size2, c_size=UtW->size2+2; - 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. - // Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); - - // Each column is H_k^{-1}y_k. - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); - - // Each dcxdc block is x_k\otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); - 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; including env but not - // including x. - 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_null1=gsl_matrix_alloc (d_size, c_size-1); - gsl_matrix *se_B_null2=gsl_matrix_alloc (d_size, c_size); - - gsl_matrix_view X_sub1=gsl_matrix_submatrix(X,0,0,c_size-1,n_size); - gsl_matrix_view B_sub1=gsl_matrix_submatrix(B,0,0,d_size,c_size-1); - gsl_matrix_view xHi_all_sub1= - gsl_matrix_submatrix(xHi_all,0,0,d_size*(c_size-1),d_size*n_size); - - gsl_matrix_view X_sub2=gsl_matrix_submatrix (X, 0, 0, c_size, n_size); - gsl_matrix_view B_sub2=gsl_matrix_submatrix (B, 0, 0, d_size, c_size); - gsl_matrix_view xHi_all_sub2= - gsl_matrix_submatrix (xHi_all, 0, 0, d_size*c_size, d_size*n_size); - - gsl_matrix_transpose_memcpy (Y, UtY); - - gsl_matrix_view X_sub0=gsl_matrix_submatrix(X,0,0,c_size-2,n_size); - gsl_matrix_transpose_memcpy (&X_sub0.matrix, UtW); - gsl_vector_view X_row0=gsl_matrix_row(X, c_size-2); - gsl_blas_dgemv (CblasTrans, 1.0, U, env, 0.0, &X_row0.vector); - - gsl_vector_view X_row1=gsl_matrix_row(X, c_size-1); - gsl_vector_set_zero(&X_row1.vector); - gsl_vector_view X_row2=gsl_matrix_row(X, c_size); - gsl_vector_set_zero(&X_row2.vector); - - gsl_vector_view B_col1=gsl_matrix_column(B, c_size-1); - gsl_vector_set_zero(&B_col1.vector); - gsl_vector_view B_col2=gsl_matrix_column(B, c_size); - gsl_vector_set_zero(&B_col2.vector); - - MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, &X_sub1.matrix, - Y, l_min, l_max, n_region, V_g, V_e, &B_sub1.matrix); - logl_H0=MphEM ('R', em_iter, em_prec, eval, &X_sub1.matrix, Y, - U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, - UltVehiU, UltVehiE, V_g, V_e, &B_sub1.matrix); - logl_H0=MphNR ('R', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, - Hi_all, &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, - Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, - &B_sub1.matrix, se_B_null1); - - 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_null1->size1; i++) { - for (size_t j=0; j<se_B_null1->size2; j++) { - beta_remle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_remle_null.push_back(gsl_matrix_get(se_B_null1, 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_sub1.matrix, Y, U_hat, - E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, - UltVehiE, V_g, V_e, &B_sub1.matrix); - logl_H0=MphNR ('L', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, - Hi_all, &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, - Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, - &B_sub1.matrix, se_B_null1); - - 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_null1->size1; i++) { - for (size_t j=0; j<se_B_null1->size2; j++) { - beta_mle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_mle_null.push_back(gsl_matrix_get(se_B_null1, 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) { - !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_row1.vector); - gsl_vector_mul (x, env); - gsl_blas_dgemv (CblasTrans, 1.0, U, x, 0.0, &X_row2.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); - - if (a_mode==2 || a_mode==3 || a_mode==4) { - if (a_mode==3 || a_mode==4) { - logl_H0=MphEM ('R', em_iter/10, em_prec*10, eval, - &X_sub2.matrix, Y, U_hat, E_hat, OmegaU, - OmegaE, UltVehiY, UltVehiBX, UltVehiU, - UltVehiE, V_g, V_e, &B_sub2.matrix); - logl_H0=MphNR ('R', nr_iter/10, nr_prec*10, eval, - &X_sub2.matrix, Y, Hi_all, - &xHi_all_sub2.matrix, Hiy_all, V_g, V_e, - Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, - &B_sub2.matrix, se_B_null2); - } - - if (a_mode==2 || a_mode==4) { - logl_H0=MphEM ('L', em_iter/10, em_prec*10, eval, - &X_sub2.matrix, Y, U_hat, E_hat, OmegaU, - OmegaE, UltVehiY, UltVehiBX, UltVehiU, - UltVehiE, V_g, V_e, &B_sub2.matrix); - logl_H0=MphNR ('L', nr_iter/10, nr_prec*10, eval, - &X_sub2.matrix, Y, Hi_all, - &xHi_all_sub2.matrix, Hiy_all, V_g, V_e, - Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, - &B_sub2.matrix, se_B_null2); - } - } - - time_start=clock(); - - // 3 is before 1. - if (a_mode==3 || a_mode==4) { - p_score=MphCalcP (eval, &X_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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. - 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_null1); - gsl_matrix_free(se_B_null2); - - return; +void MVLMM::AnalyzeBimbamGXE(const gsl_matrix *U, const gsl_vector *eval, + const gsl_matrix *UtW, const gsl_matrix *UtY, + const gsl_vector *env) { + igzstream infile(file_geno.c_str(), igzstream::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 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; + size_t n_size = UtY->size1, d_size = UtY->size2, c_size = UtW->size2 + 2; + 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. + // Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(d_size, d_size * n_size); + + // Each column is H_k^{-1}y_k. + gsl_matrix *Hiy_all = gsl_matrix_alloc(d_size, n_size); + + // Each dcxdc block is x_k\otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(dc_size, d_size * n_size); + 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; including env but not + // including x. + 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_null1 = gsl_matrix_alloc(d_size, c_size - 1); + gsl_matrix *se_B_null2 = gsl_matrix_alloc(d_size, c_size); + + gsl_matrix_view X_sub1 = gsl_matrix_submatrix(X, 0, 0, c_size - 1, n_size); + gsl_matrix_view B_sub1 = gsl_matrix_submatrix(B, 0, 0, d_size, c_size - 1); + gsl_matrix_view xHi_all_sub1 = gsl_matrix_submatrix( + xHi_all, 0, 0, d_size * (c_size - 1), d_size * n_size); + + gsl_matrix_view X_sub2 = gsl_matrix_submatrix(X, 0, 0, c_size, n_size); + gsl_matrix_view B_sub2 = gsl_matrix_submatrix(B, 0, 0, d_size, c_size); + gsl_matrix_view xHi_all_sub2 = + gsl_matrix_submatrix(xHi_all, 0, 0, d_size * c_size, d_size * n_size); + + gsl_matrix_transpose_memcpy(Y, UtY); + + gsl_matrix_view X_sub0 = gsl_matrix_submatrix(X, 0, 0, c_size - 2, n_size); + gsl_matrix_transpose_memcpy(&X_sub0.matrix, UtW); + gsl_vector_view X_row0 = gsl_matrix_row(X, c_size - 2); + gsl_blas_dgemv(CblasTrans, 1.0, U, env, 0.0, &X_row0.vector); + + gsl_vector_view X_row1 = gsl_matrix_row(X, c_size - 1); + gsl_vector_set_zero(&X_row1.vector); + gsl_vector_view X_row2 = gsl_matrix_row(X, c_size); + gsl_vector_set_zero(&X_row2.vector); + + gsl_vector_view B_col1 = gsl_matrix_column(B, c_size - 1); + gsl_vector_set_zero(&B_col1.vector); + gsl_vector_view B_col2 = gsl_matrix_column(B, c_size); + gsl_vector_set_zero(&B_col2.vector); + + MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, &X_sub1.matrix, Y, l_min, + l_max, n_region, V_g, V_e, &B_sub1.matrix); + logl_H0 = MphEM('R', em_iter, em_prec, eval, &X_sub1.matrix, Y, U_hat, E_hat, + OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, + V_e, &B_sub1.matrix); + logl_H0 = MphNR('R', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, Hi_all, + &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, + crt_b, crt_c); + MphCalcBeta(eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, &B_sub1.matrix, + se_B_null1); + + 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_null1->size1; i++) { + for (size_t j = 0; j < se_B_null1->size2; j++) { + beta_remle_null.push_back(gsl_matrix_get(B, i, j)); + se_beta_remle_null.push_back(gsl_matrix_get(se_B_null1, 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_sub1.matrix, Y, U_hat, E_hat, + OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, + V_e, &B_sub1.matrix); + logl_H0 = MphNR('L', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, Hi_all, + &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, + crt_b, crt_c); + MphCalcBeta(eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, &B_sub1.matrix, + se_B_null1); + + 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_null1->size1; i++) { + for (size_t j = 0; j < se_B_null1->size2; j++) { + beta_mle_null.push_back(gsl_matrix_get(B, i, j)); + se_beta_mle_null.push_back(gsl_matrix_get(se_B_null1, 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) { + !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_row1.vector); + gsl_vector_mul(x, env); + gsl_blas_dgemv(CblasTrans, 1.0, U, x, 0.0, &X_row2.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); + + if (a_mode == 2 || a_mode == 3 || a_mode == 4) { + if (a_mode == 3 || a_mode == 4) { + logl_H0 = MphEM('R', em_iter / 10, em_prec * 10, eval, &X_sub2.matrix, + Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, + UltVehiU, UltVehiE, V_g, V_e, &B_sub2.matrix); + logl_H0 = MphNR('R', nr_iter / 10, nr_prec * 10, eval, &X_sub2.matrix, + Y, Hi_all, &xHi_all_sub2.matrix, Hiy_all, V_g, V_e, + Hessian, crt_a, crt_b, crt_c); + MphCalcBeta(eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, &B_sub2.matrix, + se_B_null2); + } + + if (a_mode == 2 || a_mode == 4) { + logl_H0 = MphEM('L', em_iter / 10, em_prec * 10, eval, &X_sub2.matrix, + Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, + UltVehiU, UltVehiE, V_g, V_e, &B_sub2.matrix); + logl_H0 = MphNR('L', nr_iter / 10, nr_prec * 10, eval, &X_sub2.matrix, + Y, Hi_all, &xHi_all_sub2.matrix, Hiy_all, V_g, V_e, + Hessian, crt_a, crt_b, crt_c); + MphCalcBeta(eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, &B_sub2.matrix, + se_B_null2); + } + } + + time_start = clock(); + + // 3 is before 1. + if (a_mode == 3 || a_mode == 4) { + p_score = MphCalcP(eval, &X_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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. + 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_null1); + gsl_matrix_free(se_B_null2); + + return; } -void MVLMM::AnalyzePlinkGXE (const gsl_matrix *U, const gsl_vector *eval, - const gsl_matrix *UtW, const gsl_matrix *UtY, - const gsl_vector *env) { - 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 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; - size_t n_size=UtY->size1, d_size=UtY->size2, c_size=UtW->size2+2; - 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. - // Each dxd block is H_k^{-1}. - gsl_matrix *Hi_all=gsl_matrix_alloc (d_size, d_size*n_size); - - // Each column is H_k^{-1}y_k - gsl_matrix *Hiy_all=gsl_matrix_alloc (d_size, n_size); - - // Each dcxdc block is x_k\otimes H_k^{-1}. - gsl_matrix *xHi_all=gsl_matrix_alloc (dc_size, d_size*n_size); - 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_null1=gsl_matrix_alloc (d_size, c_size-1); - gsl_matrix *se_B_null2=gsl_matrix_alloc (d_size, c_size); - - gsl_matrix_view X_sub1=gsl_matrix_submatrix(X,0,0,c_size-1,n_size); - gsl_matrix_view B_sub1=gsl_matrix_submatrix(B,0,0,d_size,c_size-1); - gsl_matrix_view xHi_all_sub1= - gsl_matrix_submatrix(xHi_all,0,0,d_size*(c_size-1),d_size*n_size); - - gsl_matrix_view X_sub2=gsl_matrix_submatrix (X, 0, 0, c_size, n_size); - gsl_matrix_view B_sub2=gsl_matrix_submatrix (B, 0, 0, d_size, c_size); - gsl_matrix_view xHi_all_sub2= - gsl_matrix_submatrix (xHi_all, 0, 0, d_size*c_size, d_size*n_size); - - gsl_matrix_transpose_memcpy (Y, UtY); - - gsl_matrix_view X_sub0=gsl_matrix_submatrix(X,0,0,c_size-2,n_size); - gsl_matrix_transpose_memcpy (&X_sub0.matrix, UtW); - gsl_vector_view X_row0=gsl_matrix_row(X, c_size-2); - gsl_blas_dgemv (CblasTrans, 1.0, U, env, 0.0, &X_row0.vector); - - gsl_vector_view X_row1=gsl_matrix_row(X, c_size-1); - gsl_vector_set_zero(&X_row1.vector); - gsl_vector_view X_row2=gsl_matrix_row(X, c_size); - gsl_vector_set_zero(&X_row2.vector); - - gsl_vector_view B_col1=gsl_matrix_column(B, c_size-1); - gsl_vector_set_zero(&B_col1.vector); - gsl_vector_view B_col2=gsl_matrix_column(B, c_size); - gsl_vector_set_zero(&B_col2.vector); - - MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, &X_sub1.matrix, - Y, l_min, l_max, n_region, V_g, V_e, &B_sub1.matrix); - - logl_H0=MphEM ('R', em_iter, em_prec, eval, &X_sub1.matrix, Y, U_hat, - E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, - UltVehiE, V_g, V_e, &B_sub1.matrix); - logl_H0=MphNR ('R', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, - Hi_all, &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, - Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, - &B_sub1.matrix, se_B_null1); - - 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_null1->size1; i++) { - for (size_t j=0; j<se_B_null1->size2; j++) { - beta_remle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_remle_null.push_back(gsl_matrix_get(se_B_null1, 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_sub1.matrix, Y, - U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, - UltVehiU, UltVehiE, V_g, V_e, &B_sub1.matrix); - logl_H0=MphNR ('L', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, - Hi_all, &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, - Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, - &B_sub1.matrix, se_B_null1); - - 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_null1->size1; i++) { - for (size_t j=0; j<se_B_null1->size2; j++) { - beta_mle_null.push_back(gsl_matrix_get(B, i, j) ); - se_beta_mle_null.push_back(gsl_matrix_get(se_B_null1, 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 magic 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;} - - // n_bit, and 3 is the number of magic numbers. - infile.seekg(t*n_bit+3); - - // 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]; - - // Minor allele homozygous: 2.0; major: 0.0. - for (size_t j=0; j<4; ++j) { - - 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); - } - } - - // Calculate statistics. - time_start=clock(); - gsl_blas_dgemv (CblasTrans, 1.0, U, x, 0.0, &X_row1.vector); - gsl_vector_mul (x, env); - gsl_blas_dgemv (CblasTrans, 1.0, U, x, 0.0, &X_row2.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); - - if (a_mode==2 || a_mode==3 || a_mode==4) { - if (a_mode==3 || a_mode==4) { - logl_H0=MphEM ('R', em_iter/10, em_prec*10, eval, - &X_sub2.matrix, Y, U_hat, E_hat, OmegaU, OmegaE, - UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, - V_e, &B_sub2.matrix); - logl_H0=MphNR ('R', nr_iter/10, nr_prec*10, eval, - &X_sub2.matrix, Y, Hi_all, &xHi_all_sub2.matrix, - Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, - &B_sub2.matrix, se_B_null2); - } - - if (a_mode==2 || a_mode==4) { - logl_H0=MphEM ('L', em_iter/10, em_prec*10, eval, - &X_sub2.matrix, Y, U_hat, E_hat, OmegaU, OmegaE, - UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, - V_e, &B_sub2.matrix); - logl_H0=MphNR ('L', nr_iter/10, nr_prec*10, eval, - &X_sub2.matrix, Y, Hi_all, &xHi_all_sub2.matrix, - Hiy_all, V_g, V_e, Hessian, crt_a, crt_b, crt_c); - MphCalcBeta (eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, - &B_sub2.matrix, se_B_null2); - } - } - - time_start=clock(); - - // 3 is before 1. - if (a_mode==3 || a_mode==4) { - p_score=MphCalcP (eval, &X_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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. - 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_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_null1); - gsl_matrix_free(se_B_null2); - - return; +void MVLMM::AnalyzePlinkGXE(const gsl_matrix *U, const gsl_vector *eval, + const gsl_matrix *UtW, const gsl_matrix *UtY, + const gsl_vector *env) { + 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 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; + size_t n_size = UtY->size1, d_size = UtY->size2, c_size = UtW->size2 + 2; + 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. + // Each dxd block is H_k^{-1}. + gsl_matrix *Hi_all = gsl_matrix_alloc(d_size, d_size * n_size); + + // Each column is H_k^{-1}y_k + gsl_matrix *Hiy_all = gsl_matrix_alloc(d_size, n_size); + + // Each dcxdc block is x_k\otimes H_k^{-1}. + gsl_matrix *xHi_all = gsl_matrix_alloc(dc_size, d_size * n_size); + 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_null1 = gsl_matrix_alloc(d_size, c_size - 1); + gsl_matrix *se_B_null2 = gsl_matrix_alloc(d_size, c_size); + + gsl_matrix_view X_sub1 = gsl_matrix_submatrix(X, 0, 0, c_size - 1, n_size); + gsl_matrix_view B_sub1 = gsl_matrix_submatrix(B, 0, 0, d_size, c_size - 1); + gsl_matrix_view xHi_all_sub1 = gsl_matrix_submatrix( + xHi_all, 0, 0, d_size * (c_size - 1), d_size * n_size); + + gsl_matrix_view X_sub2 = gsl_matrix_submatrix(X, 0, 0, c_size, n_size); + gsl_matrix_view B_sub2 = gsl_matrix_submatrix(B, 0, 0, d_size, c_size); + gsl_matrix_view xHi_all_sub2 = + gsl_matrix_submatrix(xHi_all, 0, 0, d_size * c_size, d_size * n_size); + + gsl_matrix_transpose_memcpy(Y, UtY); + + gsl_matrix_view X_sub0 = gsl_matrix_submatrix(X, 0, 0, c_size - 2, n_size); + gsl_matrix_transpose_memcpy(&X_sub0.matrix, UtW); + gsl_vector_view X_row0 = gsl_matrix_row(X, c_size - 2); + gsl_blas_dgemv(CblasTrans, 1.0, U, env, 0.0, &X_row0.vector); + + gsl_vector_view X_row1 = gsl_matrix_row(X, c_size - 1); + gsl_vector_set_zero(&X_row1.vector); + gsl_vector_view X_row2 = gsl_matrix_row(X, c_size); + gsl_vector_set_zero(&X_row2.vector); + + gsl_vector_view B_col1 = gsl_matrix_column(B, c_size - 1); + gsl_vector_set_zero(&B_col1.vector); + gsl_vector_view B_col2 = gsl_matrix_column(B, c_size); + gsl_vector_set_zero(&B_col2.vector); + + MphInitial(em_iter, em_prec, nr_iter, nr_prec, eval, &X_sub1.matrix, Y, l_min, + l_max, n_region, V_g, V_e, &B_sub1.matrix); + + logl_H0 = MphEM('R', em_iter, em_prec, eval, &X_sub1.matrix, Y, U_hat, E_hat, + OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, + V_e, &B_sub1.matrix); + logl_H0 = MphNR('R', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, Hi_all, + &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, + crt_b, crt_c); + MphCalcBeta(eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, &B_sub1.matrix, + se_B_null1); + + 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_null1->size1; i++) { + for (size_t j = 0; j < se_B_null1->size2; j++) { + beta_remle_null.push_back(gsl_matrix_get(B, i, j)); + se_beta_remle_null.push_back(gsl_matrix_get(se_B_null1, 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_sub1.matrix, Y, U_hat, E_hat, + OmegaU, OmegaE, UltVehiY, UltVehiBX, UltVehiU, UltVehiE, V_g, + V_e, &B_sub1.matrix); + logl_H0 = MphNR('L', nr_iter, nr_prec, eval, &X_sub1.matrix, Y, Hi_all, + &xHi_all_sub1.matrix, Hiy_all, V_g, V_e, Hessian, crt_a, + crt_b, crt_c); + MphCalcBeta(eval, &X_sub1.matrix, Y, V_g, V_e, UltVehiY, &B_sub1.matrix, + se_B_null1); + + 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_null1->size1; i++) { + for (size_t j = 0; j < se_B_null1->size2; j++) { + beta_mle_null.push_back(gsl_matrix_get(B, i, j)); + se_beta_mle_null.push_back(gsl_matrix_get(se_B_null1, 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 magic 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; + } + + // n_bit, and 3 is the number of magic numbers. + infile.seekg(t * n_bit + 3); + + // 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]; + + // Minor allele homozygous: 2.0; major: 0.0. + for (size_t j = 0; j < 4; ++j) { + + 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); + } + } + + // Calculate statistics. + time_start = clock(); + gsl_blas_dgemv(CblasTrans, 1.0, U, x, 0.0, &X_row1.vector); + gsl_vector_mul(x, env); + gsl_blas_dgemv(CblasTrans, 1.0, U, x, 0.0, &X_row2.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); + + if (a_mode == 2 || a_mode == 3 || a_mode == 4) { + if (a_mode == 3 || a_mode == 4) { + logl_H0 = MphEM('R', em_iter / 10, em_prec * 10, eval, &X_sub2.matrix, + Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, + UltVehiU, UltVehiE, V_g, V_e, &B_sub2.matrix); + logl_H0 = MphNR('R', nr_iter / 10, nr_prec * 10, eval, &X_sub2.matrix, + Y, Hi_all, &xHi_all_sub2.matrix, Hiy_all, V_g, V_e, + Hessian, crt_a, crt_b, crt_c); + MphCalcBeta(eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, &B_sub2.matrix, + se_B_null2); + } + + if (a_mode == 2 || a_mode == 4) { + logl_H0 = MphEM('L', em_iter / 10, em_prec * 10, eval, &X_sub2.matrix, + Y, U_hat, E_hat, OmegaU, OmegaE, UltVehiY, UltVehiBX, + UltVehiU, UltVehiE, V_g, V_e, &B_sub2.matrix); + logl_H0 = MphNR('L', nr_iter / 10, nr_prec * 10, eval, &X_sub2.matrix, + Y, Hi_all, &xHi_all_sub2.matrix, Hiy_all, V_g, V_e, + Hessian, crt_a, crt_b, crt_c); + MphCalcBeta(eval, &X_sub2.matrix, Y, V_g, V_e, UltVehiY, &B_sub2.matrix, + se_B_null2); + } + } + + time_start = clock(); + + // 3 is before 1. + if (a_mode == 3 || a_mode == 4) { + p_score = MphCalcP(eval, &X_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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_row2.vector, &X_sub2.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. + 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_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_null1); + gsl_matrix_free(se_B_null2); + + return; } |