/* Tridiagonals solvers */
void solve_tridiag_qr(int n, double *D, double *E, char type){ if (type == 'N'){
printf("Using PWK variant\n");
int info = LAPACKE_dsterf(n, D, E);
assert(!info);
}
else {
double *Q = malloc(n*n*sizeof(double)); assert(Q);
int info = LAPACKE_dsteqr(LAPACK_COL_MAJOR, type, n, D, E, Q, n);
assert(!info);
free(Q);
}
}
int main(){
struct HamData *HD;
HD = (struct HamData*)malloc(sizeof(struct HamData));
HD-> num_points = 100.0; //num_points
HD-> right_endpoint = 10.0; //right_endpoint formerly known as 'a'
HD-> left_endpoint = -10.0; //left_endpoint formerly known as 'b'
double integral = 0;
int num_points = HD-> num_points;
int ii;
int jj;
int kk;
int ll;
//double elec_field[3] ={-.1,0,.1}; //this array sets the values that the electric field will take on. ex: -1*X(operator).
double e_field_max = 1.0; //upper & lower domain of the electric field.
double e_field_min = -1.0;
//double p[3] = {0,0,0}; //initializing the polarization vector.
//int m = 3; //this tells the giant for-loop how many times to go through and corresponds to the number of electric field values.
int row = 0; //setting the row value for the chebyshev differentiation matrix.
int col = 0; //setting the column value for the chebyshev differentiation matrix.
//************** INT M(AND THUS THE NUMBER OF VALUES FOR THE ELECTRIC FIELD) AND NUM_CHEBPOINTS MUST BE THE SAME***********
double sum;
double green;
double BETA = 0;
//defining the constant alpha(for the laplacian) and num_chebpoints
int num_chebpoints = 5;
double alpha = (pow(HD -> num_points + 1.0, 2.0)) / (pow(HD -> right_endpoint - HD -> left_endpoint,2.0));
double omega = 1.0;
int flag = 1.0;
int tag = 0;
//******************************************************************************************************
double *main_diag; //main diagonal for the lapack solver
main_diag = (double*)malloc(num_points*sizeof(double));
double *sub_diag; //sub diag for the lapack solver(since this matrix is symetric the sub and super diagonals are the same.
sub_diag = (double*)malloc(num_points*sizeof(double));
double *Z; // identity matrix for the lapacke solver
Z = (double*)malloc(num_points*num_points*sizeof(double));
double *psi; //a place to store the first eigenvector.
psi = (double*)malloc(num_points*sizeof(double));
double *cheb_points;//place to store the chebpoints
cheb_points = (double*)malloc(num_chebpoints*sizeof(double));
double *elec_field; //place to store the electric field points which correspond to the chebpoints.
elec_field = (double*)malloc(num_chebpoints*sizeof(double));
double *diff; //place to store the value of
diff = (double*)malloc(sizeof(double));
double *polarization; //the polarization vector.
polarization = (double*)malloc(num_chebpoints*sizeof(double));
//this assigns the electric field array chebpoints on the user defined e_min & e_max so that was it can vary the electric field using the chebyshev points.
cheb_array(num_chebpoints, &elec_field[0], e_field_max, e_field_min);
//for(ii<0;ii<num_chebpoints;ii++){
// printf("these are the chebpoints: %E \n", elec_field[ii]);
//}
//creating giant for loop in order to vary the electric field each time. **************
for(kk=0;kk<num_chebpoints;kk++){
//*****creating the hamiltonian*****
lap_explicit(HD -> num_points, &main_diag[0], &sub_diag[0], alpha, 0);
x_squared(HD -> num_points, HD-> left_endpoint, HD-> right_endpoint, &main_diag[0], omega, 1);
E_field( HD -> num_points, HD -> left_endpoint, HD-> right_endpoint, &main_diag[0], elec_field[kk] , 1);
//identity matrix(Z) Needed for lapack's eigen-solver(otherwise you won't get the correct values)
for(ii=0;ii<num_points;ii++)
{
for(jj=0;jj<num_points;jj++){
if(ii == jj) {
Z[ii*num_points+jj] = 1.0;
//printf("X[%d] = %+1.15e\n",ii,X[ii]);
}
else{
Z[ii*num_points+jj] = 0.0;
//printf("X[%d] = %+1.15e\n",jj,X[jj]);
}
}
}
//Call 1-800-LA-PACKE for a free consulatation of eigenvalues and eigenvectors.
LAPACKE_dsteqr(LAPACK_COL_MAJOR,'I', num_points, main_diag, sub_diag, Z, num_points);
for(ii=0;ii<1;ii++){
printf("first eigenvalue. %E \n", main_diag[ii]);
}
/*
pick off the first eigenvector e.g. the ground state of the Hamiltonian.
for(ii=0;ii<num_points;ii++){
//psi[ii] = Z[ii];
printf("\nThis is Psi:\n");
for(ii=0;ii<num_points;ii++){
printf("Psi[%d] = %+1.15e\n",ii,psi[ii]);
}
printf("\n");/*/
normalize_polarize(&Z[0] ,HD -> left_endpoint ,HD-> right_endpoint ,num_points ,&integral);
polarization[kk] = integral;
//printf("The polarization: %1.1e \n", integral);
}//end of the giant for loop creating the polarization vector. **************
for(kk=0;kk<num_chebpoints;kk++){
printf("The polarization: %E \n", polarization[kk]);
}
//creating the array full of cheb_points.
//cheb_array(num_chebpoints, &cheb_points[0], e_field_max, e_field_min);
/*
printf("These are the chebpoints: \n");
for(ii=0;ii<num_chebpoints;ii++){
printf("cheb_points[ii] = %+1.15e \n", cheb_points[ii]);
}
printf("\n");
/*/
//creating the first derivative chebyshev differentiation matrix.
green = chebdiff(row, col, num_chebpoints, &elec_field[0]);
printf("this is D. %+1.15e \n",green);
sum = chebdiff2(row, col, num_chebpoints, &elec_field[0]);
printf("this is D2 %+1.15e \n",sum);
BETA = beta(num_chebpoints, &elec_field[0], &polarization[0]); //&elec_field[0] was &cheb_points[0]
printf("this is beta %1.15e \n", BETA);
/*
BETA = 0;
BETA = beta(row, col, num_chebpoints, &elec_field[0], &polarization[0]);
printf("This is beta %E \n", BETA);
/*/
free(main_diag);
free(sub_diag);
free(cheb_points);
free(diff);
return 0;
}