def opt(func, bound, niter=30):
''' optimize a function in a given bounds limit, returns [min, max]'''
stepsize = None
center = []
for interval in bound:
center.append((interval[0] + interval[1]) / 2.0)
width = interval[1] - interval[0]
if stepsize is None or width < stepsize:
stepsize = width
minimum = optimize.basinhopping(func, \
center, minimizer_kwargs=dict(method='L-BFGS-B', bounds=bound),\
niter=niter, stepsize=stepsize).fun
maximum = -optimize.basinhopping(lambda x: -func(x), \
center, minimizer_kwargs=dict(method='L-BFGS-B', bounds=bound),\
niter=niter, stepsize=stepsize).fun
# scipy bug: the doc says basinhopping returns a Result object,
# but I sometimes get a float, sometimes a numpy float, some sometimes and numpy array
minimum = float(minimum)
maximum = float(maximum)
return [minimum, maximum]
def prob2():
"""Explore the documentation on the function scipy.optimize.basinhopping()
online or via IPython. Use it to find the global minimum of the multmin()
function given in the lab, with initial point x0 = np.array([-2, -2]) and
the Nelder-Mead algorithm. Try it first with stepsize=0.5, then with
stepsize=0.2.
Return the minimum value of the function with stepsize=0.2.
Print a statement answering the following question:
Why doesn't scipy.optimize.basinhopping() find the minimum the second
time (with stepsize=0.2)?
"""
def multimin(x):
r = np.sqrt((x[0]+1)**2 + x[1]**2)
return r**2 *(1+ np.sin(4*r)**2)
x0 = np.array([-2,-2])
correct_x = opt.basinhopping(multimin, x0, stepsize=0.5,
minimizer_kwargs={'method':'nelder-mead'}).x
wrong_x = opt.basinhopping(multimin, x0, stepsize=0.2,
minimizer_kwargs={'method':'nelder-mead'}).x
output_string = """
When stepsize=0.2, the step is not large enough to jump out of the
basin. Therefore, we get the incorrect answer.
"""
return multimin(wrong_x)
def minimize_negative_acquisition(self, gpreg):
# minimization of negative acquisition function
vals, par = [], []
x0 = list(self.rand.uniform(np.array(self.bounds).T[0], np.array(self.bounds).T[1],
size=(self.n_iters_aqui - 1, self.dim)
)) + [self.x[int(np.argmax(self.y))]]
for x in x0:
if self.acquisition_func == "EI":
if self.bashop:
opti = basinhopping(expected_improvement, x0=x,
minimizer_kwargs={"method": "L-BFGS-B",
"bounds": self.bounds,
"args": (self.aquis_par[-1],
np.max(self.y),
gpreg, self.dim,)})
else:
opti = minimize(expected_improvement, x0=x, method="L-BFGS-B",
args=(self.aquis_par[-1], np.max(self.y),
gpreg, self.dim,),
bounds=self.bounds)
else:
if self.bashop:
opti = basinhopping(upper_confidence_bound, x0=x,
minimizer_kwargs={"method": "L-BFGS-B",
"bounds": self.bounds,
"args": (self.aquis_par[-1],
gpreg, self.dim,)})
else:
opti = minimize(upper_confidence_bound, x0=x, method="L-BFGS-B",
args=(self.aquis_par[-1], gpreg, self.dim,),
bounds=self.bounds)
par.append(opti.x)
vals.append(opti.fun)
return np.array(vals), np.array(par)
def bench_run(self, **minimizer_kwargs):
"""
do an optimization test starting at x0 for all the optimizers
"""
kwargs = self.minimizer_kwargs
if hasattr(self.fun, "temperature"):
kwargs["T"] = self.function.temperature
if hasattr(self.fun, "stepsize"):
kwargs["stepsize"] = self.function.stepsize
minimizer_kwargs = {"method": "L-BFGS-B"}
x0 = self.get_random_configuration()
# basinhopping - with gradient
if hasattr(self.function, 'der'):
minimizer_kwargs['jac'] = True
t0 = time.time()
res = basinhopping(
self.energy_gradient, x0, accept_test=self.accept_test,
callback=self.stop_criterion, niter=1000,
minimizer_kwargs=minimizer_kwargs,
**kwargs)
t1 = time.time()
res.success = True
if not self.found_target(res):
res.success = False
self.add_result(res, t1 - t0, 'basinhopping')
# basinhopping - no gradient
x0 = self.get_random_configuration()
minimizer_kwargs['jac'] = False
t0 = time.time()
res = basinhopping(
self.fun, x0, accept_test=self.accept_test,
callback=self.stop_criterion, niter=1000,
minimizer_kwargs=minimizer_kwargs,
**kwargs)
t1 = time.time()
res.success = True
if not self.found_target(res):
res.success = False
self.add_result(res, t1 - t0, 'basinhopping - no gradient')
# differential_evolution
t0 = time.time()
res = differential_evolution(self.fun,
self.bounds,
popsize=20,
polish=True)
t1 = time.time()
if not self.found_target(res):
res.success = False
self.add_result(res, t1 - t0, 'differential_evolution')
def prob3():
"""Explore the documentation on the function scipy.optimize.basinhopping()
online or via IPython. Use it to find the global minimum of the multmin()
function given in the lab, with initial point x0 = np.array([-2, -2]) and
the Nelder-Mead algorithm. Try it first with stepsize=0.5, then with
stepsize=0.2.
Plot the multimin function and minima found using the code provided.
Print statements answering the following questions:
Which algorithms fail to find the global minimum?
Why do these algorithms fail?
Finally, return the global minimum.
"""
# Define the function to be optimized and the initial condition.
def multimin(x):
r = np.sqrt((x[0]+1)**2 + x[1]**2)
return r**2 *(1+ np.sin(4*r)**2)
x0 = np.array([-2, -1.9])
small_step = .2
large_step = .5
# Optimize using variations on Nelder-Mead. NOTE: Here, each has been stored
# seperately for ease of plotting differently colored minimums.
small = opt.basinhopping(multimin, x0, stepsize=small_step,
minimizer_kwargs={'method':'nelder-mead'})
large = opt.basinhopping(multimin, x0, stepsize=large_step,
minimizer_kwargs={'method':'nelder-mead'})
# Print the results.
print("Stepsize:\t{}\nMinimum:\t{}\nX-Values:\t{}\n".format(small_step,
small['fun'], small['x']))
print("Stepsize:\t{}\nMinimum:\t{}\nX-Values:\t{}\n".format(large_step,
large['fun'], large['x']))
# Plot the multimin graph. Here, the points are colored differently for emphasis.
xdomain = np.linspace(-3.5,1.5,70)
ydomain = np.linspace(-2.5,2.5,60)
X,Y = np.meshgrid(xdomain,ydomain)
Z = multimin((X,Y))
fig = plt.figure()
ax1 = fig.add_subplot(111, projection='3d')
ax1.plot_wireframe(X, Y, Z, linewidth=.5, color='c')
ax1.scatter(x0[0], x0[1], multimin(x0), c='b') # Initial pt: blue
# Plot the results of the algorithms.
ax1.scatter(small.x[0], small.x[1], small.fun, s=30, c='r') # Small step: red
ax1.scatter(large.x[0], large.x[1], large.fun, s=30, c='g') # Large step: green
plt.show()
# Answer the problem questions.
print("minimize() fails because it gets trapped in a basin.")
print("0.2 fails because it is too small a stepsize to escape a basin.")
# Return the correct global minimum.
return large['fun']
def test_pass_accept_test(self):
# test passing a custom accept test
# makes sure it's being used and ensures all the possible return values
# are accepted.
accept_test = MyAcceptTest()
i = 1
# there's no point in running it more than a few steps.
basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
niter=10, disp=self.disp, accept_test=accept_test)
assert_(accept_test.been_called)
def optimize_basin_hopping_multiple(crater):
# return optimize_basin_hopping(crater)
# crater = craters[0]
x0 = [crater.x,crater.y,crater.hs,crater.D2,crater.hr,crater.aRepose,crater.lema,crater.lemp]
# crater = craters[1]
x1 = [crater.hs,crater.hr,crater.aRepose]
x2 = [crater.hs,crater.hr,crater.aRepose]
x3 = [crater.hs,crater.hr,crater.aRepose]
angles = [-1,2.141592,4]
print "DOing multiple"
basinhopping(craterXY_multiple,np.hstack([x0,x1,x2,x3]),minimizer_kwargs={"method":"nelder-mead"},niter=1)
def _partial_optimize(self, optimize_nodes, evaluate_nodes, fall_to_simplex=True, minimizer='Powell', use_basin=False, debug=False, minimizer_kwargs=None, basin_kwargs=None):
"""Optimize part of the model.
:Arguments:
nodes : iterable
list nodes to optimize.
"""
if minimizer_kwargs is None:
minimizer_kwargs = {}
if basin_kwargs is None:
basin_kwargs = {}
non_observeds = filter(lambda x: not x.observed, optimize_nodes)
init_vals = [node.value for node in non_observeds]
# define function to be optimized
def opt(values):
if debug: print(values)
for value, node in zip(values, optimize_nodes):
node.set_value(value)
try:
logp_optimize = [node.logp for node in optimize_nodes]
logp_evaluate = [node.logp for node in evaluate_nodes]
neglogp = -np.sum(logp_optimize) - np.sum(logp_evaluate)
if debug: print(neglogp)
return neglogp
except pm.ZeroProbability:
if debug: print('Outside support!')
return np.inf
# optimize
if use_basin:
try:
minimizer_kwargs_passed = {'method': minimizer, 'options': minimizer_kwargs}
basinhopping(opt, init_vals, minimizer_kwargs=minimizer_kwargs_passed, **basin_kwargs)
except:
if fall_to_simplex:
print("Warning: Powell optimization failed. Falling back to simplex.")
minimizer_kwargs_passed = {'method': minimizer, 'options': minimizer_kwargs}
basinhopping(opt, init_vals, minimizer_kwargs=minimizer_kwargs_passed, **basin_kwargs)
else:
raise
else:
try:
minimize(opt, init_vals, method=minimizer, options=minimizer_kwargs)
except:
if fall_to_simplex:
print("Warning: Powell optimization failed. Falling back to simplex.")
minimize(opt, init_vals, method='Nelder-Mead', options=minimizer_kwargs)
else:
raise
def optimize(self):
mybounds = MyBounds(self._lower, self._upper)
basinhopping(
self._funcwrapped, self._xinit,
minimizer_kwargs={
'method': 'L-BFGS-B',
'bounds': [
x for x in zip(self._lower, self._upper)
]
},
accept_test=mybounds,
niter=MAX_IT,
)
def fit_gaussian_basis(x,y,angmom):
nregrid=400
xfit=np.linspace(1e-5,12.0,nregrid)
yfit=scipy.interpolate.griddata(np.array(x),np.array(y),xfit,method='cubic')
yfit=np.array(yfit)/np.array(xfit)**(angmom+1)
errfunc=lambda p,x,y: sum_gauss(p,x)-y
objfunc=lambda p,x,y: np.sum(errfunc(p,x,y)**2/len(x))
for ng in range(4,10):
p0=[]
for i in range(ng):
p0.append(0.2)
for i in range(ng):
p0.append(0.5*2**i)
#p1,cov,infodict,mesg,success=optimize.leastsq(errfunc,p0[:],args=(xfit,yfit),full_output=True)
optres=optimize.basinhopping(objfunc,p0[:],
disp=True,
minimizer_kwargs={
'args':(xfit,yfit),
'options':{'disp':True} },
stepsize=2.0
)
p1=optres.x
coeffnorm=coeff_normalization(np.array(p1[ng:]),angmom)
print("angular momentum",angmom)
for i in range(ng):
print(i+1,p1[i+ng],p1[i]/coeffnorm[i])
#print('rms',np.sqrt(np.sum(infodict['fvec']**2)/len(infodict['fvec'])),'ng',ng)
print('rms',np.sqrt(optres.fun))
def maximize(self):
"""
Maximizes the given acquisition function.
Returns
-------
np.ndarray(N,D)
Point with highest acquisition value.
"""
cand = np.zeros([self.n_restarts, self.X_lower.shape[0]])
cand_vals = np.zeros([self.n_restarts])
f = partial(self._acquisition_fkt_wrapper, acq_f=self.objective_func)
for i in range(self.n_restarts):
start = np.array([self.rng.uniform(self.X_lower,
self.X_upper,
self.X_lower.shape[0])])
res = optimize.basinhopping(
f,
start,
minimizer_kwargs={
"bounds": zip(
self.X_lower,
self.X_upper),
"method": "L-BFGS-B"},
disp=self.verbosity)
cand[i] = res.x
cand_vals[i] = res.fun
best = np.argmax(cand_vals)
return np.array([cand[best]])
def scipyBasinhopping(recipe, method='L-BFGS-B', *args, **kwargs):
# new in scipy 0.12
from scipy.optimize import basinhopping
print "Fit using scipy's basin hopping optimizer"
mybounds = MyBounds(recipe)
mystep = MyRandomDisplacement(recipe)
minimizer_kwargs = {'method': method,
# 'bounds': recipe.getBounds(),
'bounds': recipe.getBoundsFlat(),
'options': {'maxiter': 300},
}
if kwargs.has_key('maxiter'):
minimizer_kwargs['options'] = kwargs['maxiter']
bh_kwargs = {'take_step': mystep,
'accept_test': mybounds}
if kwargs.has_key('callback'):
bh_kwargs['callback'] = kwargs['callback']
if kwargs.has_key('maxxint'):
bh_kwargs['niter'] = kwargs['maxxint']
else:
bh_kwargs['niter'] = 20
res = basinhopping(recipe.scalarResidual, recipe.getValues(),
minimizer_kwargs=minimizer_kwargs,
**bh_kwargs)
return {'x': res['x'],
'raw': res}
def optimize(self,niter=100):
"""
Optimize kernel's hyperparameters using basin hopping.
Args:
niter: iterations in basin hopping function.
Returns: optimized covariance parameters for kernel.
"""
def optimized_marginal_likelihood(cov_args):
"""
Negative log marginal likelihood to be minimized.
if cov_args is out of bounds specified by kernel return inf
"""
in_bounds=True
for i in xrange(len(cov_args)):
lower=self.kernel.cov_bounds[i][0]
upper=self.kernel.cov_bounds[i][1]
if cov_args[i]<lower or cov_args[i]>upper:
in_bounds=False
if in_bounds==False:
return 1e309
else:
cov_matrix=np.matrix([[self.kernel.cov(xm,xn,cov_args) for xm in self.X] for xn in self.X])+10**-9*np.identity(len(self.X))
return -1*np.log(multivariate_normal(self.mean_vector,cov_matrix).pdf(self.Y))
opt=basinhopping(optimized_marginal_likelihood,self.kernel.cov_args,niter=niter).x
self.kernel.update_args(list(opt))
def execute(self, **minimize_options):
"""
Execute the basin-hopping minimization.
:param minimize_options: options to be passed on to
:func:`scipy.optimize.basinhopping`.
:return: :class:`symfit.core.fit_results.FitResults`
"""
if 'minimizer_kwargs' not in minimize_options:
minimize_options['minimizer_kwargs'] = {}
if 'method' not in minimize_options['minimizer_kwargs']:
# If no minimizer was set by the user upon execute, use local_minimizer
minimize_options['minimizer_kwargs']['method'] = self.local_minimizer.method_name()
if 'jac' not in minimize_options['minimizer_kwargs'] and isinstance(self.local_minimizer, GradientMinimizer):
# Assign the jacobian
minimize_options['minimizer_kwargs']['jac'] = self.local_minimizer.wrapped_jacobian
if 'constraints' not in minimize_options['minimizer_kwargs'] and isinstance(self.local_minimizer, ConstrainedMinimizer):
# Assign constraints
minimize_options['minimizer_kwargs']['constraints'] = self.local_minimizer.wrapped_constraints
if 'bounds' not in minimize_options['minimizer_kwargs'] and isinstance(self.local_minimizer, BoundedMinimizer):
# Assign bounds
minimize_options['minimizer_kwargs']['bounds'] = self.local_minimizer.bounds
ans = basinhopping(
self.objective,
self.initial_guesses,
**minimize_options
)
return self._pack_output(ans)
def eq_ellipse_calc(cutout,weight,userNSuccess):
mytakestep = MyTakeStep()
global nSuccess_basinhopping
nSuccess_basinhopping = userNSuccess
global minVals_basinhopping
minVals_basinhopping = np.empty(nSuccess_basinhopping)
minVals_basinhopping[:] = np.nan
global successCount_basinhopping
successCount_basinhopping = 0
#maxDist = max(np.hypot(*cutout.boundary.xy))
minimizer_kwargs = {"args": (cutout,weight,#maxDist,
), "method": 'BFGS' }
x0 = np.array([0,0,1,1,0])
output = basinhopping(ellipse_in_cutout,x0,
niter=1000,minimizer_kwargs=minimizer_kwargs,
take_step=mytakestep, callback=print_fun)
return output
def __tune__(self):
if self.minimizer == Minimizer.DifferentialEvolution:
bounds = [
self.spectralRadiusBound,
self.inputScalingBound,
self.reservoirScalingBound,
self.leakingRateBound,
]
result = optimize.differential_evolution(self.__reservoirTrain__, bounds=bounds)
print("The Optimization results are :" + str(result))
return result.x[0], result.x[1], result.x[2], result.x[3]
else:
bounds = [
self.spectralRadiusBound,
self.inputScalingBound,
self.reservoirScalingBound,
self.leakingRateBound,
]
minimizer_kwargs = {"method": "TNC", "bounds": bounds, "options": {"eps": 0.005}}
mytakestep = ParameterStep()
result = optimize.basinhopping(
self.__reservoirTrain__,
x0=self.initialGuess,
minimizer_kwargs=minimizer_kwargs,
take_step=mytakestep,
stepsize=0.005,
)
print("The Optimization results are :" + str(result))
return result.x[0], result.x[1], result.x[2], result.x[3]
def main():
x0 = 10.0* np.random.random(6)- 5.0
mybounds = MyBounds()
minimizer_kwargs = {"method":"L-BFGS-B"}
ret=optimize.basinhopping(rastrigin, x0, niter=500,
minimizer_kwargs=minimizer_kwargs,
callback=print_fun,
accept_test=mybounds)
print(ret.x, ret.fun)
print ret
print xiteration[499]
fig = plt.figure()
xp=[]
for i in range(0,len(xminima)):
xp.append(np.linalg.norm(xminima[i]))
plt.plot(xp, ".")
plt.show()
plt.savefig("sin.png")
fig = plt.figure()
plt.plot(fminima, ".")
plt.show()
def test_2d_nograd(self):
# test 2d minimizations without gradient
i = 1
res = basinhopping(
func2d_nograd, self.x0[i], minimizer_kwargs=self.kwargs_nograd, niter=self.niter, disp=self.disp
)
assert_almost_equal(res.x, self.sol[i], self.tol)
def fit(self, niter: int=1000) -> Tuple[float, np.ndarray]:
"""
Optimize the spectral gap using basin hopping.
Parameters
----------
niter : Number of iterations to use.
Returns
-------
coeffs : The found ideal coefficients.
"""
dim = self._data.shape[1]
rs = np.ones((dim,))
rs *= 1 / np.sqrt((rs ** 2).sum())
result = basinhopping(
func=self._score,
x0=rs,
niter=niter,
minimizer_kwargs=dict(
method='L-BFGS-B',
bounds=[(0.0001, 1.) for _ in range(dim)]
),
stepsize=0.1,
T=2.5
)
self.coeffs = result['x']
return -result['fun'], self.coeffs
def call_bh_prelim_params(trans_data):
'''This function calls the basinhopping algorithm to minimize the sum of the distances
between the data points projected onto an arbitrary plane, and the center of mass
of the projected points
Parameters
trans_data - data roughly translated to the origin
'''
minimizer_kwargs = {"method": "L-BFGS-B", "args": trans_data, "bounds": ((0,2*pi),(0,2*pi))}
x0 = [pi, pi]
ret = optimize.basinhopping(prelim_params_test, x0, minimizer_kwargs=minimizer_kwargs, niter = 200)
print("Preliminary parameters minimization: x = [%.4f, %.4f], epsilon = %.4f" %\
(ret.x[0], ret.x[1], ret.fun))
z = array([cos(ret.x[0])*sin(ret.x[1]), sin(ret.x[0])*sin(ret.x[1]), cos(ret.x[1])])
epsilon = ret.fun
n = size(trans_data[0])
r_guess = sqrt(epsilon / n ) # average distance from COM
beta_guess = pi - arctan2(-z[0],z[2])
alpha_guess = arctan2(z[1], sqrt((z[0])**2 + (z[2])**2))
print('Initial guess for alpha, beta and r from preliminary parameter test:')
print('alpha = %.4f' %alpha_guess)
print('beta = %.4f' %beta_guess)
print('r = %.4f' %r_guess)
return r_guess, beta_guess, alpha_guess, z
def BasinHop(funcToMinimize,x0,boundsBasin,method="TNC",disp=False,
interval=10,niter=30,niter_success=10,T=1,stepsize=0.001,
ftol=1e-3,xtol=1e-3,gtol=1e-3):
"""
Returns the result of basin hopping, given the arguments:
Args:
funcToMinimize: function to minimize, should take in the parameters
as described by scipy's basinhopping routine
x0: initial guessses, one per minimizer
boundsBasin: the bounds, same size as x0. open ends of intervals are
None
all others: consult basinhopping function
"""
# the minimizer itself (for each 'basin') takes keywords
# here, we are a little less 'picky' about the function tolerances
# than before
minimizer_kwargs = dict(method=method,bounds=boundsBasin,
options=dict(ftol=ftol,xtol=xtol,gtol=gtol))
# use basin-hopping to get a solid guess of where we should start
obj = basinhopping(funcToMinimize,x0=x0,disp=disp,T=T,
stepsize=stepsize,minimizer_kwargs=minimizer_kwargs,
niter_success=niter_success,interval=interval,
niter=niter)
return obj
def test_2d(self):
# test 2d minimizations with gradient
i = 1
res = basinhopping(func2d, self.x0[i], minimizer_kwargs=self.kwargs,
niter=self.niter, disp=self.disp)
assert_almost_equal(res.x, self.sol[i], self.tol)
self.assertTrue(res.nfev > 0)
def run_basinhopping(self):
"""
Do an optimization run for basinhopping
"""
kwargs = self.minimizer_kwargs
if hasattr(self.fun, "temperature"):
kwargs["T"] = self.function.temperature
if hasattr(self.fun, "stepsize"):
kwargs["stepsize"] = self.function.stepsize
minimizer_kwargs = {"method": "L-BFGS-B"}
x0 = self.function.initial_vector()
# basinhopping - no gradient
minimizer_kwargs['jac'] = False
self.function.nfev = 0
t0 = time.time()
res = basinhopping(
self.fun, x0, accept_test=self.accept_test,
minimizer_kwargs=minimizer_kwargs,
**kwargs)
t1 = time.time()
res.success = self.function.success(res.x)
res.nfev = self.function.nfev
self.add_result(res, t1 - t0, 'basinh.')
def cv():
width = 10 * 24 # predict 10 days into future
tests = 20
starts = numpy.random.randint(width, len(train) - width, 20)
for start in starts:
cv_train = train.iloc[:start]
cv_test = train.iloc[start:start + width]
nbsm = NonlinearBikeShareModel(cv_train)
res = optimize.basinhopping(
nbsm,
nbsm.beta0(),
minimizer_kwargs={
'method':'L-BFGS-B',
'jac':True,
'bounds': nbsm_train.bounds(),
'options': {'disp': False, 'maxiter': 500}
},
disp=True,
niter=2
)
print 'error:', nbsm(res.x)[0]
plt.plot_date(cv_train['dates'], cv_train['count'], label='train')
plt.plot_date(cv_train['dates'], nbsm.count(res.x), label='train fit')
plt.plot_date(cv_test['dates'], cv_test['count'], label='test')
plt.plot_date(cv_test['dates'], nbsm.predict(cv_test, res.x), label='predicted')
plt.legend()
plt.show()
plt.clf()
def register_masked(ref_mask, img_mask, niter=None, x0=None):
"""Register img_mask to ref_mask, assumes inputs are contour masks
Args:
ref_mask -- reference image
img_mask -- image to register to reference
niter -- number of iterations
x0 -- starting value for transform (dx, dy, dsx, dsy)
Returns: (matrix, image)
matrix -- skimage AffineTranform object
image -- img warped to reference
"""
assert ref_mask.ndim == img_mask.ndim == 2
if niter is None:
niter = 100
x0 = x0 or (0, 0, 1, 1)
ny, nx = ref_mask.shape
img_mask_resized = skimage.transform.resize(img_mask, ref_mask.shape)
minimizer_kwargs = dict(method='COBYLA')
res = basinhopping(CostFunc(ref_mask, img_mask_resized),
x0=x0,
niter=niter,
minimizer_kwargs=minimizer_kwargs)
tr = _x_to_affine(res.x)
img_mask_warped = resize_and_warp_mask(img_mask, ref_mask.shape, tr)
reg_res = RegistrationResult(tr, ref_mask, img_mask, img_mask_warped, res)
return img_mask_warped, reg_res
def minimize(lipids, box, stepxy=0.5, steprot=50, contactthresh=2.6):
from scipy.optimize import basinhopping
# rotate in 10deg increments
# translate in a 2x2 box in 0.25A increments
# swap lipid conformer?
headnames = [l.headname for l in lipids]
zpos = [l.xyz[2] for l in lipids]
neighbours = [l.neighbours for l in lipids]
pos = np.vstack([l.xyz[:2] for l in lipids])
x0 = pos.flatten().tolist()
numlips = len(lipids)
bounds = [(x - 1, x + 1) for x in x0]
x0 += [180] * numlips # Add the rotations
bounds += [(0, 360)] * numlips # Add the rotations
stepsizes = np.ones(numlips * 2) * stepxy
stepsizes = np.hstack((stepsizes, np.ones(numlips) * steprot)) # Add the rotations
# define the new step taking routine and pass it to basinhopping
take_step = RandomDisplacementBounds(np.vstack(bounds), stepsizes=stepsizes)
minimizer_kwargs = dict(method="L-BFGS-B", bounds=bounds,
args=(lipids, headnames, zpos, contactthresh, neighbours, numlips, box))
res = basinhopping(totalContacts, x0, minimizer_kwargs=minimizer_kwargs, disp=True, take_step=take_step, niter=10)
newpos = res.x[:numlips * 2].reshape((-1, 2))
newrot = res.x[numlips * 2:]
return newpos, newrot
def find_assignment(variable_handler, atoms, max_num_resets, tol, verbose=True):
init = variable_handler.dict_to_vector()
def func(vector):
return sum(evaluate(atom, variable_handler.vector_to_dict(vector)).norm for atom in atoms)
xs = []
fs = []
options = {'ftol': tol**2}
minimizer_kwargs = {"method": "SLSQP", "options": options}
for i in range(max_num_resets):
result = basinhopping(func, init, minimizer_kwargs=minimizer_kwargs)
if verbose:
print("iteration %d:" % (i+1))
print(result)
xs.append(result.x)
fs.append(result.fun)
if result.fun < tol:
break
init = np.random.rand(len(init))
min_idx = min(enumerate(fs), key=lambda pair: pair[1])[0]
assignment = variable_handler.vector_to_dict(xs[min_idx])
norm = fs[min_idx]
return assignment, norm
def test_basinhopping_2d_lmfit_vs_scipy():
"""Test basinhopping in lmfit versus scipy."""
# SciPy
def func2d(x):
return np.cos(14.5*x[0] - 0.3) + (x[1]+0.2) * x[1] + (x[0]+0.2) * x[0]
minimizer_kwargs = {'method': 'L-BFGS-B'}
x0 = [1.0, 1.0]
ret = basinhopping(func2d, x0, minimizer_kwargs=minimizer_kwargs, seed=7)
# lmfit
def residual_2d(params):
x0 = params['x0'].value
x1 = params['x1'].value
return np.cos(14.5*x0 - 0.3) + (x1+0.2) * x1 + (x0+0.2) * x0
pars = lmfit.Parameters()
pars.add_many(('x0', 1.), ('x1', 1.))
mini = lmfit.Minimizer(residual_2d, pars)
kws = {'minimizer_kwargs': {'method': 'L-BFGS-B'}, 'seed': 7}
out = mini.minimize(method='basinhopping', **kws)
assert_allclose(out.residual, ret.fun)
assert_allclose(out.params['x0'].value, ret.x[0], rtol=1e-5)
assert_allclose(out.params['x1'].value, ret.x[1], rtol=1e-5)
def best_position(tag_kde, all_kde, coords):
X, Y = zip(*coords)
x_max = max(X)
x_min = min(X)
y_max = max(Y)
y_min = min(Y)
# Start in the center of the map
start_x = x_min + (x_max-x_min)/2.
start_y = y_min + (y_max-y_min)/2.
# Define the function to minimize, the - is to find the maximum
def fn(pos, tag_kde=tag_kde, all_kde=all_kde):
result = -tag_kde(pos) / all_kde(pos)
return result
#print "Start:", (start_x, start_y)
peak_fit = optimize.basinhopping(
fn,
(start_x, start_y),
stepsize = 0.15,
)
peak_lon = peak_fit['x'][0]
peak_lat = peak_fit['x'][1]
return peak_lon, peak_lat, start_x, start_y
def findOptimumCurve(self):
"""
Uses basic downhill simplex optimization to find a curve with freqs target
Returns:
optpts (tuple): points (x,y) defining optimized curve
"""
x, y = self.c0
flatpts = np.append(x, y)
if self.grade == 'coarse':
ftol = 1.0
xtol = 1.0
else:
ftol = .1
xtol = .1
if self.method == 'simplex':
retvals = fmin(lambda pts: self.evalFitness(pts), flatpts,
disp=True, xtol=xtol, ftol=ftol, retall=True, maxiter=300)
elif self.method == 'basinhopping':
def test(f_new, x_new, f_old, x_old):
c = (x_new[:len(x_new) // 2], x_new[len(x_new) // 2:])
return not xy.curve_intersects(xy.interp(c)) # check for intersection
# TODO - redundant - happens inside basinhopping anyways
minimizer_kwargs = {'tol':ftol*100}
res = basinhopping(lambda pts: self.evalFitness(pts), flatpts, T=1,
accept_test=test, stepsize=20, disp=True, callback = print,
minimizer_kwargs=minimizer_kwargs)
retvals = [res.x, list(res.x)] # this is so indexing to look for xopt doesn't break
else: raise ValueError("Invalid method selected")
# save the data for lata
# TODO - live update instead of waiting til end to write - better crash recovery
labels = ['xopt','allvecs']
retdict = dict(zip(labels,retvals)) # automatically ignores allvecs if absent
retdict['fits'] = self.fits
retdict['fqs'] = self.fqs
outpts = retvals[0]
x = outpts[:len(outpts) // 2]
y = outpts[len(outpts) // 2:]
self.optpts = (x, y)
print(self.optpts)
retdict['optpts'] = self.optpts # for redundancy
retdict['target'] = self.target
retdict['c0'] = self.c0
self.allvecs = retdict['allvecs']
# TODO - this is ridiculous
# isolate best case
self.best_fit = min(self.fits)
self.best_fq = self.fqs[self.fits.index(self.best_fit)]
pickle.dump(retdict, open('vals.p','wb')) # TODO - account for overwriting
pickle.dump(self, open('bell.b','wb'))
return retdict
def get_start(self, num_walkers=1):
"""Gets an optimised `n` starting points by calculating a best fit starting point using basinhopping"""
self.logger.info("Getting start position")
def minimise(scale_params):
return -self.get_posterior(self.unscale(scale_params))
close_default = 3
start_random = self.get_raw_start()
start_close = [(s + p.default * close_default) / (1 + close_default)
for s, p in zip(start_random, self.get_active_params())]
self.logger.info(
"Starting basin hopping to find a good starting point")
res = basinhopping(
minimise,
self.scale(start_close),
niter_success=3,
niter=30,
stepsize=0.05,
minimizer_kwargs={
"method": "Nelder-Mead",
"options": {
"maxiter": 600
}
},
)
scaled_start = res.x
ratio = 0.05 # 5% of the unit hypercube
mins = np.clip(scaled_start - ratio, 0, 1)
maxes = np.clip(scaled_start + ratio, 0, 1)
samples = np.random.uniform(mins,
maxes,
size=(num_walkers, len(maxes)))
unscaled_samples = np.array([self.unscale(s) for s in samples])
self.logger.debug(f"Start samples have shape {unscaled_samples.shape}")
return unscaled_samples
def best_score_search(true_labels, predictions, f):
# https://discuss.pytorch.org/t/multilabel-classification-how-to-binarize-scores-how-to-learn-thresholds/25396
# https://github.com/mratsim/Amazon-Forest-Computer-Vision/blob/46abf834128f41f4e6d8040f474ec51973ea9332/src/p_metrics.py#L15-L53
def f_neg(threshold):
## Scipy tries to minimize the function so we must get its inverse
return - f(true_labels, pd.DataFrame(predictions).values > pd.DataFrame(threshold).values.reshape(1, len(predictions[0])))
# return - f(np.array(true_labels), pd.DataFrame(predictions).values > pd.DataFrame(threshold).values)[2]
# print(len(predictions[0]))
# Initialization of best threshold search
thr_0 = [0.20] * len(predictions[0])
constraints = [(0.,1.)] * len(predictions[0])
def bounds(**kwargs):
x = kwargs["x_new"]
tmax = bool(np.all(x <= 1))
tmin = bool(np.all(x >= 0))
return tmax and tmin
# Search using L-BFGS-B, the epsilon step must be big otherwise there is no gradient
minimizer_kwargs = {"method": "L-BFGS-B",
"bounds":constraints,
"options":{
"eps": 0.05
}
}
# We combine L-BFGS-B with Basinhopping for stochastic search with random steps
print("===> Searching optimal threshold for each label")
start_time = timer()
opt_output = basinhopping(f_neg, thr_0,
stepsize = 0.1,
minimizer_kwargs=minimizer_kwargs,
niter=10,
accept_test=bounds)
end_time = timer()
print("===> Optimal threshold for each label:\n{}".format(opt_output.x))
print("Threshold found in: %s seconds" % (end_time - start_time))
score = - opt_output.fun
return score, opt_output.x
def bhop_boxfit(data,
initial_params,
cutoff_fwhm=3,
npoints=200,
niter=100,
verbose=False):
"""Use scipy basinhopping to fit a box profile convolved
with a gaussian beam.
Args:
data: Tuple of (xdata, ydata) to be fitted
initial_params: SlabscanFitParams object for this fit.
fwhm_cutoff (float): Number of fwhm to integrate over in the
convolution.
npoints (int): Number of integration points in the convolution.
Returns:
A dict with the following keys: Time (t), minima (xmin),
basinhopping result object (res).
"""
xdata, ydata = data
param_names = ('center', 'height', 'width', 'fwhm')
params_tuple = initial_params.ndarray_of(param_names)
param_normalizers = initial_params.ndarray_of_norms_for(param_names)
err_func = get_oer_fit_err_func(xdata, ydata, param_normalizers,
cutoff_fwhm, npoints)
# bh_callback = get_bh_callback(param_normalizers, verbose)
t0 = time()
res = basinhopping(func=err_func,
x0=initial_params.normalized_ndarray_of(param_names),
T=1.0,
stepsize=0.1,
niter=niter)
if verbose:
print('Seconds', (time() - t0))
print('Initial params: ')
initial_params.pp()
print('Final params : ', boxfit_ps2str(res.x * param_normalizers))
return {'t': time() - t0, 'res': res, 'xmin': res.x * param_normalizers}
def lml_opt(train_features,
train_targets,
test_features,
kernel_dict,
regularization,
global_opt=False,
algomin='L-BFGS-B',
eval_jac=True):
"""Test Gaussian process predictions."""
# Test prediction routine with linear kernel.
N, N_D = np.shape(train_features)
regularization_bounds = (1e-3, None)
kdict, bounds = prepare_kernels(kernel_dict, regularization_bounds,
eval_gradients, N_D)
print(bounds)
# Create a list of all hyperparameters.
theta = kdicts2list(kdict, N_D=N_D)
theta = np.append(theta, regularization)
# Define fixed arguments for log_marginal_likelihood
args = (np.array(train_features), np.array(train_targets), kdict,
scale_optimizer, eval_gradients, None, eval_jac)
# Optimize
if not global_opt:
popt = minimize(lml.log_marginal_likelihood,
theta,
args=args,
method=algomin,
jac=eval_jac,
options={'disp': True},
bounds=bounds)
else:
minimizer_kwargs = {
'method': algomin,
'args': args,
'bounds': bounds,
'jac': eval_jac
}
popt = basinhopping(lml.log_marginal_likelihood,
theta,
minimizer_kwargs=minimizer_kwargs,
disp=True)
return popt
def fftfit(prof, template=None, **fftfit_kwargs):
"""Align a template to a pulse profile.
Parameters
----------
phase : array
The phases corresponding to each bin of the profile
prof : array
The pulse profile
template : array, default None
The template of the pulse used to perform the TOA calculation. If None,
a simple sinusoid is used
Returns
-------
mean_amp, std_amp : floats
Mean and standard deviation of the amplitude
mean_phase, std_phase : floats
Mean and standard deviation of the phase
Other Parameters
----------------
fftfit_kwargs : arguments
Additional arguments to be passed to error calculation
"""
prof = prof - np.mean(prof)
nbin = len(prof)
ph = np.arange(0, 1, 1/nbin)
if template is None:
template = np.cos(2 * np.pi * ph)
template = template - np.mean(template)
p0 = [np.max(prof), np.float(np.argmax(prof) / nbin)]
res = basinhopping(_fft_fun_wrap, p0,
minimizer_kwargs={'args': ([prof, template],),
'bounds': [[0, None], [0, None]]},
niter=10000, niter_success=200)
return fftfit_error(ph, prof, template, res.x, **fftfit_kwargs)
def best_f2_score(true_labels, predictions):
def f_neg(threshold):
## Scipy tries to minimize the function so we must get its inverse
return -fbeta_score(
true_labels, predictions > threshold, beta=2, average='samples')
# Initialization of best threshold search
thr_0 = [0.20] * 17
constraints = [(0., 1.)] * 17
def bounds(**kwargs):
x = kwargs["x_new"]
tmax = bool(np.all(x <= 1))
tmin = bool(np.all(x >= 0))
return tmax and tmin
# Search using L-BFGS-B, the epsilon step must be big otherwise there is no gradient
minimizer_kwargs = {
"method": "L-BFGS-B",
"bounds": constraints,
"options": {
"eps": 0.05
}
}
# We combine L-BFGS-B with Basinhopping for stochastic search with random steps
print("===> Searching optimal threshold for each label")
start_time = timer()
opt_output = basinhopping(f_neg,
thr_0,
stepsize=0.1,
minimizer_kwargs=minimizer_kwargs,
niter=10,
accept_test=bounds)
end_time = timer()
print("===> Optimal threshold for each label:\n{}".format(opt_output.x))
print("Threshold found in: %s seconds" % (end_time - start_time))
score = -opt_output.fun
return score, opt_output.x
def get_xhat(locs, N, k, inverse, pdf_ref, pdf, pdf_metric):
'''Compute xhat for given coefficient locs using basinhopping.
Parameters
----------
locs : array_like
Coefficient location indices.
N : int
Length of the desired signal (also number of coefficients in
total).
k : int
Desired sparsity level.
inverse : callable
Inverse sparsifying transform.
pdf_ref : array_like
Reference pdf of the prior to compare against.
pdf : callable
Function that estimates pixel intensity distribution.
pdf_metric : callable
Function that returns the distance between pdfs.
Returns
-------
xhat : array_like
Inverse transform of coeffs.
locs : array_like
Indices of non-zero coefficients.
coeffs : array_like
Coefficients of xhat.
'''
c0 = np.zeros(N)
ck = np.zeros(k)
res = basinhopping(obj,
ck,
minimizer_kwargs={
'args': (N, locs, inverse, pdf_ref, pdf, pdf_metric)
})
c0[locs] = res['x']
xhat = inverse(c0)
xhat /= np.max(np.abs(xhat)) + np.finfo('float').eps
return (xhat, locs, res['x'])
def get_inverse(x, y, z):
''' Funtion to get inverse kinematics
-----------------INPUT---------------
x,y,z = target end coordinates
----------------RETURN---------------
Returns list of r(theta[1]),2,3,4'''
b = (-150, 150) # Arbitrary bounds for now
bnds = (b, (-75, 70), (-95, 75), (-90, 45)
) # Bounds for r(theta[2]), r(theta[3]), theta4
# cons = [
# {'type': 'eq', 'fun': end_constraint}] # Define constraint type and function to feed into scipy constraints
def _get_theta(x, y):
'''Function to get r(theta[1])
'''
try:
t1 = degrees(arctan(y / x))
return t1
except ZeroDivisionError: # Catch Error for when y=0 raise ZeroDivisionError
return 0
# t1 = _get_theta(x, y)
x0 = array([0.3, 0.3, 0.3, 0.3])
cons = {'type': 'eq', 'fun': end_constraint}
minimizer_kwargs = {
"method": "SLSQP",
"args": (x, y, z),
"bounds": bnds,
"constraints": cons
}
# sol = minimize(objective, x0, args=(x, y, z), method='SLSQP', constraints=[cons],bounds=bnds,options={'disp': True})
# sol = minimize(objective, x0, args=(x, y, z), method='SLSQP',bounds=bnds,options={'disp': True})
sol = basinhopping(objective,
x0,
niter=50,
minimizer_kwargs=minimizer_kwargs,
disp=False)
angles = sol.x
return angles
def best_eer(val_scores, utt2len, utt2label, key_list):
def f_neg(threshold):
## Scipy tries to minimize the function
return utt_eer(val_scores, utt2len, utt2label, key_list, threshold)
# Initialization of best threshold search
thr_0 = [0.20] * 1 # binary class
constraints = [(0., 1.)] * 1 # binary class
def bounds(**kwargs):
x = kwargs["x_new"]
tmax = bool(np.all(x <= 1))
tmin = bool(np.all(x >= 0))
return tmax and tmin
# Search using L-BFGS-B, the epsilon step must be big otherwise there is no gradient
minimizer_kwargs = {
"method": "L-BFGS-B",
"bounds": constraints,
"options": {
"eps": 0.05
}
}
# We combine L-BFGS-B with Basinhopping for stochastic search with random steps
logger.info("===> Searching optimal threshold for each label")
start_time = timer()
opt_output = basinhopping(f_neg,
thr_0,
stepsize=0.1,
minimizer_kwargs=minimizer_kwargs,
niter=10,
accept_test=bounds)
end_time = timer()
logger.info("===> Optimal threshold for each label:\n{}".format(
opt_output.x))
logger.info("Threshold found in: %s seconds" % (end_time - start_time))
score = opt_output.fun
return score, opt_output.x
def solve(self,
init_value_sampler=None,
n_init=20,
n_iters=1000,
verbose=True,
multiprocessing=0):
assert self.target_stats is not None, "self.target_stats should have been set before solve."
bound = np.array([[-0.25, 0.1, 0, -0.1, 20], [0, 1, 0.2, 1, 75]])
if init_value_sampler is None:
init_value_sampler = lambda n: np.random.uniform(
low=bound[0, :], high=bound[1, :], size=[n, 5])
init = init_value_sampler(n_init)
result = np.zeros([n_init, 5])
if multiprocessing:
params = (self, [init[i] for i in range(n_init)],
[i + 1 for i in range(n_init)], True, n_iters, bound)
pool = mp.Pool(multiprocessing)
result = pool.map(SSTSolver.solve_multiprocess, params)
pool.close()
else:
for i in range(n_init):
init_value = init[i, :]
if verbose:
print(
f'{i + 1}/{n_init} is starting. Initial value: {init_value}.'
)
time_stamp = time.time()
temp_value = basinhopping(self.eval_and_compute_loss,
x0=init_value,
niter=n_iters,
stepsize=0.01).x
result[i] = minimize(self.eval_and_compute_loss,
x0=temp_value,
method='Nelder-Mead').x
if verbose:
time_elapsed = time.time() - time_stamp
formatted_time_elapsed = f'{int(time_elapsed // 3600)}:{int(time_elapsed % 3600 // 60)}:{time_elapsed % 60}'
print(
f'{i + 1}/{n_init} has completed. Optimized value: {result[i]}. Time elapsed: {formatted_time_elapsed}'
)
self.result = result
return result
def basinhopping_mode(info):
prebuild(info['c_source_list'], info['cc_options'], info['kernel_file'])
make_measure_script(int(info['threads']))
#minimizer_kwargs = {"method": "BFGS"}
#ret = basinhopping(testfunc, [1.], minimizer_kwargs=minimizer_kwargs, niter=200)
#print(ret.x)
#print(ret.fun)
#minimizer_kwargs = {"args": 1.0}
#ret = basinhopping(testfunc, [1.], minimizer_kwargs=minimizer_kwargs, stepsize=1)
#rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25))
#ret = brute(testfunc, rranges, full_output=True, finish=scipy.optimize.fmin)
#print("global minimum: x = %.4f, f(x0) = %.4f" % (ret.x, ret.fun))
#print(ret)
#x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
#res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)
#print(res)
#scipy.optimize.basinhopping(func, x0, niter=100, T=1.0, stepsize=0.5, minimizer_kwargs=None, take_step=None, accept_test=None, callback=None, interval=50, disp=False, niter_success=None, seed=None)
#x0 = [10, 10, 10, 10, 10]
#res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)
#res = minimize(rosen, x0, args=(), method='Nelder-Mead', jac=None, hess=None, hessp=None, bounds=None, constraints=(), tol=None, callback=None, options=None)
#print(res)
#params = (2, 3, 7)
#rranges = (slice(-4, 4, 0.25), slice(-4, 4, 0.25))
#ret = optimize.brute(testfunc, rranges, args=params, full_output=True, finish=optimize.fmin)
#print(ret)
#x0 = [32, 32, 32]
#ret = basinhopping(testfunc, x0, niter=30, T=1.0, stepsize=10, minimizer_kwargs=None, take_step=None, accept_test=None, callback=None, interval=50, disp=True, niter_success=None, seed=None)
#ret = basinhopping(testfunc, x0, niter=300, T=1.0, stepsize=10, minimizer_kwargs=None, take_step=None, accept_test=None, callback=None, interval=50, disp=True, niter_success=None, seed=None)
#print(ret)
minimizer_kwargs = {"args": (info, info['remote'], int(info['repetition']), info['huge_num'])}
#ret = basinhopping(testfunc, [32,32,32], niter=300, T=1.0, stepsize=10, minimizer_kwargs=minimizer_kwargs, take_step=None, accept_test=None, callback=None, interval=50, disp=True, niter_success=None, seed=None)
ret = basinhopping(evalfunc, [32,32,32], niter=10, T=1.0, stepsize=10, minimizer_kwargs=minimizer_kwargs, take_step=None, accept_test=None, callback=None, interval=50, disp=True, niter_success=None, seed=None)
print(ret)
def custom_basinhopping(self):
self.successful_results = np.empty(self.n)
self.successful_results[:] = np.nan
self.current_success_number = 0
minimizer_config = {
"method": 'BFGS',
"options": {
'gtol': self.confidence
}
}
output = basinhopping(self.to_minimise,
self.initial,
niter=1000,
minimizer_kwargs=minimizer_config,
take_step=self.step_function,
callback=self.callback_function)
return output.x
def run(self, wrapper='basinhopping'):
# maximize likelihood function by scipy.optimize.minimize function
minimizer_kwargs = {"bounds": self.paramsBounds}
if wrapper is 'minimize':
self.result = minimize(self.chi2, self.paramsInit,
**minimizer_kwargs)
if wrapper is 'basinhopping':
self.result = basinhopping(self.chi2,
self.paramsInit,
minimizer_kwargs=minimizer_kwargs)
self.paramsMax = self.result.x
self.diagnostics = {
'paramsInit': self.paramsInit,
'paramsMax': self.paramsMax,
'paramsBounds': self.paramsBounds,
'paramsNames': self.paramsNames,
'result': self.result,
'Ndim': self.Ndim
}
return self.diagnostics
def train(self):
f=self.create_lossOdeint()
bnds = ((1e-12, .2),(1e-12, .2),(5,len(self.data)-5),(1e-12, .2),
(1/120, .4),(1e-12, .4),(1e-12, .4),(1e-12, .4),(1e-12, .4),(1e-12, .4))# your bounds
x0 = [1e-3, 1e-3, 0, 1e-3, 1/120, 1e-3, 1e-3, 1e-3, 1e-3, 1e-3]
minimizer_kwargs = { "method": "L-BFGS-B","bounds":bnds }
optimal = basinhopping(f, x0, minimizer_kwargs=minimizer_kwargs,niter=10,disp=True)
point = self.s_0, self.start_date, self.i_0, self.d_0, self.r_0, self.startNCases, self.weigthCases, \
self.weigthRecov, self.weigthDeath
strSave='{}, {}, '.format(self.country, abs(optimal.fun))
strSave=strSave+', '.join(map(str,point))
self.append_new_line('./results/history_'+self.country+str(self.version)+'.csv', strSave)
del self, f, strSave, point
gc.collect()
return optimal.fun
def test_Wang_LAP():
"""Test the least action path method from Jin Wang and colleagues (http://www.pnas.org/cgi/doi/10.1073/pnas.1017017108)
Returns
-------
"""
x1_end=1
x2_end=0
x2_init=1.5
x1_init=1.5
N = 20
x1_input=np.arange(x1_init, x1_end + (x1_end-x1_init)/N, (x1_end-x1_init)/N)
x2_input=np.arange(x2_init, x2_end + (x2_end-x2_init)/N, (x2_end-x2_init)/N)
X_input=np.vstack((x1_input, x2_input))
dyn.tl.least_action(X_input, F=F, D=0.1, N=20, lamada_=1)
res = optimize.basinhopping(dyn.tl.least_action, x0=X_input,minimizer_kwargs={'args': (2, F, 0.1, 20, 1)})
res
def start(self, seq_to_optimize):
"""
@param: The starting list of values to be optimised.
Note that the value bounds per element are fixed.
"""
x0 = seq_to_optimize
assert isinstance(x0, list) and len(x0) > 0 and all([isinstance(x, Number) for x in x0]), \
"Input sequence should be a list of type numbers.Number."
# the bounds
xmin = [1.0] * len(x0)
xmax = [2.0] * len(x0)
# rewrite the bounds in the way required by L-BFGS-B
bounds = [(low, high) for low, high in zip(xmin, xmax)]
# use method L-BFGS-B because the problem is smooth and bounded
minimizer_kwargs = dict(method="L-BFGS-B", bounds=bounds)
res = basinhopping(self.f, x0, minimizer_kwargs=minimizer_kwargs)
return res
def trainMinimizer(self, input, optimizer):
flattenedWeights = self.__flattenNetwork()
print(flattenedWeights.shape)
# Minimize the cost function
res = optimize.basinhopping(func=self.__loss,
x0=flattenedWeights,
disp=True,
minimizer_kwargs={
"args": (input, input),
"method": "L-BFGS-B",
"options": {
"disp": True
}
})
# res = adam(fun=self.__loss, x0=flattenedWeights, args=(input, input))
# Rebuild the weights matrix
self.__rebuildNetwork(flattenedWeights)
# Error of the cost function
error = res.fun
print(f'Final loss is {error}')
def test_all_nograd_minimizers(self):
# test 2d minimizations without gradient. Newton-CG requires jac=True,
# so not included here.
i = 1
methods = [
'CG', 'BFGS', 'L-BFGS-B', 'TNC', 'SLSQP', 'Nelder-Mead', 'Powell',
'COBYLA'
]
minimizer_kwargs = copy.copy(self.kwargs_nograd)
for method in methods:
minimizer_kwargs["method"] = method
res = basinhopping(func2d_nograd,
self.x0[i],
minimizer_kwargs=minimizer_kwargs,
niter=self.niter,
disp=self.disp)
tol = self.tol
if method == 'COBYLA':
tol = 2
assert_almost_equal(res.x, self.sol[i], decimal=tol)
def main():
results = {}
results['shgo'] = optimize.shgo(eggholder, bounds)
results['DA'] = optimize.dual_annealing(eggholder, bounds)
results['DE'] = optimize.differential_evolution(eggholder, bounds)
# basinhopping requires initiual guess x0
x0 = np.array([randint(-512, 513), randint(-512, 513)])
kwargs = {'bounds': bounds}
results['BH'] = optimize.basinhopping(eggholder, x0, minimizer_kwargs=kwargs)
# shgo has a second method, which returns all local minima rather
# than only what it thinks is the global minimum:
results['shgo_sobol'] = optimize.shgo(eggholder, bounds, n=200, iters=5,
sampling_method='sobol')
plot_minima(results)
def _fit_basinhopping(self, X, y, X_val, Y_val, activations, deltas,
coef_grads, intercept_grads, layer_units):
# Store meta information for the parameters
self._coef_indptr = []
self._intercept_indptr = []
start = 0
# Save sizes and indices of coefficients for faster unpacking
for i in range(self.n_layers_ - 1):
n_fan_in, n_fan_out = layer_units[i], layer_units[i + 1]
end = start + (n_fan_in * n_fan_out)
self._coef_indptr.append((start, end, (n_fan_in, n_fan_out)))
start = end
# Save sizes and indices of intercepts for faster unpacking
for i in range(self.n_layers_ - 1):
end = start + layer_units[i + 1]
self._intercept_indptr.append((start, end))
start = end
# Run Basinhopping
packed_coef_inter = _pack(self.coefs_, self.intercepts_)
minimizer_kwargs = {
'method': 'L-BFGS-B',
'args': (X, y, activations, deltas, coef_grads, intercept_grads)
}
result = optimize.basinhopping(x0=packed_coef_inter,
T=self.T,
stepsize=self.stepsize,
func=self._loss_func,
niter=self.max_iter,
callback=self._callback,
minimizer_kwargs=minimizer_kwargs)
optimal_parameters = result.x
self.loss = result.fun
self._unpack(optimal_parameters)
def optimize(self, x0=None, nhops=None, polish=1e-6):
"""
Perform the optimization.
Parameters
----------
x0 : ndarray, None
Initial optimization vector. If None, use a random vector.
nhops : int, None
The number of basin hops to perform while optimizing. If None,
hop a number of times equal to the dimension of the conditioning
variable(s).
polish : float
If `polish` > 0, the found minima is improved by removing small
components and optimized with lower tolerances.
"""
from scipy.optimize import basinhopping
if x0 is not None:
x = x0
else:
x = self.construct_random_initial()
if nhops is None:
nhops = self._default_hops
minimizer_kwargs = {'method': 'L-BFGS-B',
'bounds': [(0, 1)] * x.size,
}
res = basinhopping(func=self.objective,
x0=x,
minimizer_kwargs=minimizer_kwargs,
niter=nhops,
accept_test=accept_test,
)
self._optima = res.x
if polish:
self._polish(cutoff=polish)
def optimize_bis(params, args_, distance, I_A, I_B, I_C, mybounds, obs, cumul):
"""
Optimise sur la fonction objectif avec l'algorithme du recuit simule
de gradient et renvoie le resultat de cette opt.
Args
----
params : list
Contient les parametres fixes du modele de la fonction
mdl.integrateCecidoInflo
args_ : list
Contient une initialisation des parametres a estimer du modele de
la fonction mdl.integrateCecidoInflo
distance : fonction
Fonction objectif choisie
I_ABC : ndarray
Nombre d'inflorescences vivantes au cours du temps dans chaque
sous parcelle
mybounds :
Bornes des parametres a estimer
obs : bool
Vaut 0 si on fait l'optimisation sur toutes les valeurs
journalieres, 1 si sur les valeurs observees
cumul : bool
Vaut 1 si on fait l'optimisation sur les valeurs cumulees au cours
du temps. 0 sinon.
Returns
-------
res : float
Resultat de l'optimisation
"""
res = basinhopping(objectif,
params,
minimizer_kwargs={
"args": (args_, distance, I_A, I_B, I_C, obs, cumul)
},
accept_test=mybounds)
return res
def main():
args = create_cmd_args()
if not args:
args = get_input_args()
# Select subjects for fitting
if args.subject == 'all':
# Fit model to all subjects
subjects = range(100)
elif args.subject[0] == '-':
# For leave-one-subject-out cross validation
subjects = [int(x) for x in range(100) if x != -int(args.subject)]
else:
# For single subject fitting
subjects = [int(args.subject)]
notes = 'na'
bounds = model_bounds[args.training_model]
simulator, trials = build_simulator(args.experiment_name, subjects)
logfile = 'fitting_log_' + ymdhms() + '_' + str(args.subject) + '.txt'
with open(logfile, 'a') as file:
file.write(f'experiment_name: {args.experiment_name}\nsubject: {args.subject}\ntrials: {trials}\n'
f'approach_experiment: {args.approach_experiment}\n'
f'approach_model: {args.approach_model}, avoid_model: {args.avoid_model}\n'
f'training_model: {args.training_model}\n'
f'method: {args.method}\nbounds: {bounds}\nt_start: {args.t_start}, t_end: {args.t_end}\n'
f'preferred speed: {args.ps}\nnotes: {notes}\n')
if args.method == 'nelder-mead':
res = optimize.minimize(error, x0, args=(simulator, trials, logfile, args), method='nelder-mead',
options={'xatol': 1e-6, 'disp': True, 'adaptive': True})
elif args.method == 'shgo':
res = optimize.shgo(error, bounds, args=(simulator, trials, logfile, args))
elif args.method == 'dual_annealing':
res = optimize.dual_annealing(error, bounds, args=(simulator, trials, logfile, args),
initial_temp=25000)
elif args.method == 'differential_evolution':
res = optimize.differential_evolution(error, bounds, args=(simulator, trials, logfile, args),
updating='immediate', workers=1)
elif args.method == 'basinhopping':
res = optimize.basinhopping(error, bounds, minimizer_kwargs={'args':(simulator, trials, logfile, args)})
with open(logfile, 'a') as file:
file.write(f'The optimal x: {res.x}')
print(res.x)
def findminglob(self,
pvals,
f_name='None',
email=0,
meth='TNC',
bnds='strict',
it=300,
stpsize=0.5,
temp=1.,
displ=True,
maxits=3000):
"""Function which minimizes 4DVAR cost fn. Takes an initial state
(pvals), an obs dictionary, an obs error dictionary, a dataClass and
a start and finish time step.
"""
p = np.array(pvals.tolist()[0], dtype=np.float)
self.xb = p
self.names = pvals.dtype.names
if bnds == 'strict':
bnds = self.opt_bnds(self.dC.bnds)
else:
bnds = bnds
findmin = spop.basinhopping(self.cost,
p,
niter=it,
minimizer_kwargs={
'method': meth,
'bounds': bnds,
'jac': self.gradcost2,
'options': {
'maxiter': maxits
}
},
stepsize=stpsize,
T=temp,
disp=displ)
if f_name != 'None':
if email == 1:
my_email.send_email(findmin, f_name)
return findmin
def removecoin(inputimage, startguess=[0.5, 0.5, 0.1], method='local'):
if method == 'local':
x_opt = fmin(circlecost, [0.4, 0.7, 0.1], args=(inputimage))
print(x_opt)
outermean = circlecost_outermean(x_opt, totuple(inputimage))
outputimage = drawcircle(inputimage, x_opt[0], x_opt[1], x_opt[2], 0)
if method == 'global':
minimizer_kwargs = {
'method': 'Nelder-Mead',
'args': totuple(inputimage)
}
result = basinhopping(circlecost, [0.4, 0.7, 0.1],
minimizer_kwargs=minimizer_kwargs)
x_opt = result.x
print(x_opt)
outermean = circlecost_outermean(x_opt, totuple(inputimage))
outputimage = drawcircle(inputimage, x_opt[0], x_opt[1], x_opt[2], 0)
imshow(outputimage)
return outputimage
def MSM_original(data,kbar,startingvals):
"""
Implementation of MSM close to the original one in Matlab
data = data to use for likelihood calculation
kbar = number of multipliers in the model
startingvals = 4 parameters of the MSM, recommended to set to None so that the function can
compute optimal starting values
"""
A_template = T_mat_template(kbar)
startingvals, LLs,ordered_parameters = starting_values(data,startingvals,kbar,A_template)
bnds = ((1.001,50),(1,1.99),(1e-3,0.999999),(1e-4,5))
minimizer_kwargs = dict(method = "L-BFGS-B",bounds = bnds,args = (kbar,data,A_template,None))
res = opt.basinhopping(likelihood,x0 = startingvals,minimizer_kwargs = minimizer_kwargs,
niter = 1)
parameters,LL,niters,output = res.x,res.fun,res.nit,res.message
#print(LL,parameters)
LL, LLs,pi_t = likelihood(parameters,kbar,data,A_template,None,2)
LL = -LL
return(LL,LLs,parameters,pi_t)
def fit(self, X, Y, sY):
# first we need to build a distance matrix
self.sY = sY
if type(self.sY) is float:
self.sY = self.Y * 0 + sY
self.X = X
self.Y = Y
self.dX1X1 = dmat(X.reshape(-1, 1))
fitter = basinhopping(func=self.marginal_likelihood,
x0=np.array([self.mu, self.sigma, self.length]),
niter=13)
self.mu = fitter.x[0]
self.sigma = abs(fitter.x[1])
self.length = abs(fitter.x[2])
self.tY = (Y - self.mu).reshape(-1, 1)
self.KX1X1 = rbf_kern(
self.dX1X1, self.sigma**2.0,
self.length) + np.eye(self.dX1X1.shape[0]) * self.sY
self.KX1X1_inv = np.linalg.pinv(self.KX1X1)
self.KiY = self.KX1X1_inv.dot(self.tY)
def basinhopping(self, x0=None, bounds=None, **kwargs):
if x0 is None:
x0 = [par.guess for par in self.fit_parameters]
if bounds is None:
bounds = [par.bounds for par in self.fit_parameters]
xmin = np.array(bounds)[:, 0]
xmax = np.array(bounds)[:, 1]
def bounds_enforcer(**kwargs):
x = kwargs["x_new"]
tmax = bool(np.all(x <= xmax))
tmin = bool(np.all(x >= xmin))
return tmax and tmin
from scipy.optimize import basinhopping
sol = basinhopping(
self.minimizer, x0, accept_test=bounds_enforcer, **kwargs
)
sol.x = dict(zip([par.name for par in self.fit_parameters], sol.x))
return sol
def run_basinhopping(cf, mst, links_to_add, highD_dist_matrix, debug = False):
'''
Returns new graph.
cf = cost_function
start = start x
'''
disp = False
if debug: disp = True
start = len(mst.es())
if debug: print(f"Starting optimization at {start}")
minimizer_kwargs = {'args':{'graph':mst,'list_of_links_to_add':links_to_add,'highD_dist_matrix':highD_dist_matrix,'debug':debug}}
result = optimize.basinhopping(
cf,
start,
disp=disp,
minimizer_kwargs=minimizer_kwargs
)
if debug:
print(result)
g = add_links_to_graph(mst, highD_dist_matrix, links_to_add, result.x[0])
return g
def argmaxvar(self, bounds = (-4., 4.)):
assert isinstance(bounds, tuple)
def neg_var_x(x):
assert x.shape[0] == self._kern._input_dim
X_test = x.reshape(1, x.shape[0])
K_test = self._kern.cov(self._X, X_test)
K_test_grad = self._kern.d_cov_d_X(X_test, self._X)[:,0,:].T
v = np.linalg.solve(self._chol, K_test)
v_grad = np.linalg.solve(self._chol, K_test_grad)
return - self.predict(X_test)[1][0,0], 2. * np.dot(v_grad.T, v)
bnds = (bounds,) * self._kern._input_dim
#res = minimize(neg_var_x, np.random.normal(size = (self._kern._input_dim,)), method = 'L-BFGS-B', jac = True, bounds = bnds, options = {'ftol': 1e-16, 'gtol': 1e-16, 'maxiter' : 1000})
#res = minimize(neg_var_x, x0, method = 'TNC', jac = True)
# --- Using optimize.basinhopping
minimizer_kwargs = {'method': 'L-BFGS-B', 'jac': True, 'bounds': bnds, 'options' : {'ftol': 1e-16, 'gtol': 1e-16, 'maxiter' : 1000}}
res = basinhopping(neg_var_x, np.random.uniform(size = (self._kern._input_dim,))- 0.5, minimizer_kwargs = minimizer_kwargs)
return res.x