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Tracking-of-selected-states.md
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**VERSION>=2021.09.18**
[[_TOC_]]
# Tracking the states
# Tracking the states using build in mechanism
**VERSION>=2021.09.18**
## Defining the subset
W-SLDA Toolkit allows the tracking of observables arising from selected states in time. Presently, the following quantities can be tracked:
* `subset_rho_a`:
$`n_{\uparrow}^{\textrm{(subset)}}(r)= \sum_{E_{\textrm{min}}^{\textrm{(subset)}}<E_n<E_{\textrm{max}}^{\textrm{(subset)}}}|u_{n,\uparrow}(r)|^2 f_{\beta}(E_n)`$
......@@ -21,10 +23,10 @@ In the case of spin-imbalanced systems, it is also convenient to introduce a shi
```bash
subsetShiftDmu 1 # if 1 then apply extra shift of quasiparticle energies by (mu_a-mu_b)/2, default=0
```
# Limitations
The states to be tracked and contracted into `subset_rho` and `subset_j` are tagged at the beginning of the simulations. It means that we select states based on their energies at `t=0`. However, as the dynamics proceed energies of the states can change as well, so some of them can acquire energy that is out of the given range, and some that were not included initially can acquire energy within the considered energy range. These effects are not taken into account by the presented prescription.
## Limitations
The states to be tracked and contracted into `subset_rho` and `subset_j` are tagged at the beginning of the simulations. We select states based on their energies at `t=0`. However, as the dynamics proceed, the energies of the states can change as well, so some of them can acquire energy that is out of the given range, and some that were not included initially can acquire energy within the considered energy range. These effects are not taken into account by the presented prescription.
# Example
## Example
Below we present a snapshot from a simulation with SLDA functional for the spin-symmetric system. `td-wslda-2d` has been used. The unitary Fermi gas is confined in a tube, and the vortex dipole is imprinted in the initial state. Following options for subset tracking were used
```bash
......@@ -36,5 +38,155 @@ subsetMinEn -0.35 # in eF units, deafault=0.0
subsetMaxEn 0.35 # in eF units, deafault=0.0
subsetShiftDmu 1 # if 1 then apply extra shift of quasiparticle energies by (mu_a-mu_b)/2, default=0
```
For the unitary Fermi gas $`\Delta/\varepsilon_{F}=0.5`$, thus as the subset we select only in-gap states, which in this case corresponds to Andreev vortex states. They are localized in the vortex core. It is visualized below: the left half shows $`\Delta(r)/\varepsilon_{F}`$, while the right half shows `subset_rho_a`.
![subset](uploads/448524d11f75bbd5e63179d7ba7722b9/subset.png)
\ No newline at end of file
For the unitary Fermi gas $`\Delta/\varepsilon_{F}=0.5`$, thus, as the subset, we select only in-gap states, which in this case corresponds to Andreev vortex states. They are localized in the vortex core. It is visualized below: the left half shows $`\Delta(r)/\varepsilon_{F}`$, while the right half shows `subset_rho_a`.
![subset](uploads/448524d11f75bbd5e63179d7ba7722b9/subset.png)
# Writing to files selected states
**VERSION>=2024.01.31**
# Tracking the state using write_wave_functions(...)
The use can track the selected state via `write_wave_functions(...)` function located in `logger.h`. The example below shows an example code that writes periodically to files states with quasiparticle energies smaller than the given threshold value. The example is for 2D code.
```c
static int wffileid; // line id
static int wfcall; // call id of the function
int *idx_wf_for_storage;
static int cnt_wf_for_storage;
int write_wave_functions(int it, int nxyz, int nwfip, int nwf, double beta, MPI_Comm comm,
double complex *h_wf, double *h_qpe, double *h_kky, double *h_kkz, int *h_cnt, // Host pointers
double complex *d_wf, // Device pointers
double *params, size_t extra_data_size, void *extra_data
)
{
// settings mapping
int sweep = params[11];
double delta = params[12];
// do periodically
wfcall++;
if((wfcall-1) % sweep != 0) return 0; // break
// example code demonstrating writing wave functions to data format (readable by VisIt).
int ip, np;
MPI_Comm_size(comm, &np); // np = total number of processes
MPI_Comm_rank(comm, &ip); // id of process st 0 <= ip < np
// printf("S--> %d %d %d %d\n", ip, np, nwfip, nwf);
// Copy wave functions from device to host
memcopy_gpu2host(d_wf, h_wf, (size_t)2*nxyz*nwfip*sizeof(double complex));
// set pointers to u and v components
double complex *wf_u=h_wf+(size_t)0*nxyz*nwfip; // pointer to nwfip wave functions
double complex *wf_v=h_wf+(size_t)1*nxyz*nwfip; // pointer to nwfip wave functions
int i, ixy, cnt ;
// identify only states that have e_n<Delta, where Delta is stored in delta
// and save their indices to the global array
// do it only for the firts call of the function
if(wffileid==0)
{
cnt=0;
for(i=0; i<nwfip; i++) if(fabs(h_qpe[i])<delta) {cnt++;}
cnt_wf_for_storage = cnt;
if(cnt_wf_for_storage>0) idx_wf_for_storage = (int *)malloc(cnt_wf_for_storage*sizeof(int));
else idx_wf_for_storage=NULL;
cnt=0;
for(i=0; i<nwfip; i++) if(fabs(h_qpe[i])<delta) {idx_wf_for_storage[cnt]=i; cnt++;}
}
double *my_qpe=NULL, *my_kkz=NULL;
if(cnt_wf_for_storage>0)
{
my_qpe = (double *)malloc(sizeof(double)*cnt_wf_for_storage);
my_kkz = (double *)malloc(sizeof(double)*cnt_wf_for_storage);
}
for(i=0; i<cnt_wf_for_storage; i++) my_qpe[i]=h_qpe[idx_wf_for_storage[i]]; // make local copy
for(i=0; i<cnt_wf_for_storage; i++) my_kkz[i]=h_kkz[idx_wf_for_storage[i]]; // make local copy
for(i=0; i<cnt_wf_for_storage; i++) for(ixy=0; ixy<NXY; ixy++) wf_u[i*nxyz+ixy] = wf_u[idx_wf_for_storage[i]*nxyz+ixy]; // reorganize
for(i=0; i<cnt_wf_for_storage; i++) for(ixy=0; ixy<NXY; ixy++) wf_v[i*nxyz+ixy] = wf_v[idx_wf_for_storage[i]*nxyz+ixy]; // reorganize
nwfip=cnt_wf_for_storage;
MPI_Allreduce(&nwfip, &nwf, 1, MPI_INT, MPI_SUM, comm);
if(ip==0) printf("# [write_wave_functions] IDENTIFIED %d STATES WITH |E_n|<%f\n", nwf, delta);
// get info about the number of wave functions kept by each MPI process
int * wf_tbl = (int *)malloc(np*sizeof(int));
MPI_Gather( &nwfip , 1 , MPI_INT , wf_tbl , 1 , MPI_INT , 0 , MPI_COMM_WORLD ) ;
MPI_Bcast( wf_tbl , np , MPI_INT , 0 , MPI_COMM_WORLD ) ;
// use MPI I/O to write a file
char file_name[128];
MPI_File fh;
MPI_Offset my_offset=0;
MPI_Status status;
for(i=0; i<ip; i++) my_offset+=sizeof(double complex)*nxyz*wf_tbl[i];
// u component
sprintf(file_name, "%s_%06d_wf_u.wdat", md.outprefix, wffileid);
if(ip==0) printf("# [write_wave_functions] WRITING U COMPONENTS TO FILE `%s`\n", file_name);
MPI_File_open(comm, file_name, MPI_MODE_CREATE | MPI_MODE_WRONLY, MPI_INFO_NULL, &fh);
MPI_File_seek(fh, my_offset, MPI_SEEK_SET);
MPI_File_write_all(fh, wf_u , nxyz*nwfip, MPI_DOUBLE_COMPLEX, &status);
MPI_Get_count(&status, MPI_DOUBLE_COMPLEX, &cnt);
if(cnt!=nxyz*nwfip) { printf("# PROBLEM WITH WRITING OF U COMPONENTS BY PROCESS %s!\n", ip); return 1; }
MPI_File_close(&fh);
// v component
sprintf(file_name, "%s_%06d_wf_v.wdat", md.outprefix, wffileid);
if(ip==0) printf("# [write_wave_functions] WRITING V COMPONENTS TO FILE `%s`\n", file_name);
MPI_File_open(comm, file_name, MPI_MODE_CREATE | MPI_MODE_WRONLY, MPI_INFO_NULL, &fh);
MPI_File_seek(fh, my_offset, MPI_SEEK_SET);
MPI_File_write_all(fh, wf_v , nxyz*nwfip, MPI_DOUBLE_COMPLEX, &status);
MPI_Get_count(&status, MPI_DOUBLE_COMPLEX, &cnt);
if(cnt!=nxyz*nwfip) { printf("# PROBLEM WITH WRITING OF V COMPONENTS BY PROCESS %s!\n", ip); return 2; }
MPI_File_close(&fh);
// to be able to see the wave functions in VisIt add wtxt file
// see documentation of WDATA for more details
wdata_metadata wdmd;
wdmd.datadim = CODEDIM;
wdmd.nx = NX; wdmd.ny = NY; wdmd.nz = NZ;
wdmd.dx = DX; wdmd.dy = DY; wdmd.dz = DZ;
sprintf(wdmd.prefix, "%s_%06d", md.outprefix, wffileid);
wdmd.t0 = 0.0; wdmd.dt = 1.0; wdmd.cycles=nwf; wdmd.nvar=0;
wdata_variable vwf_u = {"wf_u", "complex", "none", "wdat"}; wdata_add_variable(&wdmd, &vwf_u);
wdata_variable vwf_v = {"wf_v", "complex", "none", "wdat"}; wdata_add_variable(&wdmd, &vwf_v);
sprintf(file_name, "%s_%06d.wtxt", md.outprefix, wffileid);
if(ip==0) wdata_write_metadata_to_file(&wdmd,file_name);
// write En and kz
my_offset=0;
#define __LINE_LGHT 128
char line[__LINE_LGHT];
sprintf(line, "%5d %12.8f %12.8f \n", 0, 0.0, 0.0); // line format
int _line_lgh = strlen(line); // test its lenght to get info about number of bytes per line
for(i=0; i<ip; i++) my_offset+=sizeof(char)*_line_lgh*wf_tbl[i];
int startidx=0;
for(i=0; i<ip; i++) startidx+=wf_tbl[i];
sprintf(file_name, "%s_%06d_Ekz.txt", md.outprefix, wffileid);
if(ip==0) printf("# [write_wave_functions] WRITING En AND kz TO FILE `%s`\n", file_name);
MPI_File_open(comm, file_name, MPI_MODE_CREATE | MPI_MODE_WRONLY, MPI_INFO_NULL, &fh);
for(i=0; i<nwfip; i++)
{
sprintf(line, "%5d %12.8f %12.8f \n", startidx+i, my_kkz[i], my_qpe[i]); // prepare line
MPI_File_write_at(fh, my_offset, line , _line_lgh, MPI_CHAR, &status); // write it
MPI_Get_count(&status, MPI_CHAR, &cnt); // get status
if(cnt!=_line_lgh) { printf("# PROBLEM WITH WRITING OF En AND kz BY PROCESS %s!\n", ip); return 3; }
my_offset+=sizeof(char)*_line_lgh; // move pointer to next line
}
MPI_File_close(&fh);
#undef __LINE_LGHT
// clear memory
free(wf_tbl);
wffileid++; // store next id
free(my_kkz);
free(my_qpe);
return 0; // return OK status
}
```