def mysticCompute(self):
#for b in range(10**5, budget, ba):
for b in range(0, int(self.ba), int(self.ba / self.intermediate)):
equations = "{} <= {}".format(
"+".join(([
"x{}".format(i) for i in range(len(self.componentIndices))
])), b)
#print(equations)
cf = generate_constraint(generate_solvers(simplify(equations)))
pf = generate_penalty(generate_conditions(equations))
x0 = [
b / len(self.componentIndices) for i in self.componentIndices
]
bounds = [(0, b) for i in self.componentIndices]
result = diffev(self.sys_avail,
x0=x0,
bounds=bounds,
constraints=cf,
penalty=pf,
npop=10,
disp=True)
#print(result)
self.results.append(result)
self.avail_.append(-self.sys_avail(result))
self.budget_.append(b)
#print(self.n_gamma(result))
self.eta_.append(self.n_gamma(result))
return self.results
def _symbolic():
import mystic.symbolic as ms
eqn = """x0 - 2*x1 > 0
x3 - 3*x2 < 0"""
eqn = ms.simplify(eqn, target=['x1', 'x3'])
cons = ms.generate_constraint(ms.generate_solvers(eqn))
return cons
def impose_reweighted_variance(v, samples, weights=None, solver=None):
"""impose a variance on a list of points by reweighting weights"""
ndim = len(samples)
if weights is None:
weights = [1.0 / ndim] * ndim
if solver is None or solver == 'fmin':
from mystic.solvers import fmin as solver
elif solver == 'fmin_powell':
from mystic.solvers import fmin_powell as solver
elif solver == 'diffev':
from mystic.solvers import diffev as solver
elif solver == 'diffev2':
from mystic.solvers import diffev2 as solver
norm = sum(weights)
m = mean(samples, weights)
inequality = ""
equality = ""
equality2 = ""
equality3 = ""
for i in range(ndim):
inequality += "x%s >= 0.0\n" % (i) # positive
equality += "x%s + " % (i) # normalized
equality2 += "%s * x%s + " % (float(samples[i]), (i)) # mean
equality3 += "x%s*(%s-%s)**2 + " % ((i), float(samples[i]), m) # var
equality += "0.0 = %s\n" % float(norm)
equality += equality2 + "0.0 = %s*%s\n" % (float(norm), m)
equality += equality3 + "0.0 = %s*%s\n" % (float(norm), v)
penalties = generate_penalty(generate_conditions(inequality))
constrain = generate_constraint(generate_solvers(solve(equality)))
def cost(x):
return sum(x)
results = solver(cost, weights, constraints=constrain, \
penalty=penalties, disp=False, full_output=True)
wts = list(results[0])
_norm = results[1] # should have _norm == norm
warn = results[4] # nonzero if didn't converge
#XXX: better to fail immediately if xlo < m < xhi... or the below?
if warn or not almostEqual(_norm, norm):
print "Warning: could not impose mean through reweighting"
return None #impose_variance(v, samples, weights), weights
return wts #samples, wts # "mean-preserving"
def impose_reweighted_variance(v, samples, weights=None, solver=None):
"""impose a variance on a list of points by reweighting weights"""
ndim = len(samples)
if weights is None:
weights = [1.0/ndim] * ndim
if solver is None or solver == 'fmin':
from mystic.solvers import fmin as solver
elif solver == 'fmin_powell':
from mystic.solvers import fmin_powell as solver
elif solver == 'diffev':
from mystic.solvers import diffev as solver
elif solver == 'diffev2':
from mystic.solvers import diffev2 as solver
norm = sum(weights)
m = mean(samples, weights)
inequality = ""
equality = ""; equality2 = ""; equality3 = ""
for i in range(ndim):
inequality += "x%s >= 0.0\n" % (i) # positive
equality += "x%s + " % (i) # normalized
equality2 += "%s * x%s + " % (float(samples[i]),(i)) # mean
equality3 += "x%s*(%s-%s)**2 + " % ((i),float(samples[i]),m) # var
equality += "0.0 = %s\n" % float(norm)
equality += equality2 + "0.0 = %s*%s\n" % (float(norm),m)
equality += equality3 + "0.0 = %s*%s\n" % (float(norm),v)
penalties = generate_penalty(generate_conditions(inequality))
constrain = generate_constraint(generate_solvers(solve(equality)))
def cost(x): return sum(x)
results = solver(cost, weights, constraints=constrain, \
penalty=penalties, disp=False, full_output=True)
wts = list(results[0])
_norm = results[1] # should have _norm == norm
warn = results[4] # nonzero if didn't converge
#XXX: better to fail immediately if xlo < m < xhi... or the below?
if warn or not almostEqual(_norm, norm):
print "Warning: could not impose mean through reweighting"
return None #impose_variance(v, samples, weights), weights
return wts #samples, wts # "mean-preserving"
def mysticCompute():
#for b in range(10**5, budget, ba):
results = []
for b in range(10**5, ba, (ba-10**5)/20):
equations = "{} <= {}".format("+".join((["x{}".format(i) for i in range(len(componentIndices))])), b)
print(equations)
cf = generate_constraint(generate_solvers(simplify(equations)))
pf = generate_penalty(generate_conditions(equations))
x0 = [b/len(componentIndices) for i in componentIndices]
bounds = [(0,b) for i in componentIndices]
result = diffev(sys, x0=x0, bounds=bounds, constraints=cf, penalty=pf, npop=10, disp=True)
print(result)
results.append(result)
avail_.append(-sys(result))
budget_.append(b)
print(eta(result))
eta_.append(eta(result))
return results
-3*x0 + x1 - 6.0 <= 0.0 x0 + 2*x1 - 4.0 <= 0.0 """ bounds = [(None, None),(-3.0, None)] # with penalty='penalty' applied, solution is: xs = [10.0, -3.0] ys = -22.0 # alternately, if solving for the maximum, the solution is: _xs = [-1.14285714, 2.57142857] _ys = 11.428571428571429 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)
# generate some sparse data
xtrain = np.random.uniform(0, 100, size=(10, 4))
target = model(xtrain.T).T
xtest = np.random.uniform(0, 100, size=(10, 4))
test = model(xtest.T).T
# define some model constraints
equations = """
3*b + c > -0.75
4.5*b - d > 11.0
"""
var = list('abcd')
equations = simplify(equations, variables=var)
cf = generate_constraint(generate_solvers(equations, variables=var))
if __name__ == '__main__':
# build a kernel-transformed regressor
ta = pre.FunctionTransformer(func=vectorize(cf, axis=1))
tp = pre.PolynomialFeatures(degree=3)
e = lin.LinearRegression()
# train and score, then test and score
xtrain_ = tp.fit_transform(ta.fit_transform(xtrain))
assert 1.0 == e.fit(xtrain_, target).score(xtrain_, target)
xtest_ = tp.fit_transform(ta.fit_transform(xtest))
assert 1 - e.score(xtest_, test) <= 1e-2
# EOF
import mystic.symbolic as ms
import scipy.optimize as so
equations = """
A*B + C >= 1
B <= A
A >= -5
B >= -5
C >= -5
5 >= A
5 >= B
5 >= C
"""
var = list('ABC')
eqns = ms.simplify(equations, variables=var, all=True)
constrain = ms.generate_constraint(ms.generate_solvers(eqns, var),
join=my.constraints.and_)
def objective(x):
return 3 * x[0] + 1.e-6 * x[0]**3 + 2 * x[1] + 2.e-6 / 3 * x[1]**3 + x[2]**2
mon = my.monitors.Monitor()
def cost(x):
kx = constrain(x)
y = objective(kx)
mon(kx, y)
return y
x0, x1 = x
return x0**2 + (x1 - 1)**2
bounds = [(-1, 1)] * 2
# with penalty='penalty' applied, solution is:
xs, xs_ = [(0.5)**.5, 0.5], [-(0.5)**.5, 0.5]
ys = 0.75
from mystic.symbolic import generate_constraint, generate_solvers, solve
from mystic.symbolic import generate_penalty, generate_conditions
equations = """
x1 - x0**2 = 0.0
"""
cf = generate_constraint(generate_solvers(solve(equations, target='x1')))
pf = generate_penalty(generate_conditions(equations), k=1e12)
if __name__ == '__main__':
from mystic.solvers import diffev2
from mystic.math import almostEqual
result = diffev2(objective,
x0=bounds,
bounds=bounds,
constraints=cf,
npop=40,
disp=False,
full_output=True)
Subject to: x[0] + 1*x[1] <= 7
-x[0] + 2*x[1] <= 4
where: 0 <= x[0] <= inf
0 <= x[1] <= 4
"""
import numpy as np
import mystic.symbolic as ms
import mystic.solvers as my
import mystic.math as mm
# generate constraints and penalty for a linear system of equations
A = np.array([[1, 1],[-1, 2]])
b = np.array([7,4])
eqns = ms.linear_symbolic(G=A, h=b)
cons = ms.generate_constraint(ms.generate_solvers(ms.simplify(eqns)))
pens = ms.generate_penalty(ms.generate_conditions(eqns), k=1e3)
bounds = [(0., None), (0., 4.)]
# get the objective
def objective(x):
x = np.asarray(x)
return x[0]**2 + 4*x[1]**2 - 32*x[1] + 64
x0 = np.random.rand(2)
# compare against the exact minimum
xs = np.array([2., 3.])
ys = objective(xs)
def objective(x):
x0,x1 = x
return x0**2 + (x1 - 1)**2
bounds = [(-1,1)]*2
# with penalty='penalty' applied, solution is:
xs, xs_ = [(0.5)**.5, 0.5], [-(0.5)**.5, 0.5]
ys = 0.75
from mystic.symbolic import generate_constraint, generate_solvers, solve
from mystic.symbolic import generate_penalty, generate_conditions
equations = """
x1 - x0**2 = 0.0
"""
cf = generate_constraint(generate_solvers(solve(equations, target='x1')))
pf = generate_penalty(generate_conditions(equations), k=1e12)
if __name__ == '__main__':
from mystic.solvers import diffev2
from mystic.math import almostEqual
result = diffev2(objective, x0=bounds, bounds=bounds, constraints=cf, npop=40, 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)
def cf(len=3):
return generate_constraint(generate_solvers(solve(equations(len))))
98527*x0 + 34588*x1 + 5872*x2 + 59422*x4 + 65159*x6 - 1547604 - 30704*x3 - 29649*x5 == 0.0
98957*x1 + 83634*x2 + 69966*x3 + 62038*x4 + 37164*x5 + 85413*x6 - 1823553 - 93989*x0 == 0.0
900032 + 10949*x0 + 77761*x1 + 67052*x4 - 80197*x2 - 61944*x3 - 92964*x5 - 44550*x6 == 0.0
73947*x0 + 84391*x2 + 81310*x4 - 1164380 - 96253*x1 - 44247*x3 - 70582*x5 - 33054*x6 == 0.0
13057*x2 + 42253*x3 + 77527*x4 + 96552*x6 - 1185471 - 60152*x0 - 21103*x1 - 97932*x5 == 0.0
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?
i=0
while i<= len(list):
if list[i]==1:
return i
i=i+1
return len(list)
# Define constraints
cminconstr="x"+str(firstone(cvec))+" >= "
for i in list(range(0,len(cvec))):
if cvec[i]==1 and i!=firstone(cvec):
cminconstr=cminconstr+"x"+str(i)+" + "
cminconstr=cminconstr+"2"
solv = generate_solvers(cminconstr,nvars=len(pointvec))
constraintfunc = generate_constraint(solv)
#Run optimization
if __name__ == '__main__':
print("Powell's Method")
print("===============")
# dimensional information
from mystic.tools import random_seed
random_seed(12)
ndim = len(pointvec)
nbins = 1 #[2,1,2,1,2,1,2,1,1]
B < 0
"""
print(equations)
var = list('ABC')
eqns = ms.simplify(equations, variables=var, all=True)
if isinstance(eqns, str):
_join = join_ = None
print(eqns)
else:
_join, join_ = _or, or_
for eqn in eqns:
print(eqn + '\n----------------------')
constrain = ms.generate_constraint(ms.generate_solvers(
eqns, var, locals=dict(e_=eps)),
join=_join)
solution = constrain([1, -2, 1])
print('solved: %s' % dict(zip(var, solution)))
penalty = ms.generate_penalty(ms.generate_conditions(eqns,
var,
locals=dict(e_=eps)),
join=join_)
print('penalty: %s' % penalty(solution))
equations = """
A*(B-C) + 2*C > 1
B + C = 2*D
D < 0
ys = 24.3062091
from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.symbolic import generate_penalty, generate_conditions
equations = """
4.0*x0 + 5.0*x1 - 3.0*x6 + 9.0*x7 - 105.0 <= 0.0
10.0*x0 - 8.0*x1 - 17.0*x6 + 2.0*x7 <= 0.0
-8.0*x0 + 2.0*x1 + 5.0*x8 - 2.0*x9 - 12.0 <= 0.0
3.0*(x0-2)**2 + 4.0*(x1-3)**2 + 2.0*x2**2 - 7.0*x3 - 120.0 <= 0.0
5.0*x0**2 + 8.0*x1 + (x2-6)**2 - 2.0*x3 - 40.0 <= 0.0
0.5*(x0-8)**2 + 2.0*(x1-4)**2 + 3.0*x4**2 - x5 - 30.0 <= 0.0
x0**2 + 2.0*(x1-2)**2 - 2.0*x0*x1 + 14.0*x4 - 6.0*x5 <= 0.0
-3.0*x0 + 6.0*x1 + 12.0*(x8-8)**2 - 7.0*x9 <= 0.0
"""
cf = generate_constraint(generate_solvers(simplify(equations, target=['x5','x3'])))
pf = generate_penalty(generate_conditions(equations))
if __name__ == '__main__':
x = [0]*len(xs)
from mystic.solvers import fmin_powell
from mystic.math import almostEqual
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)
result = fmin_powell(objective, x0=x, bounds=bounds, penalty=pf, maxiter=1000, maxfun=100000, ftol=1e-12, xtol=1e-12, gtol=10, disp=False, full_output=True)
assert almostEqual(result[0], xs, tol=1e-2)
"""
import numpy as np
import mystic.symbolic as ms
import mystic.solvers as my
import mystic.math as mm
# generate constraints and penalty for a nonlinear system of equations
ieqn = '''
-2*x0 + 2*x1 <= -2
2*x0 - 4*x1 <= 0
'''
eqn = '''
x0**3 - x1 == 0
'''
cons = ms.generate_constraint(ms.generate_solvers(ms.simplify(eqn,target='x1')))
pens = ms.generate_penalty(ms.generate_conditions(ieqn), k=1e3)
bounds = [(0., None), (1., None)]
# get the objective
def objective(x, sign=1):
x = np.asarray(x)
return sign * (2*x[0]*x[1] + 2*x[0] - x[0]**2 - 2*x[1]**2)
x0 = np.random.rand(2)
# compare against the exact minimum
xs = np.array([2., 1.])
ys = objective(xs, -1)
import mystic.symbolic as ms
import mystic.constraints as mc
import mystic.models as mm
from mystic.solvers import PowellDirectionalSolver, NelderMeadSimplexSolver, \
DifferentialEvolutionSolver, \
DifferentialEvolutionSolver2, \
LatticeSolver, BuckshotSolver, SparsitySolver
almostEqual = my.math.almostEqual
rosen = mm.rosen
bounds = [(0.0001, 0.0002)] * 3
guess = [0.001, 0.001, 0.001]
# generate the constraints
_eqn = 'x0 + x1 + x2 <= .0005'
_cons = ms.generate_constraint(ms.generate_solvers(ms.simplify(_eqn)),
join=mc.and_)
# explicitly include bounds in constraints
eqn_ = '\n'.join([_eqn, ms.symbolic_bounds(*zip(*bounds))])
cons_ = ms.generate_constraint(ms.generate_solvers(ms.simplify(eqn_)),
join=mc.and_)
def test_constrained(TheSolver, tight, clip):
ndim = len(bounds)
solver = TheSolver(ndim)
if TheSolver in [PowellDirectionalSolver, NelderMeadSimplexSolver]:
solver.SetInitialPoints(guess)
elif TheSolver in [
DifferentialEvolutionSolver, DifferentialEvolutionSolver2
]:
eq_ = '''
abs(x0) - x1 > 0
x2/(x0 - x1) > 1
'''
res = ms.simplify(eq_, all=True)
#print(res[0])
#print('')
res0 = ms.simplify(eq_, all=False)
#print(res0)
#print('')
assert res0 in res
assert len(res) == 3
_eq = '''
x0**.5 == abs(x1 + x2)
abs(x0) - x1 > 0
x2**2 > 1
'''
res = ms.simplify(_eq, all=True)
import mystic.constraints as mc
c = ms.generate_constraint(ms.generate_solvers(res), join=mc.or_)
kx = c([1, 2, 3])
#print(kx)
x0, x1, x2 = kx
assert x0**.5 == abs(x1 + x2)
assert abs(x0) - x1 > 0
assert x2**2 > 1
ys = 24.3062091
from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.symbolic import generate_penalty, generate_conditions
equations = """
4.0*x0 + 5.0*x1 - 3.0*x6 + 9.0*x7 - 105.0 <= 0.0
10.0*x0 - 8.0*x1 - 17.0*x6 + 2.0*x7 <= 0.0
-8.0*x0 + 2.0*x1 + 5.0*x8 - 2.0*x9 - 12.0 <= 0.0
3.0*(x0-2)**2 + 4.0*(x1-3)**2 + 2.0*x2**2 - 7.0*x3 - 120.0 <= 0.0
5.0*x0**2 + 8.0*x1 + (x2-6)**2 - 2.0*x3 - 40.0 <= 0.0
0.5*(x0-8)**2 + 2.0*(x1-4)**2 + 3.0*x4**2 - x5 - 30.0 <= 0.0
x0**2 + 2.0*(x1-2)**2 - 2.0*x0*x1 + 14.0*x4 - 6.0*x5 <= 0.0
-3.0*x0 + 6.0*x1 + 12.0*(x8-8)**2 - 7.0*x9 <= 0.0
"""
cf = generate_constraint(
generate_solvers(simplify(equations, target=['x5', 'x3'])))
pf = generate_penalty(generate_conditions(equations))
if __name__ == '__main__':
x = [0] * len(xs)
from mystic.solvers import fmin_powell
from mystic.math import almostEqual
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)
result = fmin_powell(objective,
x0=x,
bounds=bounds,
penalty=pf,
maxiter=1000,
load = [i.mass for i in items]
invest = [i.buy for i in items]
constraints = ms.linear_symbolic(G=[load, invest], h=[max_load, max_spend])
# bounds (on x)
bounds = [(0, i.limit) for i in items]
# bounds constraints
lo = 'x%s >= %s'
lo = '\n'.join(lo % (i, str(float(j[0])).lstrip('0'))
for (i, j) in enumerate(bounds))
hi = 'x%s <= %s'
hi = '\n'.join(hi % (i, str(float(j[1])).lstrip('0'))
for (i, j) in enumerate(bounds))
constraints = '\n'.join([lo, hi]).strip() + '\n' + constraints
cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(constraints)),
join=mc.and_)
pf = ms.generate_penalty(ms.generate_conditions(ms.simplify(constraints)))
# integer constraints
#constrain = mc.and_(mc.integers(float)(lambda x:x), cf)
constrain = mc.integers(float)(lambda x: x)
# solve
mon = my.monitors.VerboseMonitor(10)
result = my.solvers.diffev2(lambda x: -profit(x),
bounds,
npop=400,
bounds=bounds,
ftol=1e-6,
gtol=100,
itermon=mon,