/usr/share/octave/packages/optim-1.4.0/private/__siman__.m is in octave-optim 1.4.0-1.
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##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.
## The simulated annealing code is translated and adapted from siman.c,
## written by Mark Galassi, of the GNU Scientific Library.
function [p_res, objf, cvg, outp] = __siman__ (f, pin, hook)
## passed constraints:
##
## hook.mc: matrix of linear constraints
##
## hook.vc: vector of linear constraints
##
## hook.f_cstr: function of all constraints
##
## hook.df_cstr: function of derivatives of all constraints
##
## hook.n_gencstr: number of non-linear constraints
##
## hook.eq_idx: logical index of equality constraints in all
## constraints
##
## hook.lbound, hook.ubound: bounds, subset of linear inequality
## constraints in mc and vc
## passed values of constraints for initial parameters
pin_cstr = hook.pin_cstr;
## passed function for complementary pivoting, currently sqp is used
## instead
##
## cpiv = hook.cpiv;
## passed simulated annealing parameters
T_init = hook.siman.T_init;
T_min = hook.siman.T_min;
mu_T = hook.siman.mu_T;
iters_fixed_T = hook.siman.iters_fixed_T;
max_rand_step = hook.max_rand_step;
## passed options
fixed = hook.fixed;
verbose = strcmp (hook.Display, "iter");
user_interaction = hook.user_interaction;
siman_log = hook.siman_log;
trace_steps = hook.trace_steps;
save_state = ! isempty (hook.save_state);
recover_state = ! isempty (hook.recover_state);
## Parallelization, if any, will be done within the iterations at a
## fixed temperature. Some parameter combinations will be tested in
## parallel, but an order will be defined for them and all results
## after the first accepted will be discarded. The time savings will
## depend on the frequency of accepted results. To limit time losses
## even in cases where the first of the parallel results is accepted,
## the number of parallel tests will not exceed the number of
## available processor cores.
if ((parallel_local = hook.parallel_local))
np = int32 (nproc ("current"));
np = ifelse (iters_fixed_T < np, iters_fixed_T, np);
if (np < 2)
parallel_local = false;
endif
endif
## some useful variables derived from passed variables
n_lconstr = length (hook.vc);
n_bounds = sum (hook.lbound != -Inf) + sum (hook.ubound != Inf);
hook.ac_idx = true (n_lconstr + hook.n_gencstr, 1);
hook.ineq_idx = ! hook.eq_idx;
hook.leq_idx = hook.eq_idx(1:n_lconstr);
hook.lineq_idx = hook.ineq_idx(1:n_lconstr);
hook.lfalse_idx = false(n_lconstr, 1);
nz = 20 * eps; # This is arbitrary. Accuracy of equality constraints.
## backend-specific checking of options and constraints
##
## equality constraints can not be met by chance
if ((any (hook.eq_idx) || any (hook.lbound == hook.ubound)) && ! hook.stoch_regain_constr)
error ("If 'stoch_regain_constr' is not set, equality constraints or identical lower and upper bounds are not allowed by simulated annealing backend.");
endif
##
if (any (pin < hook.lbound | pin > hook.ubound) ||
any (pin_cstr.inequ.lin_except_bounds < 0) ||
any (pin_cstr.inequ.gen < 0) ||
any (abs (pin_cstr.equ.lin)) >= nz ||
any (abs (pin_cstr.equ.gen)) >= nz)
error ("Initial parameters violate constraints.");
endif
##
if (all (fixed))
error ("no free parameters");
endif
##
idx = isna (max_rand_step);
max_rand_step(idx) = 0.005 * pin(idx);
## fill constant fields of hook for derivative-functions; some fields
## may be backend-specific
dfdp_hook.fixed = fixed; # this may be handled by the frontend, but
# the backend still may add to it
## set up for iterations
done = false;
if (recover_state)
state = load (hook.recover_state);
p = state.p;
best_p = state.best_p;
E = state.E;
best_E = state.best_E;
T = state.T;
n_evals = state.n_evals;
n_iter = state.n_iter;
rand ("state", state.rstate);
if (isfield (state, "log"))
log = state.log;
endif
if (isfield (state, "trace"))
trace = state.trace;
endif
else
p = best_p = pin;
E = best_E = f (pin);
T = T_init;
n_evals = 1;
n_iter = 0;
if (siman_log)
log = zeros (0, 5);
endif
if (trace_steps)
trace = [0, 0, E, pin.'];
endif
if (([stop, outp.user_interaction] = ...
__do_user_interaction__ (user_interaction, p,
struct ("iteration", 0,
"fval", E),
"init")))
p_res = p;
outp.niter = 0;
objf = E;
cvg = -1;
return;
endif
endif
cvg = 1;
unwind_protect
if (parallel_local)
parallel_ready = false;
lerrm = lasterr ();
lasterr ("");
child_data = zeros (np, 4); # pipe descriptor for reading, pipe
# descriptor for writing, pid, line
# number
child_data(:, 4) = 1 : np;
## create subprocesses
for id = 1 : np
## parameter pipe
[pdp_r, pdp_w, err, msg] = pipe ();
if (err)
error ("could not create pipe: %s", msg);
endif
## result pipe
[pdr_r, pdr_w, err, msg] = pipe ();
if (err)
error ("could not create pipe: %s", msg);
endif
child_data(id, 1) = pdr_r;
child_data(id, 2) = pdp_w;
if ((pid = fork ()) == 0)
## child
pclose (pdp_w);
pclose (pdr_r);
try
while (true)
p = __bw_prcv__ (pdp_r);
if (ismatrix (p))
error ("parent closed without sending");
endif
if (ischar (p.psend_var))
pclose (pdp_r);
pclose (pdr_w);
__internal_exit__ ();
endif
new_E = f (p.psend_var);
__bw_psend__ (pdr_w, new_E);
fflush (pdr_w);
endwhile
catch
pclose (pdp_r);
pclose (pdr_w);
__internal_exit__ ();
end_try_catch
## end child
elseif (pid > 0)
## parent
child_data(id, 3) = pid;
pclose (pdp_r);
pclose (pdr_w);
else
## fork error
error ("could not fork");
endif
endfor ## create subprocesses
endif # parallel_local
## simulated annealing
while (! done)
n_iter++;
n_accepts = n_rejects = n_eless = 0;
## rand() for potential decisions on accepting a step with an
## increase is called here for all possibly parallized tests, to
## make the course of optimization potentially reproducible
## between parallelized and non-parallelized runs
rand_store = rand (iters_fixed_T, 1);
if (parallel_local)
n_left = int32 (iters_fixed_T);
while (n_left)
## number of currently used processes
cnp = ifelse (np <= n_left, np, n_left);
## for restoration
rand_states = cell (cnp - 1, 1);
busy_children = true (cnp, 1);
tp_E = zeros (cnp, 1); # results
tp_p = cell (cnp, 1); # tested parameters
for id = 1 : cnp
## all rand() calls are done in the parent process
new_p = p + max_rand_step .* (2 * rand (size (p)) - 1);
new_p = apply_constraints (p, new_p, hook, nz, verbose);
##
tp_p{id} = new_p;
if (id < cnp)
rand_states{id} = rand ("state");
endif
__bw_psend__ (child_data(id, 2), new_p);
fflush (child_data(id, 2));
endfor
while (any (busy_children))
[~, act] = ...
select (child_data(busy_children, 1), [], [], -1);
act_idx = child_data(busy_children, 4)(act);
for id = act_idx.'
res = __bw_prcv__ (child_data(id, 1));
if (ismatrix (res))
error ("child closed pipe without sending");
endif
tp_E(id) = res.psend_var;
busy_children(id) = false;
endfor
endwhile
for (id = 1 : cnp)
id_iters = double (iters_fixed_T - n_left + id);
if (tp_E(id) < best_E)
best_p = tp_p{id};
best_E = tp_E(id);
endif
if (tp_E(id) < E)
## take a step
p = tp_p{id};
E = tp_E(id);
n_eless++;
if (trace_steps)
trace(end + 1, :) = [n_iter, id_iters, E, p.'];
endif
break;
elseif (rand_store(id_iters) < ...
exp (- (tp_E(id) - E) / T))
## take a step
p = tp_p{id};
E = tp_E(id);
n_accepts++;
if (trace_steps)
trace(end + 1, :) = [n_iter, id_iters, E, p.'];
endif
break;
else
n_rejects++;
endif
endfor
## 'id' is now the number of (ordered) parallel tests up to
## the accepted one; we discard all other tests as invalid
n_left -= id;
if (int32 (id) < cnp)
## restore random generator
rand ("state", rand_states{id})
endif
n_evals += id;
endwhile # n_left
else # ! parallel_local
for id = 1 : iters_fixed_T
new_p = p + max_rand_step .* (2 * rand (size (p)) - 1);
new_p = apply_constraints (p, new_p, hook, nz, verbose);
new_E = f (new_p);
n_evals++;
if (new_E < best_E)
best_p = new_p;
best_E = new_E;
endif
if (new_E < E)
## take a step
p = new_p;
E = new_E;
n_eless++;
if (trace_steps)
trace(end + 1, :) = [n_iter, id, E, p.'];
endif
elseif (rand_store(id) < exp (- (new_E - E) / T))
## take a step
p = new_p;
E = new_E;
n_accepts++;
if (trace_steps)
trace(end + 1, :) = [n_iter, id, E, p.'];
endif
else
n_rejects++;
endif
endfor # iters_fixed_T
endif # ! parallel_local
if (verbose)
printf ("temperature no. %i: %e, energy %e,\n", n_iter, T, E);
printf ("tries with energy less / not less but accepted / rejected:\n");
printf ("%i / %i / %i\n", n_eless, n_accepts, n_rejects);
endif
if (([stop, outp.user_interaction] = ...
__do_user_interaction__ (user_interaction, p,
struct ("iteration", n_iter,
"fval", E),
"iter")))
p_res = p;
outp.niter = n_iter;
objf = E;
cvg = -1;
return;
endif
if (siman_log)
log(end + 1, :) = [T, E, n_eless, n_accepts, n_rejects];
endif
## cooling
T /= mu_T;
if (T < T_min)
done = true;
endif
if (save_state)
rstate = rand ("state");
unwind_protect
unwind_protect_cleanup
save ("-binary", hook.save_state, "p", "best_p", "E", ...
"best_E", "T", "n_evals", "n_iter", "rstate", ...
{"log"}(siman_log){:}, {"trace"}(trace_steps){:});
end_unwind_protect
endif
endwhile
## 'regular' cleanup
if (parallel_local)
for (id = 1 : np)
__bw_psend__ (child_data(id, 2), "exit");
pclose (child_data(id, 2));
child_data(id, 2) = 0;
pclose (child_data(id, 1));
child_data(id, 1) = 0;
waitpid (child_data(id, 3));
child_data(id, 3) = 0;
endfor
parallel_ready = true; # try/catch would not handle ctrl-c
endif
unwind_protect_cleanup
if (parallel_local)
if (! parallel_ready)
for (id = 1 : np)
if (child_data(id, 1))
pclose (child_data(id, 1));
endif
if (child_data(id, 2))
pclose (child_data(id, 2));
endif
if (child_data(id, 3))
kill (child_data(id, 3), 9);
waitpid (child_data(id, 3));
endif
endfor
nerrm = lasterr ();
error ("no success, last error message: %s", nerrm);
endif
lasterr (lerrm);
endif
end_unwind_protect
## return result
p_res = best_p;
objf = best_E;
outp.niter = n_iter;
if (trace_steps)
outp.trace = trace;
endif
if (siman_log)
outp.log = log;
endif
if (([stop, outp.user_interaction] = ...
__do_user_interaction__ (user_interaction, p_res,
struct ("iteration", n_iter,
"fval", objf),
"done")))
cvg = -1;
endif
endfunction
function new_p = apply_constraints (p, new_p, hook, nz, verbose)
if (hook.stoch_regain_constr)
evidx = (abs ((ac = hook.f_cstr (new_p, hook.ac_idx))(hook.eq_idx)) >= nz);
ividx = (ac(hook.ineq_idx) < 0);
if (any (evidx) || any (ividx))
nv = sum (evidx) + sum (ividx);
if (sum (lbvidx = (new_p < hook.lbound)) + ...
sum (ubvidx = (new_p > hook.ubound)) == ...
nv)
## special case only bounds violated, set back to bound
new_p(lbvidx) = hook.lbound(lbvidx);
new_p(ubvidx) = hook.ubound(ubvidx);
elseif (nv == 1 && ...
sum (t_eq = (abs (ac(hook.leq_idx)) >= nz)) + ...
sum (t_inequ = (ac(hook.lineq_idx) < 0)) == 1)
## special case only one linear constraint violated, set back
## perpendicularly to constraint
tidx = hook.lfalse_idx;
tidx(hook.leq_idx) = t_eq;
tidx(hook.lineq_idx) = t_inequ;
c = hook.mc(:, tidx);
d = ac(tidx);
new_p -= c * (d / (c.' * c));
else
## other cases, set back keeping the distance to original
## 'new_p' minimal, using quadratic programming, or sequential
## quadratic programming for nonlinear constraints
[new_p, discarded, sqp_info] = ...
sqp (new_p, ...
{@(x)sumsq(x-new_p), ...
@(x)2*(x-new_p), ...
@(x)2*eye(numel(p))}, ...
{@(x)hook.f_cstr(x,hook.eq_idx), ...
@(x)hook.df_cstr(x,hook.eq_idx, ...
setfield(hook,"f", ...
hook.f_cstr(x,hook.ac_idx)))}, ...
{@(x)hook.f_cstr(x,hook.ineq_idx), ...
@(x)hook.df_cstr(x,hook.ineq_idx, ...
setfield(hook,"f", ...
hook.f_cstr(x,hook.ac_idx)))});
if (sqp_info != 101)
cvg = 0;
done = true;
break;
endif
endif
endif
else
n_retry_constr = 0;
while (any (abs ((ac = hook.f_cstr (new_p, hook.ac_idx))(hook.eq_idx)) >= nz) ...
|| any (ac(hook.ineq_idx) < 0))
new_p = p + hook.max_rand_step .* (2 * rand (size (p)) - 1);
n_retry_constr++;
endwhile
if (verbose && n_retry_constr)
printf ("%i additional tries of random step to meet constraints\n",
n_retry_constr);
endif
endif
endfunction
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