Python solvers.diffev2函数代码示例

solver = as_constraint(penalty)
#solver = discrete(range(11))(solver)  #XXX: MOD = range(11) instead of LARGE
#FIXME: constrain to 'int' with discrete is very fragile!  required #MODs

def constraint(x):
    from numpy import round
    return round(solver(x))

# better is to constrain to integers, penalize otherwise
from mystic.constraints import integers

@integers()
def round(x):
  return x


if __name__ == '__main__':

    from mystic.solvers import diffev2
    from mystic.math import almostEqual

    result = diffev2(objective, x0=bounds, bounds=bounds, penalty=penalty, constraints=round, npop=30, gtol=50, disp=True, full_output=True)

    print(result[0])
    assert almostEqual(result[0], xs, tol=1e-8) #XXX: fails b/c rel & zero?
    assert almostEqual(result[1], ys, tol=1e-4)


# EOF

from g11 import objective, bounds, xs, xs_, ys

from mystic.penalty import quadratic_equality
from mystic.constraints import with_penalty

@with_penalty(quadratic_equality, k=1e12)
def penalty(x): # == 0.0
    return x[1] - x[0]**2

from mystic.constraints import as_constraint

solver = as_constraint(penalty)



if __name__ == '__main__':

    from mystic.solvers import diffev2
    from mystic.math import almostEqual

    result = diffev2(objective, x0=bounds, bounds=bounds, constraints=solver, npop=40, xtol=1e-8, ftol=1e-8, disp=False, full_output=True)

    assert almostEqual(result[0], xs, tol=1e-2) \
        or almostEqual(result[0], xs_, tol=1e-2)
    assert almostEqual(result[1], ys, rel=1e-2)



# EOF

  def radius(model, point, ytol=0.0, xtol=0.0, ipop=None, imax=None):
    """graphical distance between a single point x,y and a model F(x')"""
    # given a single point x,y: find the radius = |y - F(x')| + delta
    # radius is just a minimization over x' of |y - F(x')| + delta
    # where we apply a constraints function (of box constraints) of
    # |x - x'| <= xtol  (for each i in x)
    #
    # if hausdorff = some iterable, delta = |x - x'|/hausdorff
    # if hausdorff = True, delta = |x - x'|/spread(x); using the dataset range
    # if hausdorff = False, delta = 0.0
    #
    # if ipop, then DE else Powell; ytol is used in VTR(ytol)
    # and will terminate when cost <= ytol
    x,y = _get_xy(point)
    y = asarray(y)
    # catch cases where yptp or y will cause issues in normalization
   #if not isfinite(yptp): return 0.0 #FIXME: correct?  shouldn't happen
   #if yptp == 0: from numpy import inf; return inf #FIXME: this is bad

    # build the cost function
    if hausdorff: # distance in all directions
      def cost(rv):
        '''cost = |y - F(x')| + |x - x'| for each x,y (point in dataset)'''
        _y = model(rv)
        if not isfinite(_y): return abs(_y)
        errs = seterr(invalid='ignore', divide='ignore') # turn off warning 
        z = abs((asarray(x) - rv)/ptp)  # normalize by range
        m = abs(y - _y)/yptp            # normalize by range
        seterr(invalid=errs['invalid'], divide=errs['divide']) # turn on warning
        return m + sum(z[isfinite(z)])
    else:  # vertical distance only
      def cost(rv):
        '''cost = |y - F(x')| for each x,y (point in dataset)'''
        return abs(y - model(rv))

    if debug:
      print("rv: %s" % str(x))
      print("cost: %s" % cost(x))

    # if xtol=0, radius is difference in x,y and x,F(x); skip the optimization
    try:
      if not imax or not max(xtol): #iterables
        return cost(x)
    except TypeError:
      if not xtol: #non-iterables
        return cost(x)

    # set the range constraints
    xtol = asarray(xtol)
    bounds = list(zip( x - xtol, x + xtol ))

    if debug:
      print("lower: %s" % str(zip(*bounds)[0]))
      print("upper: %s" % str(zip(*bounds)[1]))

    # optimize where initially x' = x
    stepmon = Monitor()
    if debug: stepmon = VerboseMonitor(1)
    #XXX: edit settings?
    MINMAX = 1 #XXX: confirm MINMAX=1 is minimization
    ftol = ytol
    gtol = None  # use VTRCOG
    if ipop:
      results = diffev2(cost, bounds, ipop, ftol=ftol, gtol=gtol, \
                        itermon = stepmon, maxiter=imax, bounds=bounds, \
                        full_output=1, disp=0, handler=False)
    else:
      results = fmin_powell(cost, x, ftol=ftol, gtol=gtol, \
                            itermon = stepmon, maxiter=imax, bounds=bounds, \
                            full_output=1, disp=0, handler=False)
   #solved = results[0]            # x'
    func_opt = MINMAX * results[1] # cost(x')
    if debug:
      print("solved: %s" % results[0])
      print("cost: %s" % func_opt)

    # get the minimum distance |y - F(x')|
    return func_opt

from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.symbolic import generate_penalty, generate_conditions

equations = """
-x0 + 0.0193*x2 <= 0.0
-x1 + 0.00954*x2 <= 0.0
-pi*x2**2*x3 - (4/3.)*pi*x2**3 + 1296000.0 <= 0.0
x3 - 240.0 <= 0.0
"""
cf = generate_constraint(generate_solvers(simplify(equations)))
pf = generate_penalty(generate_conditions(equations), k=1e12)



if __name__ == '__main__':

    from mystic.solvers import diffev2
    from mystic.math import almostEqual
    from mystic.monitors import VerboseMonitor
    mon = VerboseMonitor(10)

    result = diffev2(objective, x0=bounds, bounds=bounds, constraints=cf, penalty=pf, npop=40, gtol=50, disp=False, full_output=True, itermon=mon)

    assert almostEqual(result[0], xs, rel=1e-2)
    assert almostEqual(result[1], ys, rel=1e-2)



# EOF

#.........这里部分代码省略.........
    optimization termination for the sum(graphical_distances), while cutoff is
    used in defining the graphical_distance between x,y and x',F(x').
"""
  from numpy import sum as _sum, asarray
  from mystic.math.distance import graphical_distance, infeasibility, _npts
  if guess is None:
    message = "Requires a guess scenario, or a tuple of scenario dimensions."
    raise TypeError, message
  # get initial guess
  if hasattr(guess, 'pts'): # guess is a scenario
    pts = guess.pts    # number of x
    guess = guess.flatten(all=True)
  else:
    pts = guess        # guess is given as a tuple of 'pts'
    guess = None
  npts = _npts(pts)    # number of Y

  # prepare bounds for solver
  bounds = kwds.pop('bounds', None)
  # if bounds are not set, use the default optimizer bounds
  if bounds is None:
    lower_bounds = []; upper_bounds = []
    for n in pts:  # bounds for n*x in each dimension  (x2 due to weights)
      lower_bounds += [None]*n * 2
      upper_bounds += [None]*n * 2
    # also need bounds for npts*y values
    lower_bounds += [None]*npts
    upper_bounds += [None]*npts
    bounds = lower_bounds, upper_bounds
  bounds = asarray(bounds).T

  # plug in the 'constraints' function:  param' = constraints(param)
  constraints = kwds.pop('constraints', None) # default is no constraints
  if not constraints:  # if None (default), there are no constraints
    constraints = lambda x: x

  # 'wiggle room' tolerances
  ipop = kwds.pop('ipop', 10) #XXX: tune ipop (inner optimization)?
  imax = kwds.pop('imax', 10) #XXX: tune imax (inner optimization)?
  # tolerance for optimization on sum(y)
  tol = kwds.pop('tol', 0.0) # default
  npop = kwds.pop('npop', 20) #XXX: tune npop (outer optimization)?
  maxiter = kwds.pop('maxiter', 1000) #XXX: tune maxiter (outer optimization)?

  # if no guess was made, then use bounds constraints
  if guess is None:
    if npop:
      guess = bounds
    else:  # fmin_powell needs a list params (not bounds)
      guess = [(a + b)/2. for (a,b) in bounds]

  # construct cost function to reduce sum(infeasibility)
  def cost(rv):
    """compute cost from a 1-d array of model parameters,
    where: cost = | sum( infeasibility ) | """
    # converting rv to scenario
    points = scenario()
    points.load(rv, pts)
    # calculate infeasibility
    Rv = graphical_distance(model, points, ytol=cutoff, ipop=ipop, \
                                                        imax=imax, **kwds)
    v = infeasibility(Rv, cutoff)
    # converting v to E
    return _sum(v) #XXX: abs ?

  # construct and configure optimizer
  debug = False  #!!!
  maxfun = 1e+6
  crossover = 0.9; percent_change = 0.8
  ftol = abs(tol); gtol = None #XXX: optimally, should be VTRCOG...

  if debug:
    print "lower bounds: %s" % bounds.T[0]
    print "upper bounds: %s" % bounds.T[1]
  # print "initial value: %s" % guess
  # use optimization to get model-valid points
  from mystic.solvers import diffev2, fmin_powell
  from mystic.monitors import Monitor, VerboseMonitor
  from mystic.strategy import Best1Bin, Best1Exp
  evalmon = Monitor();  stepmon = Monitor(); strategy = Best1Exp
  if debug: stepmon = VerboseMonitor(2)  #!!!
  if npop: # use VTR
    results = diffev2(cost, guess, npop, ftol=ftol, gtol=gtol, bounds=bounds,\
                      maxiter=maxiter, maxfun=maxfun, constraints=constraints,\
                      cross=crossover, scale=percent_change, strategy=strategy,\
                      evalmon=evalmon, itermon=stepmon,\
                      full_output=1, disp=0, handler=False)
  else: # use VTR
    results = fmin_powell(cost, guess, ftol=ftol, gtol=gtol, bounds=bounds,\
                      maxiter=maxiter, maxfun=maxfun, constraints=constraints,\
                      evalmon=evalmon, itermon=stepmon,\
                      full_output=1, disp=0, handler=False)
  # repack the results
  pm = scenario()
  pm.load(results[0], pts)            # params: w,x,y
 #if debug: print "final cost: %s" % results[1]
  if debug and results[2] >= maxiter: # iterations
    print "Warning: constraints solver terminated at maximum iterations"
 #func_evals = results[3]           # evaluation
  return pm

"""
Maximization with a boolean variable and constraints.
"""
from mystic.solvers import diffev2
from mystic.monitors import VerboseMonitor
from mystic.constraints import impose_sum, discrete, and_
import numpy as np

N = 10
b = 5
bounds = [(0,1)] * N

def objective(x, w):
    s = 0
    for i in range(len(x)-1):
        for j in range(i, len(x)):
            s += w[i,j] * x[i] * x[j]
    return s


w = np.ones((N,N)) #XXX: replace with actual values of wij

cost = lambda x: -objective(x, w)

c = and_(lambda x: impose_sum(b, x), discrete([0,1])(lambda x:x))

mon = VerboseMonitor(10)
solution = diffev2(cost,bounds,constraints=c,bounds=bounds,itermon=mon,gtol=50, maxiter=5000, maxfun=50000, npop=10)
print(solution)

1394152 + 66920*x0 + 55679*x3 - 64234*x1 - 65337*x2 - 45581*x4 - 67707*x5 - 98038*x6 == 0.0
68550*x0 + 27886*x1 + 31716*x2 + 73597*x3 + 38835*x6 - 279091 - 88963*x4 - 76391*x5 == 0.0
76132*x1 + 71860*x2 + 22770*x3 + 68211*x4 + 78587*x5 - 480923 - 48224*x0 - 82817*x6 == 0.0
519878 + 94198*x1 + 87234*x2 + 37498*x3 - 71583*x0 - 25728*x4 - 25495*x5 - 70023*x6 == 0.0
361921 + 78693*x0 + 38592*x4 + 38478*x5 - 94129*x1 - 43188*x2 - 82528*x3 - 69025*x6 == 0.0
"""

from mystic.symbolic import generate_penalty, generate_conditions
pf = generate_penalty(generate_conditions(equations))
from mystic.symbolic import generate_constraint, generate_solvers, solve
cf = generate_constraint(generate_solvers(solve(equations)))

from numpy import round as npround


if __name__ == '__main__':

    from mystic.solvers import diffev2
    from mystic.math import almostEqual

   #result = diffev2(objective, x0=bounds, bounds=bounds, penalty=pf, npop=20, gtol=50, disp=True, full_output=True)
   #result = diffev2(objective, x0=bounds, bounds=bounds, penalty=pf, constraints=npround, npop=40, gtol=50, disp=True, full_output=True)
    result = diffev2(objective, x0=bounds, bounds=bounds, constraints=cf, npop=4, gtol=1, disp=True, full_output=True)

    print(result[0])
    assert almostEqual(result[0], xs, tol=1e-8) #XXX: fails b/c rel & zero?
    assert almostEqual(result[1], ys, tol=1e-4)


# EOF

#.........这里部分代码省略.........
  if guess is None:
    message = "Requires a guess scenario, or a tuple of scenario dimensions."
    raise TypeError, message
  # get initial guess
  if hasattr(guess, 'pts'): # guess is a scenario
    pts = guess.pts    # number of x
    guess = guess.flatten(all=True)
  else:
    pts = guess        # guess is given as a tuple of 'pts'
    guess = None
  npts = _npts(pts)    # number of Y
  long_form = len(pts) - list(pts).count(2) # can use '2^K compressed format'

  # prepare bounds for solver
  bounds = kwds.pop('bounds', None)
  # if bounds are not set, use the default optimizer bounds
  if bounds is None:
    lower_bounds = []; upper_bounds = []
    for n in pts:  # bounds for n*x in each dimension  (x2 due to weights)
      lower_bounds += [None]*n * 2
      upper_bounds += [None]*n * 2
    # also need bounds for npts*y values
    lower_bounds += [None]*npts
    upper_bounds += [None]*npts
    bounds = lower_bounds, upper_bounds
  bounds = asarray(bounds).T

  # plug in the 'constraints' function:  param' = constraints(param)
  # constraints should impose_mean(y,w), and possibly sum(weights)
  constraints = kwds.pop('constraints', None) # default is no constraints
  if not constraints:  # if None (default), there are no constraints
    constraints = lambda x: x

  _self = kwds.pop('with_self', True) # default includes self in shortness
  if _self is not False: _self = True
  # tolerance for optimization on sum(y)
  tol = kwds.pop('tol', 0.0) # default
  npop = kwds.pop('npop', 20) #XXX: tune npop?
  maxiter = kwds.pop('maxiter', 1000) #XXX: tune maxiter?

  # if no guess was made, then use bounds constraints
  if guess is None:
    if npop:
      guess = bounds
    else:  # fmin_powell needs a list params (not bounds)
      guess = [(a + b)/2. for (a,b) in bounds]

  # construct cost function to reduce sum(lipschitz_distance)
  def cost(rv):
    """compute cost from a 1-d array of model parameters,
    where:  cost = | sum(lipschitz_distance) | """
    _data = dataset()
    _pm = scenario()
    _pm.load(rv, pts)      # here rv is param: w,x,y
    if not long_form:
      positions = _pm.select(*range(npts))
    else: positions = _pm.positions
    _data.load( data.coords, data.values )                   # LOAD static
    if _self:
      _data.load( positions, _pm.values )                    # LOAD dynamic
    _data.lipschitz = data.lipschitz                         # LOAD L
    Rv = lipschitz_distance(_data.lipschitz, _pm, _data, tol=cutoff, **kwds)
    v = infeasibility(Rv, cutoff)
    return abs(sum(v))

  # construct and configure optimizer
  debug = False  #!!!
  maxfun = 1e+6
  crossover = 0.9; percent_change = 0.9
  ftol = abs(tol); gtol = None

  if debug:
    print "lower bounds: %s" % bounds.T[0]
    print "upper bounds: %s" % bounds.T[1]
  # print "initial value: %s" % guess
  # use optimization to get feasible points
  from mystic.solvers import diffev2, fmin_powell
  from mystic.monitors import Monitor, VerboseMonitor
  from mystic.strategy import Best1Bin, Best1Exp
  evalmon = Monitor();  stepmon = Monitor(); strategy = Best1Exp
  if debug: stepmon = VerboseMonitor(10)  #!!!
  if npop: # use VTR
    results = diffev2(cost, guess, npop, ftol=ftol, gtol=gtol, bounds=bounds,\
                      maxiter=maxiter, maxfun=maxfun, constraints=constraints,\
                      cross=crossover, scale=percent_change, strategy=strategy,\
                      evalmon=evalmon, itermon=stepmon,\
                      full_output=1, disp=0, handler=False)
  else: # use VTR
    results = fmin_powell(cost, guess, ftol=ftol, gtol=gtol, bounds=bounds,\
                      maxiter=maxiter, maxfun=maxfun, constraints=constraints,\
                      evalmon=evalmon, itermon=stepmon,\
                      full_output=1, disp=0, handler=False)
  # repack the results
  pm = scenario()
  pm.load(results[0], pts)            # params: w,x,y
 #if debug: print "final cost: %s" % results[1]
  if debug and results[2] >= maxiter: # iterations
    print "Warning: constraints solver terminated at maximum iterations"
 #func_evals = results[3]           # evaluation
  return pm

    assert my_x[3] == sp_x[-2]
#   # test fcalls <= maxfun
#   assert my_x[3] <= maxfun
  if maxiter is not None:
    # test iters <= maxiter
    assert my_x[2] <= maxiter
  return 

if __name__ == '__main__':
  x0 = [0,0,0]

  # check solutions versus results based on the random_seed
# print "comparing against known results"
  sol = solvers.diffev(rosen, x0, npop=40, disp=0, full_output=True)
  assert almostEqual(sol[1], 0.0020640145337293249, tol=3e-3)
  sol = solvers.diffev2(rosen, x0, npop=40, disp=0, full_output=True)
  assert almostEqual(sol[1], 0.0017516784703663288, tol=3e-3)
  sol = solvers.fmin_powell(rosen, x0, disp=0, full_output=True)
  assert almostEqual(sol[1], 8.3173488898295291e-23)
  sol = solvers.fmin(rosen, x0, disp=0, full_output=True)
  assert almostEqual(sol[1], 1.1605792769954724e-09)

  solver2 = 'diffev2'
  for solver in ['diffev']:
#   print "comparing %s and %s from mystic" % (solver, solver2)
    test_solvers(solver, solver2, x0, npop=40)
    test_solvers(solver, solver2, x0, npop=40, maxiter=None, maxfun=0)
    test_solvers(solver, solver2, x0, npop=40, maxiter=None, maxfun=1)
    test_solvers(solver, solver2, x0, npop=40, maxiter=None, maxfun=2)
    test_solvers(solver, solver2, x0, npop=40, maxiter=None, maxfun=9)
    test_solvers(solver, solver2, x0, npop=40, maxiter=0)

x0 - 2*x1 - 4.0 <= 0.0
"""
bounds = [(None, None),(0.0, None)]

# with penalty='penalty' applied, solution is:
xs = [0.5, 1.5]
ys = 2.5

from mystic.symbolic import generate_conditions, generate_penalty
pf = generate_penalty(generate_conditions(equations), k=1e3)
from mystic.symbolic import generate_constraint, generate_solvers, simplify
cf = generate_constraint(generate_solvers(simplify(equations)))



if __name__ == '__main__':

  from mystic.solvers import diffev2, fmin_powell
  from mystic.math import almostEqual

  result = diffev2(objective, x0=bounds, bounds=bounds, penalty=pf, constraint=cf, npop=40, disp=False, full_output=True, ftol=1e-10, gtol=100)
  assert almostEqual(result[0], xs, rel=1e-2)
  assert almostEqual(result[1], ys, rel=1e-2)

  result = fmin_powell(objective, x0=[0.0,0.0], bounds=bounds, penalty=pf, constraint=cf, disp=False, full_output=True, gtol=3)
  assert almostEqual(result[0], xs, rel=1e-2)
  assert almostEqual(result[1], ys, rel=1e-2)


# EOF

#x[3] is the slack variable

def func_value(d):
    curve_vec=[]
    for val in d:
        curve = (0.3 * val) + ((2 * (val ** (3/2))) / 3)
        curve_vec.append(curve)
    return curve_vec

def func(x):
    curve = func_value(x[0:3])
    return -(sum(np.dot(curve,production))-Q+x[3])

objective = lambda x: sum(np.dot(x[0:3],C))+1000*x[3]     

constraint = lambda x: func(x)

@quadratic_inequality(constraint)
def penalty(x):
    return 0.0


mon = VerboseMonitor(50)
solution = diffev2(objective,x0,penalty=penalty,bounds=bounds,itermon=mon,gtol=100, maxiter=1000, maxfun=10000, npop=40)
print(solution)

mon = VerboseMonitor(50)
solution = fmin_powell(objective,x0,penalty=penalty,bounds=bounds,itermon=mon,gtol=100, maxiter=1000, maxfun=10000)
print(solution)

def equations(len=3):
    eqn = "\nsum(["
    for i in range(len):
        eqn += 'x%s**2, ' % str(i)
    return eqn[:-2]+"]) - 1.0 = 0.0\n"

def cf(len=3):
    return generate_constraint(generate_solvers(solve(equations(len))))
def pf(len=3):
    return generate_penalty(generate_conditions(equations(len)))



if __name__ == '__main__':
    x = xs(10)
    y = ys(len(x))
    bounds = bounds(len(x))
    cf = cf(len(x))

    from mystic.solvers import diffev2
    from mystic.math import almostEqual

    result = diffev2(objective, x0=bounds, bounds=bounds, constraints=cf, npop=40, gtol=500, disp=False, full_output=True)

    assert almostEqual(result[0], x, tol=1e-2)
    assert almostEqual(result[1], y, tol=1e-2)



# EOF

from mystic.symbolic import generate_conditions, generate_penalty
pf = generate_penalty(generate_conditions(equations))
from mystic.symbolic import generate_constraint, generate_solvers, simplify
cf = generate_constraint(generate_solvers(simplify(equations)))

# inverted objective, used in solving for the maximum
_objective = lambda x: -objective(x)


if __name__ == '__main__':

  from mystic.solvers import diffev2, fmin_powell
  from mystic.math import almostEqual

  result = diffev2(objective, x0=bounds, bounds=bounds, constraint=cf, penalty=pf, npop=40, disp=False, full_output=True)
  assert almostEqual(result[0], xs, rel=1e-2)
  assert almostEqual(result[1], ys, rel=1e-2)

  result = fmin_powell(objective, x0=[0.0,0.0], bounds=bounds, constraint=cf, penalty=pf, disp=False, full_output=True)
  assert almostEqual(result[0], xs, rel=1e-2)
  assert almostEqual(result[1], ys, rel=1e-2)

  # alternately, solving for the maximum
  result = diffev2(_objective, x0=bounds, bounds=bounds, constraint=cf, penalty=pf, npop=40, disp=False, full_output=True)
  assert almostEqual( result[0], _xs, rel=1e-2)
  assert almostEqual(-result[1], _ys, rel=1e-2)

  result = fmin_powell(_objective, x0=[0,0], bounds=bounds, constraint=cf, penalty=pf, npop=40, disp=False, full_output=True)
  assert almostEqual( result[0], _xs, rel=1e-2)
  assert almostEqual(-result[1], _ys, rel=1e-2)

    p = 0.01 * p * len(x)
    if int(p) != p:
        return x[int(np.floor(p))]
    p = int(p)
    return x[p:p+2].mean()

def objective(x, p=5): # inverted objective, to find the max
    return -1*percentile(p, [np.dot(np.atleast_2d(u[i]), x)[0] for i in range(0,M-1)])


def constraint(x, p=95, v=C): # 95%(xTsx) - v <= 0
    x = np.atleast_2d(x)
    return percentile(p, [np.dot(np.dot(x,s[i]),x.T)[0,0] for i in range(0,M-1)]) - v

bounds = [(0,1) for i in range(0,N)]

from mystic.penalty import quadratic_inequality
@quadratic_inequality(constraint, k=1e4)
def penalty(x):
  return 0.0

from mystic.solvers import diffev2
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)

result = diffev2(objective, x0=bounds, penalty=penalty, npop=10, gtol=200, \
                 disp=False, full_output=True, itermon=mon, maxiter=M*N*100)

print(result[0])
print(result[1])