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Copy pathgemma_lmm.cpp
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gemma_lmm.cpp
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/*
Genome-wide Efficient Mixed Model Association (GEMMA)
Copyright (C) 2011 Xiang Zhou
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <bitset>
#include <cstring>
#include "gsl/gsl_vector.h"
#include "gsl/gsl_matrix.h"
#include "gsl/gsl_linalg.h"
#include "gsl/gsl_blas.h"
#include "gsl/gsl_cdf.h"
#include "gsl/gsl_roots.h"
#include "gsl/gsl_min.h"
#include "gsl/gsl_integration.h"
#include "gemma_io.h"
#include "gemma_lapack.h"
#include "gemma_gzstream.h"
#ifdef FORCE_FLOAT
#include "lmm_float.h"
#else
#include "gemma_lmm.h"
#endif
using namespace std;
void LMM::CopyFromParam (PARAM &cPar)
{
a_mode=cPar.a_mode;
d_pace=cPar.d_pace;
file_bfile=cPar.file_bfile;
file_geno=cPar.file_geno;
file_out=cPar.file_out;
file_gene=cPar.file_gene;
l_min=cPar.l_min;
l_max=cPar.l_max;
n_region=cPar.n_region;
l_mle_null=cPar.l_mle_null;
logl_mle_H0=cPar.logl_mle_H0;
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;
ng_total=cPar.ng_total;
ng_test=0;
indicator_idv=cPar.indicator_idv;
indicator_snp=cPar.indicator_snp;
snpInfo=cPar.snpInfo;
return;
}
void LMM::CopyToParam (PARAM &cPar)
{
cPar.time_UtX=time_UtX;
cPar.time_opt=time_opt;
cPar.ng_test=ng_test;
return;
}
void LMM::WriteFiles ()
{
string file_str;
file_str="./output/"+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;}
if (!file_gene.empty()) {
outfile<<"geneID"<<"\t";
if (a_mode==1) {
outfile<<"beta"<<"\t"<<"se"<<"\t"<<"l_remle"<<"\t"<<"p_wald"<<endl;
} else if (a_mode==2) {
outfile<<"l_mle"<<"\t"<<"p_lrt"<<endl;
} else if (a_mode==3) {
outfile<<"beta"<<"\t"<<"se"<<"\t"<<"p_score"<<endl;
} else if (a_mode==4) {
outfile<<"beta"<<"\t"<<"se"<<"\t"<<"l_remle"<<"\t"<<"l_mle"<<"\t"<<"p_wald"<<"\t"<<"p_lrt"<<"\t"<<"p_score"<<endl;
} else {}
for (vector<SUMSTAT>::size_type t=0; t<sumStat.size(); ++t) {
outfile<<snpInfo[t].rs_number<<"\t";
if (a_mode==1) {
outfile<<scientific<<setprecision(6)<<sumStat[t].beta<<"\t"<<sumStat[t].se<<"\t"<<sumStat[t].lambda_remle<<"\t"<<sumStat[t].p_wald <<endl;
} else if (a_mode==2) {
outfile<<scientific<<setprecision(6)<<sumStat[t].lambda_mle<<"\t"<<sumStat[t].p_lrt<<endl;
} else if (a_mode==3) {
outfile<<scientific<<setprecision(6)<<sumStat[t].beta<<"\t"<<sumStat[t].se<<"\t"<<sumStat[t].p_score<<endl;
} else if (a_mode==4) {
outfile<<scientific<<setprecision(6)<<sumStat[t].beta<<"\t"<<sumStat[t].se<<"\t"<<sumStat[t].lambda_remle<<"\t"<<sumStat[t].lambda_mle<<"\t"<<sumStat[t].p_wald <<"\t"<<sumStat[t].p_lrt<<"\t"<<sumStat[t].p_score<<endl;
} else {}
}
} else {
outfile<<"chr"<<"\t"<<"rs"<<"\t"<<"ps"<<"\t"<<"n_miss"<<"\t"<<"allele1"<<"\t"<<"allele0"<<"\t"<<"af"<<"\t";
if (a_mode==1) {
outfile<<"beta"<<"\t"<<"se"<<"\t"<<"l_remle"<<"\t"<<"p_wald"<<endl;
} else if (a_mode==2) {
outfile<<"l_mle"<<"\t"<<"p_lrt"<<endl;
} else if (a_mode==3) {
outfile<<"beta"<<"\t"<<"se"<<"\t"<<"p_score"<<endl;
} else if (a_mode==4) {
outfile<<"beta"<<"\t"<<"se"<<"\t"<<"l_remle"<<"\t"<<"l_mle"<<"\t"<<"p_wald"<<"\t"<<"p_lrt"<<"\t"<<"p_score"<<endl;
} else {}
size_t t=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";
if (a_mode==1) {
outfile<<scientific<<setprecision(6)<<sumStat[t].beta<<"\t"<<sumStat[t].se<<"\t"<<sumStat[t].lambda_remle<<"\t"<<sumStat[t].p_wald <<endl;
} else if (a_mode==2) {
outfile<<scientific<<setprecision(6)<<sumStat[t].lambda_mle<<"\t"<<sumStat[t].p_lrt<<endl;
} else if (a_mode==3) {
outfile<<scientific<<setprecision(6)<<sumStat[t].beta<<"\t"<<sumStat[t].se<<"\t"<<sumStat[t].p_score<<endl;
} else if (a_mode==4) {
outfile<<scientific<<setprecision(6)<<sumStat[t].beta<<"\t"<<sumStat[t].se<<"\t"<<sumStat[t].lambda_remle<<"\t"<<sumStat[t].lambda_mle<<"\t"<<sumStat[t].p_wald <<"\t"<<sumStat[t].p_lrt<<"\t"<<sumStat[t].p_score<<endl;
} else {}
t++;
}
}
outfile.close();
outfile.clear();
return;
}
//map a number 1-(n_cvt+2) to an index between 0 and [(n_c+2)^2+(n_c+2)]/2-1
size_t GetabIndex (const size_t a, const size_t b, const size_t n_cvt) {
if (a>n_cvt+2 || b>n_cvt+2 || a<=0 || b<=0) {cout<<"error in GetabIndex."<<endl; return 0;}
size_t index;
size_t l, h;
if (b>a) {l=a; h=b;} else {l=b; h=a;}
size_t n=n_cvt+2;
index=(2*n-l+2)*(l-1)/2+h-l;
return index;
}
void CalcPab (const size_t n_cvt, const size_t e_mode, const gsl_vector *Hi_eval, const gsl_matrix *Uab, const gsl_vector *ab, gsl_matrix *Pab)
{
size_t index_ab, index_aw, index_bw, index_ww;
double p_ab;
double ps_ab, ps_aw, ps_bw, ps_ww;
for (size_t p=0; p<=n_cvt+1; ++p) {
for (size_t a=p+1; a<=n_cvt+2; ++a) {
for (size_t b=a; b<=n_cvt+2; ++b) {
index_ab=GetabIndex (a, b, n_cvt);
if (p==0) {
gsl_vector_const_view Uab_col=gsl_matrix_const_column (Uab, index_ab);
gsl_blas_ddot (Hi_eval, &Uab_col.vector, &p_ab);
if (e_mode!=0) {p_ab=gsl_vector_get (ab, index_ab)-p_ab;}
gsl_matrix_set (Pab, 0, index_ab, p_ab);
}
else {
index_aw=GetabIndex (a, p, n_cvt);
index_bw=GetabIndex (b, p, n_cvt);
index_ww=GetabIndex (p, p, n_cvt);
ps_ab=gsl_matrix_get (Pab, p-1, index_ab);
ps_aw=gsl_matrix_get (Pab, p-1, index_aw);
ps_bw=gsl_matrix_get (Pab, p-1, index_bw);
ps_ww=gsl_matrix_get (Pab, p-1, index_ww);
p_ab=ps_ab-ps_aw*ps_bw/ps_ww;
gsl_matrix_set (Pab, p, index_ab, p_ab);
}
}
}
}
return;
}
void CalcPPab (const size_t n_cvt, const size_t e_mode, const gsl_vector *HiHi_eval, const gsl_matrix *Uab, const gsl_vector *ab, const gsl_matrix *Pab, gsl_matrix *PPab)
{
size_t index_ab, index_aw, index_bw, index_ww;
double p2_ab;
double ps2_ab, ps_aw, ps_bw, ps_ww, ps2_aw, ps2_bw, ps2_ww;
for (size_t p=0; p<=n_cvt+1; ++p) {
for (size_t a=p+1; a<=n_cvt+2; ++a) {
for (size_t b=a; b<=n_cvt+2; ++b) {
index_ab=GetabIndex (a, b, n_cvt);
if (p==0) {
gsl_vector_const_view Uab_col=gsl_matrix_const_column (Uab, index_ab);
gsl_blas_ddot (HiHi_eval, &Uab_col.vector, &p2_ab);
if (e_mode!=0) {p2_ab=p2_ab-gsl_vector_get (ab, index_ab)+2.0*gsl_matrix_get (Pab, 0, index_ab);}
gsl_matrix_set (PPab, 0, index_ab, p2_ab);
}
else {
index_aw=GetabIndex (a, p, n_cvt);
index_bw=GetabIndex (b, p, n_cvt);
index_ww=GetabIndex (p, p, n_cvt);
ps2_ab=gsl_matrix_get (PPab, p-1, index_ab);
ps_aw=gsl_matrix_get (Pab, p-1, index_aw);
ps_bw=gsl_matrix_get (Pab, p-1, index_bw);
ps_ww=gsl_matrix_get (Pab, p-1, index_ww);
ps2_aw=gsl_matrix_get (PPab, p-1, index_aw);
ps2_bw=gsl_matrix_get (PPab, p-1, index_bw);
ps2_ww=gsl_matrix_get (PPab, p-1, index_ww);
p2_ab=ps2_ab+ps_aw*ps_bw*ps2_ww/(ps_ww*ps_ww);
p2_ab-=(ps_aw*ps2_bw+ps_bw*ps2_aw)/ps_ww;
gsl_matrix_set (PPab, p, index_ab, p2_ab);
}
}
}
}
return;
}
void CalcPPPab (const size_t n_cvt, const size_t e_mode, const gsl_vector *HiHiHi_eval, const gsl_matrix *Uab, const gsl_vector *ab, const gsl_matrix *Pab, const gsl_matrix *PPab, gsl_matrix *PPPab)
{
size_t index_ab, index_aw, index_bw, index_ww;
double p3_ab;
double ps3_ab, ps_aw, ps_bw, ps_ww, ps2_aw, ps2_bw, ps2_ww, ps3_aw, ps3_bw, ps3_ww;
for (size_t p=0; p<=n_cvt+1; ++p) {
for (size_t a=p+1; a<=n_cvt+2; ++a) {
for (size_t b=a; b<=n_cvt+2; ++b) {
index_ab=GetabIndex (a, b, n_cvt);
if (p==0) {
gsl_vector_const_view Uab_col=gsl_matrix_const_column (Uab, index_ab);
gsl_blas_ddot (HiHiHi_eval, &Uab_col.vector, &p3_ab);
if (e_mode!=0) {p3_ab=gsl_vector_get (ab, index_ab)-p3_ab+3.0*gsl_matrix_get (PPab, 0, index_ab)-3.0*gsl_matrix_get (Pab, 0, index_ab);}
gsl_matrix_set (PPPab, 0, index_ab, p3_ab);
}
else {
index_aw=GetabIndex (a, p, n_cvt);
index_bw=GetabIndex (b, p, n_cvt);
index_ww=GetabIndex (p, p, n_cvt);
ps3_ab=gsl_matrix_get (PPPab, p-1, index_ab);
ps_aw=gsl_matrix_get (Pab, p-1, index_aw);
ps_bw=gsl_matrix_get (Pab, p-1, index_bw);
ps_ww=gsl_matrix_get (Pab, p-1, index_ww);
ps2_aw=gsl_matrix_get (PPab, p-1, index_aw);
ps2_bw=gsl_matrix_get (PPab, p-1, index_bw);
ps2_ww=gsl_matrix_get (PPab, p-1, index_ww);
ps3_aw=gsl_matrix_get (PPPab, p-1, index_aw);
ps3_bw=gsl_matrix_get (PPPab, p-1, index_bw);
ps3_ww=gsl_matrix_get (PPPab, p-1, index_ww);
p3_ab=ps3_ab-ps_aw*ps_bw*ps2_ww*ps2_ww/(ps_ww*ps_ww*ps_ww);
p3_ab-=(ps_aw*ps3_bw+ps_bw*ps3_aw+ps2_aw*ps2_bw)/ps_ww;
p3_ab+=(ps_aw*ps2_bw*ps2_ww+ps_bw*ps2_aw*ps2_ww+ps_aw*ps_bw*ps3_ww)/(ps_ww*ps_ww);
gsl_matrix_set (PPPab, p, index_ab, p3_ab);
}
}
}
}
return;
}
double LogL_f (double l, void *params)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt;} else {nc_total=n_cvt+1;}
double f=0.0, logdet_h=0.0, d;
size_t index_yy;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
for (size_t i=0; i<(p->eval)->size; ++i) {
d=gsl_vector_get (v_temp, i);
logdet_h+=log(fabs(d));
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
double c=0.5*(double)ni_test*(log((double)ni_test)-log(2*M_PI)-1.0);
index_yy=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_yy);
f=c-0.5*logdet_h-0.5*(double)ni_test*log(P_yy);
gsl_matrix_free (Pab);
gsl_vector_free (Hi_eval);
gsl_vector_free (v_temp);
return f;
}
double LogL_dev1 (double l, void *params)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt;} else {nc_total=n_cvt+1;}
double dev1=0.0, trace_Hi=0.0;
size_t index_yy;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
gsl_vector_memcpy (HiHi_eval, Hi_eval);
gsl_vector_mul (HiHi_eval, Hi_eval);
gsl_vector_set_all (v_temp, 1.0);
gsl_blas_ddot (Hi_eval, v_temp, &trace_Hi);
if (p->e_mode!=0) {trace_Hi=(double)ni_test-trace_Hi;}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
CalcPPab (n_cvt, p->e_mode, HiHi_eval, p->Uab, p->ab, Pab, PPab);
double trace_HiK=((double)ni_test-trace_Hi)/l;
index_yy=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_yy);
double PP_yy=gsl_matrix_get (PPab, nc_total, index_yy);
double yPKPy=(P_yy-PP_yy)/l;
dev1=-0.5*trace_HiK+0.5*(double)ni_test*yPKPy/P_yy;
gsl_matrix_free (Pab);
gsl_matrix_free (PPab);
gsl_vector_free (Hi_eval);
gsl_vector_free (HiHi_eval);
gsl_vector_free (v_temp);
return dev1;
}
double LogL_dev2 (double l, void *params)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt;} else {nc_total=n_cvt+1;}
double dev2=0.0, trace_Hi=0.0, trace_HiHi=0.0;
size_t index_yy;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
gsl_vector_memcpy (HiHi_eval, Hi_eval);
gsl_vector_mul (HiHi_eval, Hi_eval);
gsl_vector_memcpy (HiHiHi_eval, HiHi_eval);
gsl_vector_mul (HiHiHi_eval, Hi_eval);
gsl_vector_set_all (v_temp, 1.0);
gsl_blas_ddot (Hi_eval, v_temp, &trace_Hi);
gsl_blas_ddot (HiHi_eval, v_temp, &trace_HiHi);
if (p->e_mode!=0) {
trace_Hi=(double)ni_test-trace_Hi;
trace_HiHi=2*trace_Hi+trace_HiHi-(double)ni_test;
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
CalcPPab (n_cvt, p->e_mode, HiHi_eval, p->Uab, p->ab, Pab, PPab);
CalcPPPab (n_cvt, p->e_mode, HiHiHi_eval, p->Uab, p->ab, Pab, PPab, PPPab);
double trace_HiKHiK=((double)ni_test+trace_HiHi-2*trace_Hi)/(l*l);
index_yy=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_yy);
double PP_yy=gsl_matrix_get (PPab, nc_total, index_yy);
double PPP_yy=gsl_matrix_get (PPPab, nc_total, index_yy);
double yPKPy=(P_yy-PP_yy)/l;
double yPKPKPy=(P_yy+PPP_yy-2.0*PP_yy)/(l*l);
dev2=0.5*trace_HiKHiK-0.5*(double)ni_test*(2.0*yPKPKPy*P_yy-yPKPy*yPKPy)/(P_yy*P_yy);
gsl_matrix_free (Pab);
gsl_matrix_free (PPab);
gsl_matrix_free (PPPab);
gsl_vector_free (Hi_eval);
gsl_vector_free (HiHi_eval);
gsl_vector_free (HiHiHi_eval);
gsl_vector_free (v_temp);
return dev2;
}
void LogL_dev12 (double l, void *params, double *dev1, double *dev2)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt;} else {nc_total=n_cvt+1;}
double trace_Hi=0.0, trace_HiHi=0.0;
size_t index_yy;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
gsl_vector_memcpy (HiHi_eval, Hi_eval);
gsl_vector_mul (HiHi_eval, Hi_eval);
gsl_vector_memcpy (HiHiHi_eval, HiHi_eval);
gsl_vector_mul (HiHiHi_eval, Hi_eval);
gsl_vector_set_all (v_temp, 1.0);
gsl_blas_ddot (Hi_eval, v_temp, &trace_Hi);
gsl_blas_ddot (HiHi_eval, v_temp, &trace_HiHi);
if (p->e_mode!=0) {
trace_Hi=(double)ni_test-trace_Hi;
trace_HiHi=2*trace_Hi+trace_HiHi-(double)ni_test;
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
CalcPPab (n_cvt, p->e_mode, HiHi_eval, p->Uab, p->ab, Pab, PPab);
CalcPPPab (n_cvt, p->e_mode, HiHiHi_eval, p->Uab, p->ab, Pab, PPab, PPPab);
double trace_HiK=((double)ni_test-trace_Hi)/l;
double trace_HiKHiK=((double)ni_test+trace_HiHi-2*trace_Hi)/(l*l);
index_yy=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_yy);
double PP_yy=gsl_matrix_get (PPab, nc_total, index_yy);
double PPP_yy=gsl_matrix_get (PPPab, nc_total, index_yy);
double yPKPy=(P_yy-PP_yy)/l;
double yPKPKPy=(P_yy+PPP_yy-2.0*PP_yy)/(l*l);
*dev1=-0.5*trace_HiK+0.5*(double)ni_test*yPKPy/P_yy;
*dev2=0.5*trace_HiKHiK-0.5*(double)ni_test*(2.0*yPKPKPy*P_yy-yPKPy*yPKPy)/(P_yy*P_yy);
gsl_matrix_free (Pab);
gsl_matrix_free (PPab);
gsl_matrix_free (PPPab);
gsl_vector_free (Hi_eval);
gsl_vector_free (HiHi_eval);
gsl_vector_free (HiHiHi_eval);
gsl_vector_free (v_temp);
return;
}
double LogRL_f (double l, void *params)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
double df;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt; df=(double)ni_test-(double)n_cvt; }
else {nc_total=n_cvt+1; df=(double)ni_test-(double)n_cvt-1.0;}
double f=0.0, logdet_h=0.0, logdet_hiw=0.0, d;
size_t index_ww;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *Iab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
for (size_t i=0; i<(p->eval)->size; ++i) {
d=gsl_vector_get (v_temp, i);
logdet_h+=log(fabs(d));
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
gsl_vector_set_all (v_temp, 1.0);
CalcPab (n_cvt, p->e_mode, v_temp, p->Uab, p->ab, Iab);
//calculate |WHiW|-|WW|
logdet_hiw=0.0;
for (size_t i=0; i<nc_total; ++i) {
index_ww=GetabIndex (i+1, i+1, n_cvt);
d=gsl_matrix_get (Pab, i, index_ww);
logdet_hiw+=log(d);
d=gsl_matrix_get (Iab, i, index_ww);
logdet_hiw-=log(d);
}
index_ww=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_ww);
double c=0.5*df*(log(df)-log(2*M_PI)-1.0);
f=c-0.5*logdet_h-0.5*logdet_hiw-0.5*df*log(P_yy);
gsl_matrix_free (Pab);
gsl_matrix_free (Iab);
gsl_vector_free (Hi_eval);
gsl_vector_free (v_temp);
return f;
}
double LogRL_dev1 (double l, void *params)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
double df;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt; df=(double)ni_test-(double)n_cvt; }
else {nc_total=n_cvt+1; df=(double)ni_test-(double)n_cvt-1.0;}
double dev1=0.0, trace_Hi=0.0;
size_t index_ww;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
gsl_vector_memcpy (HiHi_eval, Hi_eval);
gsl_vector_mul (HiHi_eval, Hi_eval);
gsl_vector_set_all (v_temp, 1.0);
gsl_blas_ddot (Hi_eval, v_temp, &trace_Hi);
if (p->e_mode!=0) {
trace_Hi=(double)ni_test-trace_Hi;
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
CalcPPab (n_cvt, p->e_mode, HiHi_eval, p->Uab, p->ab, Pab, PPab);
//calculate tracePK and trace PKPK
double trace_P=trace_Hi;
double ps_ww, ps2_ww;
for (size_t i=0; i<nc_total; ++i) {
index_ww=GetabIndex (i+1, i+1, n_cvt);
ps_ww=gsl_matrix_get (Pab, i, index_ww);
ps2_ww=gsl_matrix_get (PPab, i, index_ww);
trace_P-=ps2_ww/ps_ww;
}
double trace_PK=(df-trace_P)/l;
//calculate yPKPy, yPKPKPy
index_ww=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_ww);
double PP_yy=gsl_matrix_get (PPab, nc_total, index_ww);
double yPKPy=(P_yy-PP_yy)/l;
dev1=-0.5*trace_PK+0.5*df*yPKPy/P_yy;
gsl_matrix_free (Pab);
gsl_matrix_free (PPab);
gsl_vector_free (Hi_eval);
gsl_vector_free (HiHi_eval);
gsl_vector_free (v_temp);
return dev1;
}
double LogRL_dev2 (double l, void *params)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
double df;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt; df=(double)ni_test-(double)n_cvt; }
else {nc_total=n_cvt+1; df=(double)ni_test-(double)n_cvt-1.0;}
double dev2=0.0, trace_Hi=0.0, trace_HiHi=0.0;
size_t index_ww;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
gsl_vector_memcpy (HiHi_eval, Hi_eval);
gsl_vector_mul (HiHi_eval, Hi_eval);
gsl_vector_memcpy (HiHiHi_eval, HiHi_eval);
gsl_vector_mul (HiHiHi_eval, Hi_eval);
gsl_vector_set_all (v_temp, 1.0);
gsl_blas_ddot (Hi_eval, v_temp, &trace_Hi);
gsl_blas_ddot (HiHi_eval, v_temp, &trace_HiHi);
if (p->e_mode!=0) {
trace_Hi=(double)ni_test-trace_Hi;
trace_HiHi=2*trace_Hi+trace_HiHi-(double)ni_test;
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
CalcPPab (n_cvt, p->e_mode, HiHi_eval, p->Uab, p->ab, Pab, PPab);
CalcPPPab (n_cvt, p->e_mode, HiHiHi_eval, p->Uab, p->ab, Pab, PPab, PPPab);
//calculate tracePK and trace PKPK
double trace_P=trace_Hi, trace_PP=trace_HiHi;
double ps_ww, ps2_ww, ps3_ww;
for (size_t i=0; i<nc_total; ++i) {
index_ww=GetabIndex (i+1, i+1, n_cvt);
ps_ww=gsl_matrix_get (Pab, i, index_ww);
ps2_ww=gsl_matrix_get (PPab, i, index_ww);
ps3_ww=gsl_matrix_get (PPPab, i, index_ww);
trace_P-=ps2_ww/ps_ww;
trace_PP+=ps2_ww*ps2_ww/(ps_ww*ps_ww)-2.0*ps3_ww/ps_ww;
}
double trace_PKPK=(df+trace_PP-2.0*trace_P)/(l*l);
//calculate yPKPy, yPKPKPy
index_ww=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_ww);
double PP_yy=gsl_matrix_get (PPab, nc_total, index_ww);
double PPP_yy=gsl_matrix_get (PPPab, nc_total, index_ww);
double yPKPy=(P_yy-PP_yy)/l;
double yPKPKPy=(P_yy+PPP_yy-2.0*PP_yy)/(l*l);
dev2=0.5*trace_PKPK-0.5*df*(2.0*yPKPKPy*P_yy-yPKPy*yPKPy)/(P_yy*P_yy);
gsl_matrix_free (Pab);
gsl_matrix_free (PPab);
gsl_matrix_free (PPPab);
gsl_vector_free (Hi_eval);
gsl_vector_free (HiHi_eval);
gsl_vector_free (HiHiHi_eval);
gsl_vector_free (v_temp);
return dev2;
}
void LogRL_dev12 (double l, void *params, double *dev1, double *dev2)
{
FUNC_PARAM *p=(FUNC_PARAM *) params;
size_t n_cvt=p->n_cvt;
size_t ni_test=p->ni_test;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
double df;
size_t nc_total;
if (p->calc_null==true) {nc_total=n_cvt; df=(double)ni_test-(double)n_cvt; }
else {nc_total=n_cvt+1; df=(double)ni_test-(double)n_cvt-1.0;}
double trace_Hi=0.0, trace_HiHi=0.0;
size_t index_ww;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_matrix *PPPab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *HiHiHi_eval=gsl_vector_alloc((p->eval)->size);
gsl_vector *v_temp=gsl_vector_alloc((p->eval)->size);
gsl_vector_memcpy (v_temp, p->eval);
gsl_vector_scale (v_temp, l);
if (p->e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
gsl_vector_memcpy (HiHi_eval, Hi_eval);
gsl_vector_mul (HiHi_eval, Hi_eval);
gsl_vector_memcpy (HiHiHi_eval, HiHi_eval);
gsl_vector_mul (HiHiHi_eval, Hi_eval);
gsl_vector_set_all (v_temp, 1.0);
gsl_blas_ddot (Hi_eval, v_temp, &trace_Hi);
gsl_blas_ddot (HiHi_eval, v_temp, &trace_HiHi);
if (p->e_mode!=0) {
trace_Hi=(double)ni_test-trace_Hi;
trace_HiHi=2*trace_Hi+trace_HiHi-(double)ni_test;
}
CalcPab (n_cvt, p->e_mode, Hi_eval, p->Uab, p->ab, Pab);
CalcPPab (n_cvt, p->e_mode, HiHi_eval, p->Uab, p->ab, Pab, PPab);
CalcPPPab (n_cvt, p->e_mode, HiHiHi_eval, p->Uab, p->ab, Pab, PPab, PPPab);
//calculate tracePK and trace PKPK
double trace_P=trace_Hi, trace_PP=trace_HiHi;
double ps_ww, ps2_ww, ps3_ww;
for (size_t i=0; i<nc_total; ++i) {
index_ww=GetabIndex (i+1, i+1, n_cvt);
ps_ww=gsl_matrix_get (Pab, i, index_ww);
ps2_ww=gsl_matrix_get (PPab, i, index_ww);
ps3_ww=gsl_matrix_get (PPPab, i, index_ww);
trace_P-=ps2_ww/ps_ww;
trace_PP+=ps2_ww*ps2_ww/(ps_ww*ps_ww)-2.0*ps3_ww/ps_ww;
}
double trace_PK=(df-trace_P)/l;
double trace_PKPK=(df+trace_PP-2.0*trace_P)/(l*l);
//calculate yPKPy, yPKPKPy
index_ww=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
double P_yy=gsl_matrix_get (Pab, nc_total, index_ww);
double PP_yy=gsl_matrix_get (PPab, nc_total, index_ww);
double PPP_yy=gsl_matrix_get (PPPab, nc_total, index_ww);
double yPKPy=(P_yy-PP_yy)/l;
double yPKPKPy=(P_yy+PPP_yy-2.0*PP_yy)/(l*l);
*dev1=-0.5*trace_PK+0.5*df*yPKPy/P_yy;
*dev2=0.5*trace_PKPK-0.5*df*(2.0*yPKPKPy*P_yy-yPKPy*yPKPy)/(P_yy*P_yy);
gsl_matrix_free (Pab);
gsl_matrix_free (PPab);
gsl_matrix_free (PPPab);
gsl_vector_free (Hi_eval);
gsl_vector_free (HiHi_eval);
gsl_vector_free (HiHiHi_eval);
gsl_vector_free (v_temp);
return ;
}
void LMM::CalcRLWald (const double &l, const FUNC_PARAM ¶ms, double &beta, double &se, double &p_wald)
{
size_t n_cvt=params.n_cvt;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
int df=(int)ni_test-(int)n_cvt-1;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc(params.eval->size);
gsl_vector *v_temp=gsl_vector_alloc(params.eval->size);
gsl_vector_memcpy (v_temp, params.eval);
gsl_vector_scale (v_temp, l);
if (params.e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
CalcPab (n_cvt, params.e_mode, Hi_eval, params.Uab, params.ab, Pab);
size_t index_yy=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
size_t index_xx=GetabIndex (n_cvt+1, n_cvt+1, n_cvt);
size_t index_xy=GetabIndex (n_cvt+2, n_cvt+1, n_cvt);
double P_yy=gsl_matrix_get (Pab, n_cvt, index_yy);
double P_xx=gsl_matrix_get (Pab, n_cvt, index_xx);
double P_xy=gsl_matrix_get (Pab, n_cvt, index_xy);
double Px_yy=gsl_matrix_get (Pab, n_cvt+1, index_yy);
beta=P_xy/P_xx;
double tau=(double)df/Px_yy;
se=sqrt(1.0/(tau*P_xx));
p_wald=gsl_cdf_fdist_Q ((P_yy-Px_yy)*tau, 1.0, df);
// p_wald=gsl_cdf_chisq_Q ((P_yy-Px_yy)*tau, 1);
gsl_matrix_free (Pab);
gsl_vector_free (Hi_eval);
gsl_vector_free (v_temp);
return ;
}
void LMM::CalcRLScore (const double &l, const FUNC_PARAM ¶ms, double &beta, double &se, double &p_score)
{
size_t n_cvt=params.n_cvt;
size_t n_index=(n_cvt+2+1)*(n_cvt+2)/2;
int df=(int)ni_test-(int)n_cvt-1;
gsl_matrix *Pab=gsl_matrix_alloc (n_cvt+2, n_index);
gsl_vector *Hi_eval=gsl_vector_alloc(params.eval->size);
gsl_vector *v_temp=gsl_vector_alloc(params.eval->size);
gsl_vector_memcpy (v_temp, params.eval);
gsl_vector_scale (v_temp, l);
if (params.e_mode==0) {gsl_vector_set_all (Hi_eval, 1.0);} else {gsl_vector_memcpy (Hi_eval, v_temp);}
gsl_vector_add_constant (v_temp, 1.0);
gsl_vector_div (Hi_eval, v_temp);
CalcPab (n_cvt, params.e_mode, Hi_eval, params.Uab, params.ab, Pab);
size_t index_yy=GetabIndex (n_cvt+2, n_cvt+2, n_cvt);
size_t index_xx=GetabIndex (n_cvt+1, n_cvt+1, n_cvt);
size_t index_xy=GetabIndex (n_cvt+2, n_cvt+1, n_cvt);
double P_yy=gsl_matrix_get (Pab, n_cvt, index_yy);
double P_xx=gsl_matrix_get (Pab, n_cvt, index_xx);
double P_xy=gsl_matrix_get (Pab, n_cvt, index_xy);
double Px_yy=gsl_matrix_get (Pab, n_cvt+1, index_yy);
beta=P_xy/P_xx;
double tau=(double)df/Px_yy;
se=sqrt(1.0/(tau*P_xx));
p_score=gsl_cdf_fdist_Q ((double)ni_test*P_xy*P_xy/(P_yy*P_xx), 1.0, df);
// p_score=gsl_cdf_chisq_Q ((double)ni_test*P_xy*P_xy/(P_yy*P_xx), 1);
gsl_matrix_free (Pab);
gsl_vector_free (Hi_eval);
gsl_vector_free (v_temp);
return ;
}
void CalcUab (const gsl_matrix *UtW, const gsl_vector *Uty, gsl_matrix *Uab)
{
size_t index_ab;
size_t n_cvt=UtW->size2;
gsl_vector *u_a=gsl_vector_alloc (Uty->size);
for (size_t a=1; a<=n_cvt+2; ++a) {
if (a==n_cvt+1) {continue;}
if (a==n_cvt+2) {gsl_vector_memcpy (u_a, Uty);}
else {
gsl_vector_const_view UtW_col=gsl_matrix_const_column (UtW, a-1);
gsl_vector_memcpy (u_a, &UtW_col.vector);
}
for (size_t b=a; b>=1; --b) {
if (b==n_cvt+1) {continue;}
index_ab=GetabIndex (a, b, n_cvt);
gsl_vector_view Uab_col=gsl_matrix_column (Uab, index_ab);
if (b==n_cvt+2) {gsl_vector_memcpy (&Uab_col.vector, Uty);}
else {
gsl_vector_const_view UtW_col=gsl_matrix_const_column (UtW, b-1);
gsl_vector_memcpy (&Uab_col.vector, &UtW_col.vector);
}
gsl_vector_mul(&Uab_col.vector, u_a);
}
}
gsl_vector_free (u_a);