def test_rosenbrock():
"""Test the 2-dimensional Rosenbrock function.
Testing 2-D Rosenbrock:
Expected: x=[1., 1.] and f=0
Using DifferentialEvolutionSolver:
Solution: [ 1.00000037 1.0000007 ]
f value: 2.29478683682e-13
Iterations: 99
Function evaluations: 3996
Time elapsed: 0.582273006439 seconds
Using DifferentialEvolutionSolver2:
Solution: [ 0.99999999 0.99999999]
f value: 3.84824937598e-15
Iterations: 100
Function evaluations: 4040
Time elapsed: 0.577210903168 seconds
Using NelderMeadSimplexSolver:
Solution: [ 0.99999921 1.00000171]
f value: 1.08732211477e-09
Iterations: 70
Function evaluations: 130
Time elapsed: 0.0190329551697 seconds
Using PowellDirectionalSolver:
Solution: [ 1. 1.]
f value: 0.0
Iterations: 28
Function evaluations: 859
Time elapsed: 0.113857030869 seconds
"""
print "Testing 2-D Rosenbrock:"
print "Expected: x=[1., 1.] and f=0"
from mystic.models import rosen as costfunc
ndim = 2
lb = [-5.]*ndim
ub = [5.]*ndim
x0 = [2., 3.]
maxiter = 10000
# DifferentialEvolutionSolver
print "\nUsing DifferentialEvolutionSolver:"
npop = 40
from mystic.solvers import DifferentialEvolutionSolver
from mystic.termination import ChangeOverGeneration as COG
from mystic.strategy import Rand1Bin
esow = Monitor()
ssow = Monitor()
solver = DifferentialEvolutionSolver(ndim, npop)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = COG(1e-10)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term, strategy=Rand1Bin)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 2.29478683682e-13, tol=3e-3)
# DifferentialEvolutionSolver2
print "\nUsing DifferentialEvolutionSolver2:"
npop = 40
from mystic.solvers import DifferentialEvolutionSolver2
from mystic.termination import ChangeOverGeneration as COG
from mystic.strategy import Rand1Bin
esow = Monitor()
ssow = Monitor()
solver = DifferentialEvolutionSolver2(ndim, npop)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = COG(1e-10)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term, strategy=Rand1Bin)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 3.84824937598e-15, tol=3e-3)
# NelderMeadSimplexSolver
print "\nUsing NelderMeadSimplexSolver:"
from mystic.solvers import NelderMeadSimplexSolver
from mystic.termination import CandidateRelativeTolerance as CRT
esow = Monitor()
ssow = Monitor()
solver = NelderMeadSimplexSolver(ndim)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = CRT()
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 1.08732211477e-09, tol=3e-3)
# PowellDirectionalSolver
print "\nUsing PowellDirectionalSolver:"
from mystic.solvers import PowellDirectionalSolver
from mystic.termination import NormalizedChangeOverGeneration as NCOG
esow = Monitor()
ssow = Monitor()
solver = PowellDirectionalSolver(ndim)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = NCOG(1e-10)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 0.0, tol=3e-3)
#ssow= VerboseMonitor(1)
# import random
# xinit = [random.random() for j in range(ND)]
xinit = [0.8, 1.2, 0.7]
# xinit = [0.8,1.2,1.7] #... better when using "bad" range
min = [-0.999, -0.999, 0.999] #XXX: behaves badly when large range
max = [200.001, 100.001, inf] #... for >=1 x0 out of bounds; (up xtol)
# min = [-0.999, -0.999, -0.999]
# max = [200.001, 100.001, inf]
# min = [-0.999, -0.999, 0.999] #XXX: tight range and non-randomness
# max = [2.001, 1.001, 1.001] #...: is _bad_ for DE solvers
#print(diffev(rosen,xinit,NP,retall=0,full_output=0))
solver = DifferentialEvolutionSolver(len(xinit), NP)
solver.SetInitialPoints(xinit)
solver.SetStrictRanges(min, max)
solver.SetEvaluationLimits(generations=MAX_GENERATIONS)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
solver.Solve(rosen, VTR(0.0001), \
CrossProbability=0.5, ScalingFactor=0.6, disp=1)
sol = solver.bestSolution
print(sol)
#print("Current function value: %s" % solver.bestEnergy)
#print("Iterations: %s" % solver.generations)
#print("Function evaluations: %s" % solver.evaluations)
times.append(time.time() - start)
algor.append('Differential Evolution\t')
def solve(constraints, guess=None, nvars=None, solver=None, \
lower_bounds=None, upper_bounds=None, termination=None):
"""Use optimization to find a solution to a set of constraints.
Inputs:
constraints -- a constraints solver function or a penalty function
Additional Inputs:
guess -- list of parameter values proposed to solve the constraints.
lower_bounds -- list of lower bounds on solution values.
upper_bounds -- list of upper bounds on solution values.
nvars -- number of parameter values.
solver -- the mystic solver to use in the optimization
termination -- the mystic termination to use in the optimization
NOTE: The resulting constraints will likely be more expensive to evaluate
and less accurate than writing the constraints solver from scratch.
NOTE: The ensemble solvers are available, using the default NestedSolver,
where the keyword 'guess' can be used to set the number of solvers.
NOTE: The default solver is 'diffev', with npop=min(40, ndim*5). The default
termination is ChangeOverGeneration(), and the default guess is randomly
selected points between the upper and lower bounds.
"""
npts = 8
if type(guess) is int: npts, guess = guess, None
ndim = 1 #XXX: better, increase in while loop catching IndexError ?
if nvars is not None: ndim = nvars
elif guess is not None: ndim = len(guess)
elif lower_bounds is not None: ndim = len(lower_bounds)
elif upper_bounds is not None: ndim = len(upper_bounds)
def cost(x):
return 1.
#XXX: don't allow solver string as a short-cut? #FIXME: add ensemble solvers
ensemble = False
if solver is None or solver == 'diffev':
from mystic.solvers import DifferentialEvolutionSolver as TheSolver
solver = TheSolver(ndim, min(40, ndim * 5))
elif solver == 'diffev2':
from mystic.solvers import DifferentialEvolutionSolver2 as TheSolver
solver = TheSolver(ndim, min(40, ndim * 5))
elif solver == 'fmin_powell': #XXX: better as the default? (it's not random)
from mystic.solvers import PowellDirectionalSolver as TheSolver
solver = TheSolver(ndim)
elif solver == 'fmin':
from mystic.solvers import NelderMeadSimplexSolver as TheSolver
solver = TheSolver(ndim)
elif solver == 'buckshot':
from mystic.solvers import BuckshotSolver as TheSolver
solver = TheSolver(ndim, max(8, npts)) #XXX: needs better default?
ensemble = True
elif solver == 'lattice':
from mystic.solvers import LatticeSolver as TheSolver
solver = TheSolver(ndim, max(8, npts)) #XXX: needs better default?
ensemble = True
if termination is None:
from mystic.termination import ChangeOverGeneration as COG
termination = COG()
if not ensemble:
if guess is not None:
solver.SetInitialPoints(guess) #XXX: nice if 'diffev' had methods
else:
solver.SetRandomInitialPoints(lower_bounds, upper_bounds)
if lower_bounds or upper_bounds:
solver.SetStrictRanges(lower_bounds, upper_bounds)
if hasattr(constraints, 'iter') and hasattr(constraints, 'error'):
solver.SetPenalty(constraints) #i.e. is a penalty function
else: # is a constraints solver
solver.SetConstraints(constraints)
from numpy import seterr
settings = seterr(all='ignore')
solver.Solve(cost, termination)
seterr(**settings)
soln = solver.bestSolution
from numpy import ndarray, array
if isinstance(soln, ndarray) and not isinstance(guess, ndarray):
soln = soln.tolist()
elif isinstance(guess, ndarray) and not isinstance(soln, ndarray):
soln = array(soln) #XXX: or always return a list ?
return soln #XXX: check with 'issolution' ?
def solve(constraints, guess=None, nvars=None, solver=None, \
lower_bounds=None, upper_bounds=None, termination=None):
"""Use optimization to find a solution to a set of constraints.
Inputs:
constraints -- a constraints solver function or a penalty function
Additional Inputs:
guess -- list of parameter values proposed to solve the constraints.
lower_bounds -- list of lower bounds on solution values.
upper_bounds -- list of upper bounds on solution values.
nvars -- number of parameter values.
solver -- the mystic solver to use in the optimization
termination -- the mystic termination to use in the optimization
NOTE: The resulting constraints will likely be more expensive to evaluate
and less accurate than writing the constraints solver from scratch.
"""
ndim = 1 #XXX: better, increase in while loop catching IndexError ?
if nvars is not None: ndim = nvars
elif guess is not None: ndim = len(guess)
elif lower_bounds is not None: ndim = len(lower_bounds)
elif upper_bounds is not None: ndim = len(upper_bounds)
def cost(x):
return 1.
#XXX: don't allow solver string as a short-cut?
if solver is None or solver == 'diffev':
from mystic.solvers import DifferentialEvolutionSolver as TheSolver
solver = TheSolver(ndim, min(40, ndim * 5))
elif solver == 'diffev2':
from mystic.solvers import DifferentialEvolutionSolver2 as TheSolver
solver = TheSolver(ndim, min(40, ndim * 5))
elif solver == 'fmin_powell': #XXX: better as the default? (it's not random)
from mystic.solvers import PowellDirectionalSolver as TheSolver
solver = TheSolver(ndim)
elif solver == 'fmin':
from mystic.solvers import NelderMeadSimplexSolver as TheSolver
solver = TheSolver(ndim)
if termination is None:
from mystic.termination import ChangeOverGeneration as COG
termination = COG()
if guess != None:
solver.SetInitialPoints(guess) #XXX: nice if 'diffev' also had methods
else:
solver.SetRandomInitialPoints(lower_bounds, upper_bounds)
if lower_bounds or upper_bounds:
solver.SetStrictRanges(lower_bounds, upper_bounds)
if hasattr(constraints, 'iter') and hasattr(constraints, 'error'):
solver.SetPenalty(constraints) #i.e. is a penalty function
else: # is a constraints solver
solver.SetConstraints(constraints)
solver.Solve(cost, termination)
soln = solver.bestSolution
from numpy import ndarray, array
if isinstance(soln, ndarray) and not isinstance(guess, ndarray):
soln = soln.tolist()
elif isinstance(guess, ndarray) and not isinstance(soln, ndarray):
soln = array(soln) #XXX: or always return a list ?
return soln #XXX: check with 'issolution' ?