1"""Implement the GeometricProgram class""" 

2import sys 

3import warnings as pywarnings 

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 ..small_scripts import appendsolwarning, initsolwarning 

10from ..keydict import KeyDict 

11from ..solution_array import SolutionArray 

12from .set import ConstraintSet 

13from ..exceptions import (InvalidPosynomial, Infeasible, UnknownInfeasible, 

14 PrimalInfeasible, DualInfeasible, UnboundedGP, 

15 InvalidLicense) 

16 

17 

18DEFAULT_SOLVER_KWARGS = {"cvxopt": {"kktsolver": "ldl"}} 

19SOLUTION_TOL = {"cvxopt": 1e-3, "mosek_cli": 1e-4, "mosek_conif": 1e-3} 

20 

21 

22class MonoEqualityIndexes: 

23 "Class to hold MonoEqualityIndexes" 

24 

25 def __init__(self): 

26 self.all = set() 

27 self.first_half = set() 

28 

29 

30def _get_solver(solver, kwargs): 

31 """Get the solverfn and solvername associated with solver""" 

32 if solver is None: 

33 from .. import settings 

34 try: 

35 solver = settings["default_solver"] 

36 except KeyError: 

37 raise ValueError("No default solver was set during build, so" 

38 " solvers must be manually specified.") 

39 if solver == "cvxopt": 

40 from ..solvers.cvxopt import optimize 

41 elif solver == "mosek_cli": 

42 from ..solvers.mosek_cli import optimize_generator 

43 optimize = optimize_generator(**kwargs) 

44 elif solver == "mosek_conif": 

45 from ..solvers.mosek_conif import optimize 

46 elif hasattr(solver, "__call__"): 

47 solver, optimize = solver.__name__, solver 

48 else: 

49 raise ValueError("Unknown solver '%s'." % solver) 

50 return solver, optimize 

51 

52 

53class GeometricProgram: 

54 # pylint: disable=too-many-instance-attributes 

55 """Standard mathematical representation of a GP. 

56 

57 Attributes with side effects 

58 ---------------------------- 

59 `solver_out` and `solve_log` are set during a solve 

60 `result` is set at the end of a solve if solution status is optimal 

61 

62 Examples 

63 -------- 

64 >>> gp = gpkit.constraints.gp.GeometricProgram( 

65 # minimize 

66 x, 

67 [ # subject to 

68 x >= 1, 

69 ], {}) 

70 >>> gp.solve() 

71 """ 

72 _result = solve_log = solver_out = model = v_ss = nu_by_posy = None 

73 choicevaridxs = integersolve = None 

74 

75 def __init__(self, cost, constraints, substitutions, 

76 *, checkbounds=True, **_): 

77 self.cost, self.substitutions = cost, substitutions 

78 for key, sub in self.substitutions.items(): 

79 if isinstance(sub, FixedScalar): 

80 sub = sub.value 

81 if hasattr(sub, "units"): 

82 sub = sub.to(key.units or "dimensionless").magnitude 

83 self.substitutions[key] = sub 

84 if not isinstance(sub, (Numbers, np.ndarray)): 

85 raise TypeError("substitution {%s: %s} has invalid value type" 

86 " %s." % (key, sub, type(sub))) 

87 cost_hmap = cost.hmap.sub(self.substitutions, cost.vks) 

88 if any(c <= 0 for c in cost_hmap.values()): 

89 raise InvalidPosynomial("a GP's cost must be Posynomial") 

90 hmapgen = ConstraintSet.as_hmapslt1(constraints, self.substitutions) 

91 self.hmaps = [cost_hmap] 

92 hmapset = set() 

93 for i, hmap in enumerate(hmapgen): 

94 if hmap not in hmapset: # de-duplicate hmaps 

95 hmapset.add(hmap) 

96 self.hmaps.append(hmap) 

97 self.gen() # Generate various maps into the posy- and monomials 

98 if checkbounds: 

99 self.check_bounds(err_on_missing_bounds=True) 

100 

101 def check_bounds(self, *, err_on_missing_bounds=False): 

102 "Checks if any variables are unbounded, through equality constraints." 

103 missingbounds = {} 

104 for var, locs in self.varlocs.items(): 

105 upperbound, lowerbound = False, False 

106 for i in locs: 

107 if i not in self.meq_idxs.all: 

108 if self.exps[i][var] > 0: # pylint:disable=simplifiable-if-statement 

109 upperbound = True 

110 else: 

111 lowerbound = True 

112 if upperbound and lowerbound: 

113 break 

114 if not upperbound: 

115 missingbounds[(var, "upper")] = "." 

116 if not lowerbound: 

117 missingbounds[(var, "lower")] = "." 

118 if not missingbounds: 

119 return {} # all bounds found in inequalities 

120 meq_bounds = gen_meq_bounds(missingbounds, self.exps, self.meq_idxs) 

121 fulfill_meq_bounds(missingbounds, meq_bounds) 

122 if missingbounds and err_on_missing_bounds: 

123 raise UnboundedGP( 

124 "\n\n".join("%s has no %s bound%s" % (v, b, x) 

125 for (v, b), x in missingbounds.items())) 

126 return missingbounds 

127 

128 def gen(self): 

129 """Generates nomial and solve data (A, p_idxs) from posynomials. 

130 

131 k [posys]: number of monomials (rows of A) present in each constraint 

132 m_idxs [mons]: monomial indices of each posynomial 

133 p_idxs [mons]: posynomial index of each monomial 

134 cs, exps [mons]: coefficient and exponents of each monomial 

135 varlocs: {vk: monomial indices of each variables' location} 

136 meq_idxs: {all indices of equality mons} and {the first index of each} 

137 varidxs: {vk: which column corresponds to it in A} 

138 A [mons, vks]: sparse array of each monomials' variables' exponents 

139 

140 """ 

141 self.k = [len(hmap) for hmap in self.hmaps] 

142 self.m_idxs, self.p_idxs, self.cs, self.exps = [], [], [], [] 

143 self.varkeys = self.varlocs = defaultdict(list) 

144 self.meq_idxs = MonoEqualityIndexes() 

145 m_idx = 0 

146 row, col, data = [], [], [] 

147 for p_idx, (N_mons, hmap) in enumerate(zip(self.k, self.hmaps)): 

148 self.p_idxs.extend([p_idx]*N_mons) 

149 self.m_idxs.append(slice(m_idx, m_idx+N_mons)) 

150 if getattr(self.hmaps[p_idx], "from_meq", False): 

151 self.meq_idxs.all.add(m_idx) 

152 if len(self.meq_idxs.all) > 2*len(self.meq_idxs.first_half): 

153 self.meq_idxs.first_half.add(m_idx) 

154 self.exps.extend(hmap) 

155 self.cs.extend(hmap.values()) 

156 for exp in hmap: 

157 if not exp: # space out A matrix with constants for mosek 

158 row.append(m_idx) 

159 col.append(0) 

160 data.append(0) 

161 for var in exp: 

162 self.varlocs[var].append(m_idx) 

163 m_idx += 1 

164 self.p_idxs = np.array(self.p_idxs, "int32") # to use array equalities 

165 self.varidxs = {vk: i for i, vk in enumerate(self.varlocs)} 

166 self.choicevaridxs = {vk: i for i, vk in enumerate(self.varlocs) 

167 if vk.choices} 

168 for j, (var, locs) in enumerate(self.varlocs.items()): 

169 row.extend(locs) 

170 col.extend([j]*len(locs)) 

171 data.extend(self.exps[i][var] for i in locs) 

172 self.A = CootMatrix(row, col, data) 

173 

174 # pylint: disable=too-many-statements, too-many-locals 

175 def solve(self, solver=None, *, verbosity=1, gen_result=True, **kwargs): 

176 """Solves a GeometricProgram and returns the solution. 

177 

178 Arguments 

179 --------- 

180 solver : str or function (optional) 

181 By default uses a solver found during installation. 

182 If "mosek_conif", "mosek_cli", or "cvxopt", uses that solver. 

183 If a function, passes that function cs, A, p_idxs, and k. 

184 verbosity : int (default 1) 

185 If greater than 0, prints solver name and solve time. 

186 gen_result : bool (default True) 

187 If True, makes a human-readable SolutionArray from solver output. 

188 **kwargs : 

189 Passed to solver constructor and solver function. 

190 

191 

192 Returns 

193 ------- 

194 SolutionArray (or dict if gen_result is False) 

195 """ 

196 solvername, solverfn = _get_solver(solver, kwargs) 

197 if verbosity > 0: 

198 print("Using solver '%s'" % solvername) 

199 print(" for %i free variables" % len(self.varlocs)) 

200 print(" in %i posynomial inequalities." % len(self.k)) 

201 

202 solverargs = DEFAULT_SOLVER_KWARGS.get(solvername, {}) 

203 solverargs.update(kwargs) 

204 if self.choicevaridxs and solvername == "mosek_conif": 

205 solverargs["choicevaridxs"] = self.choicevaridxs 

206 self.integersolve = True 

207 starttime = time() 

208 solver_out, infeasibility, original_stdout = {}, None, sys.stdout 

209 try: 

210 sys.stdout = SolverLog(original_stdout, verbosity=verbosity-2) 

211 solver_out = solverfn(c=self.cs, A=self.A, meq_idxs=self.meq_idxs, 

212 k=self.k, p_idxs=self.p_idxs, **solverargs) 

213 except Infeasible as e: 

214 infeasibility = e 

215 except InvalidLicense as e: 

216 raise InvalidLicense("license for solver \"%s\" is invalid." 

217 % solvername) from e 

218 except Exception as e: 

219 raise UnknownInfeasible("Something unexpected went wrong.") from e 

220 finally: 

221 self.solve_log = "\n".join(sys.stdout) 

222 sys.stdout = original_stdout 

223 self.solver_out = solver_out 

224 

225 solver_out["solver"] = solvername 

226 solver_out["soltime"] = time() - starttime 

227 if verbosity > 0: 

228 print("Solving took %.3g seconds." % solver_out["soltime"]) 

229 

230 if infeasibility: 

231 if isinstance(infeasibility, PrimalInfeasible): 

232 msg = ("The model had no feasible points; relaxing some" 

233 " constraints or constants will probably fix this.") 

234 elif isinstance(infeasibility, DualInfeasible): 

235 msg = ("The model ran to an infinitely low cost" 

236 " (or was otherwise dual infeasible); bounding" 

237 " the right variables will probably fix this.") 

238 elif isinstance(infeasibility, UnknownInfeasible): 

239 msg = ("Solver failed for an unknown reason. Relaxing" 

240 " constraints/constants, bounding variables, or" 

241 " using a different solver might fix it.") 

242 if (verbosity > 0 and solver_out["soltime"] < 1 

243 and hasattr(self, "model")): # fast, top-level model 

244 print(msg + "\nSince the model solved in less than a second," 

245 " let's run `.debug()` to analyze what happened.\n`") 

246 return self.model.debug(solver=solver) 

247 # else, raise a clarifying error 

248 msg += (" Running `.debug()` or increasing verbosity may pinpoint" 

249 " the trouble.") 

250 raise infeasibility.__class__(msg) from infeasibility 

251 

252 if not gen_result: 

253 return solver_out 

254 # else, generate a human-readable SolutionArray 

255 self._result = self.generate_result(solver_out, verbosity=verbosity-2) 

256 return self.result 

257 

258 @property 

259 def result(self): 

260 "Creates and caches a result from the raw solver_out" 

261 if not self._result: 

262 self._result = self.generate_result(self.solver_out) 

263 return self._result 

264 

265 def generate_result(self, solver_out, *, verbosity=0, dual_check=True): 

266 "Generates a full SolutionArray and checks it." 

267 if verbosity > 0: 

268 soltime = solver_out["soltime"] 

269 tic = time() 

270 # result packing # 

271 result = self._compile_result(solver_out) # NOTE: SIDE EFFECTS 

272 if verbosity > 0: 

273 print("Result packing took %.2g%% of solve time." % 

274 ((time() - tic) / soltime * 100)) 

275 tic = time() 

276 # solution checking # 

277 initsolwarning(result, "Solution Inconsistency") 

278 try: 

279 tol = SOLUTION_TOL.get(solver_out["solver"], 1e-5) 

280 self.check_solution(result["cost"], solver_out['primal'], 

281 solver_out["nu"], solver_out["la"], tol) 

282 except Infeasible as chkerror: 

283 msg = str(chkerror) 

284 if not ("Dual" in msg and not dual_check): 

285 appendsolwarning(msg, None, result, "Solution Inconsistency") 

286 if verbosity > -4: 

287 print("Solution check warning: %s" % msg) 

288 if verbosity > 0: 

289 print("Solution checking took %.2g%% of solve time." % 

290 ((time() - tic) / soltime * 100)) 

291 return result 

292 

293 def _generate_nula(self, solver_out): 

294 if "nu" in solver_out: 

295 # solver gave us monomial sensitivities, generate posynomial ones 

296 solver_out["nu"] = nu = np.ravel(solver_out["nu"]) 

297 nu_by_posy = [nu[mi] for mi in self.m_idxs] 

298 solver_out["la"] = la = np.array([sum(nup) for nup in nu_by_posy]) 

299 elif "la" in solver_out: 

300 la = np.ravel(solver_out["la"]) 

301 if len(la) == len(self.hmaps) - 1: 

302 # assume solver dropped the cost's sensitivity (always 1.0) 

303 la = np.hstack(([1.0], la)) 

304 # solver gave us posynomial sensitivities, generate monomial ones 

305 solver_out["la"] = la 

306 z = np.log(self.cs) + self.A.dot(solver_out["primal"]) 

307 m_iss = [self.p_idxs == i for i in range(len(la))] 

308 nu_by_posy = [la[p_i]*np.exp(z[m_is])/sum(np.exp(z[m_is])) 

309 for p_i, m_is in enumerate(m_iss)] 

310 solver_out["nu"] = np.hstack(nu_by_posy) 

311 else: 

312 raise RuntimeWarning("The dual solution was not returned.") 

313 return la, nu_by_posy 

314 

315 def _compile_result(self, solver_out): 

316 result = {"cost": float(solver_out["objective"])} 

317 primal = solver_out["primal"] 

318 if len(self.varlocs) != len(primal): 

319 raise RuntimeWarning("The primal solution was not returned.") 

320 result["freevariables"] = KeyDict(zip(self.varlocs, np.exp(primal))) 

321 result["constants"] = KeyDict(self.substitutions) 

322 result["variables"] = KeyDict(result["freevariables"]) 

323 result["variables"].update(result["constants"]) 

324 result["soltime"] = solver_out["soltime"] 

325 if self.integersolve: 

326 result["choicevariables"] = KeyDict( \ 

327 {k: v for k, v in result["freevariables"].items() 

328 if k in self.choicevaridxs}) 

329 result["warnings"] = {"No Dual Solution": [(\ 

330 "This model has the discretized choice variables" 

331 " %s and hence no dual solution. You can fix those variables" 

332 " to their optimal value and get sensitivities to the resulting" 

333 " continuous problem by updating your model's substitions with" 

334 " `sol[\"choicevariables\"]`." 

335 % sorted(self.choicevaridxs.keys()), self.choicevaridxs)]} 

336 return SolutionArray(result) 

337 if self.choicevaridxs: 

338 result["warnings"] = {"Freed Choice Variables": [(\ 

339 "This model has the discretized choice variables" 

340 " %s, but since the '%s' solver doesn't support discretization" 

341 " they were treated as continuous variables." 

342 % (sorted(self.choicevaridxs.keys()), solver_out["solver"]), 

343 self.choicevaridxs)]} 

344 

345 result["sensitivities"] = {"constraints": {}} 

346 la, self.nu_by_posy = self._generate_nula(solver_out) 

347 cost_senss = sum(nu_i*exp for (nu_i, exp) in zip(self.nu_by_posy[0], 

348 self.cost.hmap)) 

349 gpv_ss = cost_senss.copy() 

350 m_senss = defaultdict(float) 

351 for las, nus, c in zip(la[1:], self.nu_by_posy[1:], self.hmaps[1:]): 

352 while getattr(c, "parent", None) is not None: 

353 c = c.parent 

354 v_ss, c_senss = c.sens_from_dual(las, nus, result) 

355 for vk, x in v_ss.items(): 

356 gpv_ss[vk] = x + gpv_ss.get(vk, 0) 

357 while getattr(c, "generated_by", None): 

358 c = c.generated_by 

359 result["sensitivities"]["constraints"][c] = abs(c_senss) 

360 m_senss[lineagestr(c)] += abs(c_senss) 

361 # add fixed variables sensitivities to models 

362 for vk, senss in gpv_ss.items(): 

363 m_senss[lineagestr(vk)] += abs(senss) 

364 result["sensitivities"]["models"] = dict(m_senss) 

365 # carry linked sensitivities over to their constants 

366 for v in list(v for v in gpv_ss if v.gradients): 

367 dlogcost_dlogv = gpv_ss.pop(v) 

368 val = np.array(result["constants"][v]) 

369 for c, dv_dc in v.gradients.items(): 

370 with pywarnings.catch_warnings(): # skip pesky divide-by-zeros 

371 pywarnings.simplefilter("ignore") 

372 dlogv_dlogc = dv_dc * result["constants"][c]/val 

373 gpv_ss[c] = gpv_ss.get(c, 0) + dlogcost_dlogv*dlogv_dlogc 

374 if v in cost_senss: 

375 if c in self.cost.vks: 

376 dlogcost_dlogv = cost_senss.pop(v) 

377 before = cost_senss.get(c, 0) 

378 cost_senss[c] = before + dlogcost_dlogv*dlogv_dlogc 

379 result["sensitivities"]["cost"] = cost_senss 

380 result["sensitivities"]["variables"] = KeyDict(gpv_ss) 

381 result["sensitivities"]["constants"] = \ 

382 result["sensitivities"]["variables"] # NOTE: backwards compat. 

383 return SolutionArray(result) 

384 

385 def check_solution(self, cost, primal, nu, la, tol, abstol=1e-20): 

386 """Run checks to mathematically confirm solution solves this GP 

387 

388 Arguments 

389 --------- 

390 cost: float 

391 cost returned by solver 

392 primal: list 

393 primal solution returned by solver 

394 nu: numpy.ndarray 

395 monomial lagrange multiplier 

396 la: numpy.ndarray 

397 posynomial lagrange multiplier 

398 

399 Raises 

400 ------ 

401 Infeasible if any problems are found 

402 """ 

403 A = self.A.tocsr() 

404 def almost_equal(num1, num2): 

405 "local almost equal test" 

406 return (num1 == num2 or abs((num1 - num2) / (num1 + num2)) < tol 

407 or abs(num1 - num2) < abstol) 

408 # check primal sol # 

409 primal_exp_vals = self.cs * np.exp(A.dot(primal)) # c*e^Ax 

410 if not almost_equal(primal_exp_vals[self.m_idxs[0]].sum(), cost): 

411 raise Infeasible("Primal solution computed cost did not match" 

412 " solver-returned cost: %s vs %s." % 

413 (primal_exp_vals[self.m_idxs[0]].sum(), cost)) 

414 for mi in self.m_idxs[1:]: 

415 if primal_exp_vals[mi].sum() > 1 + tol: 

416 raise Infeasible("Primal solution violates constraint: %s is " 

417 "greater than 1" % primal_exp_vals[mi].sum()) 

418 # check dual sol # 

419 if self.integersolve: 

420 return 

421 # note: follows dual formulation in section 3.1 of 

422 # http://web.mit.edu/~whoburg/www/papers/hoburg_phd_thesis.pdf 

423 if not almost_equal(self.nu_by_posy[0].sum(), 1): 

424 raise Infeasible("Dual variables associated with objective sum" 

425 " to %s, not 1" % self.nu_by_posy[0].sum()) 

426 if any(nu < 0): 

427 minnu = min(nu) 

428 if minnu < -tol/1000: 

429 raise Infeasible("Dual solution has negative entries as" 

430 " large as %s." % minnu) 

431 if any(np.abs(A.T.dot(nu)) > tol): 

432 raise Infeasible("Dual: sum of nu^T * A did not vanish.") 

433 b = np.log(self.cs) 

434 dual_cost = sum( 

435 self.nu_by_posy[i].dot( 

436 b[mi] - np.log(self.nu_by_posy[i]/la[i])) 

437 for i, mi in enumerate(self.m_idxs) if la[i]) 

438 if not almost_equal(np.exp(dual_cost), cost): 

439 raise Infeasible("Dual cost %s does not match primal cost %s" 

440 % (np.exp(dual_cost), cost)) 

441 

442 

443def gen_meq_bounds(missingbounds, exps, meq_idxs): # pylint: disable=too-many-locals,too-many-branches 

444 "Generate conditional monomial equality bounds" 

445 meq_bounds = defaultdict(set) 

446 for i in meq_idxs.first_half: 

447 p_upper, p_lower, n_upper, n_lower = set(), set(), set(), set() 

448 for key, x in exps[i].items(): 

449 if (key, "upper") in missingbounds: 

450 if x > 0: 

451 p_upper.add((key, "upper")) 

452 else: 

453 n_upper.add((key, "upper")) 

454 if (key, "lower") in missingbounds: 

455 if x > 0: 

456 p_lower.add((key, "lower")) 

457 else: 

458 n_lower.add((key, "lower")) 

459 # (consider x*y/z == 1) 

460 # for a var (e.g. x) to be upper bounded by this monomial equality, 

461 # - vars of the same sign (y) must be lower bounded 

462 # - AND vars of the opposite sign (z) must be upper bounded 

463 p_ub = n_lb = frozenset(n_upper).union(p_lower) 

464 n_ub = p_lb = frozenset(p_upper).union(n_lower) 

465 for keys, ub in ((p_upper, p_ub), (n_upper, n_ub)): 

466 for key, _ in keys: 

467 needed = ub.difference([(key, "lower")]) 

468 if needed: 

469 meq_bounds[(key, "upper")].add(needed) 

470 else: 

471 del missingbounds[(key, "upper")] 

472 for keys, lb in ((p_lower, p_lb), (n_lower, n_lb)): 

473 for key, _ in keys: 

474 needed = lb.difference([(key, "upper")]) 

475 if needed: 

476 meq_bounds[(key, "lower")].add(needed) 

477 else: 

478 del missingbounds[(key, "lower")] 

479 return meq_bounds 

480 

481 

482def fulfill_meq_bounds(missingbounds, meq_bounds): 

483 "Bounds variables with monomial equalities" 

484 still_alive = True 

485 while still_alive: 

486 still_alive = False # if no changes are made, the loop exits 

487 for bound in set(meq_bounds): 

488 if bound not in missingbounds: 

489 del meq_bounds[bound] 

490 continue 

491 for condition in meq_bounds[bound]: 

492 if not any(bound in missingbounds for bound in condition): 

493 del meq_bounds[bound] 

494 del missingbounds[bound] 

495 still_alive = True 

496 break 

497 for (var, bound) in meq_bounds: 

498 boundstr = (", but would gain it from any of these sets: ") 

499 for condition in list(meq_bounds[(var, bound)]): 

500 meq_bounds[(var, bound)].remove(condition) 

501 newcond = condition.intersection(missingbounds) 

502 if newcond and not any(c.issubset(newcond) 

503 for c in meq_bounds[(var, bound)]): 

504 meq_bounds[(var, bound)].add(newcond) 

505 boundstr += " or ".join(str(list(condition)) 

506 for condition in meq_bounds[(var, bound)]) 

507 missingbounds[(var, bound)] = boundstr