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1"""Implement the GeometricProgram class"""
2import sys
3import warnings
4from time import time
5from collections import defaultdict
6import numpy as np
7from ..repr_conventions import lineagestr
8from ..small_classes import CootMatrix, SolverLog, Numbers, FixedScalar
9from ..keydict import KeyDict
10from ..solution_array import SolutionArray
11from .set import ConstraintSet
12from ..exceptions import (InvalidPosynomial, Infeasible, UnknownInfeasible,
13 PrimalInfeasible, DualInfeasible, UnboundedGP,
14 InvalidLicense)
17DEFAULT_SOLVER_KWARGS = {"cvxopt": {"kktsolver": "ldl"}}
18SOLUTION_TOL = {"cvxopt": 1e-3, "mosek_cli": 1e-4, "mosek_conif": 1e-3}
21class MonoEqualityIndexes:
22 "Class to hold MonoEqualityIndexes"
24 def __init__(self):
25 self.all = set()
26 self.first_half = set()
29def _get_solver(solver, kwargs):
30 """Get the solverfn and solvername associated with solver"""
31 if solver is None:
32 from .. import settings
33 try:
34 solver = settings["default_solver"]
35 except KeyError:
36 raise ValueError("No default solver was set during build, so"
37 " solvers must be manually specified.")
38 if solver == "cvxopt":
39 from ..solvers.cvxopt import optimize
40 elif solver == "mosek_cli":
41 from ..solvers.mosek_cli import optimize_generator
42 optimize = optimize_generator(**kwargs)
43 elif solver == "mosek_conif":
44 from ..solvers.mosek_conif import optimize
45 elif hasattr(solver, "__call__"):
46 solver, optimize = solver.__name__, solver
47 else:
48 raise ValueError("Unknown solver '%s'." % solver)
49 return solver, optimize
52class GeometricProgram:
53 # pylint: disable=too-many-instance-attributes
54 """Standard mathematical representation of a GP.
56 Attributes with side effects
57 ----------------------------
58 `solver_out` and `solve_log` are set during a solve
59 `result` is set at the end of a solve if solution status is optimal
61 Examples
62 --------
63 >>> gp = gpkit.constraints.gp.GeometricProgram(
64 # minimize
65 x,
66 [ # subject to
67 x >= 1,
68 ], {})
69 >>> gp.solve()
70 """
71 _result = solve_log = solver_out = model = v_ss = nu_by_posy = None
73 def __init__(self, cost, constraints, substitutions, *, checkbounds=True):
74 self.cost, self.substitutions = cost, substitutions
75 for key, sub in self.substitutions.items():
76 if isinstance(sub, FixedScalar):
77 sub = sub.value
78 if hasattr(sub, "units"):
79 sub = sub.to(key.units or "dimensionless").magnitude
80 self.substitutions[key] = sub
81 if not isinstance(sub, (Numbers, np.ndarray)):
82 raise TypeError("substitution {%s: %s} has invalid value type"
83 " %s." % (key, sub, type(sub)))
84 cost_hmap = cost.hmap.sub(self.substitutions, cost.vks)
85 if any(c <= 0 for c in cost_hmap.values()):
86 raise InvalidPosynomial("a GP's cost must be Posynomial")
87 hmapgen = ConstraintSet.as_hmapslt1(constraints, self.substitutions)
88 self.hmaps = [cost_hmap] + list(hmapgen)
89 self.gen() # Generate various maps into the posy- and monomials
90 if checkbounds:
91 self.check_bounds(err_on_missing_bounds=True)
93 def check_bounds(self, *, err_on_missing_bounds=False):
94 "Checks if any variables are unbounded, through equality constraints."
95 missingbounds = {}
96 for var, locs in self.varlocs.items():
97 upperbound, lowerbound = False, False
98 for i in locs:
99 if i not in self.meq_idxs.all:
100 if self.exps[i][var] > 0: # pylint:disable=simplifiable-if-statement
101 upperbound = True
102 else:
103 lowerbound = True
104 if upperbound and lowerbound:
105 break
106 if not upperbound:
107 missingbounds[(var, "upper")] = "."
108 if not lowerbound:
109 missingbounds[(var, "lower")] = "."
110 if not missingbounds:
111 return {} # all bounds found in inequalities
112 meq_bounds = gen_meq_bounds(missingbounds, self.exps, self.meq_idxs)
113 fulfill_meq_bounds(missingbounds, meq_bounds)
114 if missingbounds and err_on_missing_bounds:
115 raise UnboundedGP(
116 "\n\n".join("%s has no %s bound%s" % (v, b, x)
117 for (v, b), x in missingbounds.items()))
118 return missingbounds
120 def gen(self):
121 """Generates nomial and solve data (A, p_idxs) from posynomials.
123 k [posys]: number of monomials (rows of A) present in each constraint
124 m_idxs [mons]: monomial indices of each posynomial
125 p_idxs [mons]: posynomial index of each monomial
126 cs, exps [mons]: coefficient and exponents of each monomial
127 varlocs: {vk: monomial indices of each variables' location}
128 meq_idxs: {all indices of equality mons} and {the first index of each}
129 varidxs: {vk: which column corresponds to it in A}
130 A [mons, vks]: sparse array of each monomials' variables' exponents
132 """
133 self.k = [len(hmap) for hmap in self.hmaps]
134 self.m_idxs, self.p_idxs, self.cs, self.exps = [], [], [], []
135 self.varkeys = self.varlocs = defaultdict(list)
136 self.meq_idxs = MonoEqualityIndexes()
137 m_idx = 0
138 row, col, data = [], [], []
139 for p_idx, (N_mons, hmap) in enumerate(zip(self.k, self.hmaps)):
140 self.p_idxs.extend([p_idx]*N_mons)
141 self.m_idxs.append(slice(m_idx, m_idx+N_mons))
142 if getattr(self.hmaps[p_idx], "from_meq", False):
143 self.meq_idxs.all.add(m_idx)
144 if len(self.meq_idxs.all) > 2*len(self.meq_idxs.first_half):
145 self.meq_idxs.first_half.add(m_idx)
146 self.exps.extend(hmap)
147 self.cs.extend(hmap.values())
148 for exp in hmap:
149 if not exp: # space out A matrix with constants for mosek
150 row.append(m_idx)
151 col.append(0)
152 data.append(0)
153 for var in exp:
154 self.varlocs[var].append(m_idx)
155 m_idx += 1
156 self.p_idxs = np.array(self.p_idxs, "int32") # to use array equalities
157 self.varidxs = {vk: i for i, vk in enumerate(self.varlocs)}
158 for j, (var, locs) in enumerate(self.varlocs.items()):
159 row.extend(locs)
160 col.extend([j]*len(locs))
161 data.extend(self.exps[i][var] for i in locs)
162 self.A = CootMatrix(row, col, data)
164 # pylint: disable=too-many-statements, too-many-locals
165 def solve(self, solver=None, *, verbosity=1, gen_result=True, **kwargs):
166 """Solves a GeometricProgram and returns the solution.
168 Arguments
169 ---------
170 solver : str or function (optional)
171 By default uses a solver found during installation.
172 If "mosek_conif", "mosek_cli", or "cvxopt", uses that solver.
173 If a function, passes that function cs, A, p_idxs, and k.
174 verbosity : int (default 1)
175 If greater than 0, prints solver name and solve time.
176 gen_result : bool (default True)
177 If True, makes a human-readable SolutionArray from solver output.
178 **kwargs :
179 Passed to solver constructor and solver function.
182 Returns
183 -------
184 SolutionArray (or dict if gen_result is False)
185 """
186 solvername, solverfn = _get_solver(solver, kwargs)
187 if verbosity > 0:
188 print("Using solver '%s'" % solvername)
189 print(" for %i free variables" % len(self.varlocs))
190 print(" in %i posynomial inequalities." % len(self.k))
192 solverargs = DEFAULT_SOLVER_KWARGS.get(solvername, {})
193 solverargs.update(kwargs)
194 starttime = time()
195 solver_out, infeasibility, original_stdout = {}, None, sys.stdout
196 try:
197 sys.stdout = SolverLog(original_stdout, verbosity=verbosity-2)
198 solver_out = solverfn(c=self.cs, A=self.A, meq_idxs=self.meq_idxs,
199 k=self.k, p_idxs=self.p_idxs, **solverargs)
200 except Infeasible as e:
201 infeasibility = e
202 except InvalidLicense as e:
203 raise InvalidLicense("license for solver \"%s\" is invalid."
204 % solvername) from e
205 except Exception as e:
206 raise UnknownInfeasible("Something unexpected went wrong.") from e
207 finally:
208 self.solve_log = "\n".join(sys.stdout)
209 sys.stdout = original_stdout
210 self.solver_out = solver_out
212 solver_out["solver"] = solvername
213 solver_out["soltime"] = time() - starttime
214 if verbosity > 0:
215 print("Solving took %.3g seconds." % solver_out["soltime"])
217 if infeasibility:
218 if isinstance(infeasibility, PrimalInfeasible):
219 msg = ("The model had no feasible points; "
220 "you may wish to relax some constraints or constants.")
221 elif isinstance(infeasibility, DualInfeasible):
222 msg = ("The model ran to an infinitely low cost;"
223 " bounding the right variables would prevent this.")
224 elif isinstance(infeasibility, UnknownInfeasible):
225 msg = "The solver failed for an unknown reason."
226 if (verbosity > 0 and solver_out["soltime"] < 1
227 and hasattr(self, "model")): # fast, top-level model
228 print(msg + "\nSince the model solved in less than a second,"
229 " let's run `.debug()` to analyze what happened.\n`")
230 return self.model.debug(solver=solver)
231 # else, raise a clarifying error
232 msg += (" Running `.debug()` may pinpoint the trouble. You can"
233 " also try another solver, or increase the verbosity.")
234 raise infeasibility.__class__(msg) from infeasibility
236 if not gen_result:
237 return solver_out
238 # else, generate a human-readable SolutionArray
239 self._result = self.generate_result(solver_out, verbosity=verbosity-2)
240 return self.result
242 @property
243 def result(self):
244 "Creates and caches a result from the raw solver_out"
245 if not self._result:
246 self._result = self.generate_result(self.solver_out)
247 return self._result
249 def generate_result(self, solver_out, *, verbosity=0, dual_check=True):
250 "Generates a full SolutionArray and checks it."
251 if verbosity > 0:
252 soltime = solver_out["soltime"]
253 tic = time()
254 # result packing #
255 result = self._compile_result(solver_out) # NOTE: SIDE EFFECTS
256 if verbosity > 0:
257 print("Result packing took %.2g%% of solve time." %
258 ((time() - tic) / soltime * 100))
259 tic = time()
260 # solution checking #
261 try:
262 tol = SOLUTION_TOL.get(solver_out["solver"], 1e-5)
263 self.check_solution(result["cost"], solver_out['primal'],
264 solver_out["nu"], solver_out["la"], tol)
265 except Infeasible as chkerror:
266 chkwarn = str(chkerror)
267 if not ("Dual" in chkwarn and not dual_check):
268 print("Solution check warning: %s" % chkwarn)
269 if verbosity > 0:
270 print("Solution checking took %.2g%% of solve time." %
271 ((time() - tic) / soltime * 100))
272 return result
274 def _generate_nula(self, solver_out):
275 if "nu" in solver_out:
276 # solver gave us monomial sensitivities, generate posynomial ones
277 solver_out["nu"] = nu = np.ravel(solver_out["nu"])
278 nu_by_posy = [nu[mi] for mi in self.m_idxs]
279 solver_out["la"] = la = np.array([sum(nup) for nup in nu_by_posy])
280 elif "la" in solver_out:
281 la = np.ravel(solver_out["la"])
282 if len(la) == len(self.hmaps) - 1:
283 # assume solver dropped the cost's sensitivity (always 1.0)
284 la = np.hstack(([1.0], la))
285 # solver gave us posynomial sensitivities, generate monomial ones
286 solver_out["la"] = la
287 z = np.log(self.cs) + self.A.dot(solver_out["primal"])
288 m_iss = [self.p_idxs == i for i in range(len(la))]
289 nu_by_posy = [la[p_i]*np.exp(z[m_is])/sum(np.exp(z[m_is]))
290 for p_i, m_is in enumerate(m_iss)]
291 solver_out["nu"] = np.hstack(nu_by_posy)
292 else:
293 raise RuntimeWarning("The dual solution was not returned.")
294 return la, nu_by_posy
296 def _compile_result(self, solver_out):
297 result = {"cost": float(solver_out["objective"])}
298 primal = solver_out["primal"]
299 if len(self.varlocs) != len(primal):
300 raise RuntimeWarning("The primal solution was not returned.")
301 result["freevariables"] = KeyDict(zip(self.varlocs, np.exp(primal)))
302 result["constants"] = KeyDict(self.substitutions)
303 result["variables"] = KeyDict(result["freevariables"])
304 result["variables"].update(result["constants"])
305 result["sensitivities"] = {"constraints": {}}
306 la, self.nu_by_posy = self._generate_nula(solver_out)
307 cost_senss = sum(nu_i*exp for (nu_i, exp) in zip(self.nu_by_posy[0],
308 self.cost.hmap))
309 gpv_ss = cost_senss.copy()
310 m_senss = defaultdict(float)
311 for las, nus, c in zip(la[1:], self.nu_by_posy[1:], self.hmaps[1:]):
312 while getattr(c, "parent", None) is not None:
313 c = c.parent
314 v_ss, c_senss = c.sens_from_dual(las, nus, result)
315 for vk, x in v_ss.items():
316 gpv_ss[vk] = x + gpv_ss.get(vk, 0)
317 while getattr(c, "generated_by", None):
318 c = c.generated_by
319 result["sensitivities"]["constraints"][c] = abs(c_senss)
320 m_senss[lineagestr(c)] += c_senss
321 # add fixed variables sensitivities to models
322 for vk, senss in gpv_ss.items():
323 m_senss[lineagestr(vk)] += abs(senss)
324 result["sensitivities"]["models"] = dict(m_senss)
325 # carry linked sensitivities over to their constants
326 for v in list(v for v in gpv_ss if v.gradients):
327 dlogcost_dlogv = gpv_ss.pop(v)
328 val = np.array(result["constants"][v])
329 for c, dv_dc in v.gradients.items():
330 with warnings.catch_warnings(): # skip pesky divide-by-zeros
331 warnings.simplefilter("ignore")
332 dlogv_dlogc = dv_dc * result["constants"][c]/val
333 before = gpv_ss.get(c, 0)
334 gpv_ss[c] = before + dlogcost_dlogv*dlogv_dlogc
335 if v in cost_senss:
336 if c in self.cost.vks:
337 dlogcost_dlogv = cost_senss.pop(v)
338 before = cost_senss.get(c, 0)
339 cost_senss[c] = before + dlogcost_dlogv*dlogv_dlogc
340 result["sensitivities"]["cost"] = cost_senss
341 result["sensitivities"]["variables"] = KeyDict(gpv_ss)
342 result["sensitivities"]["constants"] = \
343 result["sensitivities"]["variables"] # NOTE: backwards compat.
344 result["soltime"] = solver_out["soltime"]
345 return SolutionArray(result)
347 def check_solution(self, cost, primal, nu, la, tol, abstol=1e-20):
348 """Run checks to mathematically confirm solution solves this GP
350 Arguments
351 ---------
352 cost: float
353 cost returned by solver
354 primal: list
355 primal solution returned by solver
356 nu: numpy.ndarray
357 monomial lagrange multiplier
358 la: numpy.ndarray
359 posynomial lagrange multiplier
361 Raises
362 ------
363 Infeasible if any problems are found
364 """
365 A = self.A.tocsr()
366 def almost_equal(num1, num2):
367 "local almost equal test"
368 return (num1 == num2 or abs((num1 - num2) / (num1 + num2)) < tol
369 or abs(num1 - num2) < abstol)
370 # check primal sol #
371 primal_exp_vals = self.cs * np.exp(A.dot(primal)) # c*e^Ax
372 if not almost_equal(primal_exp_vals[self.m_idxs[0]].sum(), cost):
373 raise Infeasible("Primal solution computed cost did not match"
374 " solver-returned cost: %s vs %s." %
375 (primal_exp_vals[self.m_idxs[0]].sum(), cost))
376 for mi in self.m_idxs[1:]:
377 if primal_exp_vals[mi].sum() > 1 + tol:
378 raise Infeasible("Primal solution violates constraint: %s is "
379 "greater than 1" % primal_exp_vals[mi].sum())
380 # check dual sol #
381 # note: follows dual formulation in section 3.1 of
382 # http://web.mit.edu/~whoburg/www/papers/hoburg_phd_thesis.pdf
383 if not almost_equal(self.nu_by_posy[0].sum(), 1):
384 raise Infeasible("Dual variables associated with objective sum"
385 " to %s, not 1" % self.nu_by_posy[0].sum())
386 if any(nu < 0):
387 minnu = min(nu)
388 if minnu < -tol/1000:
389 raise Infeasible("Dual solution has negative entries as"
390 " large as %s." % minnu)
391 if any(np.abs(A.T.dot(nu)) > tol):
392 raise Infeasible("Dual: sum of nu^T * A did not vanish.")
393 b = np.log(self.cs)
394 dual_cost = sum(
395 self.nu_by_posy[i].dot(
396 b[mi] - np.log(self.nu_by_posy[i]/la[i]))
397 for i, mi in enumerate(self.m_idxs) if la[i])
398 if not almost_equal(np.exp(dual_cost), cost):
399 raise Infeasible("Dual cost %s does not match primal cost %s"
400 % (np.exp(dual_cost), cost))
403def gen_meq_bounds(missingbounds, exps, meq_idxs): # pylint: disable=too-many-locals,too-many-branches
404 "Generate conditional monomial equality bounds"
405 meq_bounds = defaultdict(set)
406 for i in meq_idxs.first_half:
407 p_upper, p_lower, n_upper, n_lower = set(), set(), set(), set()
408 for key, x in exps[i].items():
409 if (key, "upper") in missingbounds:
410 if x > 0:
411 p_upper.add((key, "upper"))
412 else:
413 n_upper.add((key, "upper"))
414 if (key, "lower") in missingbounds:
415 if x > 0:
416 p_lower.add((key, "lower"))
417 else:
418 n_lower.add((key, "lower"))
419 # (consider x*y/z == 1)
420 # for a var (e.g. x) to be upper bounded by this monomial equality,
421 # - vars of the same sign (y) must be lower bounded
422 # - AND vars of the opposite sign (z) must be upper bounded
423 p_ub = n_lb = frozenset(n_upper).union(p_lower)
424 n_ub = p_lb = frozenset(p_upper).union(n_lower)
425 for keys, ub in ((p_upper, p_ub), (n_upper, n_ub)):
426 for key, _ in keys:
427 needed = ub.difference([(key, "lower")])
428 if needed:
429 meq_bounds[(key, "upper")].add(needed)
430 else:
431 del missingbounds[(key, "upper")]
432 for keys, lb in ((p_lower, p_lb), (n_lower, n_lb)):
433 for key, _ in keys:
434 needed = lb.difference([(key, "upper")])
435 if needed:
436 meq_bounds[(key, "lower")].add(needed)
437 else:
438 del missingbounds[(key, "lower")]
439 return meq_bounds
442def fulfill_meq_bounds(missingbounds, meq_bounds):
443 "Bounds variables with monomial equalities"
444 still_alive = True
445 while still_alive:
446 still_alive = False # if no changes are made, the loop exits
447 for bound in set(meq_bounds):
448 if bound not in missingbounds:
449 del meq_bounds[bound]
450 continue
451 for condition in meq_bounds[bound]:
452 if not any(bound in missingbounds for bound in condition):
453 del meq_bounds[bound]
454 del missingbounds[bound]
455 still_alive = True
456 break
457 for (var, bound) in meq_bounds:
458 boundstr = (", but would gain it from any of these sets: ")
459 for condition in list(meq_bounds[(var, bound)]):
460 meq_bounds[(var, bound)].remove(condition)
461 newcond = condition.intersection(missingbounds)
462 if newcond and not any(c.issubset(newcond)
463 for c in meq_bounds[(var, bound)]):
464 meq_bounds[(var, bound)].add(newcond)
465 boundstr += " or ".join(str(list(condition))
466 for condition in meq_bounds[(var, bound)])
467 missingbounds[(var, bound)] = boundstr