def optimizationSC():
from scipy.optimize import fmin_cobyla
objectiveSC = lambda x: objectNL(x, grad=0)
f1Dev = lambda x: x[0]
f2Dev = lambda x: x[1]
lc1Cstrt = lambda x: x[2] - 1
lc2Cstrt = lambda x: x[3] - 1
fmin_cobyla(objectiveSC, [0.18, 0.09, 1.1, 1.1],
[f1Dev, f2Dev, lc1Cstrt, lc2Cstrt],
rhobeg=0.2,
rhoend=1e-4)
def main():
parse_args()
mpm.mp.prec = PREC
runtime = str(datetime.datetime.now())
time_start = timeit.default_timer()
# filename = "cobyla_wavesolve_run" + str(NSIZE) + runtime
fmin_cobyla(objective, [A1, A2, B1, B2, G1, G2],
get_constraints,
maxfun=MAXFUN,
rhobeg=RHOBEG,
rhoend=RHOEND)
def mindist(cobramodel,x0,FBAobjval, optreq = 0, tol = 0.001):
cobmodel = CobylaModel(cobramodel, tol = tol)
if x0 is None:
x0 = [0 for element in cobmodel.C]
if optreq == 0:
minsol = optimize.fmin_cobyla(compdistcomplete,x0,cobmodel.allconstr,args = (cobramodel,),consargs = ())
else:
objcon = lambda x, objective = cobmodel.C , value = FBAobjval, optreq = optreq : np.dot(C,x) - FBAobjval*optreq #+ 0.0001
allconstr2 = cobmodel.allconstr + [objcon]
minsol = optimize.fmin_cobyla(compdistcomplete,x0,allconstr2,args = (cobramodel,),consargs = ())
return minsol
def fitting(Eqm, Eel, ljd, uniform_weight, output=True):
if uniform_weight == True:
x = fmin_cobyla(f_opt_LB_cobyla,
opt_p_LB,
cons,
args=(Eqm, Eel, np.array(weight0(Eqm)),
np.transpose(ljd)),
maxfun=100000,
iprint=0)
opt_LJ = ljeval_LB(np.transpose(ljdists), x)
if output:
output_parameters(x)
output_goodness(opt_LJ)
if out != '': output_energies(opt_LJ)
return x
else:
# 1st iteration
x = fmin_cobyla(f_opt_LB_cobyla,
opt_p_LB,
cons,
args=(Eqm, Eel, np.array(weight1(Eqm - Eel)),
np.transpose(ljd)),
maxfun=100000,
iprint=0)
opt_LJ = ljeval_LB(np.transpose(ljdists), x)
if ver:
print "Iteration #1:"
output_parameters(x)
output_goodness(opt_LJ)
# 2nd iteration
x = fmin_cobyla(f_opt_LB_cobyla,
opt_p_LB,
cons,
args=(Eqm, Eel, np.array(weight2(Eqm, Eel, opt_LJ)),
np.transpose(ljd)),
maxfun=100000,
iprint=0)
opt_LJ2 = ljeval_LB(np.transpose(ljdists), x)
if ver: print "Iteration #2:"
if output:
output_parameters(x)
output_goodness(opt_LJ2)
if out != '': output_energies(opt_LJ2)
return x
def fit(self, lX, ly, sample_weight=None):
n_cols = lX.shape[1]
x0 = np.ones((n_cols, 1))
constr_lb = [
lambda x, z=i: x[z] - self.lowerbound for i in range(n_cols)
]
constr_ub = [
lambda x, z=i: self.upperbound - x[z] for i in range(n_cols)
]
constr = constr_lb + constr_ub
# constr=constr_lb
self.coef_ = fmin_cobyla(self.fopt,
x0,
constr,
args=(lX, ly),
consargs=(),
rhoend=1e-10,
maxfun=10000,
disp=0)
# coef_ = minimize(fopt, x0,method='COBYLA',constraints=self.constr)
# normalize coefficient
if self.normalize:
self.coef_ = self.coef_ / np.sum(self.coef_)
# print "Normalizing coefficients:",self.coef_
if np.isnan(np.sum(self.coef_)):
print("We have NaN here...")
def local_refine(f, gts, eqs, x0, rhobeg=1, rhoend=1e-7, maxfun=1e4):
"""
Use SciPy's COBYLA solver in an attempt to find a minimizer of ``f`` subject to
inequality constraints in ``gts`` and equality constraints in ``eqs``.
Parameters
----------
f : a callable function
The minimization objective.
gts : a list of callable functions
Each ``g in gts`` specifies an inequality constraint ``g(x) >= 0``.
eqs : a list of callable functions
Each ``g in eqs`` specifies an equality constraint ``g(x) == 0``.
x0 : ndarray
An initial point for COBYLA.
rhobeg : float
Controls the size of COBYLA's initial search space.
rhoend : float
Termination criteria, controlling the size of COBYLA's smallest search space.
maxfun : int
Termination criteria, bounding the number of COBYLA's iterations.
Returns
-------
x : ndarray
The solution returned by COBYLA.
"""
maxfun = int(maxfun)
x = fmin_cobyla(f, x0, gts + eqs + [-g for g in eqs],
rhobeg=rhobeg, rhoend=rhoend, maxfun=maxfun)
return x
def garchfit(self,initvalue):
"""
estimate GARCH(1,1) paramters by maximum likelihood method.
Optimization should be under the following constraints:
ARCH + GARCH < 1 (Stationarity)
All parameters >= 0 (Non-negative)
-------------------------------------------------------------------------
InitValue = [ARCH; GARCH; Constant]
"""
try:
from openopt import NLP
lb = [0.0001, 0.0001, 0.] #lower bound
A = [1, 1, 0]
b = 1.0
p = NLP(self.f,initvalue,lb=lb,A=A,b=b)
r = p.solve('ralg')
return r.xf
except ImportError:
print "Openopt is not installed, will use scipy.fmin_cobyla instead"
print "the result may not accurate though"
params = fmin_cobyla(self.f,initvalue,cons=[lambda x:1-(x[0]+x[1]),
lambda x:x[0],
lambda x:x[2],
lambda x:x[1]])
return params
def q4():
r = 0.05 # annual interest rate (with 6 month compounding)
recrate = [0.1, 0.25, 0.5, 0.1, 0.2]
coupon = [0.05, 0.02, 0.05, 0.05, 0.1]
nperiod = [2 * x for x in range(1, 6)]
fs = [fdb(r / 2, c, rec, nper) for c, rec, nper in zip(coupon, recrate, nperiod)]
h0 = np.linspace(0.1, 0.9, nperiod[-1])
h0 = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99])
h0 = 0.05 * np.ones((nperiod[-1] + 1,))
bondprices = np.array([100.92, 91.56, 105.60, 98.90, 137.48]) / 100
def nonneg(h):
h = copy.deepcopy(h)
h[h > 0] = 0
return np.sum(h)
def monotonic(h):
x = h[1:] - h[:-1]
x[x > 0] = 0
return np.sum(x)
hopt = fmin_cobyla(lambda hr: np.sum(([f(hr) for f in fs] - bondprices) ** 2), h0, [nonneg, monotonic], disp=0)
return hopt
def test_simple(self):
x = fmin_cobyla(self.fun,
self.x0, [self.con1, self.con2],
rhobeg=1,
rhoend=1e-5,
maxfun=100)
assert_allclose(x, self.solution, atol=1e-4)
def fullA_Xing(X,S,D):
#X: the data matrix
#S: the similarity Matrix
#D: the dissimilarty Matrix
#Creating the objective function and the constraints function here
def objective(A):
values = []
for i in range(S.shape[0]):
for j in range(S.shape[1]):
if S[i,j] == 0:
continue
M = np.matrix(X[i] - X[j])
values.append(np.sum((M*A)*M.T))
return np.sum(np.array(values))
def constraint(A):
values = []
for i in range(D.shape[0]):
for j in range(D.shape[1]):
if D[i,j] == 0:
continue
M = np.matrix(X[i]-X[j])
values.append(np.sqrt(np.sum((M*A)*M.T)))
return np.sum(np.array(values))
A0 = np.random.rand(X.shape[1], X.shape[1])
return fmin_cobyla(objective, A0, [constraint], rhoend=1e-7)
def fit_adsorption_kinetics_fmin_cobyla(self):
from scipy.optimize import fmin_cobyla
def constr0(params):
return params[0]
def constr1(params):
return params[1]
def constr2(params):
return params[2]
error = self.compute_error(self.initial_parameters,
self.concentrations, self.mean_surf_conc,
self.times)
self.initial_sse = error
self.fitted_parameters = fmin_cobyla(self.compute_error,
self.initial_parameters, [],
args=self.model_parameters,
consargs=(),
rhobeg=min(
self.initial_parameters),
rhoend=1e-9,
iprint=2)
error = self.compute_error(self.fitted_parameters, self.concentrations,
self.mean_surf_conc, self.times)
self.final_sse = error
def get_weights():
# Read validation labels
_, labels, _, _, _ = utils.load_data()
skf = StratifiedKFold(labels, n_folds=5, random_state=23)
test_index = None
for _, test_idx in skf:
test_index = np.append(
test_index, test_idx) if test_index is not None else test_idx
val_labels = labels[test_index]
# Read predictions on validation set
val_predictions = []
prediction_files = utils.get_prediction_files()
for preds_file in prediction_files:
vp = np.genfromtxt(os.path.join(consts.BLEND_PATH, preds_file),
delimiter=',')
val_predictions.append(vp)
# Minimize blending function
p0 = [1.] * len(prediction_files)
p = fmin_cobyla(error,
p0,
args=(val_predictions, val_labels),
cons=[constraint],
rhoend=1e-5)
return p
def calc_variable_arrays(self, trend_mod, data, periods):
"""
Function to calculate arrays that depend on changing starting variables, i.e. trend modifier
Parameters
----------
trend_modifier : float
Trend modifier value for exponential dampened smoothing function.
data : array
Data array that needs to be forecasted
periods : integer
Number of periods to forecast.
"""
self.xs = data
self.fcast_periods = periods
self.data_N = self.xs.size
self.warmUp = self.data_N / 2 # Going with a warm-up of half the data, instead of 6
self.zero_len = self.data_N + self.fcast_periods # Length of arrays with one missing value
self.lvlArr = np.zeros(self.zero_len + 1)
self.errors = np.zeros(self.data_N)
self.trendArr = np.zeros(self.zero_len + 1)
self.fcasts = np.zeros(self.zero_len)
avg_first_four_diffs = np.average(np.diff(self.xs[:4 + 1]))
self.trendArr[0] = avg_first_four_diffs
self.lvlArr[0] = self.xs[0] - avg_first_four_diffs
self.trend_modifier = trend_mod
self.trend_exp = np.ones(self.zero_len + 1)
self.trend_exp[self.data_N:] = np.power(
self.trend_modifier, (np.arange(self.data_N + 1, self.zero_len + 2) - self.data_N)
)
self.trend_multiplier = np.zeros(self.zero_len + 1)
self.trend_multiplier[self.data_N:] = np.cumsum(self.trend_exp[self.data_N:])
return optimize.fmin_cobyla(self.exp_smooth_forecast, self.x0, self.constrs, iprint=0)
def main(self,
fit_params=None,
par=None,
Rd=None,
Ci=None,
N_p=None,
Tleaf=None,
Q10=None,
Eaj=None,
Eav=None,
deltaSj=None,
deltaSv=None,
r25=None,
Hdv=200000.0,
Hdj=200000.0,
Tref=None):
""" figure out the optimal allocation of nitrogen """
result = opt.fmin_cobyla(self.objective,
x0=fit_params,
disp=0,
cons=[
self.constraint_Np, self.constraint_Nc,
self.constraint_Ne, self.constraint_Nr
],
args=(par, Rd, Ci, N_p, Tleaf, Q10, Eaj, Eav,
deltaSj, deltaSv, r25, Hdv, Hdj, Tref),
consargs=(N_p, ))
return result
def find_min_dist_residual(f, points, dis_threshold):
def objective(X, P):
# print "objective:",X,P
# P is point and X is a point on curve
x, y = np.ndarray.tolist(np.asarray(X).reshape((2)))
return np.sqrt((x - P[0])**2 + (y - P[1])**2)
def c1(X, P):
X = np.asarray(X).reshape((2))
P = np.asarray(P).reshape((2))
return f(X, P)
summation = 0
indices = []
for i in range(points.shape[0]):
P = points[i, :]
# print "point of cloud:", P
X = fmin_cobyla(objective,
x0=[P],
cons=[c1],
args=([P]),
consargs=([P]))
# print objective(X, P)
dist = objective(X, P)
if dist <= dis_threshold:
summation += objective(X, P)
indices.append(i)
return summation / points.shape[0], indices
def _fit_sphere(points, disp='auto'):
"""Aux function to fit a sphere to an arbitrary set of points"""
from scipy.optimize import fmin_cobyla
if isinstance(disp, string_types) and disp == 'auto':
disp = True if logger.level <= 20 else False
# initial guess for center and radius
radii = (np.max(points, axis=1) - np.min(points, axis=1)) / 2.
radius_init = radii.mean()
center_init = np.median(points, axis=0)
# optimization
x0 = np.concatenate([center_init, [radius_init]])
def cost_fun(center_rad):
d = points - center_rad[:3]
d = (np.sqrt(np.sum(d * d, axis=1)) - center_rad[3])
return np.sum(d * d)
def constraint(center_rad):
return center_rad[3] # radius must be >= 0
x_opt = fmin_cobyla(cost_fun, x0, constraint, rhobeg=radius_init,
rhoend=radius_init * 1e-6, disp=disp)
origin = x_opt[:3]
radius = x_opt[3]
return radius, origin
def getCostPerformanceCurve():
X_opt = []
f_opt = []
TP_opt = []
cost_opt = []
for i in range(len(weights)):
OP.W = weights[i]
X_opt.append([])
TP_opt.append([])
cost_opt.append([])
f_opt.append([])
for j in initial_guesses:
x = fmin_cobyla(func=OP.ObjectiveFunction,
x0=j,
cons=OP.constraints,
rhobeg=1,
rhoend=1e-3)
X_opt[i].append(x)
TP_opt[i].append(OP.NormalizedThroughput(OP.Clip(x)))
cost_opt[i].append(OP.NormalizedCost(OP.Clip(x)))
f_opt[i].append(OP.ObjectiveFunction(x))
#write the arrays out to a file
with open("RESULT_X_opt.py", "w") as f:
print >> f, "X_opt=", X_opt
with open("RESULT_TP_opt.py", "w") as f:
print >> f, "TP_opt=", TP_opt
with open("RESULT_cost_opt.py", "w") as f:
print >> f, "cost_opt=", cost_opt
with open("RESULT_f_opt.py", "w") as f:
print >> f, "f_opt=", f_opt
def aim_point(self,
model,
params,
dataX,
dataY,
delta=0.001,
return_dist=False,
**kwargs):
dist2 = list()
aim_points = list()
for index, row in np.ndenumerate(dataX):
p = (dataX[index], dataY[index])
funct = lambda x: model.eval(params, x)
obj = lambda X: self.evaldist2(model, params, p[0], X[0], p[1], X[
1])
greater_coeff = 1 if dataY[index] - funct(dataX[index]) > 0 else -1
def c1(X):
x, y = X
return greater_coeff * (y - funct(x))
p0 = (dataX[index], funct(dataX[index]))
X = fmin_cobyla(obj, x0=p0, cons=[c1])
aim_points.append(X[0])
if return_dist: dist2.append(obj(X))
self.logger.debug(f"Aim: {aim_points}")
if return_dist:
return dist2, aim_points
return aim_points
def blend_predictions(train_preds, test_preds, labels, ids_sub, skf, save_results=False):
test_index = None
for _, test_idx in skf:
test_index = np.append(test_index, test_idx) if test_index is not None else test_idx
val_labels = labels[test_index]
val_predictions, val_submission = [], []
for i in range(np.shape(train_preds)[1]):
val_predictions.append(train_preds[:,i])
for i in range(np.shape(test_preds)[1]):
val_submission.append(test_preds[:, i])
p0 = [1.] * len(val_predictions)
p = fmin_cobyla(error, p0, args=(val_predictions, val_labels), cons=[constraint], rhoend=1e-5)
err = error(p, val_predictions, val_labels)
print 'error:', err
y_submission = blended(p, val_submission)
if save_results:
csv_output = 'submission_{}.csv'.format(time.strftime("%Y%m%d-%H%M%S"))
pd.DataFrame({"ID": ids_sub, "PredictedProb": y_submission}).to_csv(csv_output, index=False)
print 'saving:', csv_output
return err
def COBYLAEstimator(S, binnedTrain, abg_init):
from scipy.optimize import fmin_cobyla
print 'COBYLA method: '
constraints = [lambda p: p[0]- .01,
lambda p: 8. - p[0],
lambda p: p[1] - .01,
lambda p: 5. - p[1],
lambda p: p[2] - .01,
lambda p: 8. - p[2]]
# lbounds = ((.01, 5.),
# (.01, 5.),
# (.0 , 5.) );
#
def func(abg):
'Solve it:'
Fs = S.solve(abg, visualize=False)
Ss = S.transformSurvivorData(binnedTrain)
Ls = Fs[:,:,-1] - Ss
'Return '
G = .5*sum(Ls*Ls)*S._dt
return G
abg_est = fmin_cobyla(func, abg_init, constraints, disp=0);
return abg_est
def __solver__(self, p):
#p.kernelIterFuncs.pop(SMALL_DELTA_X)
#p.kernelIterFuncs.pop(SMALL_DELTA_F)
xBounds2Matrix(p)
p.cobyla = EmptyClass()
if p.userProvided.c: p.cobyla.nc = p.c(p.x0).size
else: p.cobyla.nc = 0
if p.userProvided.h: p.cobyla.nh = p.h(p.x0).size
else: p.cobyla.nh = 0
det_arr = cumsum(array((p.cobyla.nc, p.cobyla.nh, p.b.size, p.beq.size, p.cobyla.nh, p.beq.size)))
cons = []
for i in range(det_arr[-1]):
if i < det_arr[0]:
c = lambda x, i=i: - p.c(x)[i] # cobyla requires positive constraints!
elif det_arr[0] <= i < det_arr[1]:
j = i - det_arr[0]
c = lambda x, j=j: p.h(x)[j]
elif det_arr[1] <= i < det_arr[2]:
j = i - det_arr[1]
#assert 0<= j <p.cobyla.nb
c = lambda x, j=j: p.b[j] - p.dotmult(p.A[j], x).sum() # cobyla requires positive constraints!
elif det_arr[2] <= i < det_arr[3]:
j = i - det_arr[2]
#assert 0<= j <p.cobyla.nbeq
c = lambda x, j=j: p.dotmult(p.Aeq[j], x).sum() - p.beq[j]
elif det_arr[3] <= i < det_arr[4]:
j = i - det_arr[3]
c = lambda x, j=j: - p.h(x)[j]
elif det_arr[4] <= i < det_arr[5]:
j = i - det_arr[4]
#assert 0<= j <p.cobyla.nbeq
c = lambda x, j=j: p.dotmult(p.Aeq[j], x).sum() - p.beq[j]
else:
p.err('error in connection cobyla to openopt')
cons.append(c)
## def oo_cobyla_cons(x):
## c0 = -p.c(x)
## c1 = p.h(x)
## c2 = -(p.matmult(p.A, x) - p.b)
## c3 = p.matmult(p.Aeq, x) - p.beq
## return hstack((c0, c1, -c1, c2, c3, -c3))
# p.xk = p.x0.copy()
# p.fk = p.f(p.x0)
#
# p.iterfcn()
# if p.istop:
# p.xf = p.xk
# p.ff = p.fk
# return
xf = fmin_cobyla(p.f, p.x0, cons = tuple(cons), iprint = 0, maxfun = p.maxFunEvals, rhoend = p.xtol )
p.xk = xf
p.fk = p.f(xf)
p.istop = 1000
def fitting(Eqm,Eel,ljd,uniform_weight,output=True):
if uniform_weight == True:
x = fmin_cobyla(f_opt_LB_cobyla, opt_p_LB,
cons, args=(Eqm, Eel,
np.array(weight0(Eqm)),
np.transpose(ljd)),
maxfun=100000, iprint=0)
opt_LJ = ljeval_LB(np.transpose(ljdists),x)
if output:
output_parameters(x)
output_goodness(opt_LJ)
if out != '': output_energies(opt_LJ)
return x
else:
# 1st iteration
x = fmin_cobyla(f_opt_LB_cobyla, opt_p_LB,
cons, args=(Eqm, Eel,
np.array(weight1(Eqm-Eel)),
np.transpose(ljd)),
maxfun=100000, iprint=0)
opt_LJ = ljeval_LB(np.transpose(ljdists),x)
if ver:
print "Iteration #1:"
output_parameters(x)
output_goodness(opt_LJ)
# 2nd iteration
x = fmin_cobyla(f_opt_LB_cobyla, opt_p_LB,
cons, args=(Eqm, Eel,
np.array(weight2(Eqm,Eel,opt_LJ)),
np.transpose(ljd)),
maxfun=100000, iprint=0)
opt_LJ2 = ljeval_LB(np.transpose(ljdists),x)
if ver: print "Iteration #2:"
if output:
output_parameters(x)
output_goodness(opt_LJ2)
if out != '': output_energies(opt_LJ2)
return x
def _from_samples(histogram, alpha, ordered=False):
"""
Reference:
T. Denoeux (2006), "Constructing belief functions from sample data using multinomial confidence regions",
International Journal of Approximate Reasoning 42, 228-252.
"""
p_lower, p_upper = MassFunction._confidence_intervals(histogram, alpha)
def p_lower_set(hs):
l = u = 0
for h in H:
if h in hs:
l += p_lower[h]
else:
u += p_upper[h]
return max(l, 1 - u)
if ordered:
H = sorted(histogram.keys())
m = MassFunction()
for i1, h1 in enumerate(H):
m[(h1, )] = p_lower[h1]
for i2, h2 in enumerate(H[i1 + 1:]):
i2 += i1 + 1
if i2 == i1 + 1:
v = p_lower_set(
H[i1:i2 + 1]) - p_lower[h1] - p_lower[h2]
else:
v = p_lower_set(H[i1:i2 + 1]) - p_lower_set(
H[i1 + 1:i2 + 1]) - p_lower_set(
H[i1:i2]) + p_lower_set(H[i1 + 1:i2])
if v > 0:
m[H[i1:i2 + 1]] = v
return m
else:
H = list(histogram.keys())
L = 2**len(H)
initial = numpy.zeros(L)
cons = []
singletons = lambda index: [
i for i in range(len(H)) if 2**i & index
]
# constraint (24)
bel = lambda index, m: fsum(m[sum([2**i for i in h_ind])] for h_ind
in powerset(singletons(index)))
c24 = lambda m, i: p_lower_set(MassFunction._from_array_index(
i, H)) - bel(i, m)
for i in range(L):
cons.append(partial(c24, i=i))
# constraint (25)
cons.append(lambda m: m.sum() - 1.0)
cons.append(lambda m: 1.0 - m.sum())
# constraint (26)
for i in range(L):
cons.append(partial(lambda m, i_s: m[i_s], i_s=i))
f = lambda m: -1 * 2**len(H) * fsum(
[m[i] * 2**(-len(singletons(i))) for i in range(L)])
m_optimal = fmin_cobyla(f, initial, cons, disp=0)
return MassFunction.from_array(m_optimal, H)
def _fit_chpi_pos(est_pos_dev, hpi_head_rrs, x0):
"""Fit rotation and translation parameters for cHPI coils"""
from scipy.optimize import fmin_cobyla
denom = np.sum((hpi_head_rrs - np.mean(hpi_head_rrs, axis=0)) ** 2)
objective = partial(_chpi_objective, est_pos_dev=est_pos_dev,
hpi_head_rrs=hpi_head_rrs)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-2, rhoend=1e-6, disp=False)
return x, 1. - objective(x) / denom
def _fit_chpi_pos(est_pos_dev, hpi_head_rrs, x0):
"""Fit rotation and translation parameters for cHPI coils"""
from scipy.optimize import fmin_cobyla
denom = np.sum((hpi_head_rrs - np.mean(hpi_head_rrs, axis=0)) ** 2)
objective = partial(_chpi_objective, est_pos_dev=est_pos_dev,
hpi_head_rrs=hpi_head_rrs)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-2, rhoend=1e-6, disp=False)
return x, 1. - objective(x) / denom
def fitPspCobyla(x, y, guess, bounds, risePower=1.0):
def cons(v, *args):
ret = 1 if all(v > bounds[:,0]) and all(v < bounds[:,1]) else 0
#print "Constraint:", v, ret
return ret
fit = opt.fmin_cobyla(errFn, guess, [cons], args=(x,y,risePower), disp=0)
return fit
def get_offset_cost(self): # Get closest point from the curve X = fmin_cobyla(offset_obj, x0=[self.state[0], self.state[1]], cons=[c1]) x_r, y_r = X state_diff = np.array([state[0]-x_r, state[1]-y_r]) Qk = np.array([[1,0,0],[0,1,0],[0,0,self.args.w_vel]]) return np.matmul(np.matmul(state_diff.T*Q),state_diff)
def fitPspCobyla(x, y, guess, bounds, risePower=1.0):
def cons(v, *args):
ret = 1 if all(v > bounds[:, 0]) and all(v < bounds[:, 1]) else 0
#print "Constraint:", v, ret
return ret
fit = opt.fmin_cobyla(errFn, guess, [cons], args=(x, y, risePower), disp=0)
return fit
def _fit_dipole(min_dist_to_inner_skull, B_orig, t, rrs, guess_fwd_svd, fwd_data, whitener, proj_op, fmin_cobyla):
"""Fit a single bit of data"""
B = np.dot(whitener, B_orig)
surf = None
# make constraint function to keep the solver within the inner skull
if isinstance(fwd_data["inner_skull"], dict): # bem
surf = fwd_data["inner_skull"]
def constraint(rd):
dist = _compute_nearest(surf["rr"], rd[np.newaxis, :], return_dists=True)[1][0]
if _points_outside_surface(rd[np.newaxis, :], surf, 1)[0]:
dist *= -1.0
# Once we know the dipole is below the inner skull,
# let's check if its distance to the inner skull is at least
# min_dist_to_inner_skull. This can be enforced by adding a
# constrain proportional to its distance.
dist -= min_dist_to_inner_skull
return dist
else: # sphere
R, r0 = fwd_data["inner_skull"]
R_adj = R - 1e-3 # to be sure we don't hit the innermost surf
def constraint(rd):
return R_adj - np.sqrt(np.sum((rd - r0) ** 2))
# Find a good starting point (find_best_guess in C)
B2 = np.dot(B, B)
if B2 == 0:
logger.warning("Zero field found for time %s" % t)
return np.zeros(3), 0, np.zeros(3), 0
x0 = rrs[np.argmin([_fit_eval(rrs[fi][np.newaxis, :], B, B2, fwd_svd) for fi, fwd_svd in enumerate(guess_fwd_svd)])]
fun = partial(_fit_eval, B=B, B2=B2, fwd_data=fwd_data, whitener=whitener, constraint=constraint)
# Tested minimizers:
# Simplex, BFGS, CG, COBYLA, L-BFGS-B, Powell, SLSQP, TNC
# Several were similar, but COBYLA won for having a handy constraint
# function we can use to ensure we stay inside the inner skull /
# smallest sphere
rd_final = fmin_cobyla(fun, x0, (constraint,), consargs=(), rhobeg=5e-2, rhoend=1e-4, disp=False)
# Compute the dipole moment at the final point
Q, gof, residual = _fit_Q(fwd_data, whitener, proj_op, B, B2, B_orig, rd_final)
amp = np.sqrt(np.dot(Q, Q))
norm = 1.0 if amp == 0.0 else amp
ori = Q / norm
msg = "---- Fitted : %7.1f ms" % (1000.0 * t)
if surf is not None:
dist_to_inner_skull = _compute_nearest(surf["rr"], rd_final[np.newaxis, :], return_dists=True)[1][0]
msg += ", distance to inner skull : %2.4f mm" % (dist_to_inner_skull * 1000.0)
logger.info(msg)
return rd_final, amp, ori, gof, residual
def _from_samples_consonant(histogram, alpha, approximate=False):
"""
Reference:
A. Aregui, T. Denoeux (2008), "Constructing consonant belief functions from sample data using confidence
sets of pignistic probabilities", International Journal of Approximate Reasoning 49, 575-594.
"""
p_lower, p_upper = MassFunction._confidence_intervals(histogram, alpha)
H = list(histogram.keys())
if approximate:
# approximate possibility distribution
poss = {
h1: min(1, fsum([min(p_upper[h1], p_upper[h2]) for h2 in H]))
for h1 in H
}
else:
# optimal possibility distribution (based on linear programming)
poss = {h: 0 for h in H}
for k, h_k in enumerate(H):
S_k = {
l
for l in range(len(H)) if p_lower[H[l]] >= p_upper[h_k]
}
S_k.add(k)
I_k = {
l
for l in range(len(H)) if p_upper[H[l]] < p_lower[h_k]
}
P_k = set(range(len(H))).difference(S_k.union(I_k))
for A in powerset(P_k):
G = S_k.union(A)
G_c = set(range(len(H))).difference(G)
cons = []
# constraint (26)
for i, h in enumerate(H):
cons.append(
partial(lambda p, i_s, p_s: p[i_s] - p_s,
i_s=i,
p_s=p_lower[h])) # lower bound
cons.append(
partial(lambda p, i_s, p_s: p_s - p[i_s],
i_s=i,
p_s=p_upper[h])) # upper bound
# constraint (27)
cons.append(lambda p: 1 - sum(p))
cons.append(lambda p: sum(p) - 1)
# constraint (30)
for i in G:
cons.append(
partial(lambda p, i_s: p[i_s] - p[k], i_s=i))
# constraint (31)
for i in G_c:
cons.append(
partial(lambda p, i_s: p[k] - p[i_s], i_s=i))
initial = [1.0 / len(H)] * len(H)
f = lambda p: -(fsum([p[i] for i in G_c]) + len(G) * p[k])
poss_optimal = fmin_cobyla(f, initial, cons, disp=0)
poss[h_k] = max(poss[h_k], -f(poss_optimal))
return MassFunction.from_possibility(poss)
def _fit_dipole(min_dist_to_inner_skull, B_orig, t, guess_rrs,
guess_data, fwd_data, whitener, proj_op,
fmin_cobyla, ori):
"""Fit a single bit of data."""
B = np.dot(whitener, B_orig)
# make constraint function to keep the solver within the inner skull
if isinstance(fwd_data['inner_skull'], dict): # bem
surf = fwd_data['inner_skull']
constraint = partial(_surface_constraint, surf=surf,
min_dist_to_inner_skull=min_dist_to_inner_skull)
else: # sphere
surf = None
R, r0 = fwd_data['inner_skull']
constraint = partial(_sphere_constraint, r0=r0,
R_adj=R - min_dist_to_inner_skull)
del R, r0
# Find a good starting point (find_best_guess in C)
B2 = np.dot(B, B)
if B2 == 0:
warn('Zero field found for time %s' % t)
return np.zeros(3), 0, np.zeros(3), 0, B
idx = np.argmin([_fit_eval(guess_rrs[[fi], :], B, B2, fwd_svd)
for fi, fwd_svd in enumerate(guess_data['fwd_svd'])])
x0 = guess_rrs[idx]
fun = partial(_fit_eval, B=B, B2=B2, fwd_data=fwd_data, whitener=whitener)
# Tested minimizers:
# Simplex, BFGS, CG, COBYLA, L-BFGS-B, Powell, SLSQP, TNC
# Several were similar, but COBYLA won for having a handy constraint
# function we can use to ensure we stay inside the inner skull /
# smallest sphere
rd_final = fmin_cobyla(fun, x0, (constraint,), consargs=(),
rhobeg=5e-2, rhoend=5e-5, disp=False)
# simplex = _make_tetra_simplex() + x0
# _simplex_minimize(simplex, 1e-4, 2e-4, fun)
# rd_final = simplex[0]
# Compute the dipole moment at the final point
Q, gof, residual = _fit_Q(fwd_data, whitener, proj_op, B, B2, B_orig,
rd_final, ori=ori)
amp = np.sqrt(np.dot(Q, Q))
norm = 1. if amp == 0. else amp
ori = Q / norm
msg = '---- Fitted : %7.1f ms' % (1000. * t)
if surf is not None:
dist_to_inner_skull = _compute_nearest(
surf['rr'], rd_final[np.newaxis, :], return_dists=True)[1][0]
msg += (", distance to inner skull : %2.4f mm"
% (dist_to_inner_skull * 1000.))
logger.info(msg)
return rd_final, amp, ori, gof, residual
def _fit_chpi_pos(coil_dev_rrs, coil_head_rrs, x0):
"""Fit rotation and translation parameters for cHPI coils"""
from scipy.optimize import fmin_cobyla
denom = np.sum((coil_head_rrs - np.mean(coil_head_rrs, axis=0)) ** 2)
objective = partial(_chpi_objective, coil_dev_rrs=coil_dev_rrs,
coil_head_rrs=coil_head_rrs)
x = fmin_cobyla(objective, x0, _unit_quat_constraint,
rhobeg=1e-2, rhoend=1e-6, disp=False)
return x, 1. - objective(x) / denom
def _fit_magnetic_dipole(B_orig, w, coils, x0):
"""Fit a single bit of data (x0 = pos)"""
from scipy.optimize import fmin_cobyla
B = np.dot(w, B_orig)
B2 = np.dot(B, B)
objective = partial(_magnetic_dipole_objective, B=B, B2=B2,
w=w, coils=coils)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-2, rhoend=1e-4, disp=False)
return x, 1. - objective(x) / B2
def train(self, inp, out, t):
from scipy.optimize import fmin_cobyla
self.t = t
self.b = out.mean()
constr = [lambda p, inp, out: self.t - sum(p)]
for i in range(self.params.shape[0]):
constr.append(Pick(i))
self.updateparams(fmin_cobyla(self.objective,self.params.copy(),\
constr,(inp,out),maxfun=100000))
def test_simple(self):
# use disp=True as smoke test for gh-8118
x = fmin_cobyla(self.fun,
self.x0, [self.con1, self.con2],
rhobeg=1,
rhoend=1e-5,
maxfun=100,
disp=True)
assert_allclose(x, self.solution, atol=1e-4)
def _fit_chpi_pos(coil_dev_rrs, coil_head_rrs, x0):
"""Fit rotation and translation parameters for cHPI coils"""
from scipy.optimize import fmin_cobyla
denom = np.sum((coil_head_rrs - np.mean(coil_head_rrs, axis=0)) ** 2)
objective = partial(_chpi_objective, coil_dev_rrs=coil_dev_rrs,
coil_head_rrs=coil_head_rrs)
x = fmin_cobyla(objective, x0, _unit_quat_constraint,
rhobeg=1e-2, rhoend=1e-6, disp=False)
return x, 1. - objective(x) / denom
def _fit_magnetic_dipole(B_orig, x0, coils, scale, method):
"""Fit a single bit of data (x0 = pos)."""
from scipy.optimize import fmin_cobyla
B = np.dot(scale, B_orig)
B2 = np.dot(B, B)
objective = partial(_magnetic_dipole_objective, B=B, B2=B2,
coils=coils, scale=scale, method=method)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-4, rhoend=1e-5, disp=False)
return x, 1. - objective(x) / B2
def _fit_magnetic_dipole(B_orig, x0, coils, scale, method):
"""Fit a single bit of data (x0 = pos)."""
from scipy.optimize import fmin_cobyla
B = np.dot(scale, B_orig)
B2 = np.dot(B, B)
objective = partial(_magnetic_dipole_objective, B=B, B2=B2,
coils=coils, scale=scale, method=method)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-4, rhoend=1e-5, disp=False)
return x, 1. - objective(x) / B2
def _fit_magnetic_dipole(B_orig, w, coils, x0):
"""Fit a single bit of data (x0 = pos)"""
from scipy.optimize import fmin_cobyla
B = np.dot(w, B_orig)
B2 = np.dot(B, B)
objective = partial(_magnetic_dipole_objective, B=B, B2=B2,
w=w, coils=coils)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-2, rhoend=1e-4, disp=False)
return x, 1. - objective(x) / B2
def _optimize(self, left: FitData, right: FitData, kwa, params):
if self.symmetry is Symmetry.both:
cost = lambda x: self._sym(left, right, x[0], x[1])
elif self.symmetry is Symmetry.left:
cost = lambda x: self._asym(left, right, x[0], x[1])
else:
cost = lambda x: self._asym(left, right, 1. / x[0], -x[0] * x[1])
tmp = fmin_cobyla(cost, params, **kwa)
return (cost(tmp), tmp[0], tmp[1])
def _minimize(x_0: np.array) -> np.array:
return fmin_cobyla(objective,
x_0,
constraints,
rhobeg=self._rhobeg,
rhoend=self._rhoend,
maxfun=self._maxfun,
disp=self._disp,
catol=self._catol)
def train(self,inp,out,t):
from scipy.optimize import fmin_cobyla
self.t = t
self.b = out.mean()
constr = [lambda p, inp, out: self.t - sum(p)]
for i in range(self.params.shape[0]):
constr.append(Pick(i))
self.updateparams(fmin_cobyla(self.objective,self.params.copy(),\
constr,(inp,out),maxfun=100000))
def _fit_dipole(min_dist_to_inner_skull, B_orig, t, guess_rrs,
guess_data, fwd_data, whitener, proj_op,
fmin_cobyla, ori):
"""Fit a single bit of data."""
B = np.dot(whitener, B_orig)
# make constraint function to keep the solver within the inner skull
if isinstance(fwd_data['inner_skull'], dict): # bem
surf = fwd_data['inner_skull']
constraint = partial(_surface_constraint, surf=surf,
min_dist_to_inner_skull=min_dist_to_inner_skull)
else: # sphere
surf = None
R, r0 = fwd_data['inner_skull']
constraint = partial(_sphere_constraint, r0=r0,
R_adj=R - min_dist_to_inner_skull)
del R, r0
# Find a good starting point (find_best_guess in C)
B2 = np.dot(B, B)
if B2 == 0:
warn('Zero field found for time %s' % t)
return np.zeros(3), 0, np.zeros(3), 0, B
idx = np.argmin([_fit_eval(guess_rrs[[fi], :], B, B2, fwd_svd)
for fi, fwd_svd in enumerate(guess_data['fwd_svd'])])
x0 = guess_rrs[idx]
fun = partial(_fit_eval, B=B, B2=B2, fwd_data=fwd_data, whitener=whitener)
# Tested minimizers:
# Simplex, BFGS, CG, COBYLA, L-BFGS-B, Powell, SLSQP, TNC
# Several were similar, but COBYLA won for having a handy constraint
# function we can use to ensure we stay inside the inner skull /
# smallest sphere
rd_final = fmin_cobyla(fun, x0, (constraint,), consargs=(),
rhobeg=5e-2, rhoend=5e-5, disp=False)
# simplex = _make_tetra_simplex() + x0
# _simplex_minimize(simplex, 1e-4, 2e-4, fun)
# rd_final = simplex[0]
# Compute the dipole moment at the final point
Q, gof, residual = _fit_Q(fwd_data, whitener, proj_op, B, B2, B_orig,
rd_final, ori=ori)
amp = np.sqrt(np.dot(Q, Q))
norm = 1. if amp == 0. else amp
ori = Q / norm
msg = '---- Fitted : %7.1f ms' % (1000. * t)
if surf is not None:
dist_to_inner_skull = _compute_nearest(
surf['rr'], rd_final[np.newaxis, :], return_dists=True)[1][0]
msg += (", distance to inner skull : %2.4f mm"
% (dist_to_inner_skull * 1000.))
logger.info(msg)
return rd_final, amp, ori, gof, residual
def _minimize(x_0: np.ndarray) -> Tuple[np.ndarray, Any]:
x = fmin_cobyla(objective,
x_0,
constraints,
rhobeg=self._rhobeg,
rhoend=self._rhoend,
maxfun=self._maxfun,
disp=self._disp,
catol=self._catol)
return x, None
def similarity_correction(sim, reads, N, negative_correction=True):
""" Calculate corrected abundances given a similarity matrix and observations using optimization.
Copied from GASiC, for metaproteomic experiments replace the term 'reads' with 'spectra'.
Input:
sim: [numpy.array (M,M)] with pairwise similarities between species
reads: [numpy.array (M,)] with number of observed reads for each species
N: [int] total number of reads
negative_correction: [boolean] whether numerical errors (negative values) should be corrected or not
Output:
abundances: [numpy.array (M,)] estimated abundance of each species in the sample
"""
# transform reads to abundances and rename similarity matrix
A = np.transpose(sim)
r = reads.astype(np.float) / N
rng = range(len(reads))
# Now solve the optimization problem: min_c |Ac-r|^2 s.t. c_i >= 0 and 1-sum(c_i) >= 0
# construct objective function
def objective(c):
# numpy implementation of objective function |A*c-r|^2
return np.sum(np.square(np.dot(A, c) - r))
# construct constraints
def build_con(k):
# constraint: k'th component of x should be >0
return lambda c: c[k]
cons = [build_con(k) for k in rng]
# constraint: the sum of all components of x should not exceed 1
cons.append(lambda c: 1 - np.sum(c))
# initial guess
c_0 = np.array([0.5 for i in range(len(reads))])
# finally: optimization procedure
abundances = opt.fmin_cobyla(objective,
c_0,
cons,
disp=0,
rhoend=1e-10,
maxfun=10000)
if negative_correction:
for i in range(len(abundances)):
if abundances[i] < 0:
print "warning: correcting negative similarity ", abundances[
i], " -> 0"
abundances[i] = 0
return abundances
def _fit_magnetic_dipole(B_orig, x0, coils, scale, method, too_close):
"""Fit a single bit of data (x0 = pos)."""
from scipy.optimize import fmin_cobyla
B = dgemv(alpha=1, a=scale, x=B_orig) # np.dot(scale, B_orig)
B2 = ddot(B, B) # np.dot(B, B)
lwork = _svd_lwork((3, B_orig.shape[0]))
objective = partial(_magnetic_dipole_objective, B=B, B2=B2,
coils=coils, scale=scale, method=method,
too_close=too_close, lwork=lwork)
x = fmin_cobyla(objective, x0, (), rhobeg=1e-4, rhoend=1e-5, disp=False)
return x, 1. - objective(x) / B2
def setGravity(self):
window_size = 15
d = self.aConfigs[len(self.aConfigs)-window_size:]
def func(x):
return (np.sum(np.dot(d-x,x))/np.linalg.norm(x))**2
def constr(x):
return np.linalg.norm(x) - CONST_GRAVITY
self.gravity = fmin_cobyla(func, [0., 0., 0.], constr, rhoend=1e-7)
def test_vector_constraints():
# test that fmin_cobyla and minimize can take a combination
# of constraints, some returning a number and others an array
def fun(x):
return (x[0] - 1)**2 + (x[1] - 2.5)**2
def fmin(x):
return fun(x) - 1
def cons1(x):
a = np.array([[1, -2, 2], [-1, -2, 6], [-1, 2, 2]])
return np.array([a[i, 0] * x[0] + a[i, 1] * x[1] +
a[i, 2] for i in range(len(a))])
def cons2(x):
return x # identity, acts as bounds x > 0
x0 = np.array([2, 0])
cons_list = [fun, cons1, cons2]
xsol = [1.4, 1.7]
fsol = 0.8
# testing fmin_cobyla
sol = fmin_cobyla(fun, x0, cons_list, rhoend=1e-5, iprint=0)
assert_allclose(sol, xsol, atol=1e-4)
sol = fmin_cobyla(fun, x0, fmin, rhoend=1e-5, iprint=0)
assert_allclose(fun(sol), 1, atol=1e-4)
# testing minimize
constraints = [{'type': 'ineq', 'fun': cons} for cons in cons_list]
sol = minimize(fun, x0, constraints=constraints, tol=1e-5)
assert_allclose(sol.x, xsol, atol=1e-4)
assert_(sol.success, sol.message)
assert_allclose(sol.fun, fsol, atol=1e-4)
constraints = {'type': 'ineq', 'fun': fmin}
sol = minimize(fun, x0, constraints=constraints, tol=1e-5)
assert_allclose(sol.fun, 1, atol=1e-4)
def __call__(self):
self.first_guess()
self.current_solution = opt.fmin_cobyla(self.criterion,
self.current_solution,
self.cons,
args=self.args,
**self.kwargs)
# output depends on kwargs ...
if isinstance(self.optimizer_output, tuple):
self.current_solution = self.optimizer_output[0]
else:
self.current_solution = self.optimizer_output
return self.current_solution
def _fit_chpi_pos(coil_dev_rrs, coil_head_rrs, x0):
"""Fit rotation and translation parameters for cHPI coils."""
from scipy.optimize import fmin_cobyla
denom = np.sum((coil_head_rrs - np.mean(coil_head_rrs, axis=0)) ** 2)
objective = partial(_chpi_objective, coil_dev_rrs=coil_dev_rrs,
coil_head_rrs=coil_head_rrs)
x0 = x0.copy()
x0[3:] *= 10. # decimeters to get quats and head units close
x = fmin_cobyla(objective, x0, _unit_quat_constraint,
rhobeg=1e-3, rhoend=1e-5, disp=False)
result = objective(x)
x[3:] /= 10.
return x, 1. - result / denom
def main(self, fit_params=None, par=None, Rd=None,
Ci=None, N_p=None, Tleaf=None, Q10=None, Eaj=None, Eav=None,
deltaSj=None, deltaSv=None, r25=None, Hdv=200000.0,
Hdj=200000.0, Tref=None):
""" figure out the optimal allocation of nitrogen """
result = opt.fmin_cobyla(self.objective, x0=fit_params, disp=0,
cons=[self.constraint_Np, self.constraint_Nc,
self.constraint_Ne, self.constraint_Nr],
args=(par, Rd, Ci, N_p, Tleaf, Q10,
Eaj, Eav, deltaSj, deltaSv, r25,
Hdv, Hdj, Tref), consargs=(N_p,))
return result
def sell_captial(self):
""" 1. take a random price (can be learned)
2. calculate for this price how much of the good should be sold to maximize profit.
3. offers to sell the according amount.
"""
price = np.random.uniform(0, 10, 1)
objective = lambda x: - (self.sales_price_consumption_good
* (self.possession('K') - x[0])
+ x[0] * price
)
constraint = lambda x: self.possession('K') - x[0]
x = fmin_cobyla(func=objective, x0=(0, 0), cons=[constraint], disp=0)
quantity = x[0]
self.sell('downfirm', random.randint(0, self.num_downfirms), 'K', float(quantity), price)
def _fit_dipole(B_orig, t, rrs, guess_fwd_svd, fwd_data, whitener, proj_op,
fmin_cobyla):
"""Fit a single bit of data"""
logger.info('---- Fitting : %7.1f ms' % (1000 * t,))
B = np.dot(whitener, B_orig)
# make constraint function to keep the solver within the inner skull
if isinstance(fwd_data['inner_skull'], dict): # bem
surf = fwd_data['inner_skull']
def constraint(rd):
if _points_outside_surface(rd[np.newaxis, :], surf, 1)[0]:
dist = _compute_nearest(surf['rr'], rd[np.newaxis, :],
return_dists=True)[1][0]
return -dist
else:
return 1.
else: # sphere
R, r0 = fwd_data['inner_skull']
R_adj = R - 1e-5 # to be sure we don't hit the innermost surf
def constraint(rd):
return R_adj - np.sqrt(np.sum((rd - r0) ** 2))
# Find a good starting point (find_best_guess in C)
B2 = np.dot(B, B)
if B2 == 0:
logger.warning('Zero field found for time %s' % t)
return np.zeros(3), 0, np.zeros(3), 0
x0 = rrs[np.argmin([_fit_eval(rrs[fi][np.newaxis, :], B, B2, fwd_svd)
for fi, fwd_svd in enumerate(guess_fwd_svd)])]
fun = partial(_fit_eval, B=B, B2=B2, fwd_data=fwd_data, whitener=whitener,
constraint=constraint)
# Tested minimizers:
# Simplex, BFGS, CG, COBYLA, L-BFGS-B, Powell, SLSQP, TNC
# Several were similar, but COBYLA won for having a handy constraint
# function we can use to ensure we stay inside the inner skull /
# smallest sphere
rd_final = fmin_cobyla(fun, x0, (constraint,), consargs=(),
rhobeg=5e-2, rhoend=1e-4, disp=False)
# Compute the dipole moment at the final point
Q, gof, residual = _fit_Q(fwd_data, whitener, proj_op, B, B2, B_orig,
rd_final)
amp = np.sqrt(np.sum(Q * Q))
norm = 1 if amp == 0 else amp
ori = Q / norm
return rd_final, amp, ori, gof, residual
def _from_samples(histogram, alpha, ordered=False):
"""
Reference:
T. Denoeux (2006), "Constructing belief functions from sample data using multinomial confidence regions",
International Journal of Approximate Reasoning 42, 228-252.
"""
p_lower, p_upper = MassFunction._confidence_intervals(histogram, alpha)
def p_lower_set(hs):
l = u = 0
for h in H:
if h in hs:
l += p_lower[h]
else:
u += p_upper[h]
return max(l, 1 - u)
if ordered:
H = sorted(histogram.keys())
m = MassFunction()
for i1, h1 in enumerate(H):
m[(h1,)] = p_lower[h1]
for i2, h2 in enumerate(H[i1 + 1:]):
i2 += i1 + 1
if i2 == i1 + 1:
v = p_lower_set(H[i1:i2 + 1]) - p_lower[h1] - p_lower[h2]
else:
v = p_lower_set(H[i1:i2 + 1]) - p_lower_set(H[i1 + 1:i2 + 1]) - p_lower_set(H[i1:i2]) + p_lower_set(H[i1 + 1:i2])
if v > 0:
m[H[i1:i2 + 1]] = v
return m
else:
H = list(histogram.keys())
L = 2**len(H)
initial = numpy.zeros(L)
cons = []
singletons = lambda index: [i for i in range(len(H)) if 2**i & index]
# constraint (24)
bel = lambda index, m: fsum(m[sum([2**i for i in h_ind])] for h_ind in powerset(singletons(index)))
c24 = lambda m, i: p_lower_set(MassFunction._from_array_index(i, H)) - bel(i, m)
for i in range(L):
cons.append(partial(c24, i=i))
# constraint (25)
cons.append(lambda m: m.sum() - 1.0)
cons.append(lambda m: 1.0 - m.sum())
# constraint (26)
for i in range(L):
cons.append(partial(lambda m, i_s: m[i_s], i_s=i))
f = lambda m: -1 * 2**len(H) * fsum([m[i] * 2**(-len(singletons(i))) for i in range(L)])
m_optimal = fmin_cobyla(f, initial, cons, disp=0)
return MassFunction.from_array(m_optimal, H)
def utility(init_w, delta, blacklit_r, blacklit_sigma):
def objective(w):
return -np.dot(w,r)+0.5*delta*np.dot(np.dot(w,sigma),w)
constraints = []
for i in range(np.array(init_w).size):
constraints.append(lambda w: 1 - w[i] )
constraints.append(lambda w: 3-sum(abs(w)))
constraints.append(lambda w: sum(w)-1)
constraints.append(lambda w: -sum(w)+1)
return optimize.fmin_cobyla(objective,init_w,constraints,rhoend=1e-7,maxfun=1000)
def __init__(self, samples):
n = len(samples) - 1
tot = sum(samples)
pmf = super(BetaBinomMLEst, self).pmf
# function to minimize
def f(x):
pred = (tot * pmf(n, k, x[0], x[1]) for k in range(len(samples)))
diff = ((p - samples[k]) ** 2 for k, p in enumerate(pred))
return sum(diff) # L2 error
# initial guess with method of moments
mom = BetaBinomMoMEst(samples)
x0 = np.array([mom.alpha, mom.beta])
xn = fmin_cobyla(f, x0, [lambda x: x[0], lambda x: x[1]], rhobeg=1e-1, rhoend=1e-10, disp=0)
self._ah = xn[0]
self._bh = xn[1]
def opt_wlf_coeffs(self, df, ref_temp, wlf_coeffs, opt):
"""Generate the optimized master curve"""
temps = np.unique(df['Temp'])
if len(temps) == 1:
# only one data set
return np.zeros(2)
if wlf_coeffs is None:
wlf_coeffs = self.get_wlf_coeffs(df, ref_temp)
if opt is None:
opt = self.optwlf
if not opt:
return wlf_coeffs
def func(xopt, *args):
"""Objective function returning the area between the fitted curve
and shifted data
"""
if np.any(np.abs(xopt[1] + temps - ref_temp) < EPS):
self.fiterr = 1000.
return self.fiterr
df1 = self.shift_data(df.copy(), ref_temp, xopt)
fit = self.fit_shifted_data(df1)
# determine error between fitted curve and master curve
yvals = []
for logx in df1['Log[X/aT]']:
yvals.append(self.cf.eval(fit, logx))
yvals = np.asarray(yvals)
error = np.sqrt(np.mean((yvals - df1['Y']) ** 2))
self.fiterr = error # / area(data[:,0],data[:,1])
return self.fiterr
if self.optimizer == COBYLA:
cons = [lambda x: 1 if abs(x[1]+temp-ref_temp) > EPS else -1
for temp in temps]
wlf_coeffs = sciopt.fmin_cobyla(func, wlf_coeffs, cons, disp=0)
elif self.optimizer == POWELL:
wlf_coeffs = sciopt.fmin_powell(func, wlf_coeffs, disp=0)
else:
wlf_coeffs = sciopt.fmin(func, wlf_coeffs, disp=0)
return wlf_coeffs
def optimize_spacing(x0, dx):
x0 = np.asarray(x0)
sorted_index = np.argsort(x0)
x1 = x0[sorted_index]
dx = np.asarray(dx)[sorted_index]
objective, constraints = get_objective_constraints(x1, dx)
x1_optimized = fmin_cobyla(objective, x1, constraints, rhoend=1e-7,
iprint=0)
x0_optimized = np.empty_like(x1_optimized)
x0_optimized[sorted_index] = x1_optimized
return x0_optimized
def fit(self, lX, ly, sample_weight=None):
n_cols = lX.shape[1]
x0 = np.ones((n_cols, 1))
constr_lb = [lambda x, z=i: x[z] - self.lowerbound for i in range(n_cols)]
constr_ub = [lambda x, z=i: self.upperbound - x[z] for i in range(n_cols)]
constr = constr_lb + constr_ub
# constr=constr_lb
self.coef_ = fmin_cobyla(self.fopt, x0, constr, args=(lX, ly), consargs=(), rhoend=1e-10, maxfun=10000, disp=0)
# coef_ = minimize(fopt, x0,method='COBYLA',constraints=self.constr)
# normalize coefficient
if self.normalize:
self.coef_ = self.coef_ / np.sum(self.coef_)
# print "Normalizing coefficients:",self.coef_
if np.isnan(np.sum(self.coef_)):
print "We have NaN here..."