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Band_DFT_NonCol_GB.c
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Band_DFT_NonCol_GB.c
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/**********************************************************************
Band_DFT_NonCol_GB.c:
Band_DFT_NonCol_GB.c is a subroutine to perform band calculations based on a non-collinear DFT by including generalized Bloch theorem. This subroutine is a modified version of Band_DFT_NonCol.c released previously by Prof. T. Ozaki
Log of Band_DFT_NonCol_GB.c:
Modified by T. B. Prayitno (supervised by Prof. F. Ishii)
***********************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include "openmx_common.h"
#include "mpi.h"
#include <omp.h>
#define measure_time 0
double Band_DFT_NonCol_GB(int SCF_iter,
double *koSU,
double *koSL,
dcomplex **SU,
dcomplex **SL,
int knum_i, int knum_j, int knum_k,
int SpinP_switch,
double *****nh,
double *****ImNL,
double ****CntOLP,
double *****CDM,
double *****EDM,
double Eele0[2], double Eele1[2])
{
static int firsttime=1;
int i,j,k,l,n,n2,wan;
int ii1,m,mn,lmn,lmax;
int i1,j1,jj1,jj2,po,spin,n1;
int ia,ib,ja,jb;
int num2,RnB,l1,l2,l3,loop_num;
int ct_AN,h_AN,wanA,tnoA,wanB,tnoB;
int MA_AN,GA_AN,Anum;
double time0,sum_weights;
double Imdum2,Imsum,ImsumE;
int LB_AN,GB_AN,Bnum;
double EV_cut0;
double snum_i,snum_j,snum_k,k1,k2,k3,sum,sumi,Num_State,FermiF;
double sum_r0,sum_i0;
double sum_r1,sum_i1;
double sum_r00,sum_i00;
double sum_r01,sum_i01;
double sum_r10,sum_i10;
double sum_r11,sum_i11;
double av_num;
double x,Dnum,Dnum2,AcP,ChemP_MAX,ChemP_MIN;
double **EIGEN;
double d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d12,d13,d14,d15,d16;
double *VecFkw;
double *VecFkwE;
dcomplex **H,**C;
dcomplex Ctmp1,Ctmp2;
int ***k_op,*T_k_op,*T_k_ID;
int ii,ij,ik;
int S_knum,E_knum,T_knum,e1,s1,kloop,kloop0,num_kloop0;
double *KGrids1,*KGrids2,*KGrids3;
double *T_KGrids1,*T_KGrids2,*T_KGrids3;
double u2,v2,uv,vu,tmp,tmp1;
double My_Eele1[2];
double kw,eig,Fkw;
double TZ,dum,sumE,kRn,qRn,si1,co1,si2,co2;
double Resum,ResumE,Redum,Redum2,Imdum;
double ResumA,ResumEA,RedumA,Redum2A,ImdumA;
double ResumB,RedumB,Redum2B,ImdumB;
double ResumC,RedumC,Redum2C,ImdumC;
double RedumD,ImdumD;
double Imdum2D,ImsumED;
double u2A,v2A,uvA,vuA;
double u2B,v2B,uvB,vuB;
double u2C,v2C,uvC,vuC;
double TStime,TEtime,SiloopTime,EiloopTime;
double Stime,Etime;
double FermiEps=1.0e-14;
double x_cut=30.0;
char file_EV[YOUSO10];
FILE *fp_EV;
char buf[fp_bsize]; /* setvbuf */
int *MP;
int *order_GA;
double *ko;
double *koU;
double *koL;
double *S1;
double *RH0;
double *RH1;
double *RH2;
double *RH3;
double *IH0;
double *IH1;
double *IH2;
double *CDM0;
double *CDM1;
double *CDM2;
double *CDM3;
double *EDM0;
double *EDM1;
double *EDM2;
double *EDM3;
double *iDM0;
double *iDM1;
int *is1,*ie1;
int *is12,*ie12;
int *is2,*ie2;
MPI_Status *stat_send;
MPI_Request *request_send;
MPI_Request *request_recv;
int *My_NZeros;
int *SP_NZeros;
int *SP_Atoms;
MPI_Comm *MPI_CommWD_CDM1;
int *MPI_CDM1_flag;
double lumos;
int Rn,AN;
int size_H1;
int all_knum;
int MaxN,ks,i0;
int ID,ID0,ID1;
int numprocs0,myid0;
int numprocs1,myid1;
int myworld1;
int parallel_mode;
int Num_Comm_World1;
int *NPROCS_ID1;
int *NPROCS_WD1;
int *Comm_World1;
int *Comm_World_StartID1;
MPI_Comm *MPI_CommWD1;
double time1,time2,time3;
double time4,time5,time6;
double time7,time8,time9;
double time10,time11,time12;
double time13,time14,time15;
double time16,time17,time18;
/* for OpenMP */
int OMPID,Nthrds,Nprocs;
/* MPI */
MPI_Comm_size(mpi_comm_level1,&numprocs0);
MPI_Comm_rank(mpi_comm_level1,&myid0);
dtime(&TStime);
if (myid0==Host_ID){
printf ("Generalized Bloch Theorem is included with q1 = %lf, q2 = %lf, q3 = %lf",q1_GB,q2_GB,q3_GB);
printf("\n");
}
time1 = 0.0;
time2 = 0.0;
time3 = 0.0;
time4 = 0.0;
time5 = 0.0;
time6 = 0.0;
time7 = 0.0;
time8 = 0.0;
time9 = 0.0;
time10 = 0.0;
time11 = 0.0;
time12 = 0.0;
time13 = 0.0;
time14 = 0.0;
time15 = 0.0;
time16 = 0.0;
time17 = 0.0;
time18 = 0.0;
/****************************************************
calculation of the array size
****************************************************/
n = 0;
for (i=1; i<=atomnum; i++){
wanA = WhatSpecies[i];
n += Spe_Total_CNO[wanA];
}
n2 = 2*n + 2;
/****************************************************
find TZ
****************************************************/
TZ = 0.0;
for (i=1; i<=atomnum; i++){
wan = WhatSpecies[i];
TZ += Spe_Core_Charge[wan];
}
/***********************************************
find the number of states to be solved
***********************************************/
lumos = (double)(TZ-system_charge)*0.200;
if (lumos<60.0) lumos = 200.0;
MaxN = (TZ-system_charge) + (int)lumos;
if (n2<MaxN) MaxN = n2;
/****************************************************
Allocation
int MP[List_YOUSO[1]]
double ko[n2]
double koS[n+1];
dcomplex H[n2][n2]
dcomplex S[n2][n2]
double M1[n2]
dcomplex C[n2][n2]
double EIGEN[T_knum]
[n2]
double KGrids1[knum_i]
double KGrids2[knum_j]
double KGrids3[knum_k]
int k_op[knum_i][knum_j][knum_k]
****************************************************/
VecFkw = (double*)malloc(sizeof(double)*n2);
VecFkwE = (double*)malloc(sizeof(double)*n2);
H = (dcomplex**)malloc(sizeof(dcomplex*)*n2);
for (j=0; j<n2; j++){
H[j] = (dcomplex*)malloc(sizeof(dcomplex)*n2);
}
C = (dcomplex**)malloc(sizeof(dcomplex*)*n2);
for (j=0; j<n2; j++){
C[j] = (dcomplex*)malloc(sizeof(dcomplex)*n2);
}
KGrids1 = (double*)malloc(sizeof(double)*knum_i);
KGrids2 = (double*)malloc(sizeof(double)*knum_j);
KGrids3 = (double*)malloc(sizeof(double)*knum_k);
k_op=(int***)malloc(sizeof(int**)*knum_i);
for (i=0;i<knum_i; i++) {
k_op[i]=(int**)malloc(sizeof(int*)*knum_j);
for (j=0;j<knum_j; j++) {
k_op[i][j]=(int*)malloc(sizeof(int)*knum_k);
}
}
/* k_op[0:knum_i-1][0:knum_j-1][0:knum_k-1] */
MP = (int*)malloc(sizeof(int)*List_YOUSO[1]);
order_GA = (int*)malloc(sizeof(int)*(List_YOUSO[1]+1));
My_NZeros = (int*)malloc(sizeof(int)*numprocs0);
SP_NZeros = (int*)malloc(sizeof(int)*numprocs0);
SP_Atoms = (int*)malloc(sizeof(int)*numprocs0);
MPI_CommWD_CDM1 = (MPI_Comm*)malloc(sizeof(MPI_Comm)*numprocs0);
MPI_CDM1_flag = (int*)malloc(sizeof(int)*numprocs0);
for (i=0; i<numprocs0; i++) MPI_CDM1_flag[i] = 0;
ko = (double*)malloc(sizeof(double)*n2);
koU = (double*)malloc(sizeof(double)*n2);
koL = (double*)malloc(sizeof(double)*n2);
/****************************************************
PrintMemory
****************************************************/
if (firsttime){
PrintMemory("Band_DFT: ko",sizeof(double)*n2,NULL);
PrintMemory("Band_DFT: koU",sizeof(double)*n2,NULL);
PrintMemory("Band_DFT: koL",sizeof(double)*n2,NULL);
PrintMemory("Band_DFT: H",sizeof(dcomplex)*n2*n2,NULL);
PrintMemory("Band_DFT: SU",sizeof(dcomplex)*n2*n2,NULL);
PrintMemory("Band_DFT: SL",sizeof(dcomplex)*n2*n2,NULL);
PrintMemory("Band_DFT: C",sizeof(dcomplex)*n2*n2,NULL);
PrintMemory("Band_DFT: M1",sizeof(double)*n2,NULL);
PrintMemory("Band_DFT: EIGEN",
sizeof(double)*List_YOUSO[27]*
List_YOUSO[28]*
List_YOUSO[29]*n2,NULL);
PrintMemory("Band_DFT: ko_op",
sizeof(int)*knum_i*knum_j*knum_k,NULL);
}
/* for PrintMemory */
firsttime=0;
/***********************************************
k-points by regular mesh
***********************************************/
if (way_of_kpoint==1){
snum_i = (double)knum_i;
snum_j = (double)knum_j;
snum_k = (double)knum_k;
for (i=0; i<knum_i; i++){
if (knum_i==1){
k1 = 0.0;
}
else {
k1 = -0.5 + (2.0*(double)i+1.0)/(2.0*snum_i) + Shift_K_Point;
}
KGrids1[i]=k1;
}
for (i=0; i<knum_j; i++){
if (knum_j==1){
k1 = 0.0;
}
else {
k1 = -0.5 + (2.0*(double)i+1.0)/(2.0*snum_j) - Shift_K_Point;
}
KGrids2[i] = k1;
}
for (i=0; i<knum_k; i++){
if (knum_k==1){
k1 = 0.0;
}
else {
k1 = -0.5 + (2.0*(double)i+1.0)/(2.0*snum_k) + 2.0*Shift_K_Point;
}
KGrids3[i]=k1;
}
if (myid0==Host_ID && 0<level_stdout){
printf(" KGrids1: ");
for (i=0;i<=knum_i-1;i++) printf("%9.5f ",KGrids1[i]);
printf("\n");
printf(" KGrids2: ");
for (i=0;i<=knum_j-1;i++) printf("%9.5f ",KGrids2[i]);
printf("\n");
printf(" KGrids3: ");
for (i=0;i<=knum_k-1;i++) printf("%9.5f ",KGrids3[i]);
printf("\n");
}
/**************************************************************
k_op[i][j][k]: weight of DOS
=0 no calc.
=1 G-point
note that there is no simple inversion symmetry for
the wave functions in noncollinear case
=1 other
*************************************************************/
for (i=0; i<knum_i; i++) {
for (j=0; j<knum_j; j++) {
for (k=0; k<knum_k; k++) {
k_op[i][j][k]=-999;
}
}
}
for (i=0;i<=knum_i-1;i++) {
for (j=0;j<=knum_j-1;j++) {
for (k=0;k<=knum_k-1;k++) {
if ( k_op[i][j][k]==-999 ) {
k_inversion(i,j,k,knum_i,knum_j,knum_k,&ii,&ij,&ik);
if ( i==ii && j==ij && k==ik ) {
/*
printf("* : %d %d %d (%f %f %f)\n",i,j,k,
KGrids1[i], KGrids2[j], KGrids3[k]);
*/
k_op[i][j][k] = 1;
}
else {
/* note that there is no simple inversion symmetry for
the wave functions in noncollinear case */
k_op[i][j][k] = 1;
k_op[ii][ij][ik] = 1;
}
}
} /* k */
} /* j */
} /* i */
/***********************************
one-dimentionalize for MPI
************************************/
T_knum = 0;
for (i=0; i<knum_i; i++){
for (j=0; j<knum_j; j++){
for (k=0; k<knum_k; k++){
if (0<k_op[i][j][k]){
T_knum++;
}
}
}
}
/* allocation of arrays */
T_KGrids1 = (double*)malloc(sizeof(double)*T_knum);
T_KGrids2 = (double*)malloc(sizeof(double)*T_knum);
T_KGrids3 = (double*)malloc(sizeof(double)*T_knum);
T_k_op = (int*)malloc(sizeof(int)*T_knum);
T_k_ID = (int*)malloc(sizeof(int)*T_knum);
EIGEN = (double**)malloc(sizeof(double*)*T_knum);
for (j=0; j<T_knum; j++){
EIGEN[j] = (double*)malloc(sizeof(double)*n2);
for (i=0; i<n2; i++) EIGEN[j][i] = 1.0e+5;
}
/* set T_KGrid1,2,3 and T_k_op */
T_knum = 0;
for (i=0; i<=(knum_i-1); i++){
for (j=0; j<=(knum_j-1); j++){
for (k=0; k<=(knum_k-1); k++){
if (0<k_op[i][j][k]){
T_KGrids1[T_knum] = KGrids1[i];
T_KGrids2[T_knum] = KGrids2[j];
T_KGrids3[T_knum] = KGrids3[k];
T_k_op[T_knum] = k_op[i][j][k];
T_knum++;
}
}
}
}
}
/***********************************************
Monkhorst-Pack k-points
***********************************************/
else if (way_of_kpoint==2){
T_knum = num_non_eq_kpt;
T_KGrids1 = (double*)malloc(sizeof(double)*T_knum);
T_KGrids2 = (double*)malloc(sizeof(double)*T_knum);
T_KGrids3 = (double*)malloc(sizeof(double)*T_knum);
T_k_op = (int*)malloc(sizeof(int)*T_knum);
T_k_ID = (int*)malloc(sizeof(int)*T_knum);
EIGEN = (double**)malloc(sizeof(double*)*T_knum);
for (j=0; j<T_knum; j++){
EIGEN[j] = (double*)malloc(sizeof(double)*n2);
for (i=0; i<n2; i++) EIGEN[j][i] = 1.0e+5;
}
for (k=0; k<T_knum; k++){
T_KGrids1[k] = NE_KGrids1[k];
T_KGrids2[k] = NE_KGrids2[k];
T_KGrids3[k] = NE_KGrids3[k];
T_k_op[k] = NE_T_k_op[k];
}
}
/***********************************************
calculate the sum of weights
***********************************************/
sum_weights = 0.0;
for (k=0; k<T_knum; k++){
sum_weights += (double)T_k_op[k];
}
/***********************************************
allocate k-points into processors
***********************************************/
if (numprocs0<T_knum){
/* set parallel_mode */
parallel_mode = 0;
/* allocation of kloop to ID */
for (ID=0; ID<numprocs0; ID++){
tmp = (double)T_knum/(double)numprocs0;
S_knum = (int)((double)ID*(tmp+1.0e-12));
E_knum = (int)((double)(ID+1)*(tmp+1.0e-12)) - 1;
if (ID==(numprocs0-1)) E_knum = T_knum - 1;
if (E_knum<0) E_knum = 0;
for (k=S_knum; k<=E_knum; k++){
/* ID in the zeroth level world */
T_k_ID[k] = ID;
}
}
/* find own informations */
tmp = (double)T_knum/(double)numprocs0;
S_knum = (int)((double)myid0*(tmp+1.0e-12));
E_knum = (int)((double)(myid0+1)*(tmp+1.0e-12)) - 1;
if (myid0==(numprocs0-1)) E_knum = T_knum - 1;
if (E_knum<0) E_knum = 0;
num_kloop0 = E_knum - S_knum + 1;
}
else {
/* set parallel_mode */
parallel_mode = 1;
num_kloop0 = 1;
Num_Comm_World1 = T_knum;
NPROCS_ID1 = (int*)malloc(sizeof(int)*numprocs0);
Comm_World1 = (int*)malloc(sizeof(int)*numprocs0);
NPROCS_WD1 = (int*)malloc(sizeof(int)*Num_Comm_World1);
Comm_World_StartID1 = (int*)malloc(sizeof(int)*Num_Comm_World1);
MPI_CommWD1 = (MPI_Comm*)malloc(sizeof(MPI_Comm)*Num_Comm_World1);
Make_Comm_Worlds(mpi_comm_level1, myid0, numprocs0, Num_Comm_World1, &myworld1, MPI_CommWD1,
NPROCS_ID1, Comm_World1, NPROCS_WD1, Comm_World_StartID1);
MPI_Comm_size(MPI_CommWD1[myworld1],&numprocs1);
MPI_Comm_rank(MPI_CommWD1[myworld1],&myid1);
S_knum = myworld1;
/* allocate k-points into processors */
for (k=0; k<T_knum; k++){
/* ID in the first level world */
T_k_ID[k] = Comm_World_StartID1[k];
}
}
/****************************************************
find all_knum
if (all_knum==1), all the calculation will be made
by the first diagonalization loop, and the second
diagonalization will be skipped.
****************************************************/
MPI_Allreduce(&num_kloop0, &all_knum, 1, MPI_INT, MPI_PROD, mpi_comm_level1);
if (all_knum==1){
/* allocation */
stat_send = malloc(sizeof(MPI_Status)*numprocs1);
request_send = malloc(sizeof(MPI_Request)*numprocs1);
request_recv = malloc(sizeof(MPI_Request)*numprocs1);
is1 = (int*)malloc(sizeof(int)*numprocs1);
ie1 = (int*)malloc(sizeof(int)*numprocs1);
is12 = (int*)malloc(sizeof(int)*numprocs1);
ie12 = (int*)malloc(sizeof(int)*numprocs1);
is2 = (int*)malloc(sizeof(int)*numprocs1);
ie2 = (int*)malloc(sizeof(int)*numprocs1);
/* make is1 and ie1, is12 and ie12 */
if ( numprocs1<=n ){
av_num = (double)n/(double)numprocs1;
for (ID=0; ID<numprocs1; ID++){
is1[ID] = (int)(av_num*(double)ID) + 1;
ie1[ID] = (int)(av_num*(double)(ID+1));
}
is1[0] = 1;
ie1[numprocs1-1] = n;
}
else{
for (ID=0; ID<n; ID++){
is1[ID] = ID + 1;
ie1[ID] = ID + 1;
}
for (ID=n; ID<numprocs1; ID++){
is1[ID] = 1;
ie1[ID] = -2;
}
}
for (ID=0; ID<numprocs1; ID++){
is12[ID] = 2*is1[ID] - 1;
ie12[ID] = 2*ie1[ID];
}
/* make is2 and ie2 */
if ( numprocs1<=MaxN ){
av_num = (double)MaxN/(double)numprocs1;
for (ID=0; ID<numprocs1; ID++){
is2[ID] = (int)(av_num*(double)ID) + 1;
ie2[ID] = (int)(av_num*(double)(ID+1));
}
is2[0] = 1;
ie2[numprocs1-1] = MaxN;
}
else{
for (ID=0; ID<MaxN; ID++){
is2[ID] = ID + 1;
ie2[ID] = ID + 1;
}
for (ID=MaxN; ID<numprocs1; ID++){
is2[ID] = 1;
ie2[ID] = -2;
}
}
/**********************************************
for MPI communication of CDM1 and EDM1
**********************************************/
{
MPI_Group new_group,old_group;
int *new_ranks;
new_ranks = (int*)malloc(sizeof(int)*T_knum);
/* ID: zeroth world */
for (ID=0; ID<numprocs0; ID++){
for (i=0; i<T_knum; i++){
if (Comm_World_StartID1[i]<=ID){
ks = i;
}
}
new_ranks[0] = ID;
if (myid0==ID) MPI_CDM1_flag[ID] = 1;
for (i=(ks+1); i<(T_knum+ks); i++){
i0 = i % T_knum;
/* id in the zeroth world */
ID0 = Comm_World_StartID1[i0] + (ID % NPROCS_WD1[i0]);
new_ranks[i-ks] = ID0;
if (myid0==ID0) MPI_CDM1_flag[ID] = 1;
}
MPI_Comm_group(mpi_comm_level1, &old_group);
/* define a new group */
MPI_Group_incl(old_group,T_knum,new_ranks,&new_group);
MPI_Comm_create(mpi_comm_level1, new_group, &MPI_CommWD_CDM1[ID]);
MPI_Group_free(&new_group);
}
free(new_ranks); /* never forget cleaning! */
}
} /* if (all_knum==1) */
/****************************************************
store in each processor all the matrix elements
for overlap and Hamiltonian matrices
****************************************************/
dtime(&Stime);
/* get size_H1 */
size_H1 = Get_OneD_HS_Col(0, CntOLP, &tmp, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
S1 = (double*)malloc(sizeof(double)*size_H1);
RH0 = (double*)malloc(sizeof(double)*size_H1);
RH1 = (double*)malloc(sizeof(double)*size_H1);
RH2 = (double*)malloc(sizeof(double)*size_H1);
RH3 = (double*)malloc(sizeof(double)*size_H1);
IH0 = (double*)malloc(sizeof(double)*size_H1);
IH1 = (double*)malloc(sizeof(double)*size_H1);
IH2 = (double*)malloc(sizeof(double)*size_H1);
/* set S1, RH0, RH1, RH2, RH3, IH0, IH1, IH2 */
size_H1 = Get_OneD_HS_Col(1, CntOLP, S1, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
size_H1 = Get_OneD_HS_Col(1, nh[0], RH0, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
size_H1 = Get_OneD_HS_Col(1, nh[1], RH1, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
size_H1 = Get_OneD_HS_Col(1, nh[2], RH2, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
size_H1 = Get_OneD_HS_Col(1, nh[3], RH3, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
if (SO_switch==0 && Hub_U_switch==0 && Constraint_NCS_switch==0
&& Zeeman_NCS_switch==0 && Zeeman_NCO_switch==0){
/* nothing is done. */
}
else {
size_H1 = Get_OneD_HS_Col(1, ImNL[0], IH0, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
size_H1 = Get_OneD_HS_Col(1, ImNL[1], IH1, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
size_H1 = Get_OneD_HS_Col(1, ImNL[2], IH2, MP, order_GA, My_NZeros, SP_NZeros, SP_Atoms);
}
/* allocate
CDM0, CDM1, CDM2, CDM3
EDM0, EDM1, EDM2, EDM3
iDM0, iDM1
*/
CDM0 = (double*)malloc(sizeof(double)*size_H1);
CDM1 = (double*)malloc(sizeof(double)*size_H1);
CDM2 = (double*)malloc(sizeof(double)*size_H1);
CDM3 = (double*)malloc(sizeof(double)*size_H1);
EDM0 = (double*)malloc(sizeof(double)*size_H1);
EDM1 = (double*)malloc(sizeof(double)*size_H1);
EDM2 = (double*)malloc(sizeof(double)*size_H1);
EDM3 = (double*)malloc(sizeof(double)*size_H1);
iDM0 = (double*)malloc(sizeof(double)*size_H1);
iDM1 = (double*)malloc(sizeof(double)*size_H1);
dtime(&Etime);
time1 += Etime - Stime;
/****************************************************
start kloop
****************************************************/
dtime(&SiloopTime);
for (kloop0=0; kloop0<num_kloop0; kloop0++){
dtime(&Stime);
kloop = S_knum + kloop0;
k1 = T_KGrids1[kloop];
k2 = T_KGrids2[kloop];
k3 = T_KGrids3[kloop];
/* make S and H */
if (SCF_iter==1 || rediagonalize_flag_overlap_matrix==1 || all_knum!=1){
for (i=1; i<=n; i++){
for (j=1; j<=n; j++){
SU[i][j] = Complex(0.0,0.0);
SL[i][j] = Complex(0.0,0.0);
}
}
}
for (i=1; i<=2*n; i++){
for (j=1; j<=2*n; j++){
H[i][j] = Complex(0.0,0.0);
}
}
/* non-spin-orbit coupling and non-LDA+U */
if (SO_switch==0 && Hub_U_switch==0 && Constraint_NCS_switch==0
&& Zeeman_NCS_switch==0 && Zeeman_NCO_switch==0){
k = 0;
for (AN=1; AN<=atomnum; AN++){
GA_AN = order_GA[AN];
wanA = WhatSpecies[GA_AN];
tnoA = Spe_Total_CNO[wanA];
Anum = MP[GA_AN];
for (LB_AN=0; LB_AN<=FNAN[GA_AN]; LB_AN++){
GB_AN = natn[GA_AN][LB_AN];
Rn = ncn[GA_AN][LB_AN];
wanB = WhatSpecies[GB_AN];
tnoB = Spe_Total_CNO[wanB];
Bnum = MP[GB_AN];
l1 = atv_ijk[Rn][1];
l2 = atv_ijk[Rn][2];
l3 = atv_ijk[Rn][3];
kRn = k1*(double)l1 + k2*(double)l2 + k3*(double)l3;
qRn = q1_GB*(double)l1 + q2_GB*(double)l2 + q3_GB*(double)l3;
si1 = sin(2.0*PI*(kRn-0.5*qRn));
co1 = cos(2.0*PI*(kRn-0.5*qRn));
si2 = sin(2.0*PI*(kRn+0.5*qRn));
co2 = cos(2.0*PI*(kRn+0.5*qRn));
for (i=0; i<tnoA; i++){
for (j=0; j<tnoB; j++){
H[Anum+i ][Bnum+j ].r += co1*RH0[k];
H[Anum+i ][Bnum+j ].i += si1*RH0[k];
H[Anum+i+n][Bnum+j+n].r += co2*RH1[k];
H[Anum+i+n][Bnum+j+n].i += si2*RH1[k];
H[Anum+i ][Bnum+j+n].r += co1*RH2[k] - si1*RH3[k];
H[Anum+i ][Bnum+j+n].i += si1*RH2[k] + co1*RH3[k];
k++;
}
if (SCF_iter==1 || rediagonalize_flag_overlap_matrix==1 || all_knum!=1){
k -= tnoB;
for (j=0; j<tnoB; j++){
SU[Anum+i ][Bnum+j ].r += co1*S1[k];
SU[Anum+i ][Bnum+j ].i += si1*S1[k];
SL[Anum+i ][Bnum+j ].r += co2*S1[k];
SL[Anum+i ][Bnum+j ].i += si2*S1[k];
k++;
}
}
}
}
}
}
/* spin-orbit coupling or LDA+U */
else {
k = 0;
for (AN=1; AN<=atomnum; AN++){
GA_AN = order_GA[AN];
wanA = WhatSpecies[GA_AN];
tnoA = Spe_Total_CNO[wanA];
Anum = MP[GA_AN];
for (LB_AN=0; LB_AN<=FNAN[GA_AN]; LB_AN++){
GB_AN = natn[GA_AN][LB_AN];
Rn = ncn[GA_AN][LB_AN];
wanB = WhatSpecies[GB_AN];
tnoB = Spe_Total_CNO[wanB];
Bnum = MP[GB_AN];
l1 = atv_ijk[Rn][1];
l2 = atv_ijk[Rn][2];
l3 = atv_ijk[Rn][3];
kRn = k1*(double)l1 + k2*(double)l2 + k3*(double)l3;
qRn = q1_GB*(double)l1 + q2_GB*(double)l2 + q3_GB*(double)l3;
si1 = sin(2.0*PI*(kRn-0.5*qRn));
co1 = cos(2.0*PI*(kRn-0.5*qRn));
si2 = sin(2.0*PI*(kRn+0.5*qRn));
co2 = cos(2.0*PI*(kRn+0.5*qRn));
for (i=0; i<tnoA; i++){
for (j=0; j<tnoB; j++){
H[Anum+i ][Bnum+j ].r += co1*RH0[k] - si1*IH0[k];
H[Anum+i ][Bnum+j ].i += si1*RH0[k] + co1*IH0[k];
H[Anum+i+n][Bnum+j+n].r += co2*RH1[k] - si2*IH1[k];
H[Anum+i+n][Bnum+j+n].i += si2*RH1[k] + co2*IH1[k];
H[Anum+i ][Bnum+j+n].r += co1*RH2[k] - si1*(RH3[k]+IH2[k]);
H[Anum+i ][Bnum+j+n].i += si1*RH2[k] + co1*(RH3[k]+IH2[k]);
k++;
}
if (SCF_iter==1 || rediagonalize_flag_overlap_matrix==1 || all_knum!=1){
k -= tnoB;
for (j=0; j<tnoB; j++){
SU[Anum+i ][Bnum+j ].r += co1*S1[k];
SU[Anum+i ][Bnum+j ].i += si1*S1[k];
SL[Anum+i ][Bnum+j ].r += co2*S1[k];
SL[Anum+i ][Bnum+j ].i += si2*S1[k];
k++;
}
}
}
}
}
}
/* set off-diagonal part */
for (i=1; i<=n; i++){
for (j=1; j<=n; j++){
H[j+n][i].r = H[i][j+n].r;
H[j+n][i].i =-H[i][j+n].i;
}
}
/*
if (myid0==0){
for (i=1; i<=n; i++){
for (j=1; j<=n; j++){
printf("i=%2d j=%2d SU.r=%18.15f SU.i=%18.15f\n",i,j,SU[i][j].r,SU[i][j].i);
printf("i=%2d j=%2d SL.r=%18.15f SL.i=%18.15f\n",i,j,SL[i][j].r,SL[i][j].i);
}
}
for (i=1; i<=2*n; i++){
for (j=1; j<=2*n; j++){
printf("i=%2d j=%2d H.r=%18.15f H.i=%18.15f\n",i,j,H[i][j].r,H[i][j].i);
}
}
}
MPI_Finalize();
exit(0);
*/
dtime(&Etime);
time2 += Etime - Stime;
/* diagonalize S */
dtime(&Stime);
if (parallel_mode==0){
EigenBand_lapack(SU,koU,n,n,1);
EigenBand_lapack(SL,koL,n,n,1);
}
else if (SCF_iter==1 || all_knum!=1){
Eigen_PHH(MPI_CommWD1[myworld1],SU,koU,n,n,1);
Eigen_PHH(MPI_CommWD1[myworld1],SL,koL,n,n,1);
}
dtime(&Etime);
time3 += Etime - Stime;
if (SCF_iter==1 || rediagonalize_flag_overlap_matrix==1 || all_knum!=1){
if (3<=level_stdout){
printf(" myid0=%2d kloop %2d k1 k2 k3 %10.6f %10.6f %10.6f\n",
myid0,kloop,T_KGrids1[kloop],T_KGrids2[kloop],T_KGrids3[kloop]);
for (i=1; i<=n; i++){
printf(" Eigenvalues of Up-OLP %2d %15.12f\n",i,koU[i]);
printf(" Eigenvalues of Down-OLP %2d %15.12f\n",i,koL[i]);
}
}
/* minus eigenvalues to 1.0e-14 */
for (l=1; l<=n; l++){
if (koU[l]<0.0) koU[l] = 1.0e-14;
koSU[l] = koU[l];
if (koL[l]<0.0) koL[l] = 1.0e-14;
koSL[l] = koL[l];
}
/* calculate S*1/sqrt(koU) and S*1/sqrt(koL)*/
for (l=1; l<=n; l++){
koU[l] = 1.0/sqrt(koU[l]);
koL[l] = 1.0/sqrt(koL[l]);
}
/* S * 1.0/sqrt(ko[l]) */
for (i1=1; i1<=n; i1++){
for (j1=1; j1<=n; j1++){
SU[i1][j1].r = SU[i1][j1].r*koU[j1];
SU[i1][j1].i = SU[i1][j1].i*koU[j1];
SL[i1][j1].r = SL[i1][j1].r*koL[j1];
SL[i1][j1].i = SL[i1][j1].i*koL[j1];
}
}
}
/****************************************************
set H' and diagonalize it
****************************************************/
/* U'^+ * H * U * M1 */