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iterative_dia_band.cpp
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#include<iostream>
#include<iomanip>
#include<fstream>
#include<cstdlib>
#include<math.h>
#include<mkl.h>
#include<omp.h>
#include<string.h>
#include"setup.h"
#include"struct.h"
using namespace std;
void genoutput(void);
void occu_imp_operator(int);
int func_delta(int a, int b){
if (a==b){
return 1;
}else{
return 0;
}
}
void iterative_dia_band(void)
{
int N_tmp;
int num_block;
int * num_basis_block;
BASIS ** block;
double *** H_bij;
double ** temp1;
double ** temp2;
double ** temp3;
double ** temp4;
double *** vect;
NEW_BASIS *** basis_kj;
cout << " ";cout << "Iteriterative_dia_band(): ";date_time();cout << endl;
ifstream f_input("input_band");
f_input >> temperature ;
f_input >> Lambda ;
f_input >> num_kept ;
f_input >> dim_imp ;
f_input >> dim_dot ;
f_input >> Beta_bar ;
f_input >> Q ;
f_input >> Q_Sz ;
f_input >> N_up_N_down ;
f_input >> N_tmp ;
Beta=1.0/temperature;//1.0/(k_B*T/D)
N = int(1-(2.0*log(Beta_bar/Beta)/log(Lambda)));//site -1,0,...,N_max
N_max = N+15;//!!!!!!!!!!!!!!!!!!!!
if (N_tmp!=0) N_max=N_tmp;
double coupling_imp_dot_up;
double coupling_imp_dot_down;
double * pe_up = new double [N_max+1];
double * pe_down = new double [N_max+1];
double * ptn_up = new double [N_max+1];
double * ptn_down = new double [N_max+1];
E_GS=new double [N_max];
num_basis=new int [N_max+1];
num_eigen_kept=new int [N_max+1];
ifstream fin_chain("chain_band.dat");
cout << " chain parameter:" << endl;
cout << setw(13) << " #site" << setw(29) << " tn_up" << setw(29) << " tn_down" << setw(29) << " en_up" << setw(29) << " en_down" << endl;
for (int i=-1;i<N_max+1;i++){//from second line: coupling, t0, t1,...
double temp;
fin_chain >> scientific;
if (i==-1){
fin_chain >> temp >> coupling_imp_dot_up >> coupling_imp_dot_down;
cout << " " << scientific << setw(5) << i << setw(30) << setprecision(20) << coupling_imp_dot_up << setw(30) << setprecision(20) << coupling_imp_dot_down << endl;
}else{
//fin_chain >> setprecision(20) >> temp >> setprecision(20) >> ptn_up[i] >> setprecision(20) >> ptn_down[i] >> setprecision(20) >> pe_up[i] >> pe_down[i] >> setprecision(20) >> temp;
fin_chain >> setprecision(20) >> temp >> setprecision(20) >> ptn_up[i] >> setprecision(20) >> ptn_down[i] >> setprecision(20) >> pe_up[i] >> pe_down[i];
cout << " " << scientific << setw(5) << i << setw(30) << setprecision(20) << ptn_up[i] << setw(30) << setprecision(20) << ptn_down[i] << setw(30) << setprecision(20) << pe_up[i] << setw(30) << setprecision(20) << pe_down[i] << endl;
}
}
N_max=N_max-1;
Ed_up=pe_up[0];
Ed_down=pe_down[0];
U=0;
genoutput();
cout << " " << " n " << " num_basis[n] " << " num_eigen_kept[n] " << " n0 " << endl;
for (int n=0;n<N_max+1;n++){
if (n<10){
if (dim_imp*pow(dim_dot,n)<num_kept){
num_basis[n]=dim_imp*pow(dim_dot,n); //n=0,1,...
num_eigen_kept[n]=dim_imp*pow(dim_dot,n);
}else{
if (dim_imp*pow(dim_dot,n) >= dim_dot*num_kept){
num_basis[n]=dim_dot*num_kept;
}else{
num_basis[n]=dim_imp*pow(dim_dot,n); //n=0,1,...
}
num_eigen_kept[n]=num_kept;
}
if (num_basis[n]<=num_kept){
n0=n+1;
}
}else{
num_basis[n]=num_basis[9]; // 9 means big enough.
num_eigen_kept[n]=num_eigen_kept[9];//n=0,1,... 9 means big enough.
}
}
//for (int n=0;n<N_max+1;n++){
for (int n=0;n<8;n++){
cout << " " << setw(3) << n << " " << setw(7) << num_basis[n] << " " << setw(7) << num_eigen_kept[n] << " " << setw(3) << n0 << endl;
}
cout << " step starting to discard state: " << n0 << endl;
int quant_num_totalnum_dot[4]={0,1,1,2};//{0,up,down,updown}
int quant_num_upnum_dot[4]={0,1,0,1};
int quant_num_downnum_dot[4]={0,0,1,1};
double c_up_imp[4][4]={{0,1,0,0},{0,0,0,0},{0,0,0,1},{0,0,0,0}};
double c_down_imp[4][4]={{0,0,1,0},{0,0,0,-1},{0,0,0,0},{0,0,0,0}};
double c_up_dot[4][4]={{0,1,0,0},{0,0,0,0},{0,0,0,1},{0,0,0,0}};
double c_down_dot[4][4]={{0,0,1,0},{0,0,0,-1},{0,0,0,0},{0,0,0,0}};
double c_up_eigen_0[4][4];
double c_down_eigen_0[4][4];
for (int i=0;i<4;i++){
for (int j=0;j<4;j++){
c_up_eigen_0[i][j]=0;
c_down_eigen_0[i][j]=0;
}
}
basis_ordered=new BASIS * [N_max];
basis_kj=new NEW_BASIS ** [N_max];
eigen=new EIGEN_STATE * [N_max];
vect=new double ** [N_max];
for (int n=0;n<1;n++){//basis_kj[0] shouldn't be used!
basis_kj[n]=new NEW_BASIS * [dim_dot];
for (int i=0;i<dim_dot;i++){
basis_kj[n][i]=new NEW_BASIS [dim_dot];
}
}
for (int n=1;n<N_max;n++){//basis_kj[n]
basis_kj[n]=new NEW_BASIS * [num_eigen_kept[n-1]];
for (int i=0;i<num_eigen_kept[n-1];i++){
basis_kj[n][i]=new NEW_BASIS [dim_dot];
}
}
for (int n=0;n<N_max;n++){
basis_ordered[n]=new BASIS [num_basis[n]];// 二维可变数组.储存基矢排序.4,16,64,
eigen[n]=new EIGEN_STATE [num_basis[n]];// eigen[0][k] --> |k;-1>
vect[n]=new double * [num_basis[n]];
for (int i=0;i<num_basis[n];i++){
vect[n][i]=new double [num_basis[n]];
for (int j=0;j<num_basis[n];j++){
vect[n][i][j]=0;
}
}
}
BASIS basis_temp0={0,1,-1,0,0,0};basis_ordered[0][0]=basis_temp0;//|0>=|1,0;-1>
BASIS basis_temp1={0,2,-1,1,1,0};basis_ordered[0][1]=basis_temp1;//|up>=|2,0;-1>
BASIS basis_temp2={0,3,-1,1,0,1};basis_ordered[0][2]=basis_temp2;//|down>=|3,0;-1>
BASIS basis_temp3={0,4,-1,2,1,1};basis_ordered[0][3]=basis_temp3;//|up down>=|4,0;-1>
vect[0][0][0]=1;vect[0][0][1]=0;vect[0][0][2]=0;vect[0][0][3]=0;
vect[0][1][0]=0;vect[0][1][1]=1;vect[0][1][2]=0;vect[0][1][3]=0;
vect[0][2][0]=0;vect[0][2][1]=0;vect[0][2][2]=1;vect[0][2][3]=0;
vect[0][3][0]=0;vect[0][3][1]=0;vect[0][3][2]=0;vect[0][3][3]=1;
double temp[4]={0,Ed_up,Ed_down,Ed_up+Ed_down+U};//sorting of eigenvalue
for (int j=0;j<num_basis[0]-1;j++){
if (temp[j]<temp[j+1]){
double tempp=temp[j];
temp[j]=temp[j+1];
temp[j+1]=tempp;
}
}
EIGEN_STATE eig_temp0={1,1,0,1,1,0,(Ed_up)/sqrt(Lambda),(Ed_up-temp[3])/sqrt(Lambda),vect[0][1]};
EIGEN_STATE eig_temp1={2,2,0,1,0,1,(Ed_down)/sqrt(Lambda),(Ed_down-temp[3])/sqrt(Lambda),vect[0][2]};
EIGEN_STATE eig_temp2={3,3,0,0,0,0,0,(0-temp[3])/sqrt(Lambda),vect[0][0]};
EIGEN_STATE eig_temp3={4,4,0,2,1,1,(Ed_up+Ed_down+U)/sqrt(Lambda),(Ed_up+Ed_down+U-temp[3])/sqrt(Lambda),vect[0][3]};
eigen[0][0]=eig_temp0;//| up > = |1,0>
eigen[0][1]=eig_temp1;//| down > = |2,0>
eigen[0][2]=eig_temp2;//| 0 > = |3,0>
eigen[0][3]=eig_temp3;//| updown > = |4,0>
E_GS[0]=temp[3]/sqrt(Lambda);
//exit(0);
temp1=new double * [dim_dot];
temp2=new double * [dim_dot];
temp3=new double * [dim_dot];
temp4=new double * [dim_dot];
for (int i=0;i<dim_dot;i++){
temp1[i]=new double [dim_dot];
temp2[i]=new double [dim_dot];
temp3[i]=new double [dim_dot];
temp4[i]=new double [dim_dot];
for (int j=0;j<dim_dot;j++){
temp1[i][j]=0;
temp2[i][j]=0;
temp3[i][j]=0;
temp4[i][j]=0;
}
}
for (int i=0;i<num_basis[0];i++){
for (int j=0;j<num_basis[0];j++){
for (int k=0;k<num_basis[0];k++){
temp1[i][j]=temp1[i][j]+eigen[0][i].eigen_vect[k]*c_up_imp[k][j];
temp2[i][j]=temp2[i][j]+eigen[0][i].eigen_vect[k]*c_down_imp[k][j];
}
}
}
for (int i=0;i<num_basis[0];i++){
for (int j=0;j<num_basis[0];j++){
for (int k=0;k<num_basis[0];k++){
c_up_eigen_0[i][j]=c_up_eigen_0[i][j]+temp1[i][k]*eigen[0][j].eigen_vect[k];
c_down_eigen_0[i][j]=c_down_eigen_0[i][j]+temp2[i][k]*eigen[0][j].eigen_vect[k];
}
}
}
for (int i=0;i<dim_dot;i++){
delete [] temp1[i];
delete [] temp2[i];
delete [] temp3[i];
delete [] temp4[i];
}
delete [] temp1;
delete [] temp2;
delete [] temp3;
delete [] temp4;
ofstream f_E_GS("E_GS.dat",ios_base::out|ios_base::app);
for (int n=1;n<N_max;n++){
{int i=0;
for (int k=0;k<num_eigen_kept[n-1];k++){
for (int j=0;j<dim_dot;j++){
basis_ordered[n][i].k=k+1;
basis_ordered[n][i].j=j+1;
basis_ordered[n][i].n=n-1;
basis_ordered[n][i].quant_num_totalnum=eigen[n-1][k].quant_num_totalnum + quant_num_totalnum_dot[j];
basis_ordered[n][i].quant_num_upnum=eigen[n-1][k].quant_num_upnum + quant_num_upnum_dot[j];
basis_ordered[n][i].quant_num_downnum=eigen[n-1][k].quant_num_downnum+quant_num_downnum_dot[j];
basis_kj[n][k][j].k=k+1;
basis_kj[n][k][j].j=j+1;
basis_kj[n][k][j].n=n-1;
basis_kj[n][k][j].quant_num_totalnum=eigen[n-1][k].quant_num_totalnum+quant_num_totalnum_dot[j];
basis_kj[n][k][j].quant_num_upnum=eigen[n-1][k].quant_num_upnum+quant_num_upnum_dot[j];
basis_kj[n][k][j].quant_num_downnum=eigen[n-1][k].quant_num_downnum+quant_num_downnum_dot[j];
i++;
}
}}
if (Q){
for (int i=1;i<num_basis[n];i++){//sorting of quantum number: Q.
for (int ii=1;ii<=num_basis[n]-i;ii++){
if (basis_ordered[n][ii-1].quant_num_totalnum > basis_ordered[n][ii].quant_num_totalnum){
BASIS temp = basis_ordered[n][ii-1];
basis_ordered[n][ii-1]=basis_ordered[n][ii];
basis_ordered[n][ii]=temp;
}
}
}
num_block=0;
for (int i=1;i<=num_basis[n];i++){
basis_kj[n][basis_ordered[n][i-1].k-1][basis_ordered[n][i-1].j-1].sort=i-1;
if (basis_ordered[n][i-1].quant_num_totalnum != basis_ordered[n][i].quant_num_totalnum){
num_block=num_block+1;
}
}
num_basis_block=new int [num_block];
for (int i=0;i<num_block;i++){
num_basis_block[i]=0;
}
{int ii=0;
for (int i=1;i<=num_basis[n];i++){
if (basis_ordered[n][i-1].quant_num_totalnum != basis_ordered[n][i].quant_num_totalnum){
num_basis_block[ii]=i;//-num_basis_block[ii-2];
ii++;
}
}}
}else if(Q_Sz){
for (int i=1;i<num_basis[n];i++){//sorting of quantum number: Q, S_z.
for (int ii=1;ii<=num_basis[n]-i;ii++){
if (quant_tmp*basis_ordered[n][ii-1].quant_num_totalnum+(basis_ordered[n][ii-1].quant_num_upnum-basis_ordered[n][ii-1].quant_num_downnum) > quant_tmp*basis_ordered[n][ii].quant_num_totalnum+(basis_ordered[n][ii].quant_num_upnum-basis_ordered[n][ii].quant_num_downnum)){
BASIS temp = basis_ordered[n][ii-1];
basis_ordered[n][ii-1]=basis_ordered[n][ii];
basis_ordered[n][ii]=temp;
}
}
}
num_block=0;
for (int i=1;i<=num_basis[n];i++){
//cout << basis_ordered[n][i-1].quant_num_totalnum << " N " << i-1 << endl;
basis_kj[n][basis_ordered[n][i-1].k-1][basis_ordered[n][i-1].j-1].sort=i-1;
if (quant_tmp*basis_ordered[n][i-1].quant_num_totalnum+(basis_ordered[n][i-1].quant_num_upnum-basis_ordered[n][i-1].quant_num_downnum) != quant_tmp*basis_ordered[n][i].quant_num_totalnum+(basis_ordered[n][i].quant_num_upnum-basis_ordered[n][i].quant_num_downnum)){// Q, Sz
num_block=num_block+1;
}
}
num_basis_block=new int [num_block];
for (int i=0;i<num_block;i++){
num_basis_block[i]=0;
}
{int ii=0;
for (int i=1;i<=num_basis[n];i++){
if (quant_tmp*basis_ordered[n][i-1].quant_num_totalnum+(basis_ordered[n][i-1].quant_num_upnum-basis_ordered[n][i-1].quant_num_downnum) != quant_tmp*basis_ordered[n][i].quant_num_totalnum+(basis_ordered[n][i].quant_num_upnum-basis_ordered[n][i].quant_num_downnum)){
num_basis_block[ii]=i;//-num_basis_block[ii-2];
ii++;
}
}}
}else if(N_up_N_down){
for (int i=1;i<num_basis[n];i++){//sorting of quantum number: up, down.
for (int ii=1;ii<=num_basis[n]-i;ii++){
if (quant_tmp*basis_ordered[n][ii-1].quant_num_upnum+(basis_ordered[n][ii-1].quant_num_downnum) > quant_tmp*basis_ordered[n][ii].quant_num_upnum+(basis_ordered[n][ii].quant_num_downnum)){
BASIS temp = basis_ordered[n][ii-1];
basis_ordered[n][ii-1]=basis_ordered[n][ii];
basis_ordered[n][ii]=temp;
}
}
}
num_block=0;
for (int i=1;i<=num_basis[n];i++){
//cout << basis_ordered[n][i-1].quant_num_totalnum << " N " << i-1 << endl;
basis_kj[n][basis_ordered[n][i-1].k-1][basis_ordered[n][i-1].j-1].sort=i-1;
if (quant_tmp*basis_ordered[n][i-1].quant_num_upnum+(basis_ordered[n][i-1].quant_num_downnum) != quant_tmp*basis_ordered[n][i].quant_num_upnum+(basis_ordered[n][i].quant_num_downnum)){// N_up, N_down
num_block=num_block+1;
}
}
num_basis_block=new int [num_block];
for (int i=0;i<num_block;i++){
num_basis_block[i]=0;
}
{int ii=0;
for (int i=1;i<=num_basis[n];i++){
if (quant_tmp*basis_ordered[n][i-1].quant_num_upnum+(basis_ordered[n][i-1].quant_num_downnum) != quant_tmp*basis_ordered[n][i].quant_num_upnum+(basis_ordered[n][i].quant_num_downnum)){
num_basis_block[ii]=i;//-num_basis_block[ii-2];
ii++;
}
}}
}
/*
*for (int i=0;i<num_basis[n];i++){
* cout << "basis " << basis_ordered[n][i].quant_num_totalnum << " " << basis_ordered[n][i].quant_num_upnum << " " << basis_ordered[n][i].quant_num_downnum << endl;
*}
*/
for (int i=num_block-1;i>0;i--){
num_basis_block[i]=num_basis_block[i]-num_basis_block[i-1];
}//1,4,6,4,1.
/*
*for (int i=1;i<=num_block;i++){
* cout << num_basis_block[i-1] << " xxx" << endl;
*}
*/
block=new BASIS * [num_block];
for (int i=0;i<num_block;i++){
block[i]=new BASIS [num_basis_block[i]];
}
{int ii=0;//initialization of block.
for (int i=0;i<num_block;i++){
for (int j=0;j<num_basis_block[i];j++){
block[i][j]=basis_ordered[n][ii];
//cout << block[i][j].quant_num_totalnum << " xxxx" << endl;
ii++;
}
}}
H_bij=new double ** [num_block];
for (int b=0;b<num_block;b++){
H_bij[b]=new double * [num_basis_block[b]];
for (int i=0;i<num_basis_block[b];i++){
H_bij[b][i]=new double [num_basis_block[b]];
for (int j=0;j<num_basis_block[b];j++){
H_bij[b][i][j]=0;
}
}
}
//cout << " Dot "<< n;cout << "; Number of blocks: " << setw(4) << num_block << "; Total number of basis: " << num_basis[n] << endl;
if (n==1){
int sum=0;
int kk=0;
for (int b=0;b<num_block;b++){
//cout << " ";cout << "Basis number in block "<< setw(4) << left << b << " : " << setw(4) << num_basis_block[b] << "; Total electon number: " << setw(4) << block[b][0].quant_num_totalnum << endl;
for (int i=0;i<num_basis_block[b];i++){
//cout << "| " << block[b][i].k << " , " << block[b][i].j << " ; " << n-1 << " > " << block[b][i].quant_num_totalnum << " " << eigen[n-1][block[b][i].k-1].quant_num_totalnum << " " << quant_num_totalnum_dot[block[b][i].j-1] << " " << eigen[n-1][block[b][i].k-1].eig_val_relat << endl;
//cout<<"i= "<< i <<" "<< block[b][i].quant_num_totalnum << " " << block[b][i].k << " " << block[b][i].j << " " << block[b][i].n << endl;
for (int j=0;j<num_basis_block[b];j++){
double sum_up=0;double sum_down=0;
sum_up=sum_up+c_up_dot[block[b][i].j-1][block[b][j].j-1]*c_up_eigen_0[block[b][j].k-1][block[b][i].k-1]*pow(-1,eigen[n-1][block[b][j].k-1].quant_num_totalnum);
sum_up=sum_up+c_up_dot[block[b][j].j-1][block[b][i].j-1]*c_up_eigen_0[block[b][i].k-1][block[b][j].k-1]*pow(-1,eigen[n-1][block[b][i].k-1].quant_num_totalnum);
sum_down=sum_down+c_down_dot[block[b][i].j-1][block[b][j].j-1]*c_down_eigen_0[block[b][j].k-1][block[b][i].k-1]*pow(-1,eigen[n-1][block[b][j].k-1].quant_num_totalnum);
sum_down=sum_down+c_down_dot[block[b][j].j-1][block[b][i].j-1]*c_down_eigen_0[block[b][i].k-1][block[b][j].k-1]*pow(-1,eigen[n-1][block[b][i].k-1].quant_num_totalnum);
H_bij[b][i][j]=(sqrt(Lambda)*eigen[n-1][block[b][i].k-1].eig_val_relat + pow(Lambda,(n-1)/2.0)*(pe_up[n]*quant_num_upnum_dot[block[b][i].j-1] + pe_down[n]*quant_num_downnum_dot[block[b][i].j-1]))*func_delta(block[b][i].k,block[b][j].k)*func_delta(block[b][i].j,block[b][j].j) + pow(Lambda,(n-1)/2.0)*(ptn_up[0]*sum_up+ptn_down[0]*sum_down); // H_bij=<block[b][i]|H|block[b][j]>. Attention! eigen[n+1][block[b][i].k-1].eigen_value?截断后重新连续排序!
if (fabs(H_bij[b][i][j]) < 1e-30){
H_bij[b][i][j]=0;
}
//cout << setw(8) << H_bij[b][i][j] << " | " << block[b][i].k << " " << block[b][i].j << " " << block[b][i].n << " | " << block[b][j].k << " " << block[b][j].j << " " << block[b][j].n << " | " << block[b][0].quant_num_totalnum << endl;
}
//cout << " eigen_value: " << eigen[n-1][block[b][i].k-1].eig_val_relat << endl;
}
int lda=num_basis_block[b];
//double * vect_temp=new double [num_basis_block[b]*num_basis_block[b]];
MKL_Complex16 * vect_temp=new MKL_Complex16 [num_basis_block[b]*num_basis_block[b]];
double * value=new double [num_basis_block[b]];
{int k=0;
for (int i=0;i<num_basis_block[b];i++){
for (int j=0;j<num_basis_block[b];j++){
vect_temp[k].real = H_bij[b][i][j];
vect_temp[k].imag = 0;
k++;
}
}}
double abstol=1e-10;
int * isuppz=new int [2*num_basis_block[b]];
double vl,vu;
int il,iu;
int * m;
m=&num_basis_block[b];
int info=LAPACKE_zheevr(LAPACK_ROW_MAJOR,'V','A','U',num_basis_block[b],vect_temp,num_basis_block[b],vl,vu,il,iu,abstol,m,value,vect_temp,num_basis_block[b],isuppz);
//LAPACKE_dsyevd(LAPACK_ROW_MAJOR,'V','U',num_basis_block[b],vect_temp,lda,value);
for (int i=0;i<num_basis_block[b];i++){
eigen[n][kk].eig_val=value[i];
//eigen_ordered[n+1][kk].eigen_value=value[i];
//eigen_ordered[n+1][kk].quant_num_totalnum=block[b][0].quant_num_totalnum;
int k=0;
//for (int j=i*num_basis_block[b];j<(i+1)*num_basis_block[b];j++){
for (int j=0;j<num_basis_block[b];j++){
vect[n][kk][sum+k]=vect_temp[i+j*num_basis_block[b]].real;
if (fabs(vect_temp[i+j*num_basis_block[b]].imag) > 1e-30){
cout << vect_temp[i+j*num_basis_block[b]].imag << endl;
}
//vect[n][kk][sum+k]=vect_temp[j+i*num_basis_block[b]];
//vect[n][kk][sum+k]=vect_temp[j];
k++;
}
eigen[n][kk].eigen_vect=vect[n][kk];
//eigen_ordered[n+1][kk].eigen_vect=vect[n+2][kk];
kk++;
//cout << " ";cout << " ";cout << "eigenvalue: " << setw(9) << value[i] << endl;
}
sum=sum+num_basis_block[b];
//cout << " ";cout << "Basis number in block "<< setw(4) << left << b << " : " << setw(4) << num_basis_block[b] << "; Total electon number: " << setw(4) << block[b][0].quant_num_totalnum << scientific << "; min_eigenvalue: " << setw(15) << setprecision(10) << value[0] << "; max_eigenvalue: " << setw(15) << value[num_basis_block[b]-1] << endl;
delete [] vect_temp;
delete [] value;
}
}else{
double ** c_up_dot_basis=new double * [num_basis[n-1]];
double ** c_down_dot_basis=new double * [num_basis[n-1]];
double ** c_up_dot_eigen=new double * [num_eigen_kept[n-1]];
double ** c_down_dot_eigen=new double * [num_eigen_kept[n-1]];
for (int i=0;i<num_basis[n-1];i++){
c_up_dot_basis[i]=new double [num_basis[n-1]];
c_down_dot_basis[i]=new double [num_basis[n-1]];
for (int j=0;j<num_basis[n-1];j++){
c_up_dot_basis[i][j]=0;
c_down_dot_basis[i][j]=0;
}
}
for (int i=0;i<num_eigen_kept[n-1];i++){
c_up_dot_eigen[i]=new double [num_eigen_kept[n-1]];
c_down_dot_eigen[i]=new double [num_eigen_kept[n-1]];
for (int j=0;j<num_eigen_kept[n-1];j++){
c_up_dot_eigen[i][j]=0;
c_down_dot_eigen[i][j]=0;
}
}
#pragma omp parallel for
for (int i=0;i<num_basis[n-1];i++){
for (int j=0;j<num_basis[n-1];j++){
c_up_dot_basis[i][j]=func_delta(basis_ordered[n-1][i].k,basis_ordered[n-1][j].k)*c_up_dot[basis_ordered[n-1][i].j-1][basis_ordered[n-1][j].j-1]*pow(-1,basis_ordered[n-1][j].quant_num_totalnum-quant_num_totalnum_dot[basis_ordered[n-1][j].j-1]);//eigen[n-2][basis_ordered[n-1][j].k-1].quant_num_totalnum);
c_down_dot_basis[i][j]=func_delta(basis_ordered[n-1][i].k,basis_ordered[n-1][j].k)*c_down_dot[basis_ordered[n-1][i].j-1][basis_ordered[n-1][j].j-1]*pow(-1,basis_ordered[n-1][j].quant_num_totalnum-quant_num_totalnum_dot[basis_ordered[n-1][j].j-1]);//eigen[n-2][basis_ordered[n-1][j].k-1].quant_num_totalnum);
}
}
double * matrix_U=new double [num_basis[n-1]*num_eigen_kept[n-1]];
double * matrix_c=new double [num_basis[n-1]*num_basis[n-1]];
double * matrix_cc=new double [num_eigen_kept[n-1]*num_basis[n-1]];
double * matrix_ccc=new double [num_eigen_kept[n-1]*num_eigen_kept[n-1]];
{int k=0;
for (int i=0;i<num_eigen_kept[n-1];i++){
for (int j=0;j<num_basis[n-1];j++){
matrix_U[k]=eigen[n-1][i].eigen_vect[j];
k++;
}
}}
{int k=0;
for (int i=0;i<num_basis[n-1];i++){
for (int j=0;j<num_basis[n-1];j++){
matrix_c[k]=c_up_dot_basis[j][i];
k++;
}
}}
cblas_dgemm(CblasColMajor,CblasTrans,CblasNoTrans,num_eigen_kept[n-1],num_basis[n-1],num_basis[n-1],1,matrix_U,num_basis[n-1],matrix_c,num_basis[n-1],0,matrix_cc,num_eigen_kept[n-1]);
cblas_dgemm(CblasColMajor,CblasNoTrans,CblasNoTrans,num_eigen_kept[n-1],num_eigen_kept[n-1],num_basis[n-1],1,matrix_cc,num_eigen_kept[n-1],matrix_U,num_basis[n-1],0,matrix_ccc,num_eigen_kept[n-1]);
for (int i=0;i<num_eigen_kept[n-1];i++){
for (int j=0;j<num_eigen_kept[n-1];j++){
c_up_dot_eigen[j][i]=matrix_ccc[num_eigen_kept[n-1]*i+j];
}
}
{int k=0;
for (int i=0;i<num_basis[n-1];i++){
for (int j=0;j<num_basis[n-1];j++){
matrix_c[k]=c_down_dot_basis[j][i];
k++;
}
}}
cblas_dgemm(CblasColMajor,CblasTrans,CblasNoTrans,num_eigen_kept[n-1],num_basis[n-1],num_basis[n-1],1,matrix_U,num_basis[n-1],matrix_c,num_basis[n-1],0,matrix_cc,num_eigen_kept[n-1]);
cblas_dgemm(CblasColMajor,CblasNoTrans,CblasNoTrans,num_eigen_kept[n-1],num_eigen_kept[n-1],num_basis[n-1],1,matrix_cc,num_eigen_kept[n-1],matrix_U,num_basis[n-1],0,matrix_ccc,num_eigen_kept[n-1]);
for (int i=0;i<num_eigen_kept[n-1];i++){
for (int j=0;j<num_eigen_kept[n-1];j++){
c_down_dot_eigen[j][i]=matrix_ccc[num_eigen_kept[n-1]*i+j];
}
}
delete [] matrix_U;
delete [] matrix_c;
delete [] matrix_cc;
delete [] matrix_ccc;
int sum=0;
int kk=0;
BASIS * basis_old=new BASIS [num_basis[n-1]];//n=0
for (int i=0;i<num_basis[n-1];i++){
basis_old[i]=basis_ordered[n-1][i];
}
for (int b=0;b<num_block;b++){
#pragma omp parallel for
for (int i=0;i<num_basis_block[b];i++){
//cout << "| " << block[b][i].k << " , " << block[b][i].j << " ; " << n-1 << " > " << block[b][i].quant_num_totalnum << " " << eigen[n-1][block[b][i].k-1].quant_num_totalnum << " " << quant_num_totalnum_dot[block[b][i].j-1] << " " << eigen[n-1][block[b][i].k-1].eig_val_relat << endl;
for (int j=0;j<num_basis_block[b];j++){
double sum_up2=0;double sum_down2=0;double sum_up=0;double sum_down=0;
sum_up=pow(-1,eigen[n-1][block[b][j].k-1].quant_num_totalnum)*c_up_dot_eigen[block[b][j].k-1][block[b][i].k-1]*c_up_dot[block[b][i].j-1][block[b][j].j-1] + pow(-1,eigen[n-1][block[b][i].k-1].quant_num_totalnum)*c_up_dot[block[b][j].j-1][block[b][i].j-1]*c_up_dot_eigen[block[b][i].k-1][block[b][j].k-1];
sum_down=pow(-1,eigen[n-1][block[b][j].k-1].quant_num_totalnum)*c_down_dot_eigen[block[b][j].k-1][block[b][i].k-1]*c_down_dot[block[b][i].j-1][block[b][j].j-1] + pow(-1,eigen[n-1][block[b][i].k-1].quant_num_totalnum)*c_down_dot[block[b][j].j-1][block[b][i].j-1]*c_down_dot_eigen[block[b][i].k-1][block[b][j].k-1];
//H_bij[b][i][j]=(sqrt(Lambda)*eigen[n-1][block[b][i].k-1].eig_val_relat )*func_delta(block[b][i].k,block[b][j].k)*func_delta(block[b][i].j,block[b][j].j) + pow(Lambda,(n-2)/2.0)*(ptn_up[n-2]*sum_up+ptn_down[n-2]*sum_down); // H_bij=<block[b][i]|H|block[b][j]>. Attention! eigen[n+1][block[b][i].k-1].eigen_value?截断后重新连续排序!
H_bij[b][i][j]=(sqrt(Lambda)*eigen[n-1][block[b][i].k-1].eig_val_relat + pow(Lambda,(n-1)/2.0)*(pe_up[n]*quant_num_upnum_dot[block[b][i].j-1] +pe_down[n]*quant_num_downnum_dot[block[b][i].j-1]))*func_delta(block[b][i].k,block[b][j].k)*func_delta(block[b][i].j,block[b][j].j) + pow(Lambda,(n-1)/2.0)*(ptn_up[n-1]*sum_up+ptn_down[n-1]*sum_down); // H_bij=<block[b][i]|H|block[b][j]>. Attention! eigen[n+1][block[b][i].k-1].eigen_value?截断后重新连续排序!
if (fabs(H_bij[b][i][j]) < 1e-30){
H_bij[b][i][j]=0;
}
}
//cout << " eigen_value: " << eigen[n-1][block[b][i].k-1].eig_val << endl;
}
int lda=num_basis_block[b];
//double * vect_temp=new double [num_basis_block[b]*num_basis_block[b]];
MKL_Complex16 * vect_temp=new MKL_Complex16 [num_basis_block[b]*num_basis_block[b]];
double * value=new double [num_basis_block[b]];
{int k=0;
for (int i=0;i<num_basis_block[b];i++){
for (int j=0;j<num_basis_block[b];j++){
vect_temp[k].real = H_bij[b][i][j];
vect_temp[k].imag = 0;
k++;
}
}}
double abstol=1e-10;
int * isuppz=new int [2*num_basis_block[b]];
double vl,vu;
int il,iu;
int * m;
m=&num_basis_block[b];
int info=LAPACKE_zheevr(LAPACK_ROW_MAJOR,'V','A','U',num_basis_block[b],vect_temp,num_basis_block[b],vl,vu,il,iu,abstol,m,value,vect_temp,num_basis_block[b],isuppz);
//LAPACKE_dsyevd(LAPACK_ROW_MAJOR,'V','U',num_basis_block[b],vect_temp,lda,value);
for (int i=0;i<num_basis_block[b];i++){
eigen[n][kk].eig_val=value[i];
//cout << "eigenvalue: " << setw(3) << i << setw(9) << value[i] << endl;
//cout << "eigval " << setw(3) << i << setw(9) << eigen[n][kk].eig_val << endl;
int k=0;
for (int j=0;j<num_basis_block[b];j++){//row-wise
vect[n][kk][sum+k]=vect_temp[i+j*num_basis_block[b]].real;
if (fabs(vect_temp[i+j*num_basis_block[b]].imag) > 1e-30){
cout << vect_temp[i+j*num_basis_block[b]].imag << endl;
}
//vect[n][kk][sum+k]=vect_temp[j];
k++;
}
eigen[n][kk].eigen_vect=vect[n][kk];
kk++;
}
sum=sum+num_basis_block[b];
//cout << " ";cout << "Basis number in block "<< setw(4) << left << b << " : " << setw(4) << num_basis_block[b] << "; Total electon number: " << setw(4) << block[b][0].quant_num_totalnum << scientific << "; min_eigenvalue: " << setw(15) << setprecision(10) << value[0] << "; max_eigenvalue: " << setw(15) << value[num_basis_block[b]-1] << endl;
delete [] vect_temp;
delete [] value;
}
for (int i=0;i<num_eigen_kept[n-1];i++){
delete [] c_up_dot_eigen[i];
delete [] c_down_dot_eigen[i];
}
for (int i=0;i<num_basis[n-1];i++){
delete [] c_up_dot_basis[i];
delete [] c_down_dot_basis[i];
}
delete [] c_up_dot_eigen;
delete [] c_down_dot_eigen;
delete [] basis_old;
delete [] c_up_dot_basis;
delete [] c_down_dot_basis;
}
for (int k=0;k<num_basis[n];k++){//initionialization of sort,k,n.
eigen[n][k].sort=k+1;
eigen[n][k].k=k+1;
eigen[n][k].n=n;
}
{int sum1=0,sum2=0;
for(int b=0;b<1;b++){//initionialization of quantum number.
sum2=sum2+num_basis_block[b];
for (int i=0;i<num_basis_block[b];i++){
eigen[n][i].quant_num_totalnum=block[b][0].quant_num_totalnum;
eigen[n][i].quant_num_upnum=block[b][0].quant_num_upnum;
eigen[n][i].quant_num_downnum=block[b][0].quant_num_downnum;
//cout << "basi " << block[b][0].quant_num_totalnum << " " << block[b][0].quant_num_upnum << " " << block[b][0].quant_num_downnum << endl;
//cout << "basi " << eigen[n][i].quant_num_totalnum << " " << eigen[n][i].quant_num_upnum << " " << eigen[n][i].quant_num_downnum << endl;
//cout << " before sort " << i+1 << " " << eigen[n][i].quant_num_totalnum << " " << eigen[n][i].quant_num_upnum-eigen[n][i].quant_num_downnum << " " << setprecision(12) << eigen[n][i].eig_val << endl;
}
}
for(int b=1;b<num_block;b++){//initionialization of quantum number.
sum2=sum2+num_basis_block[b];
sum1=sum1+num_basis_block[b-1];
for (int i=sum1;i<sum2;i++){
eigen[n][i].quant_num_totalnum=block[b][0].quant_num_totalnum;
eigen[n][i].quant_num_upnum=block[b][0].quant_num_upnum;
eigen[n][i].quant_num_downnum=block[b][0].quant_num_downnum;
//cout << "basis " << block[b][0].quant_num_totalnum << " " << block[b][0].quant_num_upnum << " " << block[b][0].quant_num_downnum << endl;
//cout << "basis " << eigen[n][i].quant_num_totalnum << " " << eigen[n][i].quant_num_upnum << " " << eigen[n][i].quant_num_downnum << endl;
//cout << " before sort " << i+1 << " " << eigen[n][i].quant_num_totalnum << " " << eigen[n][i].quant_num_upnum-eigen[n][i].quant_num_downnum << " " << setprecision(12) << eigen[n][i].eig_val << endl;
}
}}
for (int k=1;k<=num_basis[n]-1;k++){//sort of eigen_value.
for (int ii=1;ii<=num_basis[n]-k;ii++){
if (eigen[n][ii-1].eig_val > eigen[n][ii].eig_val){
EIGEN_STATE temp = eigen[n][ii-1];//.quant_num_totalnum;
eigen[n][ii-1]=eigen[n][ii];
eigen[n][ii]=temp;
}
}
eigen[n][num_basis[n]-k].k=num_basis[n]-k+1;
}
//cout << eigen[n][0].k << endl;
eigen[n][0].k=1;
for (int i=0;i<num_basis[n];i++){
eigen[n][i].eig_val_relat=eigen[n][i].eig_val-eigen[n][0].eig_val;
//cout << "in eigen " << eigen[n][i].k-1 << endl;
//cout << n << " " << basis_ordered[n][i].quant_num_totalnum <<" | "<< basis_ordered[n][i].k <<" "<< basis_ordered[n][i].j << " | " << eigen[n][i].sort << endl;
}
//ofstream cup("cup",ios::binary);
E_GS[n]=sqrt(Lambda)*E_GS[n-1]+eigen[n][0].eig_val;
f_E_GS << "Dot " << n << scientific << setw(25) << setprecision(15) << E_GS[n] << setw(25) << E_GS[n]*pow(Lambda,-1.0*(n-1)/2.0) << endl;
//cout << " ";cout << "Time leaved: ";date_time();cout << endl;
for (int i=0;i<num_block;i++){
delete [] block[i];
}
delete [] block;
for (int b=0;b<num_block;b++){
for (int i=0;i<num_basis_block[b];i++){
delete [] H_bij[b][i];
}
delete [] H_bij[b];
}
delete [] H_bij;
delete [] num_basis_block;
//if (n==6) exit(0);
}
cout << "Time leaved: ";date_time();cout << endl;
}