void ps_dump()
{
DIR *d;
struct dirent *de;
char *namefilter = 0;
int pidfilter = 0;
int threads = 0;
d = opendir("/proc");
if(d == 0) return;
if(filter_by_system == 1)
{
process_info psinfo;
memset(&psinfo, 0, sizeof(process_info));
psinfo.uid = 0;
strcpy(psinfo.owner, "root");
strcpy(psinfo.name, "System");
psinfo.status = 'S';
ps_list_add(&psinfo);
}
while((de = readdir(d)) != 0)
{
if(isdigit(de->d_name[0]))
{
int pid = atoi(de->d_name);
ps_instance_dump(pid);
}
}
closedir(d);
}
int main(int argc, char **argv) {
int i;
if (2 != argc) {
printf("test_ls_list infile\n");
return 1;
}
char* infname = argv[1];
FILE *infile = fopen(infname, "r");
PS_DATA data = ps_data_read_bin(infile);
fclose(infile);
PS_SOLUTION *solution;
PS_LIST list = ps_list_create();
for(i=0; i<5; i++) {
solution = (PS_SOLUTION*)malloc(sizeof(PS_SOLUTION));
solution->energy = i;
solution->wavefunction = ps_data_copy(data);
ps_list_add(list, solution);
printf("List Size=%i\n", ps_list_size(list));
}
free(data);
PS_SOLUTION *listnode = ps_list_front(list);
i = 0;
while (listnode != NULL) {
printf("Node %i\n", ++i);
printf("Energy=%f\n", listnode->energy);
ps_data_write_ascii(listnode->wavefunction, stdout);
listnode = ps_list_next(list);
}
ps_list_destroy_all(list);
return 0;
}
void ps_instance_dump(int pid)
{
char statline[BUFFERSIZE*2];
struct stat stats;
process_info psinfo;
FILE *ps;
struct passwd *pw;
int n;
memset(&psinfo, 0, sizeof(process_info));
psinfo.pid = pid;
snprintf(statline, BUFFERSIZE*2, "/proc/%d", pid);
stat(statline, &stats);
psinfo.uid = (int) stats.st_uid;
pw = getpwuid(stats.st_uid);
if(pw == 0)
{
snprintf(psinfo.owner, 80, "%d", (int)stats.st_uid);
}
else
{
strncpy(psinfo.owner, pw->pw_name, 80);
}
snprintf(statline, BUFFERSIZE*2, "/proc/%d/stat", pid);
ps = fopen(statline, "r");
if (ps != 0)
{
/* Scan rest of string. */
fscanf(ps, "%*d %*s %c %*d %*d %*d %*d %*d %*d %*d %*d %*d %*d "
"%lu %lu %*d %*d %*d %*d %d %*lu %lu %*lu %ld",
&psinfo.status, &psinfo.delta_utime, &psinfo.delta_stime,
&psinfo.threadnum, &psinfo.start_time, &psinfo.rss);
fclose(ps);
}
snprintf(statline, BUFFERSIZE*2, "/proc/%d/cmdline", pid);
ps = fopen(statline, "r");
if(ps == 0) {
n = 0;
}
else
{
n = fread(psinfo.name, 1, 80, ps);
fclose(ps);
if(n < 0) n = 0;
}
psinfo.name[n] = 0;
if(strlen(psinfo.name) == 0)
{
snprintf(statline, BUFFERSIZE*2, "/proc/%d/stat", pid);
ps = fopen(statline, "r");
if(ps!= 0)
{
n = fscanf(ps, "%d (%s)", &pid, psinfo.name);
fclose(ps);
if(n == 2)
psinfo.name[strlen(psinfo.name)-1] = 0;
}
}
psinfo.nice = getpriority(PRIO_PROCESS, psinfo.pid);
if(filter_by_system == 1)
{
if((strcmp(psinfo.owner, "root") != 0) &&
(strstr(psinfo.name, "/system/") == 0) &&
(strstr(psinfo.name, "/sbin/") == 0))
ps_list_add(&psinfo);
else
ps_system_add(&psinfo);
}
else
{
ps_list_add(&psinfo);
}
}
/*
//
//The 2D version of the solving engine.
//
//intial eqn
//--> Div*F = G/M
//
//convert to finite diff eqn, use a uniform mesh, Let, dx = dy = d and Let P[x,y] = G[x,y]/M[x,y] = G*m
//--> (F[x+d,y]-2F[x,y]+F[x-d,y])/d^2 + (F[x,y+d]-2F[x,y]+F[x,y-d])/d^2 = P[x,y]
//
//rearrange:
//--> F[x+d,y] + F[x-d,y] + F[x,y+d] + F[x,y-d] - 4F[x,y] = d^2 * P[x,y]
//
//convert to c style: Let x = x0+j*d and y = y0+l*d
// where j = 0,1,2...J and l = 0,1,2...L
//--> F[j+1,l] + F[j-1,l] + F[j,l+1] + F[j,l-1] - 4F[j,l] = d^2 * P[j,l]y
//
//Goal: make a linear system of eqns in matrix form -- firstly we make a vector out of F. i.e. map j,l to a linear index 'i'
// Let, i = j(L+1) + l ...where j = 0,1,...J and l = 0,1,...L
//--> F[i+L+1] + F[i-(L+1)] + F[i+1] + F[i-1] - 4F[i] = d^2 * P[i]
// ...where this eqn holds for the interior points: j = 1,2,...,J and l = 1,2,...,L
//
//On the boundries F should be specified, i.e. where:
// j = 0 or i = 0, 1, 2, ..,L
// j = J or i = J(L+1), J(L+1)+1, J(L+1)+2, ...,J(L+1)+L
// l = 0 or i = 0, (L+1), 2(L+1), ..., J(L+1)
// l = L or i = L, (L+1)+L, 2(L+1)+L, ..., J(L+1)+L */
PS_LIST ps_solve_2D(PS_DATA potential, PS_SOLVE_PARAMETERS *params) {
char log_message[256];
ps_log("PsiShooter -- a shooting method solver for the time independant Schrodinger equation under the effective mass approximation.\n");
// This is a linked list for storing solutions
PS_LIST solution_list = ps_list_create();
ps_log("Iterate through Energy Eigenvalues to find the lowest bound state.\n");
// wavefunction storage.
int Nx = potential->xsize; // used for generating strings with sprintf for sending to ps_log
int Ny = potential->ysize; // used for generating strings with sprintf for sending to ps_log
// double dx = potential->xstep; //cm, size of differential length
//(TODO: Compute dx inside loop in order to support meshes with non-uniform differential steps)
double dx = ps_data_dx_at(potential, 2);
double dy = ps_data_dy_at(potential, 2); // 0 to 1 is wierd, maybe.
double dx_dy = dx/dy;
double dy_dx = dy/dx;
//F
//intial eqn --> Div*F = G * m_eff
//convert to finite diff eqn --> (F[x+dx,y]-F[x,y])/dx + (F[x,y]-F[x,y-dy])/dy = G[x,y]M[x,y]
//rearrange --> F[x+dx,y]-F[x,y] + dx*(F[x,y]-F[x,y-dy])/dy = dx*G[x,y]/M[x,y]
// --> F[x+dx,y] = dx*G[x,y]/M[x,y]+F[x,y]-dx/dy*(F[x,y]-F[x,y-dy])
// What does this mean for our 2D simulations? The more closely spaced the y
// Coordinate mesh points are, the more significant their effects will be. That
// Is pretty terrible for us.
//
// We need to decouple the coordinates so we don't need to know future F and G from
// from future calculated y mesh points...
// Is there some other way we can decouple them? We can't just look back instead of forward.
//
// How about we fill the array with 1D shots across the 1 direction, and then refill
// with the 2D shots? Then the array will have some approximate knowledge of the future
// and the algorithm might work.
//convert to c style --> F[x+dx,y] = F[i][j+1]
// *****README******* --> (NOTE: x is iterated over with j index. x=columns, i=rows) -jns
//in 2D --> F[i][j+1] = dx*G[i][j]/M[i][j] + F[i][j] - dx/dy*(F[i][j]-F[i-1][j])
//convert to 1D --> (F[x+dx]-F[x-dx])/(2dx) = G[x]/M[x]
//rearrange --> F[x+dx] = (2dx)*G[x]/M[x] + F[x-dx]
//convert to c style --> F[i+1] = (2dx)*G[i]*m[i] + F[i-1]
// F[i+1] = F_coeff*G[i]*m[i] + F[i-1]
double F_coeff = dx; //handy prefactor that would otherwise be for every point evaluated
//from dx to 2*dx jh sometime in may
//G
//intial eqn --> Div*G = F * 2*(V-E)/h_bar^2
//convert to finite diff eqn --> (G[x+dx,y]-G[x-dx,y])/(2dx) + (G[x,y+dy]-G[x,y-dy])/(2dy) = F[x,y]*2*(V[x,y]-E[x,y])/h_bar^2
//in 2d: --> G[x+dx,y] = (2dx)*F[x,y]*2*(V[x,y]-e[x,y])/h_bar^2+G[x-dx][y]-(2dx)/(2dy)(G[x,y+dy]-G[x,y-dy])
// --> G[i][j+1] = G_coeff * F[i][j]*(V[i][j]-E) + G[i][j-1] - dx/dy(G[i+1][j] + G[i-1][j])
//
// The equivalent FWD DIFFEQ --> G[x+dx][y] = dx*F[x,y]*2*(V[x,y] - e[x,y])/h_bar^2 + G[x,y] - dx/dy(G[x,y] - G[x,y-dy])
// --> G[i][j+1] = dx*F[i][j]*2*(V[i][j] - e[i][j])/h_bar^2 + G[i][j] - dx/dy(G[i][j] - G[i-1][j])
//convert to 1D --> G[x+dx]-G[x-dx]/(2dx) = F[x]*2*(V[x]-E)/h_bar^2
//rearrange --> G[x+dx] = (2dx)*F[x]*2*(V[x]-E)/h_bar^2 + G[x-dx]
//convert to c style --> G[i+1] = 4*dx/hbar^2 * F[i]*(V[i]-E) + G[i-1]
// G[i+1] = G_coeff * F[i]*(V[i]-E) + G[i-1]
// double G_coeff = 2*dx/(HBAR_PLANCK_SQ); //handy prefactor that would otherwise be computed for every point evaluated
//from 4*dx to 2*dx jh sometime in may
double G_coeff = 2*dx*G_COEFF;
//dx = dy here.
double F[Nx][Ny]; //the envelope function (wavefunction)
double f_cache[params->n_iter]; // We cache the last value of the envelope for each solution
double G[Nx][Ny]; //the aux function
int bound_state_count = 0;
int threshold_set_flag = 0;
double F_threshold = 0;
int i, j, iter;
double E = params->energy_min;
double Estep = (params->energy_max - params->energy_min)/(params->n_iter);
double V; //meV, Current potential
// double m_eff = MASS_ELECTRON*M_EFF_GAAS;
double m_eff = M_EFF_GAAS;
// To Do: make the electron mass be part of the structure that we are simulating. i.e.
//in general it can be a position dependant quantity just like the potential
//(think heterostructures with different band edge curvatures)
for (iter = 0; iter < params->n_iter; iter++) {
//Going to try filling the array with y-direction shots and then running the 2D shots based on those.
//initial conditions
for (j=0; j<Nx; j++){
F[0][j] = 0;
G[0][j] = 1;
F[1][j] = 1;
G[1][j] = 1;
}
for(i=1; i<Ny-1; i++) {
for(j=1; j<Nx-1; j++) {
V = ps_data_value(potential, i,j); //V[i][j]
// 5-point stencil in X and Y
F[i+1][j] = dx*dx*m_eff*G[i][j] - F[i][j+1] - F[i][j-1] - F[i-1][j] + 4*F[i][j];
G[i+1][j] = 2*dx*dx*G_COEFF*(V-E)*F[i][j] - G[i][j+1] - G[i][j-1] - G[i-1][j] + 4*G[i][j];
}
// For First and last point, Compute slope in x direction for F and G directly
// F[x+3] = F[x] + 3h*F'[x] + (3h)^2/2!*F''[x] (Taylor Expansion)
// F'[x] = 1/(12*h)*[-F[x+2] + 8*F[x+1] - 8*F[x-1] + F[x-2]] (5-point stencil)
// F''[x] = 1/(12*h*h)*[-F[x+2] + 16*F[x+1] -30*F[x] +16*F[x+1] - F[x-2]] (5-point stencil)
G[i+1][j] = G[i+1][j-3] + 0.25*(-G[i+1][j-1] + 8*G[i+1][j-2] - 8*G[i+1][j-4] + G[i+1][j-5]) + 9.0/24.0*(-G[i+1][j-5] + 16*G[i+1][j-4] - 30*G[i+1][j-3] + 16*G[i+1][j-2] - G[i+1][j-1]);
F[i+1][j] = F[i+1][j-3] + 0.25*(-F[i+1][j-1] + 8*F[i+1][j-2] - 8*F[i+1][j-4] + F[i+1][j-5]) + 9.0/24.0*(-F[i+1][j-5] + 16*F[i+1][j-4] - 30*F[i+1][j-3] + 16*F[i+1][j-2] - F[i+1][j-1]);
// F[x-3] = F[x] - 3h*F'[x] + (3h)^2/2!*F''[x] (Taylor Expansion)
// F'[x] = 1/(12*h)*[-F[x+2] + 8*F[x+1] - 8*F[x-1] + F[x-2]]
// F''[x] = 1/(12*h*h)*[-F[x+2] + 16*F[x+1] -30*F[x] +16*F[x+1] - F[x-2]]
G[i+1][0] = G[i+1][3] - 0.25*(-G[i+1][5] + 8*G[i+1][4] - 8*G[i+1][2] + G[i+1][1]) + 9.0/24.0*(-G[i+1][5] + 16*G[i+1][4] - 30*G[i+1][3] + 16*G[i+1][2] - G[i+1][1]);
F[i+1][0] = F[i+1][3] - 0.25*(-F[i+1][5] + 8*F[i+1][4] - 8*F[i+1][2] + F[i+1][1]) + 9.0/24.0*(-F[i+1][5] + 16*F[i+1][4] - 30*F[i+1][3] + 16*F[i+1][2] - F[i+1][1]);
}
//Why not just look at the change on the very last point? This definitely won't be representative, but it
//might be useful during debugging.
// It needs to check the entire boundary. (jns)
f_cache[iter] = F[Nx-1][Ny-1];
// Consider removing this for speed
// sprintf(log_message, "\tE=%g eV\tF[N-1]=%g\n", E/EV_TO_ERGS, F[N-1]);
// ps_log(log_message);
//Try to detect which solutions are eigen states (bound states)
//if((iter > 0) && ((f_cache[iter] > 0 && f_cache[iter-1] < 0) || (f_cache[iter] < 0 && f_cache[iter-1] > 0))) {
//if there was a change in sign between the last point of the prev
// and current envelope function then there was a zero crossing and there a solution
// test for a sign crossing
PS_DATA wavefunction = ps_data_copy(potential); // copy the potential
ps_data_set_data(wavefunction, (double*)F); // Overwrite the potential with the wavefunction
PS_SOLUTION *solution = (PS_SOLUTION*)malloc(sizeof(PS_SOLUTION));
solution->energy = E;
solution->wavefunction = wavefunction;
// Add the solution to the list of bound states
ps_list_add(solution_list, solution);
// Save the g solutions
PS_DATA g = ps_data_copy(potential);
ps_data_set_data(g, (double*)G);
PS_SOLUTION *gsolution = (PS_SOLUTION*)malloc(sizeof(PS_SOLUTION));
gsolution->energy = E;
gsolution->wavefunction = g;
ps_list_add(g_solutions, gsolution);
// print a log message
sprintf(log_message, "\tBoundstate number %d with E=%e found, F[Nx][Ny]=%e < F_threshold=%e\n", ++bound_state_count, solution->energy/EV_TO_ERGS, F[Nx][Ny], F_threshold);
ps_log(log_message);
//}
// Increment the energy
E += Estep;
}
return solution_list;
}
/*
//
// Solve for the bound energies given by the potential.
// energies is a buffer of energies to test.
// bound_energies is where the actual bound energies will be stored. It should be the same size as energies.
// both buffers should be of size buf_size.
// returns the number of bound energies found, 0 or negative for error
//
////////////////////////
//Solving the 1D TISE //
////////////////////////
//
//(0) H * Psi = E * Psi
//
//E is the eignenvalue
//H is the hamiltonian operator: H = T + V = p^2/(2m) + V
// ... where p is the momentum operator, p = h/i * Div
//
//Moving to the effective mass regime we no longer solve for the wavefunction
//but instead we sove for an envelope function. Careful consideration shows that
//if mass is allowed to vary with positon, m -> m(x), then simple subsitution of
//m(x) for m in H causes H to become non-Hermitian.
//Fortunately that can be worked around, the result is:
//
//(1) T * F = -h_bar^2/2 * Div * ( m_eff(x,y,E)^-1 * Div * F )
// ...note: F is the envelope function that is replacing the role of Psi
//
//Put it all together to get the effective mass equation that we are going to
//use:
// +--------------------------------------------------------------+
//(2) | -h_bar^2/2 * Div * (1/m_eff * Div * F) + V * F = E * F |
// +--------------------------------------------------------------+----> This is the main equation
//
//Note: Skip to equations (14) & (15) to see how we are going to proceed in the actual solver we are implenting.
//
//Rearranging (2):
//(3) Div * (M * Div * F) = 2*(V-E)*F/h_bar^2
// ... note: Let 1/m_eff(x,y,E) = M (For compactness of these notes only, it is still the effective mass that is position dependant)
//take the coordinate system to be cartesisian and Div becomes: Div = d/dx + d/dy --> Div*F = dF/dx + dF/dy
//(4) Div * { M(dF/dx) + M(dF/dy) } = 2*(V-E)*F/h_bar^2
//
//The LHS of (4) has a (2D) divergance of 2 terms that each have a product of two functions (M, dF), both of which depend on x and y.
//The chain rule will get invoked and there will be quite a few terms after we expand this
//(5) Div*(M(dF/dx)) + Div*(M(dF/dy)) = ... ...note: I am leaving off the RHS for awhile
//(6) (d/dx + d/dy)*(M(dF/dx)) + (d/dx + d/dy)*(M(dF/dy)) = ...
//(7) (d/dx)*(M(dF/dx)) + (d/dy)*(M(dF/dx)) + (d/dx)*(M(dF/dy)) + (d/dy)*(M(dF/dy))= ...
//(8) (M)(d^2F/dx^2) + (dF/dx)(dM/dx) + (M)(d^2F/(dxdy)) + (dF/dx)(dM/dy) + (M)(d^2F/(dydx)) + (dF/dy)(dM/dx) + (M)(d^2F/dy^2) + (dF/dy)(dM/dy) = ...
//(9) (M)(d^2F/dx^2) + (M)(d^2F/dy^2) + 2(M)(d^2F/(dxdy)) + (dF/dx)(dM/dx) + (dF/dx)(dM/dy) + (dF/dy)(dM/dx) + (dF/dy)(dM/dy) = ...
//
//The next step is to expand (9) out in terms of finite differences, here are some pieces that will be used:
//(10) dF/dx = (F[x+dx]-F[x-dx])/(2dx)
//(11) d^2F/dx^2 = ((F[x+dx+dx]-F[x+dx-dx])/(2dx) - (F[x-dx+dx]-F[x-dx-dx])/(2dx)) / (2dx)
// = (F[x+2dx] - 2F[x] + F[x-2dx])*(2dx)^-2
//(12) d^2F/(dxdy) = (d/dy) * dF/dx
// = (d/dy) * (F[x+dx]-F[x-dx])/(2dx)
// = ((F[x+dx,y+dy]-F[x-dx,y+dy])/(2dx) - (F[x+dx,y-dy]-F[x-dx,y-dy])/(2dx)) / (2dy)
// = ((F[x+dx,y+dy]-F[x-dx,y+dy]) - (F[x+dx,y-dy]-F[x-dx,y-dy])) / (2dx2dy)
//
//Using the finite differencing versions (10)-(12) of the derivatives in (9) and making M & F explcit functions of x & y:
//(9) (M)(d^2F/dx^2) + --> (13) M[x,y] * (F[x+2dx,y] - 2F[x,y] + F[x-2dx,y])*(2dx)^-2 +
// (M)(d^2F/dy^2) + --> M[x,y] * (F[x,y+2dy] - 2F[x,y] + F[x,y-2dy])*(2dy)^-2 +
// 2(M)(d^2F/(dxdy)) + --> 2*M[x,y] * ((F[x+dx,y+dy]-F[x-dx,y+dy])-(F[x+dx,y-dy]-F[x-dx,y-dy]))/(2dx2dy) +
// (dF/dx)(dM/dx) + --> (F[x+dx,y]-F[x-dx,y])/(2dx) * (M[x+dx,y]-M[x-dx,y])/(2dx) +
// (dF/dx)(dM/dy) + --> (F[x+dx,y]-F[x-dx,y])/(2dx) * (M[x,y+dy]-M[x,y-dy])/(2dy) +
// (dF/dy)(dM/dx) + --> (F[x,y+dy]-F[x,y-dy])/(2dy) * (M[x+dx,y]-M[x-dx,y])/(2dx) +
// (dF/dy)(dM/dy) = ... --> (F[x,y+dy]-F[x,y-dy])/(2dy) * (M[x,y+dy]-M[x,y-dy])/(2dy) = 2*(V[x,y]-E)*F[x,y]/h_bar^2
//
//The form in (13) can be rearranged so that you can use the shooting method.
//
//Instead of proceeding directly with that we are going to first write the
//orginal 2nd order differential equation (3) as a system of coupled ODEs
//(3) Div * (1/m_eff * Div * F) = 2*(V-E)*F/h_bar^2
//
//Choose simplifying units, such as:
// hbar = 1
// m_electron = 1/2 ...note: 1/m_eff = 1/(m_electron * m_relative) = 2/m_relative
//
//The equation in (3) becomes simpler:
// Div * (1/m_r * Div * F) = (V-E)*F
// ...note that m_relative has been shortened to m_r
//
//Let:
//(14) G = (1/m_r) * Div * F
//Then (3) becomes:
//(15) Div * G = (V-E)*F
//
//Rearranging (14) and (15) slightly:
// +--------------------------------------------------------------+
//(16) | Div*F = G * m_r |
//(17) | Div*G = F * (V-E) |
// +--------------------------------------------------------------+----> These are the useful equations the solver will implement
//
//Expanding (16) with finite differencing:
// Div*F = G*m_r
// = dF/dx + dF/dy = G*m_r
//(18) = (F[x+dx,y]-F[x-dx,y])/(2dx) + (F[x,y+dy]-F[x,y-dy])/(2dy) = G[x,y]*m_r[x,y]
//
//Expanding (17) with finite differencing:
// Div*G = F * (V-E)
// = dG/dx + dG/dy = F * (V-E)
//(19) = (G[x+dx,y]-G[x-dx,y])/(2dx) + (G[x,y+dy]-G[x,y-dy])/(2dy) = F[x,y]*(V[x,y]-E)
//
//
/////////////////////
//Initial Conditons//
/////////////////////
//
//Take the structure to start in a barrier high enough enough to warrant using:
//(20) F[0,0] = 0
//
//As for the initial value of G: G is porportional to the slope of F (the envelope function)
//solutions for the envelope function will be approx. exponentials inside barrier regions.
//Exponentials are fast functions so any reasonable value of G will get the value of F going
//to where it is going to converge too. i.e. the overall tragectory will not be sensitive to
//the intial value of G if we are starting deep enough inside a tall barrier.
//
//(21) G[0,0] = 1
//
//additional FD notes:
/////////////////////////////////////////////////////////////////////////////////////////
//Consider three points on the x axis separated by distance "h" and indexed by "i" ... i.e. i-1, i, i+1 --> x-h, x, x+h
//The function F(x) has the values at those positions: F[i-1], F[i], F[i+1]
//Taylor expand F(x) at the i-1 and the i+1 point:
//(22) F[i-1] = F[i] - dF/dx|i * h + d^2F/dx^2|i * h^2/2! - d^3F/dx^3|i * h^3/3 + ...
//(23) F[i+1] = F[i] + dF/dx|i * h + d^2F/dx^2|i * h^2/2! + d^3F/dx^3|i * h^3/3 + ...
// ...where dF/dx|i means take the derivative with respect to x at point i
//If you add (22) and (23) every other term in the expansions cancel, such that:
//(24) F[i-1] + F[i+1] = 2*F[i] + d^2F/dx^2|i * h^2 + d^4F/dx^4|i + ...
//Rearrange (24) to put the seconcd derivative of F with respect to x on the LHS
//(25) d^2F/dx^2|i = (F[i+1] - 2*F[i] + F[i-1]) / h^2 - d^4F/dx^4|i + ...
//Drop the higher order corrections b/c a second order finite differencing approx of d^2F/dx^2|i is all we should need
// +----------------------------------------------------------------+
//(26) | d^2F/dx^2|i = (F[i+1] - 2*F[i] + F[i-1]) / h^2 + O(h^2) |
// +----------------------------------------------------------------+-------->
//The error contained in O(h^2) is of the order h^2 and therefore will be small.
//BTW, subtracting (22) and (23) you can rearrange to get an accurate approx for dF/dx|i
// +---------------------------------------------------------+
//(27) | dF/dx|i = (F[i+1] - F[i-1]) / (2h) + O(h^2) |
// +---------------------------------------------------------+-------->
*/
PS_LIST ps_solve_1D(PS_DATA potential, PS_DATA effective_mass, PS_SOLVE_PARAMETERS *params) {
char log_message[256];
ps_log("PsiShooter -- a shooting method solver for the time independant Schrodinger equation under the effective mass approximation.\n");
ps_log("Iterate through Energy Eigenvalues to find the lowest bound state.\n");
PS_LIST solution_list = ps_list_create(); // This is a linked list for storing solutions
// wavefunction storage.
int N = potential->xsize; // used for generating strings with sprintf for sending to ps_log
// double dx = potential->xstep; //cm, size of differential length (TODO: Compute dx inside loop)
double dx = ps_data_dx_at(potential, 2); // in case 0 to 1 is wierd, this will do 1 to 2
//sanity checks, the effective mass should be on the same grid as the potential
if(N != effective_mass->xsize) {
//problem
sprintf(log_message, "\tThat's wierd... there are %d elements in the x axis mesh for the potential, but %d elements in the effective mass x axis mesh. Check to make sure the files for potential and effective mass have the same mesh. \n", N, effective_mass->xsize);
ps_log(log_message);
return NULL;
}
if(dx != ps_data_dx_at(effective_mass, 2)) {
//more problems
sprintf(log_message, "\tThat's wierd... the step size for the potential x axis is %e nm, and the the step size for the effective mass x axis mesh is %e nm. They need the same meshes to work", dx, ps_data_dx_at(effective_mass, 2));
ps_log(log_message);
return NULL;
}
double F[N]; //the envelope function (wavefunction)
double F_endpoint[params->n_iter]; // We save the last value of the envelope for each solution
double G[N]; //the aux function
//F
//intial eqn --> Div*F = G*m_r
//convert to finite diff eqn --> (F[x+dx,y]-F[x-dx,y])/(2dx) + (F[x,y+dy]-F[x,y-dy])/(2dy) = G[x,y]/M[x,y]
//convert to 1D --> (F[x+dx]-F[x-dx])/(2dx) = G[x]/M[x]
//rearrange --> F[x+dx] = (2dx)*G[x]/M[x] + F[x-dx]
//convert to c style --> F[i+1] = (2dx)*G[i]*m[i] + F[i-1]
// F[i+1] = F_coeff*G[i]*m[i] + F[i-1]
double F_coeff = 2*dx; //handy prefactor that would otherwise be for every point evaluated
//G
//intial eqn --> Div*G = F * 2*(V-E)/h_bar^2
//convert to finite diff eqn --> (G[x+dx,y]-G[x-dx,y])/(2dx) + (G[x,y+dy]-G[x,y-dy])/(2dy) = F[x,y]*2*(V[x,y]-E[x,y])/h_bar^2
//convert to 1D --> G[x+dx]-G[x-dx]/(2dx) = F[x]*2*(V[x]-E)/h_bar^2
//rearrange --> G[x+dx] = (2dx)*F[x]*2*(V[x]-E)/h_bar^2 + G[x-dx]
//convert to c style --> G[i+1] = 4*dx/hbar^2 * F[i]*(V[i]-E) + G[i-1]
// G[i+1] = G_coeff * F[i]*(V[i]-E) + G[i-1]
//double G_coeff = 4*dx/(HBAR_PLANCK_SQ); //handy prefactor that would otherwise be computed for every point evaluated
double G_coeff = 4*dx*G_COEFF; // Redefined to use M_ELECTRON/HBAR^2 using assuming units of nm and eV
int bound_state_count = 0;
int i, iter;
double E = params->energy_min;
double Estep = (params->energy_max - params->energy_min)/(params->n_iter);
double V; //eV, Current potential
double m_eff;
for (iter = 0; iter < params->n_iter; iter++) {
//initial conditions
F[0] = 0;
G[0] = 1;
F[1] = F_coeff * G[0] * m_eff + 0;
G[1] = G_coeff * F[0] * (V-E) + G[0];
for(i=1; i<N; i++) {
V = ps_data_value(potential, 0,i); //V[i]
m_eff = ps_data_value(effective_mass, 0,i); //m_eff[i]
//Lets eliminate bad solutions by checking if the forward and backwards solutions overlap
F[i+1] = F_coeff * G[i] * m_eff + F[i-1]; //subbed in m_eff for m[i], To Do: support a position dependant
G[i+1] = G_coeff * F[i] * (V-E) + G[i-1]; // mass by storing different masses at different locations (add to the PS_DATA structure probably)
/*
//Mix the bidirectional and forward derivatives to prevent two seperate solutions from forming. This
//Makes the upper solutions stable and oscillation free. (Probably only required on the i==1 index -jns)
// TODO compare results of this branching statement with IF (1==i) ... ELSE ...
if (i%2==1){
F[i+1] = F_coeff * G[i] * m_eff + F[i];
//subbed in m_eff for m[i], To Do: support a position dependant
// mass by storing different masses at different locations (add to the PS_DATA structure probably)
G[i+1] = G_coeff * F[i] * (V-E) + G[i];
}
if (i%2==0){
F[i+1] = 2*F_coeff * G[i] * m_eff + F[i-1];
//subbed in m_eff for m[i], To Do: support a position dependant
// mass by storing different masses at different locations (add to the PS_DATA structure probably)
G[i+1] = 2*G_coeff * F[i] * (V-E) + G[i-1];
}
*/
}
F_endpoint[iter] = F[N-1]; //store the last point of the solution in an array, use this to bracket roots by looking for sign changes (zero crossings)
//Try to detect which solutions are eigen states (bound states)
if((iter > 0) &&
((F_endpoint[iter] > 0 && F_endpoint[iter-1] < 0) ||
(F_endpoint[iter] < 0 && F_endpoint[iter-1] > 0)))
{
/*
//if there was a change in sign between the last point of the prev and current envelope function then there probably was a zero crossing and there a solution test for a sign crossing
//in order to reject solutions that appear to just be amplified/oscillating numerical error run
//shoot solutions backwards to see if you get basically the same enevelope function. If they really
//are just amplified error then the shots will look like this:
// forwards: ----.'.'. increasing amplitude in this direcion-->
// backwards: .'.'.---- <--increasing amplitude in this direcion
F[N] = 0;
G[N] = 1;
F[N-1] = F_coeff * G[0] * m_eff + 0;
G[N-1] = G_coeff * F[0] * (V-E) + G[0];
//Lets eliminate bad solutions by checking if the forward and backwards solutions overlap
for(i=N-1; i>0; i--) {
V = ps_data_value(potential, 0,i); //V[i]
F[i-1] = F[i+1] - F_coeff * G[i] * m_eff; //subbed in m_eff for m[i], To Do: support a position dependant
G[i-1] = G[i+1] + G_coeff * F[i] * (E-V); // mass by storing different masses at different locations (add to the PS_DATA structure probably)
}
//ToDo:
//see if the overlap is about unity.
*/
// Add the solution to the list of bound states
PS_DATA wavefunction = ps_data_copy(potential); // copy the potential to get the x,y coordinate stuff and sizes
ps_data_set_data(wavefunction, F); // Overwrite the potential with the wavefunction
PS_SOLUTION *solution = (PS_SOLUTION*)malloc(sizeof(PS_SOLUTION));
solution->energy = E;
solution->wavefunction = wavefunction;
ps_list_add(solution_list, solution);
bound_state_count++;
// print a log message
sprintf(log_message, "\tBoundstate number %d with E=%e found, F[N]=%e\n", bound_state_count, solution->energy, F[N]);
ps_log(log_message);
}
// Consider removing this for speed
// sprintf(log_message, "\tE=%g eV\tF[N-1]=%g\n", E, F[N-1]);
// ps_log(log_message);
E += Estep; // Increment the energy
}
return solution_list;
}
void ps_instance_dump(int pid)
{
__android_log_print(ANDROID_LOG_INFO, "JNIMsg", "run JNI function: %s ", "ps_instance_dump");
char statline[BUFFERSIZE * 2];
struct stat stats;
process_info psinfo;
FILE *ps;
struct passwd *pw;
int n;
memset(&psinfo, 0, sizeof(process_info));
psinfo.pid = pid;
snprintf(statline, BUFFERSIZE * 2, "/proc/%d", pid);
stat(statline, &stats);
psinfo.uid = (int) stats.st_uid;
pw = getpwuid(stats.st_uid);
if (pw == 0)
{
snprintf(psinfo.owner, 80, "%d", (int) stats.st_uid);
}
else
{
strncpy(psinfo.owner, pw->pw_name, 80);
}
snprintf(statline, BUFFERSIZE * 2, "/proc/%d/stat", pid);
ps = fopen(statline, "r");
if (ps != 0)
{
/* Scan rest of string. */
fscanf(ps, "%*d %*s %c %*d %*d %*d %*d %*d %*d %*d %*d %*d %*d "
"%lu %lu %*d %*d %*d %*d %d %*d %*d %*lu %ld", &psinfo.status,
&psinfo.delta_utime, &psinfo.delta_stime, &psinfo.threadnum,
&psinfo.rss);
fclose(ps);
}
snprintf(statline, BUFFERSIZE * 2, "/proc/%d/cmdline", pid);
ps = fopen(statline, "r");
if (ps == 0)
{
n = 0;
}
else
{
n = fread(psinfo.name, 1, 80, ps);
fclose(ps);
if (n < 0)
n = 0;
}
psinfo.name[n] = 0;
if (strlen(psinfo.name) == 0)
{
snprintf(statline, BUFFERSIZE * 2, "/proc/%d/stat", pid);
ps = fopen(statline, "r");
if (ps != 0)
{
n = fscanf(ps, "%d (%s)", &pid, psinfo.name);
fclose(ps);
if (n == 2)
psinfo.name[strlen(psinfo.name) - 1] = 0;
}
}
if ((strcmp(psinfo.owner, "root") != 0)
&& (strstr(psinfo.name, "/system/") == 0)
&& (strstr(psinfo.name, "/sbin/") == 0)
&& (strcmp(psinfo.name, "sh") != 0)
&& (strcmp(psinfo.name, "logcat") != 0)
&& (strcmp(psinfo.name, "watchdog") != 0)
&& (strcmp(psinfo.name, "sleep") != 0)
&& (strcmp(psinfo.name, "system_server") != 0))
ps_list_add(&psinfo);
}