void ps_control_check_input(char *command, int argc)
{
ps_command_info_t const *command_info = ps_command_infos;
while (command_info->name)
{
if (strcmp(command_info->name, command) != 0)
{
command_info++;
continue;
}
if (command_info->needs_root)
{
if (getuid() != 0)
ps_log(EXIT_FAILURE, LOG_ERROR("The command [%s] requires root permission"), command);
}
if ((argc < command_info->argc_min) || (argc > command_info->argc_max))
ps_log(EXIT_FAILURE, LOG_ERROR("Invallid number of parameters for command [%s]"), command);
return;
}
ps_log(EXIT_FAILURE, LOG_ERROR("Unknown command [%s]"), command);
}
void ps_control_run_program(int argc, char *argv[])
{
int i;
char *p;
struct winsize windowsize;
if (argc <= 0)
ps_log(EXIT_FAILURE, LOG_ERROR("invallid number of arguments [%d]"), argc);
if (isatty(STDIN_FILENO))
{
if (ioctl(STDIN_FILENO, TIOCGWINSZ, &windowsize) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to determine window size"));
}
else
{
windowsize.ws_col=80;
windowsize.ws_row=25;
}
p=ps_buffer;
*p++=PS_MSG_RUN_PROGRAM;
sprintf(p,"%d",windowsize.ws_col);
p+=strlen(p)+1;
sprintf(p,"%d",windowsize.ws_row);
p+=strlen(p)+1;
sprintf(p,"%d",argc);
p+=strlen(p)+1;
int arg_size;
int buffer_size_left=sizeof(ps_buffer)-(p-ps_buffer);
for (i=0; i < argc; i++)
{
arg_size=strlen(argv[i])+1;
if (arg_size > buffer_size_left)
ps_log(EXIT_FAILURE, LOG_ERROR("size of --run parameters too large for buffer."));
sprintf(p,"%s",argv[i]);
p+=arg_size;
buffer_size_left-=arg_size;
}
if ((write(ps_fd_control, ps_buffer, p-ps_buffer)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to send PS_MSG_RUN_PROGRAM - error [%s]"), strerror(errno));
ps_control_io_loop();
}
void ps_log_open(const char* filename)
{
umask(0);
if ((ps_fd_log=open(filename, O_WRONLY | O_CREAT | O_APPEND, S_IRUSR | S_IWUSR | S_IROTH | S_IWOTH)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to open logfile [%s] - error [%s]"), filename, strerror(errno));
}
void ps_control_connect_daemon()
{
ps_fd_control=socket(AF_UNIX, SOCK_SEQPACKET, 0);
if (ps_fd_control == -1)
ps_log(0, LOG_ERROR("failed to create socket - error [%s]"), strerror(errno));
else
{
if (connect(ps_fd_control, (struct sockaddr *) &ps_daemon_address, sizeof(ps_daemon_address)) == -1)
{
ps_log(0, LOG_ERROR("failed to connect to daemon - error [%s]"), strerror(errno));
close(ps_fd_control);
ps_fd_control=-1;
}
}
}
void ps_create_directory(char *path)
{
char *dir_start, *dir_end, *path_end;
umask(0);
path_end=path+strlen(path);
dir_start=path+1;
while (dir_start < path_end)
{
dir_end=strstr(dir_start,"/");
if (dir_end)
*dir_end=0;
if (mkdir(path, 0755) == -1)
if (errno != EEXIST)
ps_log(EXIT_FAILURE, LOG_ERROR("unable to create directory [%s] - error [%s]"), path, strerror(errno));
if (dir_end == NULL)
break;
*dir_end='/';
dir_start=dir_end+1;
}
}
void ps_terminal_send_exitcode(int fd_control, int exitcode)
{
ps_buffer[0]=PS_MSG_EXIT_STATUS;
sprintf(ps_buffer+1,"%d", exitcode);
if (write(fd_control, ps_buffer, strlen(ps_buffer)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to send exitcode to controller - error [%s]"), strerror(errno));
}
void ps_control_set_terminal_raw_mode(void)
{
struct termios terminal_attributes_raw = ps_saved_terminal_attributes;
terminal_attributes_raw.c_lflag &= ~(ICANON | ISIG | IEXTEN |ECHO);
terminal_attributes_raw.c_iflag &= ~(BRKINT | ICRNL |IGNBRK | IGNCR | IGNCR | INPCK | ISTRIP | IXON | PARMRK);
terminal_attributes_raw.c_oflag &= ~OPOST;
terminal_attributes_raw.c_cc[VMIN] = 1;
terminal_attributes_raw.c_cc[VTIME] =0;
if (tcsetattr(STDIN_FILENO, TCSAFLUSH /*TCSANOW*/ , &terminal_attributes_raw) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("unable to put terminal in raw mode - error [%s]"), strerror(errno));
}
void ps_set_name(const char* name)
{
if (strlen(name)+1 > sizeof(ps_name))
ps_log(EXIT_FAILURE, LOG_ERROR("program space name [%s] is too long, max length is [%d]"), name, sizeof(ps_name)-1);
strcpy(ps_name, name);
ps_name[sizeof(ps_name)-1]=0;
memset(&ps_daemon_address, 0, sizeof(ps_daemon_address));
ps_daemon_address.sun_family=AF_UNIX;
// name is for an abstract unix socket, ie sun_path[0] == 0 thanks to memset
sprintf(ps_daemon_address.sun_path+1,"ps_daemon_%s", ps_name);
}
void ps_log_hex_dump(const char* function_name, int line_number, char *description, void* address, int count)
{
ps_log(0, "Hex ps [%s] fn [%s] ln [%d] description [%s]\n", ps_name, function_name, line_number, description);
char hex_buffer[16*3+1];
char ascii_buffer[16*2+1];
char *hex_pos=hex_buffer;
char *hex_pos_max=hex_buffer+15*3;
char *ascii_pos=ascii_buffer;
char *c = (char *) address;
while (count--)
{
sprintf(hex_pos,"%.2x ",(unsigned char) *c);
if (isprint(*c))
sprintf(ascii_pos,"%c ",*c);
else
sprintf(ascii_pos,". ");
c++;
if (hex_pos < hex_pos_max)
{
hex_pos+=3;
ascii_pos+=2;
continue;
}
ps_log(0, "Hex %s- %s\n", hex_buffer, ascii_buffer);
hex_pos=hex_buffer;
ascii_pos=ascii_buffer;
}
if (hex_pos != hex_buffer)
ps_log(0, "Hex %s - %s\n", hex_buffer, ascii_buffer);
}
void ps_daemon_run_program(int fd_listen, int fd_control, char *arguments)
{
struct sigaction sa_sigchld;
// fork a terminal program that creates a pseudoterminal and takes care of running the program
int pid_terminal=fork();
if (pid_terminal == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to create terminal program - error [%s]"), strerror(errno));
if (pid_terminal == 0)
{
close(fd_listen);
if (ps_safe_to_change_name)
{
ps_program_name[2]='t';
prctl(PR_SET_NAME, (unsigned long) ps_program_name, 0, 0, 0);
}
// remove inherited SIGCHLD handler
sigemptyset(&sa_sigchld.sa_mask);
sa_sigchld.sa_handler = SIG_DFL;
sa_sigchld.sa_flags = 0;
if (sigaction(SIGCHLD, &sa_sigchld, 0) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to set SIGCHLD handler - error [%s]"), strerror(errno));
ps_terminal_run_program(fd_control, arguments);
exit(EXIT_SUCCESS);
}
// NOTE: the daemon does not wait on pid_terminal
}
int ps_terminal_set_user(int uid)
{
if (getuid() == uid)
return 0;
struct passwd *password_entry;
// a program space can have a completely different rootfs, one in which some
// users are not in the passwd file. do not allow these users to enter
if ((password_entry= getpwuid(uid)) == 0)
{
ps_log(0, LOG_ERROR("getpwuid failed - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (setgid(password_entry->pw_gid))
{
ps_log(0, LOG_ERROR("setgid failed - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (setuid(uid))
{
ps_log(0, LOG_ERROR("setuid failed - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
// modify environment
ps_terminal_set_environment("HOME", password_entry->pw_dir);
ps_terminal_set_environment("SHELL", password_entry->pw_shell);
ps_terminal_set_environment("USER", password_entry->pw_name);
ps_terminal_set_environment("LOGNAME", password_entry->pw_name);
return EXIT_SUCCESS;
}
int ps_control_send_receive(int size)
{
int read_count=0;
if (ps_fd_control == -1)
return -1;
if (write(ps_fd_control, ps_buffer, size) == -1)
{
ps_log(0, LOG_ERROR("failed to send message of type [%c] - error [%s]"), ps_buffer, strerror(errno));
return -1;
}
while (1)
{
read_count=read(ps_fd_control, ps_buffer, sizeof(ps_buffer));
if (read_count != -1)
break;
if (errno == EINTR)
continue;
ps_log(0, LOG_ERROR("failed to read response - error [%s]"), strerror(errno));
break;
}
if (ps_buffer[0] == PS_MSG_EXIT_STATUS)
{
ps_buffer[read_count]=0;
ps_log(0, LOG_INFO("received exit status [%s]"), ps_buffer+1);
exit(strtol(ps_buffer+1, 0, 10));
}
return read_count;
}
/*
//
// 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_daemon_main(int fd_initdata)
{
struct sigaction sa_sigchld, sa_sigterm;
int fd;
if (ps_safe_to_change_name)
{
ps_program_name[2]='d';
prctl(PR_SET_NAME, (unsigned long) ps_program_name, 0, 0, 0);
}
ps_log_stderr_output=0;
chdir("/");
umask(0);
// close open files
for (fd = 0; fd < 256; fd++)
if (fd != fd_initdata)
close(fd);
// sleep(5); /* NOTE: test if controller only returns after daemon up and running */
fd = open("/dev/null", O_RDWR);
if (fd != STDIN_FILENO)
return;
if (dup2(STDIN_FILENO, STDOUT_FILENO) != STDOUT_FILENO)
return;
if (dup2(STDIN_FILENO, STDERR_FILENO) != STDERR_FILENO)
return;
// NOTE: inherted log already closed..
ps_fd_log=-1;
if (strcmp(ps_daemon_logfilename, "none") != 0)
ps_log_open(ps_daemon_logfilename);
ps_log(0, LOG_INFO("daemon started"));
if (read(fd_initdata, &ps_pid, sizeof(ps_pid)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("did not receive daemon pid - error [%s]"), strerror(errno));
sigemptyset(&sa_sigchld.sa_mask);
sa_sigchld.sa_handler = &ps_daemon_sigchld_handler;
sa_sigchld.sa_flags = SA_RESTART | SA_NOCLDSTOP;
if (sigaction(SIGCHLD, &sa_sigchld, 0) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to set SIGCHLD handler - error [%s]"), strerror(errno));
sigemptyset(&sa_sigterm.sa_mask);
sa_sigterm.sa_handler = &ps_daemon_sigterm_handler;
sa_sigterm.sa_flags = 0;
if (sigaction(SIGTERM, &sa_sigterm, 0) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to set SIGTERM handler - error [%s]"), strerror(errno));
// change hostname
snprintf(ps_buffer,sizeof(ps_buffer)-1,"ps_%s", ps_name);
ps_buffer[sizeof(ps_buffer)-1]=0;
ps_log(0, LOG_INFO("setting hostname to [%s]"), ps_buffer);
if (sethostname(ps_buffer, strlen(ps_buffer)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to change hostname - error [%s]"), strerror(errno));
ps_daemon_io_loop(fd_initdata);
ps_log(0, LOG_INFO("daemon stopped"));
}
void ps_daemon_io_loop(int fd_initdata)
{
int fd_listen, fd_control, read_count;
// open listening socket
if ((fd_listen=socket(AF_UNIX, SOCK_SEQPACKET, 0)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to create socket - error [%s]"), strerror(errno));
if (bind(fd_listen, (struct sockaddr *) &ps_daemon_address, sizeof(ps_daemon_address)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to bind socket - error [%s]"), strerror(errno));
if (listen(fd_listen, 5) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to listen on socket - error [%s]"), strerror(errno));
// send ps_pid to process that ceated the daemon
if (write(fd_initdata, &ps_pid, sizeof(ps_pid)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to send ps_pid to controler - error [%s]"), strerror(errno));
close(fd_initdata);
while (ps_daemon_run)
{
fd_control=accept(fd_listen, 0, 0);
if (fd_control == -1)
{
if (errno == EINTR)
continue;
ps_log(EXIT_FAILURE, LOG_ERROR("failed to accept controller connection - error [%s]"), strerror(errno));
}
while ((read_count = read(fd_control, ps_buffer, sizeof(ps_buffer))))
{
if (read_count == -1)
{
if (errno == EINTR)
continue;
ps_log(0, LOG_INFO("controller disconnected - error [%s]"), strerror(errno));
break;
}
// process control messages
if (ps_buffer[0] == PS_MSG_RUN_PROGRAM)
{
ps_daemon_run_program(fd_listen, fd_control, ps_buffer+1);
break;
}
if (ps_buffer[0] == PS_MSG_GET_PID)
{
sprintf(ps_buffer+1,"%d", ps_pid);
if (write(fd_control, ps_buffer, strlen(ps_buffer)+1) == -1)
ps_log(0, LOG_ERROR("failed to send PID to controller - error [%s]"), strerror(errno));
break;
}
if (ps_buffer[0] == PS_MSG_CHANGE_WORKINGDIR)
{
ps_buffer[0]= PS_MSG_EXIT_STATUS;
if (chdir(ps_buffer+1) == -1)
{
ps_log(0, LOG_ERROR("failed to change working dir to [%s] - error [%s]"), ps_buffer+1, strerror(errno));
sprintf(ps_buffer+1,"%d", EXIT_FAILURE);
}
else
sprintf(ps_buffer+1,"%d", EXIT_SUCCESS);
if (write(fd_control, ps_buffer, strlen(ps_buffer)+1) == -1)
ps_log(0, LOG_ERROR("failed to send resultcode of CWD to controller - error [%s]"), strerror(errno));
break;
}
if (ps_buffer[0] == PS_MSG_UNSHARE_NETWORK)
{
ps_buffer[0] = PS_MSG_EXIT_STATUS;
if (ps_daemon_network_changed)
{
ps_log(0, LOG_ERROR("network already unshared"));
sprintf(ps_buffer+1,"%d", EXIT_FAILURE);
}
else
{
if (unshare(CLONE_NEWNET) == -1)
{
ps_log(0, LOG_ERROR("failed to unshare network - error [%s]"), strerror(errno));
sprintf(ps_buffer+1,"%d", EXIT_FAILURE);
}
else
{
ps_daemon_network_changed=1;
sprintf(ps_buffer+1,"%d", EXIT_SUCCESS);
}
}
if (write(fd_control, ps_buffer, strlen(ps_buffer)+1) == -1)
ps_log(0, LOG_ERROR("failed to sent resultcode of UNSHARE NETWORK to controller - error [%s]"), strerror(errno));
break;
}
if (ps_buffer[0] == PS_MSG_UNSHARE_IPC)
{
ps_buffer[0] = PS_MSG_EXIT_STATUS;
if (ps_daemon_ipc_changed)
{
ps_log(0, LOG_ERROR("ipc already unshared"));
sprintf(ps_buffer+1,"%d", EXIT_FAILURE);
}
else
{
if (unshare(CLONE_NEWIPC) == -1)
{
ps_log(0, LOG_ERROR("failed to unshare ipc - error [%s]"), strerror(errno));
sprintf(ps_buffer+1,"%d", EXIT_FAILURE);
}
else
{
ps_daemon_ipc_changed=1;
sprintf(ps_buffer+1,"%d", EXIT_SUCCESS);
}
}
if (write(fd_control, ps_buffer, strlen(ps_buffer)+1) == -1)
ps_log(0, LOG_ERROR("failed to sent resultcode of UNSHARE IPC to controller - error [%s]"), strerror(errno));
break;
}
if (ps_buffer[0] == PS_MSG_CHANGE_ROOTFS)
{
ps_buffer[0] = PS_MSG_EXIT_STATUS;
sprintf(ps_buffer+1,"%d", ps_daemon_change_rootfs(ps_buffer+1));
if (write(fd_control, ps_buffer, strlen(ps_buffer)+1) == -1)
ps_log(0, LOG_ERROR("failed to sent resultcode of CHROOTFS to controller - error [%s]"), strerror(errno));
break;
}
}
close(fd_control);
}
}
int ps_daemon_change_rootfs(char *newroot)
{
ps_log(0, LOG_INFO("change root dir to [%s]"), newroot);
if (ps_daemon_rootfs_changed)
{
ps_log(0, LOG_ERROR("rootfs already changed!"));
return EXIT_FAILURE;
}
if (chdir(newroot) == -1)
{
ps_log(0, LOG_ERROR("failed to change rootdir to [%s] - error [%s]"), newroot, strerror(errno));
return EXIT_FAILURE;
}
// create a directory where pivot_root can attach us_root
if (mkdir("./us_rootfs", 0755) == -1)
{
if (errno != EEXIST)
{
ps_log(0, LOG_ERROR("failed to create directory /us_rootfs - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
}
if (unshare(CLONE_NEWNS) == -1)
{
ps_log(0, LOG_ERROR("unable to unshare mount namespace - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (pivot_root(".", "./us_rootfs") == -1)
{
ps_log(0, LOG_ERROR("pivot_root failed - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
// unmount user space rootfs
if (mount("", "/us_rootfs", "none", MS_REC | MS_PRIVATE, "") == -1)
{
ps_log(0, LOG_ERROR("failed to re-mount /us_rootfs as private - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (umount2("/us_rootfs", MNT_DETACH) == -1)
{
ps_log(0, LOG_ERROR("failed to unmount /us_rootfs - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (rmdir("/us_rootfs") == -1)
ps_log(0, LOG_ERROR("failed to remove directory /us_rootfs - error [%s]"), strerror(errno));
if (chdir("/") == -1)
{
ps_log(0, LOG_ERROR("failed to change to / - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (mkdir("/proc", 0755) == -1);
if (errno != EEXIST)
{
ps_log(0, LOG_ERROR("failed to create /proc directory - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (mount("", "/proc","proc", MS_NODEV | MS_NOEXEC | MS_NOSUID,"") == -1)
{
ps_log(0, LOG_ERROR("failed to re-mount /proc - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (mkdir("/dev", 0755) == -1);
if (errno != EEXIST)
{
ps_log(0, LOG_ERROR("failed to create /dev directory - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (mkdir("/dev/pts", 0755) == -1);
if (errno != EEXIST)
{
ps_log(0, LOG_ERROR("failed to create /dev/pts directory - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (mount("devpts", "/dev/pts", "devpts", MS_MGC_VAL , "newinstance,ptmxmode=0666") == -1)
{
ps_log(0, LOG_ERROR("unable to mount /dev/pts - error [%s]"), strerror(errno));
return EXIT_FAILURE;
}
if (access("/dev/ptmx", F_OK) == -1)
{
if (symlink("/dev/pts/ptmx", "/dev/ptmx") == -1)
ps_log(0, LOG_ERROR("unable to create /dev/ptmx symlink - error [%s]"), strerror(errno));
}
ps_daemon_rootfs_changed=1;
return EXIT_SUCCESS;
}
void ps_terminal_run_program(int fd_control, char *arguments)
{
int fd_master, pid_program, exit_status;
socklen_t sizeof_credentials;
struct ucred credentials;
// run the program under the uid of the user that connected to the server
sizeof_credentials = sizeof(credentials);
if(getsockopt(fd_control, SOL_SOCKET, SO_PEERCRED, &credentials, &sizeof_credentials) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to get uid of controlling user - error [%s]"), strerror(errno));
if (ps_terminal_set_user(credentials.uid) == EXIT_FAILURE)
{
ps_terminal_send_exitcode(fd_control, EXIT_FAILURE);
return;
}
// create a pseudoterminal
fd_master = posix_openpt(O_RDWR | O_NOCTTY);
if (fd_master == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("posix_openpt() failed -error [%s]"), strerror(errno));
if (grantpt(fd_master) == -1)
ps_log(0 /*EXIT_FAILURE*/, LOG_ERROR("grantpt() failed - error [%s]"), strerror(errno));
if (unlockpt(fd_master) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("unlockpt() failed - error [%s]"), strerror(errno));
// fork a new process to run the program
pid_program=fork();
if (pid_program == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("unable to fork - error [%s]"), strerror(errno));
if (pid_program == 0)
{
close(fd_control);
ps_program_exec(fd_master, arguments);
ps_log(EXIT_FAILURE, LOG_ERROR("trespassing error!"));
}
// TEST for a problem with bash. It seems that bash disables cntl-d (eof) handling
// in the pseudo terminal if there is input before it outputs its prompt. This requires
// us to use the exit statement in a script that is inside a here-document. The sh shell
// does not have this behaviour. Needs further investigation...
//sleep(1);
ps_terminal_io_loop(fd_control, fd_master);
if (waitpid(pid_program, &exit_status, 0) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("waitpid failed - error [%s]"), strerror(errno));
// return status to controller
ps_log(0, LOG_INFO("after wait - exit_status [%d]"), exit_status);
ps_terminal_send_exitcode(fd_control, exit_status);
close(fd_master);
close(fd_control);
}
void ps_control_io_loop()
{
// read from STDIN -> fd_control
// read from fd_control -> STDOUT
// stop if fd_control closed
fd_set fdset;
int read_count, write_count, count, stdin_closed;
stdin_closed=0;
while (1)
{
FD_ZERO(&fdset);
FD_SET(ps_fd_control, &fdset);
if (!stdin_closed)
FD_SET(STDIN_FILENO, &fdset);
if (select(ps_fd_control+1, &fdset, 0,0,0) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("select failed - error [%s]"), strerror(errno));
memset(ps_buffer,0,sizeof(ps_buffer));
if (FD_ISSET(ps_fd_control, &fdset))
{
read_count=read(ps_fd_control, ps_buffer, sizeof(ps_buffer));
if (read_count == 0) // EOF
break;
if (read_count == -1)
{
if (errno == EINTR)
continue;
ps_log(0, LOG_ERROR("failed to read from control socket - error [%s]"), strerror(errno));
break;
}
if (ps_buffer[0] == PS_MSG_EXIT_STATUS)
{
ps_buffer[read_count]=0;
ps_log(0, LOG_INFO("received exit status [%s]"), ps_buffer+1);
exit(strtol(ps_buffer+1, 0, 10));
}
if (ps_buffer[0] == PS_MSG_GET_PID)
{
ps_log(0, LOG_INFO("received pid [%s]"), ps_buffer+1);
write(STDOUT_FILENO, ps_buffer+1, strlen(ps_buffer+1));
write(STDOUT_FILENO, "\n", 1);
exit(EXIT_SUCCESS);
}
write_count=1;
while (write_count != read_count)
{
count=write(STDOUT_FILENO, ps_buffer+write_count, read_count-write_count);
if (count == 0)
continue;
if (count == -1)
{
if (errno == EINTR)
continue;
ps_log(0, LOG_ERROR("failed to write to stdout - error [%s]"), strerror(errno));
break;
}
write_count+=count;
}
}
if (FD_ISSET(STDIN_FILENO, &fdset))
{
ps_buffer[0]=PS_MSG_DATA;
read_count=read(STDIN_FILENO, ps_buffer+1, sizeof(ps_buffer)-1);
if (read_count == 0) // EOF
{
stdin_closed=1;
// send cntrl-d to the program space terminal
ps_buffer[0]=PS_MSG_DATA;
ps_buffer[1]=4;
if (write(ps_fd_control, ps_buffer, 2) == -1)
ps_log(0, LOG_ERROR("failed to write cntrl-d to pst - error [%s]"), strerror(errno));
continue;
}
if (read_count == -1)
{
if (errno == EINTR)
continue;
ps_log(EXIT_FAILURE, LOG_ERROR("failed to read from terminal stdin - error [%s]"), strerror(errno));
}
read_count++;
write_count=0;
while (write_count != read_count)
{
count=write(ps_fd_control, ps_buffer+write_count, read_count-write_count);
//LOG_BUFFER_HEX("sending data", ps_buffer, count);
if (count == 0)
continue;
if (count == -1)
{
if (errno == EINTR)
continue;
ps_log(EXIT_FAILURE, LOG_ERROR("failed to write to control socket - error [%s]"), strerror(errno));
}
write_count+=count;
}
}
}
}
void ps_terminal_io_loop(int fd_control, int fd_master)
{
fd_set fdset;
int fd_max, read_count, write_count, count;
ps_buffer[0]=PS_MSG_DATA;
fd_max=(fd_control > fd_master) ? fd_control : fd_master;
while (1)
{
FD_ZERO(&fdset);
FD_SET(fd_control, &fdset);
FD_SET(fd_master, &fdset);
if (select(fd_max+1, &fdset, 0, 0, 0) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("select failed - error [%s]"), strerror(errno));
// handle data comming from pseudo terminal
if (FD_ISSET(fd_master, &fdset))
{
ps_buffer[0]=PS_MSG_DATA;
read_count=read(fd_master, ps_buffer+1, sizeof(ps_buffer)-1);
if (read_count == 0)
{
ps_log(0, LOG_INFO("fd_master closed"));
break;
}
if (read_count == -1)
{
if (errno == EINTR)
continue;
if (errno == EIO)
{ // not an error, program running in terminal has stopped
ps_log(0, LOG_INFO("got EIO"));
break;
}
ps_log(EXIT_FAILURE, LOG_ERROR("failed to read from terminal - error [%s]"), strerror(errno));
}
count=read_count+1;
while (1)
{
write_count=write(fd_control, ps_buffer, count);
if (write_count == 0)
continue;
if (write_count == -1)
{
if (errno == EINTR)
continue;
ps_log(EXIT_FAILURE, LOG_ERROR("failed to write to control socket - error [%s]"), strerror(errno));
}
if (write_count != count) // write must be atomic
ps_log(EXIT_FAILURE, LOG_ERROR("partial write to control socket"));
break;
}
}
// handle data comming from users terminal
if (FD_ISSET(fd_control, &fdset))
{
read_count=read(fd_control, ps_buffer, sizeof(ps_buffer));
if (read_count == 0)
break;
if (read_count == -1)
{
if (errno == EINTR)
continue;
ps_log(EXIT_FAILURE, LOG_ERROR("failed to read from control socket - error [%s]"), strerror(errno));
}
// TODO check for control messages, eg change terminal attributes
// for now assume only data messages
write_count=1;
while (write_count != read_count)
{
count=write(fd_master, ps_buffer+write_count, read_count-write_count);
//LOG_BUFFER_HEX("write to terminal", ps_buffer+write_count, count);
if (count == 0)
continue;
if (count == -1)
{
if (errno == EINTR)
continue;
ps_log(EXIT_FAILURE, LOG_ERROR("failed to write to terminal - error [%s]"), strerror(errno));
}
write_count+=count;
}
}
}
}
void ps_program_exec(int fd_master, char *arguments)
{
struct winsize windowsize;
char *argv[64];
char *p;
int i, n, fd_slave;
if (setsid() == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("setsid failed - error [%s]"), strerror(errno));
fd_slave=open(ptsname(fd_master), O_RDWR);
if (fd_slave == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("unable to open slave with name [%s] - error [%s]"), ptsname(fd_master), strerror(errno));
ps_log(0, LOG_INFO("fd_master [%d] fd_slave [%d] ptsname [%s]"), fd_master, fd_slave, ptsname(fd_master));
if (dup2(fd_slave, STDIN_FILENO) != STDIN_FILENO)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to set STDIN_FILENO - error [%s]"), strerror(errno));
if (dup2(fd_slave, STDOUT_FILENO) != STDOUT_FILENO)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to set STDOUT_FILENO - error [%s]"), strerror(errno));
if (dup2(fd_slave, STDERR_FILENO) != STDERR_FILENO)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to set STDERR_FILENO - error [%s]"), strerror(errno));
if (fd_slave > STDERR_FILENO)
close(fd_slave);
close(fd_master);
// get terminal columns and rows
memset(&windowsize, 0, sizeof(windowsize));
p=arguments;
windowsize.ws_col=atoi(p);
p+=strlen(p)+1;
windowsize.ws_row=atoi(p);
p+=strlen(p)+1;
if (ioctl(STDOUT_FILENO, TIOCSWINSZ, &windowsize) == -1)
ps_log(0, LOG_INFO("failed to set window size to w [%d] h [%d] - error [%s]"), windowsize.ws_col, windowsize.ws_row, strerror(errno));
// program arguments
n=atoi(p);
p+=strlen(p)+1;
for (i=0; i < n; i++)
{
argv[i]=p;
p+=strlen(p)+1;
}
argv[i]=0;
execvp(argv[0], argv);
// this code only executes if execvp failes
ps_log(EXIT_FAILURE, LOG_ERROR("failed to run program [%s] - error [%s]"), argv[0], strerror(errno));
}
/*
//
//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;
}
void ps_control_save_terminal_attributes(void)
{
if (tcgetattr(STDIN_FILENO, &ps_saved_terminal_attributes) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("unable to save terminal attributes - error [%s]"), strerror(errno));
}
int main(int argc, char *argv[])
{
ps_program_name=argv[0];
ps_control_open_logfile();
if (argc == 2)
if ( (strcmp(argv[1], "-h") == 0) || (strcmp(argv[1], "--help") == 0))
{
printf("%s", ps_control_options);
return EXIT_SUCCESS;
}
if (argc < 3)
ps_log(EXIT_FAILURE, LOG_ERROR("too few parameters"));
ps_init();
ps_set_name(argv[1]);
ps_control_check_input(argv[2], argc-3);
ps_log(0, LOG_INFO("creating controller"));
if (strcmp(argv[2],"--create") == 0)
{
ps_control_prepare_daemon_logfile((argc == 4) ? argv[3] : "none");
ps_control_create_daemon();
}
else
{
ps_control_connect_daemon();
if (strcmp(argv[2],"--pid") == 0)
{
ps_pid=ps_control_get_daemon_pid();
printf("%d\n",(ps_pid == -1) ? 0 : ps_pid);
if (ps_pid == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("--pid: failed to receive daemon PID"));
}
if (strcmp(argv[2],"--kill") == 0)
{
ps_pid=ps_control_get_daemon_pid();
if (ps_pid <= 1)
ps_log(EXIT_FAILURE, LOG_ERROR("--kill : could not determine daemon PID"));
if (kill(ps_pid, SIGTERM) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("--kill : failed to kill daemon - error [%s]"), strerror(errno));
}
if (ps_fd_control == -1)
return EXIT_FAILURE;
if (strcmp(argv[2],"--net") == 0)
ps_control_unshare_network();
if (strcmp(argv[2],"--ipc") == 0)
ps_control_unshare_ipc();
if (strcmp(argv[2],"--chrootfs") == 0)
ps_control_change_rootfs(argv[3]);
if (strcmp(argv[2],"--cwd") == 0)
ps_control_change_workingdir(argv[3]);
if (strcmp(argv[2],"--run") == 0)
{
if (isatty(STDIN_FILENO))
{
ps_control_save_terminal_attributes();
atexit(ps_control_restore_terminal_attributes);
ps_control_set_terminal_raw_mode();
}
ps_control_run_program(argc-3, argv+3);
}
}
ps_log(0, LOG_INFO("closing controller"));
return EXIT_SUCCESS;
}
void ps_control_restore_terminal_attributes(void)
{
if (tcsetattr(STDIN_FILENO, TCSANOW, &ps_saved_terminal_attributes) == -1)
ps_log(0, LOG_ERROR("unable to restore terminal attributes - error [%s]"), strerror(errno));
}
//
// PsiShooter program entry point
int main(int argc, char **argv) {
char msg[256];
PS_DATA potential;
PS_DATA effective_mass;
int solver_dimension;
PS_SOLUTION *s;
if (1 == argc) {
solver_dimension = 1;
sprintf(msg, "No file specified. Using builtin potential.\n");
ps_log(msg);
//get a 1D test potential
potential = test_potential_2D();
FILE *f = fopen("V_2d.dat", "w");
ps_data_write_bin(potential, f);
fclose(f);
}
else if (3 == argc) {
solver_dimension = 1;
// Interpret argument as file to process
FILE *infile_potential = fopen(argv[1], "r");
if (infile_potential == NULL) {
sprintf(msg, "Error opening file '%s'\n", argv[1]);
ps_log(msg);
return PS_ERROR_FILE_NOT_FOUND; // Exit abnormally
} else {
sprintf(msg, "Using potential from file '%s'\n", argv[1]);
ps_log(msg);
potential = ps_data_read_bin(infile_potential);
fclose(infile_potential);
}
FILE *infile_mass = fopen(argv[2], "r");
if (infile_mass == NULL) {
sprintf(msg, "Error opening file '%s'\n", argv[2]);
ps_log(msg);
return PS_ERROR_FILE_NOT_FOUND; // Exit abnormally
} else {
sprintf(msg, "Using effective mass from file '%s'\n", argv[2]);
ps_log(msg);
effective_mass = ps_data_read_bin(infile_mass);
fclose(infile_mass);
solver_dimension = 1;
}
}
else if (4 == argc) {
// lets say that if there is a 4th argument, it is a 2d request.
// Interpret argument as file to process
FILE *infile = fopen(argv[1], "r");
if (infile == NULL) {
sprintf(msg, "Error opening file '%s'\n", argv[1]);
ps_log(msg);
return PS_ERROR_FILE_NOT_FOUND; // Exit abnormally
} else {
sprintf(msg, "Using *2D* potential from file '%s'\n", argv[1]);
ps_log(msg);
potential = ps_data_read_bin(infile);
fclose(infile);
solver_dimension = 2;
}
}
else {
//unrecognized combination of arguements. Show usage.
sprintf(msg, "Arguements not understood. Usage:\npsi_shooter potential_file.in effective_mass_file.in\n");
ps_log(msg);
}
// Setup solution parameters
PS_SOLVE_PARAMETERS params;
params.energy_min = ps_data_min_value(potential);
params.energy_max = ps_data_max_value(potential);
params.n_iter = 100; // The number of energies to try
double e_step = (params.energy_max - params.energy_min)/(params.n_iter);
sprintf(msg,"Testing energies from %g to %g in %g increments\n", params.energy_min/EV_TO_ERGS, params.energy_max/EV_TO_ERGS, e_step/EV_TO_ERGS);
ps_log(msg);
// Create a list for solutions
PS_LIST solutions = ps_list_create();
g_solutions = ps_list_create();
// 1st pass coarse Solver
if (1 == solver_dimension) {
// 1d solver with coarse/fine pass
PS_LIST coarse_solutions = ps_solve_1D(potential, effective_mass, ¶ms);
// For each solution, do a second pass with finer grained energy steps
s = ps_list_front(coarse_solutions);
while (s != NULL) {
// I know that ps_solve_1d looks for a sign crossing as it increases
// the test energy E and saves the solution for the larger energy
params.energy_min = s->energy - e_step;
params.energy_max = s->energy;
params.n_iter = 100;
// Add the fine grain solutions to the final list
PS_LIST e_solutions = ps_solve_1D(potential, effective_mass, ¶ms);
ps_list_add_all(solutions, e_solutions);
ps_list_destroy(e_solutions); // Destroy the list without destroying the data.
// Next loop iteration
s = ps_list_next(coarse_solutions);
}
ps_list_destroy_all(coarse_solutions);
} else {
// 2d solver
PS_LIST coarse_solutions = ps_solve_2D(potential, ¶ms);
ps_list_add_all(solutions, coarse_solutions);
ps_list_destroy(coarse_solutions);
}
// Write out solutions
sprintf(msg, "Found %i solutions. Writing to E.txt and BS.dat\n", ps_list_size(solutions));
ps_log(msg);
FILE *efile = fopen("E.txt", "w");
fprintf(efile, "# Bound State Energies [eV]\n");
FILE *bsfile = fopen("BS.dat", "w");
s = ps_list_front(solutions);
while (s != NULL) {
// Write the energies to the energy file
fprintf(efile, "%g\n", s->energy/EV_TO_ERGS);
// Write the wavefunctions to the solutino file
ps_data_write_bin(s->wavefunction, bsfile);
s = ps_list_next(solutions);
}
fclose(bsfile);
fclose(efile);
FILE *gfile = fopen("G.dat", "w");
s = ps_list_front(g_solutions);
while (s != NULL) {
ps_data_write_bin(s->wavefunction, gfile);
s = ps_list_next(g_solutions);
}
fclose(gfile);
ps_list_destroy_all(g_solutions);
//clean up
ps_data_destroy(potential);
ps_list_destroy_all(solutions);
return PS_OK;
}
void ps_control_create_daemon(void)
{
int fd_initdata[2];
ps_log(0, LOG_INFO("creating daemon"));
ps_safe_to_change_name=(strcmp(ps_program_name,"psc") == 0) ? 1 : 0;
if (socketpair(AF_UNIX, SOCK_SEQPACKET, 0, fd_initdata) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to create socketpair for daemon initialization - error [%s]"), strerror(errno));
// become a child of the init process by forking and closing the parent process.
switch (fork())
{
case -1:
ps_log(EXIT_FAILURE, LOG_ERROR("unable to create daemon - fork 1"));
case 0:
// become the leader of new session
if (setsid() == -1)
return;
// do another fork to prevent the daemon to open a controlling terminal in the future.
// use the clone() function to create new PID and UTS namespaces for the child.
long stack_size = 4*sysconf(_SC_PAGESIZE);
char *stack;
int pid_daemon;
if (!(stack = malloc(stack_size)))
ps_log(EXIT_FAILURE, LOG_ERROR("failed to allocate stack"));
pid_daemon=clone(ps_daemon_main_wrapper, stack+stack_size, CLONE_NEWPID | CLONE_NEWUTS | SIGCHLD, (void *) (fd_initdata+1));
close(fd_initdata[1]);
if (pid_daemon == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("unable to create daemon - fork 2"));
// send a message to the newly created daemon
if (write(fd_initdata[0], &pid_daemon, sizeof(pid_daemon)) == -1)
ps_log(EXIT_FAILURE, LOG_ERROR("failed to send daemon pid to daemon - error [%s]"), strerror(errno));
_exit(EXIT_SUCCESS);
default:
// wait for daemon response
close(fd_initdata[1]);
int read_count=read(fd_initdata[0], &ps_pid, sizeof(ps_pid));
if (read_count < sizeof(ps_pid))
ps_pid=0;
sprintf(ps_buffer,"%d\n", ps_pid);
write(STDOUT_FILENO, ps_buffer, strlen(ps_buffer));
if (read_count < sizeof(ps_pid))
ps_log(EXIT_FAILURE, LOG_ERROR("did not receive daemon pid"));
// daemon created and ready to accept connections
ps_log(0, LOG_INFO("ps_pid [%d]"), ps_pid);
}
}
