def test_NelderMeadSimplexSolver_CRT(self): # Default for this solver
from mystic.solvers import NelderMeadSimplexSolver
from mystic.termination import CandidateRelativeTolerance as CRT
self.solver = NelderMeadSimplexSolver(self.ND)
self.term = CRT()
self._run_solver()
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)
def test_DifferentialEvolutionSolver2_CRT(self):
from mystic.solvers import DifferentialEvolutionSolver2
from mystic.termination import CandidateRelativeTolerance as CRT
self.solver = DifferentialEvolutionSolver2(self.ND, self.NP)
self.term = CRT()
self._run_solver()
min_bounds = [0, -1, -300, -1, 0, -1, -100, -inf, -inf]
max_bounds = [200, 1, 0, 1, 200, 1, 0, inf, inf]
# configure monitors
stepmon = VerboseMonitor(100)
evalmon = Monitor()
# use Nelder-Mead to solve 8th-order Chebyshev coefficients
solver = NelderMeadSimplexSolver(ndim)
solver.SetInitialPoints(x0)
solver.SetEvaluationLimits(generations=999)
solver.SetEvaluationMonitor(evalmon)
solver.SetGenerationMonitor(stepmon)
solver.SetStrictRanges(min_bounds, max_bounds)
solver.enable_signal_handler()
solver.Solve(chebyshev8cost, termination=CRT(1e-4,1e-4), \
sigint_callback=plot_solution)
solution = solver.bestSolution
# get solved coefficients and Chi-Squared (from solver members)
iterations = solver.generations
cost = solver.bestEnergy
print("Generation %d has best Chi-Squared: %f" % (iterations, cost))
print("Solved Coefficients:\n %s\n" % poly1d(solver.bestSolution))
# compare solution with actual 8th-order Chebyshev coefficients
print("Actual Coefficients:\n %s\n" % poly1d(chebyshev8coeffs))
# plot solution versus exact coefficients
plot_solution(solution)
getch()
print "desol: ", desol
print "dstepmon 50: ", dstepmon.x[50]
print "dstepmon 100: ", dstepmon.x[100]
#
# this will try to use nelder_mean from a relatively "near by" point (very sensitive)
point = [1234., -500., 10., 0.001] # both cg and nm does fine
point = [1000, -100, 0, 1] # cg will do badly on this one
# this will try nelder-mead from an unconverged DE solution
#point = dstepmon.x[-150]
#
simplex, esow = Monitor(), Monitor()
solver = fmin(len(point))
solver.SetInitialPoints(point)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(simplex)
solver.Solve(cost_function, CRT())
sol = solver.Solution()
print "\nsimplex solution: ", sol
#
solcg = fmin_cg(cost_function, point)
print "\nConjugate-Gradient (Polak Rubiere) : ", solcg
#
if leastsq:
sollsq = leastsq(vec_cost_function, point)
sollsq = sollsq[0]
print "\nLeast Squares (Levenberg Marquardt) : ", sollsq
#
legend = [
'Noisy data', 'Differential Evolution', 'Nelder Mead', 'Polak Ribiere'
]
CrossProbability=0.3, ScalingFactor=1.0)
solution = solver.Solution()
print solution
if __name__ == '__main__':
from timeit import Timer
t = Timer("main()", "from __main__ import main")
timetaken = t.timeit(number=1)
print "CPU Time: %s" % timetaken
from mystic.monitors import Monitor
from mystic.solvers import NelderMeadSimplexSolver as fmin
from mystic.termination import CandidateRelativeTolerance as CRT
simplex = Monitor()
esow = Monitor()
xinit = [random.uniform(0, 5) for j in range(ND)]
solver = fmin(len(xinit))
solver.SetInitialPoints(xinit)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(simplex)
solver.Solve(CostFunction, CRT())
sol = solver.Solution()
print "fmin solution: ", sol
# end of file
def fmin(cost,
x0,
args=(),
bounds=None,
xtol=1e-4,
ftol=1e-4,
maxiter=None,
maxfun=None,
full_output=0,
disp=1,
retall=0,
callback=None,
**kwds):
"""Minimize a function using the downhill simplex algorithm.
Description:
Uses a Nelder-Mead simplex algorithm to find the minimum of
a function of one or more variables. Mimics the scipy.optimize.fmin
interface.
Inputs:
cost -- the Python function or method to be minimized.
x0 -- ndarray - the initial guess.
Additional Inputs:
args -- extra arguments for cost.
bounds -- list - n pairs of bounds (min,max), one pair for each parameter.
xtol -- number - acceptable relative error in xopt for convergence.
ftol -- number - acceptable relative error in cost(xopt) for
convergence.
maxiter -- number - the maximum number of iterations to perform.
maxfun -- number - the maximum number of function evaluations.
full_output -- number - non-zero if fval and warnflag outputs are
desired.
disp -- number - non-zero to print convergence messages.
retall -- number - non-zero to return list of solutions at each
iteration.
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.
handler -- boolean - enable/disable handling of interrupt signal
itermon -- monitor - override the default GenerationMonitor
evalmon -- monitor - override the default EvaluationMonitor
constraints -- an optional user-supplied function. It is called as
constraints(xk), where xk is the current parameter vector.
This function must return xk', a parameter vector that satisfies
the encoded constraints.
penalty -- an optional user-supplied function. It is called as
penalty(xk), where xk is the current parameter vector.
This function should return y', with y' == 0 when the encoded
constraints are satisfied, and y' > 0 otherwise.
Returns: (xopt, {fopt, iter, funcalls, warnflag}, {allvecs})
xopt -- ndarray - minimizer of function
fopt -- number - value of function at minimum: fopt = cost(xopt)
iter -- number - number of iterations
funcalls -- number - number of function calls
warnflag -- number - Integer warning flag:
1 : 'Maximum number of function evaluations.'
2 : 'Maximum number of iterations.'
allvecs -- list - a list of solutions at each iteration
"""
handler = False
if kwds.has_key('handler'):
handler = kwds['handler']
from mystic.monitors import Monitor
stepmon = Monitor()
evalmon = Monitor()
if kwds.has_key('itermon'):
stepmon = kwds['itermon']
if kwds.has_key('evalmon'):
evalmon = kwds['evalmon']
if xtol: #if tolerance in x is provided, use CandidateRelativeTolerance
from mystic.termination import CandidateRelativeTolerance as CRT
termination = CRT(xtol, ftol)
else:
from mystic.termination import VTRChangeOverGeneration
termination = VTRChangeOverGeneration(ftol)
solver = NelderMeadSimplexSolver(len(x0))
solver.SetInitialPoints(x0)
solver.SetEvaluationLimits(maxiter, maxfun)
solver.SetEvaluationMonitor(evalmon)
solver.SetGenerationMonitor(stepmon)
if kwds.has_key('penalty'):
penalty = kwds['penalty']
solver.SetPenalty(penalty)
if kwds.has_key('constraints'):
constraints = kwds['constraints']
solver.SetConstraints(constraints)
if bounds is not None:
minb, maxb = unpair(bounds)
solver.SetStrictRanges(minb, maxb)
if handler: solver.enable_signal_handler()
solver.Solve(cost,termination=termination,\
disp=disp, ExtraArgs=args, callback=callback)
solution = solver.Solution()
# code below here pushes output to scipy.optimize.fmin interface
#x = list(solver.bestSolution)
x = solver.bestSolution
fval = solver.bestEnergy
warnflag = 0
fcalls = solver.evaluations
iterations = solver.generations
allvecs = stepmon.x
if fcalls >= solver._maxfun:
warnflag = 1
elif iterations >= solver._maxiter:
warnflag = 2
if full_output:
retlist = x, fval, iterations, fcalls, warnflag
if retall:
retlist += (allvecs, )
else:
retlist = x
if retall:
retlist = (x, allvecs)
return retlist
def test_PowellDirectionalSolver_CRT(self):
from mystic.solvers import PowellDirectionalSolver
from mystic.termination import CandidateRelativeTolerance as CRT
self.solver = PowellDirectionalSolver(self.ND)
self.term = CRT()
self._run_solver(early_terminate=True)
print("Nelder-Mead Simplex")
print("===================")
start = time.time()
from mystic.monitors import Monitor, VerboseMonitor
#stepmon = VerboseMonitor(1)
stepmon = Monitor() #VerboseMonitor(10)
from mystic.termination import CandidateRelativeTolerance as CRT
#from mystic._scipyoptimize import fmin
from mystic.solvers import fmin, NelderMeadSimplexSolver
#print(fmin(rosen,x0,retall=0,full_output=0,maxiter=121))
solver = NelderMeadSimplexSolver(len(x0))
solver.SetInitialPoints(x0)
solver.SetStrictRanges(min,max)
solver.SetEvaluationLimits(generations=146)
solver.SetGenerationMonitor(stepmon)
solver.enable_signal_handler()
solver.Solve(rosen, CRT(xtol=4e-5), disp=1)
print(solver.bestSolution)
#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('Nelder-Mead Simplex\t')
for k,t in zip(algor,times):
print("%s\t -- took %s" % (k, t))
# end of file
def fmin(cost,
x0,
args=(),
bounds=None,
xtol=1e-4,
ftol=1e-4,
maxiter=None,
maxfun=None,
full_output=0,
disp=1,
retall=0,
callback=None,
**kwds):
"""Minimize a function using the downhill simplex algorithm.
Uses a Nelder-Mead simplex algorithm to find the minimum of a function of one
or more variables. This algorithm only uses function values, not derivatives or second derivatives. Mimics the ``scipy.optimize.fmin`` interface.
This algorithm has a long history of successful use in applications. It will
usually be slower than an algorithm that uses first or second derivative
information. In practice it can have poor performance in high-dimensional
problems and is not robust to minimizing complicated functions. Additionally,
there currently is no complete theory describing when the algorithm will
successfully converge to the minimum, or how fast it will if it does. Both the
ftol and xtol criteria must be met for convergence.
Args:
cost (func): the function or method to be minimized: ``y = cost(x)``.
x0 (ndarray): the initial guess parameter vector ``x``.
args (tuple, default=()): extra arguments for cost.
bounds (list(tuple), default=None): list of pairs of bounds (min,max),
one for each parameter.
xtol (float, default=1e-4): acceptable absolute error in ``xopt`` for
convergence.
ftol (float, default=1e-4): acceptable absolute error in ``cost(xopt)``
for convergence.
maxiter (int, default=None): the maximum number of iterations to perform.
maxfun (int, default=None): the maximum number of function evaluations.
full_output (bool, default=False): True if fval and warnflag are desired.
disp (bool, default=True): if True, print convergence messages.
retall (bool, default=False): if True, return list of solutions at each
iteration.
callback (func, default=None): function to call after each iteration. The
interface is ``callback(xk)``, with xk the current parameter vector.
handler (bool, default=False): if True, enable handling interrupt signals.
itermon (monitor, default=None): override the default GenerationMonitor.
evalmon (monitor, default=None): override the default EvaluationMonitor.
constraints (func, default=None): a function ``xk' = constraints(xk)``,
where xk is the current parameter vector, and xk' is a parameter
vector that satisfies the encoded constraints.
penalty (func, default=None): a function ``y = penalty(xk)``, where xk is
the current parameter vector, and ``y' == 0`` when the encoded
constraints are satisfied (and ``y' > 0`` otherwise).
Returns:
``(xopt, {fopt, iter, funcalls, warnflag}, {allvecs})``
Notes:
- xopt (*ndarray*): the minimizer of the cost function
- fopt (*float*): value of cost function at minimum: ``fopt = cost(xopt)``
- iter (*int*): number of iterations
- funcalls (*int*): number of function calls
- warnflag (*int*): warning flag:
- ``1 : Maximum number of function evaluations``
- ``2 : Maximum number of iterations``
- allvecs (*list*): a list of solutions at each iteration
"""
handler = kwds['handler'] if 'handler' in kwds else False
from mystic.monitors import Monitor
stepmon = kwds['itermon'] if 'itermon' in kwds else Monitor()
evalmon = kwds['evalmon'] if 'evalmon' in kwds else Monitor()
if xtol: #if tolerance in x is provided, use CandidateRelativeTolerance
from mystic.termination import CandidateRelativeTolerance as CRT
termination = CRT(xtol, ftol)
else:
from mystic.termination import VTRChangeOverGeneration
termination = VTRChangeOverGeneration(ftol)
solver = NelderMeadSimplexSolver(len(x0))
solver.SetInitialPoints(x0)
solver.SetEvaluationLimits(maxiter, maxfun)
solver.SetEvaluationMonitor(evalmon)
solver.SetGenerationMonitor(stepmon)
if 'penalty' in kwds:
solver.SetPenalty(kwds['penalty'])
if 'constraints' in kwds:
solver.SetConstraints(kwds['constraints'])
if bounds is not None:
minb, maxb = unpair(bounds)
solver.SetStrictRanges(minb, maxb)
if handler: solver.enable_signal_handler()
solver.Solve(cost, termination=termination, \
disp=disp, ExtraArgs=args, callback=callback)
solution = solver.Solution()
# code below here pushes output to scipy.optimize.fmin interface
#x = list(solver.bestSolution)
x = solver.bestSolution
fval = solver.bestEnergy
warnflag = 0
fcalls = solver.evaluations
iterations = solver.generations
allvecs = stepmon.x
if fcalls >= solver._maxfun:
warnflag = 1
elif iterations >= solver._maxiter:
warnflag = 2
if full_output:
retlist = x, fval, iterations, fcalls, warnflag
if retall:
retlist += (allvecs, )
else:
retlist = x
if retall:
retlist = (x, allvecs)
return retlist
