def findMin(self, x, y, numIters = 100):
meanfunc = self.model.meanfunc
covfunc = self.model.covfunc
likfunc = self.model.likfunc
inffunc = self.model.inffunc
hypInArray = self._convert_to_array()
try:
opt = simplex(self._nlml, hypInArray, maxiter=numIters, disp=False, full_output=True)
optimalHyp = deepcopy(opt[0])
funcValue = opt[1]
warnFlag = opt[4]
if warnFlag == 1:
self.logger.warning("Maximum number of function evaluations made")
elif warnFlag == 2:
self.logger.warning("Maximum number of iterations exceeded.")
except:
self.errorCounter += 1
if not self.searchConfig:
raise Exception("Can not learn hyperparamters using Nelder-Mead.")
self.trailsCounter += 1
if self.searchConfig:
searchRange = self.searchConfig.meanRange + self.searchConfig.covRange + self.searchConfig.likRange
if not (self.searchConfig.num_restarts or self.searchConfig.min_threshold):
raise Exception('Specify at least one of the stop conditions')
while True:
self.trailsCounter += 1 # increase counter
for i in range(hypInArray.shape[0]): # random init of hyp
hypInArray[i] = np.random.uniform(low=searchRange[i][0], high=searchRange[i][1])
# value this time is better than optiaml min value
try:
thisopt = simplex(self._nlml, hypInArray, maxiter=numIters, disp=False, full_output=True)
if thisopt[1] < funcValue:
funcValue = thisopt[1]
optimalHyp = thisopt[0]
except:
self.errorCounter += 1
if self.searchConfig.num_restarts and self.errorCounter > old_div(self.searchConfig.num_restarts, 2):
self.logger.warning("[Simplex] %d out of %d trails failed during optimization", self.errorCounter, self.trailsCounter)
raise Exception("Over half of the trails failed for Nelder-Mead")
if self.searchConfig.num_restarts and self.trailsCounter > self.searchConfig.num_restarts-1: # if exceed num_restarts
self.logger.warning("[Simplex] %d out of %d trails failed during optimization", self.errorCounter, self.trailsCounter)
return optimalHyp, funcValue
if self.searchConfig.min_threshold and funcValue <= self.searchConfig.min_threshold: # reach provided mininal
self.logger.warning("[Simplex] %d out of %d trails failed during optimization", self.errorCounter, self.trailsCounter)
return optimalHyp, funcValue
return optimalHyp, funcValue
def simplex_fit(x, y, fitFunction, p0=None, y_sigmas=None):
"""Optimizes fit parameters using assuming least-square using simplex algo.
Returns array with fit parameters and the sum of the deviations squared (fit quality)"""
yNominal = np.array(y)
yError = [0.0001 for i in y] # assuming 1 if no stdDev is given
if isinstance(y[0], uncertainties.UFloat):
yNominal = [i.nominal_value for i in y]
yError = [i.std_dev for i in y]
if y_sigmas is not None:
yError = y_sigmas
fitParameterCount = len(inspect.getargspec(fitFunction).args) - 1
if p0 is None:
p0 = [0 for i in range(fitParameterCount)
] # starting from 0 if no initial guess is given
squareErrorForFitFunction = lambda params, xData, yData, error: squareError(
fitFunction, fitParameterCount, params, xData, yData, error)
fitParams = simplex(squareErrorForFitFunction,
p0,
args=(x, y, yError),
disp=True,
full_output=0,
maxfun=1000000,
maxiter=1000000)
fitQual = fitQuality(x, y, lambda xIn: fitFunction(xIn, *fitParams))
return [fitParams, fitQual]
def orientate_octahedra(S0, O, x0, y0, z0, n1, n2, n3, n1p, n2p, n3p):
xinit = [0, 0, 0, 0, 0, 0]
opt = simplex(func2,
xinit,
args=(S0, O, x0, y0, z0, n1, n2, n3, n1p, n2p, n3p),
full_output=0)
return opt
def get_rotation_angles(Sub1, n1, n2, Sub2, n3, n4, R):
x0 = [0, 0, 0, 0, 0, 0]
opt = simplex(func,
x0,
args=(Sub1, n1, n2, Sub2, n3, n4, R),
full_output=0)
return opt
def turn_alkyl(xo, yo, zo, xab, yab, zab):
xinit = [0, 0, 0]
opt = simplex(func3,
xinit,
args=(xo, yo, zo, xab, yab, zab),
full_output=0)
return opt
def turn_methyl(ux, uy, uz, x0, y0, z0, xc, yc, zc, lcc):
xinit = [0, 0, 0]
opt = simplex(func4,
xinit,
args=(ux, uy, uz, x0, y0, z0, xc, yc, zc, lcc),
full_output=0)
return opt
def simplex(self):
"""
NUMERICAL RECIPES: https://www.google.com/url?q=https://drive.google.com/file/d/1K6tg_um1G-5X-5hdgwKb8vKyBD5oz4vX/view?usp%3Dsharing&sa=D&ust=1606856195190000&usg=AFQjCNH2Sc8A5HVZrZb72T-DrPM2-1kRtQ
"""
from scipy.optimize import fmin as simplex
self.param = simplex(self.error,
5 * [5],
xtol=1e-50,
ftol=1e-50,
maxfun=1e6)
print(self.param)
self.fit = lambda x: func(x, *self.param)
self._measureGoodness()
def go_simplex(func,xdata,ydata,lb,ub,errors=None):
params = -999. ; chi2n = -999.
# Check that the degrees of freedom is larger than 1
dof = len(xdata)-len(lb)
if (dof<=1):
sys.exit('HOD_FIT.py: The degrees of freedom should be >1')
# Get random initial values within the boundaries given
p1 = random.rand(len(lb))
p1 = lb + p1*(ub-lb)
params = simplex(f_chi2,p1,args=(xdata,ydata,errors,func),full_output=0)
model = func(xdata,*params)
chi2n = chi2(ydata,model,errors)/dof
return params,chi2n
def optimize(x, y, fitFunction, p0=None):
"""Optimizes fit parameters using assuming least-square using simplex algo.
Returns array with fit parameters and the sum of the deviations squared (fit quality)"""
yNominal = np.array(y)
yError = [0.0001 for i in y] # assuming 1 if no stdDev is given
if isinstance(y[0], uncertainties.UFloat):
yNominal = [i.nominal_value for i in y]
yError = [i.std_dev for i in y]
fitParameterCount = len(inspect.getargspec(fitFunction).args) - 1
if p0 is None:
p0 = [0 for i in range(fitParameterCount)] # starting from 0 if no initial guess is given
squareErrorForFitFunction = lambda params, xData, yData, error: squareError(fitFunction, fitParameterCount, params, xData, yData, error)
fitParams = simplex(squareErrorForFitFunction, p0, args=(x, y, yError), disp=True, full_output=0, maxfun=1000000)
fitQual = fitQuality(x, y, lambda xIn: fitFunction(xIn, *fitParams))
return [fitParams, fitQual]
def scatter(residuals_np,
s_peculiar_vel_np,
s_appmagTBmax_np,
InitialGuess=0.15):
"""
Function to compute the intrinsic scatter from the Hubble residuals by
minimizing the -2*log(Likelihood) function in Eq. (6) of Blondin et al 2011.
:param residuals_np : numpy array of Hubble residuals.
:type residuals_np : ndarray.
:param s_peculiar_vel_np : numpy array of peculiar-velocity uncertainties.
:type s_peculiar_vel_np : ndarray.
:param s_appmagTBmax_np : numpy array of apparent magnitude at t_Bmax
uncertainties.
:type s_appmagTBmax_np : ndarray.
:param InitialGuess : Initial guess about the value of the intrinsic scatter.
Default value = 0.15.
:type InitialGuess : float.
"""
int_scatter = simplex(neg2lnLikelihood,
InitialGuess,
args=(residuals_np, s_peculiar_vel_np,
s_appmagTBmax_np))
return int_scatter[0]
def scale_sky(sky_spec, sci_spec):
"""
Fit the 1D sky spectrum to the 1D science spectrum allowing
different families of OH lines to be scaled differently and
the continuum to be scaled separately.
This module is code hijacked from the OSIRIS data redcution
pipeline.
"""
sky, sky_hdr = pyfits.getdata(sky_spec, header=True)
sci, sci_hdr = pyfits.getdata(sci_spec, header=True)
# Make a wavelength array for the sky object.
sky_lambda = np.arange(len(sky), dtype=float)
sky_lambda -= sky_hdr['CRPIX1'] - 1
sky_lambda *= sky_hdr['CRDELT1']
sky_lambda += sky_hdr['CRVAL1']
# Full width in pixels of unresolved emission line
line_half_width = 2
npixw = 2 * line_half_width
# Median filter the sky to get an estimate of the continuum.
# Remove this continuum.
backgnd = filters.median(sky, size=10 * line_half_width, mode='nearest')
sky2 = sky - backgnd
for ii in range(len(l_boundary) - 1):
lr = np.where((sky_lambda >= l_boundary[ii])
& (sky_lambda < l_boundary[ii + 1]))[0]
if len(lr) == 0:
continue
sky_lr = sky[lr]
sky2_lr = sky2[lr]
sci_lr = sci[lr]
lam_lr = sky_lamda[lr]
sky_median = np.median(sky2_lr)
sky_stddev = np.std(sky2)
w_skylines = np.where(sky2_lr > (10 * sky_median) + sky_stddev)[0]
if len(w_skylines) > 0:
# Make a mask for where line regions are and for where the
# continuum is.
line_mask = np.zeros(len(lr), dtype=float)
line_mask[w_skylines] = 10.0
# Convolve the mask with a "resolution-width" window.
window = np.ones(npixw)
line_mask = np.convolve(line_mask, window, mode='same')
line_regions = line_mask > 0
line_count = line_regions.sum()
if (line_count >= 3) and ((len(line_regions) - line_count) >= 3):
# Remove the continuum from the science and object
f_sci = interp1d(lam_lr[~line_regions], sci_lr[~line_regions])
f_obj = inpterp1d(lam_lr[~line_regions], sky2[~line_regions])
sci_no_cont = sci_lr[line_regions] - f_sci([lam_lr])
out = simplex(fit_sky, init, args=(sci, sky))
def scale_sky(sky_spec, sci_spec):
"""
Fit the 1D sky spectrum to the 1D science spectrum allowing
different families of OH lines to be scaled differently and
the continuum to be scaled separately.
This module is code hijacked from the OSIRIS data redcution
pipeline.
"""
sky, sky_hdr = pyfits.getdata(sky_spec, header=True)
sci, sci_hdr = pyfits.getdata(sci_spec, header=True)
# Make a wavelength array for the sky object.
sky_lambda = np.arange(len(sky), dtype=float)
sky_lambda -= sky_hdr['CRPIX1'] - 1
sky_lambda *= sky_hdr['CRDELT1']
sky_lambda += sky_hdr['CRVAL1']
# Full width in pixels of unresolved emission line
line_half_width = 2
npixw = 2 * line_half_width
# Median filter the sky to get an estimate of the continuum.
# Remove this continuum.
backgnd = filters.median(sky, size=10*line_half_width, mode='nearest')
sky2 = sky - backgnd
for ii in range(len(l_boundary)-1):
lr = np.where((sky_lambda >= l_boundary[ii]) & (sky_lambda < l_boundary[ii+1]))[0]
if len(lr) == 0:
continue
sky_lr = sky[lr]
sky2_lr = sky2[lr]
sci_lr = sci[lr]
lam_lr = sky_lamda[lr]
sky_median = np.median(sky2_lr)
sky_stddev = np.std(sky2)
w_skylines = np.where(sky2_lr > (10 * sky_median) + sky_stddev)[0]
if len(w_skylines) > 0:
# Make a mask for where line regions are and for where the
# continuum is.
line_mask = np.zeros(len(lr), dtype=float)
line_mask[w_skylines] = 10.0
# Convolve the mask with a "resolution-width" window.
window = np.ones(npixw)
line_mask = np.convolve(line_mask, window, mode='same')
line_regions = line_mask > 0
line_count = line_regions.sum()
if (line_count >= 3) and ((len(line_regions) - line_count) >= 3):
# Remove the continuum from the science and object
f_sci = interp1d(lam_lr[~line_regions], sci_lr[~line_regions])
f_obj = inpterp1d(lam_lr[~line_regions], sky2[~line_regions])
sci_no_cont = sci_lr[line_regions] - f_sci([lam_lr])
out = simplex(fit_sky, init, args=(sci, sky))
print fof(56.9)
plt.tight_layout()
#plt.savefig('atlas5.png', dpi=200)
plt.show()
if 1:
C3 = 19.79 #km2s2
DEC = 56.917 # deg
lus = ext_LUS('mb')
lus.set_boiloff(0.002)
lus.set_time(4)
lus.compute_stack_mass()
lus.hit_from_incl(fof(DEC))
#lus.print_info()
pl = simplex(c3, 37000, args=(lus, C3))[0]
print "2x MB-60 ext-LUS:", round(pl, -2)
lus2 = ext_LUS('rl')
lus2.set_boiloff(0.002)
lus2.set_time(4)
lus2.compute_stack_mass()
lus2.hit_from_incl(fof(DEC))
#lus.print_info()
pl = simplex(c3, 37000, args=(lus2, C3))[0]
print "2x RL-10 ext-LUS:", round(pl, -2)
def all_the_rest(lus, offset, loiter, save = 0):
lus.set_launch_date(offset)
lus.set_time(offset+loiter)
lus.print_info()
print "Launching numerical simualtion..."
C3_target = allc3req[offset+loiter]
ext_LUS_payload = simplex(c3, 27000, args=(lus, C3_target))[0]
print " Payload: {0} kg @ [{1}off, {2}loi] ".format(round(ext_LUS_payload,2), offset, loiter)
# Get parking orbit parameters
__, __, pery, apo, transorb_period, br_time_1, br_time_2 = c3(ext_LUS_payload, lus, target_C3 = C3_target, rich_return = 1)
# Plot generation
print "\nDeploying C3@{0}% boiloff rate chart...".format(100*lus.Boiloff)
# C3 plot data generation.
allc3 = []
newt = []
for day in range(loiter+1):
lus.set_time(offset+day)
allc3.append(c3(ext_LUS_payload, lus))
newt.append(day+offset)
# Chart name.
name = "C3 @ [{0}%/d boiloff rate, {1}-day loiter time]".format(lus.Boiloff*100, loiter)
# ext_LUS C3 curve annotation text at start.
anno2_text = r"$Diff:\ {0} \ km^{{2}}s^{{-2}}$".format(round(allc3[0]-allc3req[offset], 2))
# ext_LUS C3 curve annotation text at end.
anno3_text = r"$Diff:\ {0} \ km^{{2}}s^{{-2}}$".format(round(allc3[loiter]-allc3req[offset+loiter], 2))
# Additional information.
anno4_text = ("Payload: {0} kg \n".format(round(ext_LUS_payload,-2))
+"Engines: {0}\n".format(lus.Engines)
+"Initial T/W: {0}\n".format(round(lus.Thrust/lus.Stack_mass, 3))
+"Burns: {0} s + {1} s\n".format(round(br_time_1,2), round(br_time_2,2))
+"Parking orbit: {0} x {1} km\n".format(round(pery/1000,1), round(apo/1000,1))
+"Orbital period: {0} hour".format(round(transorb_period,2)) )
# Name of chart file.
filename = ("C3-{0}-[{1}, {2}]-".format(lus.Boiloff, offset, loiter)
+"{0}kg-{1}-{1}kg_add".format(round(ext_LUS_payload,2), lus.Engines, lus.Stage_additions) )
# Creating plot.
plt.figure(figsize=(7.5, 4.5), dpi=180) # (11, 8) 80dpi dla full, (7.5, 4.5) 180dpi dla small
# Plot ext_LUS C3
plt.plot([swp_time(i) for i in newt],
allc3,
label="Instantaneous C3")
# Plot required C3
plt.plot([swp_time(i) for i in alltc3req],
allc3req,
label='Required C3')
# Plot reentry speed barrier line
plt.plot([swp_time(20)]*2,
[38, 44],
color='red',
linewidth=1.5,
linestyle="--")
# Annotate reentry speed barrier line
plt.annotate(r'Capsule Ventry barrier',
xy=(swp_time(20), 43.2),
xycoords='data',
xytext=(-150, +20),
textcoords='offset points',
fontsize=12,
bbox=dict(facecolor='white', edgecolor='None', alpha=0.65),
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2") )
# Annotate ext_LUS C3 curve at start
plt.annotate(anno2_text,
xy=(swp_time(newt[0]), allc3[0]),
xycoords='data',
xytext=(swp_time(8.5), 41.5),
textcoords='data',
fontsize=12,
bbox=dict(facecolor='white', edgecolor='None', alpha=0.65),
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.1") )
# Annotate ext_LUS C3 curve at end
plt.annotate(anno3_text,
xy=(swp_time(newt[loiter]), allc3[loiter] ),
xycoords='data',
xytext=(swp_time(15), 41.0),
textcoords='data',
fontsize=12,
bbox=dict(facecolor='white', edgecolor='None', alpha=0.65),
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.1") )
# Put additional information in place
plt.text(swp_time(0.6), 38.2,
anno4_text,
style='italic',
fontsize=10,
bbox={'facecolor':'white', 'alpha':0.5, 'pad':10} )
# Add labels, tittle, legend
#plt.xlabel('Date')
plt.ylabel('C3 [$km^2s^{-2}$]')
#plt.title(name)
plt.legend(loc='upper left', prop={'size':12})
# Axis and grid modyfications
rc('xtick', labelsize=8)
plt.gca().xaxis.set_major_formatter(mdates.DateFormatter('%Y-%m-%d'))
plt.gca().xaxis.set_major_locator(mdates.AutoDateLocator(minticks=6, maxticks=10))
plt.gca().xaxis.set_minor_locator(mdates.DayLocator())
plt.gcf().autofmt_xdate()
plt.gca().yaxis.set_major_locator(plt.MultipleLocator(1.0))
#plt.gca().yaxis.set_minor_locator(plt.MultipleLocator(0.1)
plt.gca().xaxis.grid(True,'minor')
#plt.gca().yaxis.grid(True,'minor')
plt.gca().xaxis.grid(True,'major', linewidth=1)
plt.gca().yaxis.grid(True,'major', linewidth=1)
plt.tight_layout()
if save:
plt.savefig(filename+'.png', dpi=200)
plt.show()
return numpy.exp(-residual*residual/2.0)
# Create data.
X = []
Y = []
for x in range(-5, 6, 1):
X.append(x)
Y.append(math.exp(-x*x/2.0))
# Add Gaussian noise to data.
Y = Y + numpy.random.normal(0.0, 0.1, len(Y))
import scipy.optimize as optimization
guess = [1.0, 2.0]
print optimization.curve_fit(func4curve_fit, X, Y, guess)
def func4Simplex(params, X, Y):
mu = params[0]
sigma = params[1]
chi2 = 0.0
for n in range(len(X)):
residual = Y[n] - func4curve_fit(X[n], mu, sigma)
chi2 = chi2 + residual*residual
return chi2
from scipy.optimize import fmin as simplex
print simplex(func4Simplex, guess, args=(X, Y))
def __call__(self, indiv):
from numpy import arange, average, arrays, zeros
from scipy.optimize import fmin as simplex
# from scipy.optimize import fmin_powell as simplex
from ...ce import leave_many_out, leave_one_out
assert len(self._mlclasses) - self._fixed == len(indiv.genes),\
"Individual is of incorrect size.\n"
self.nfun = 0
def callable_loo(x):
from math import sqrt, log as ln, fabs, exp
if self.nfun > EvalFitPairs.max_nfuncs: raise StopIteration
if fabs(x[0]) > EvalFitPairs.max_pow: raise ValueError
if fabs(x[1]) > EvalFitPairs.max_pow: raise ValueError
self.nfun += 1
self.fitter.alpha = x[0]
self.fitter.tcoef = 100*exp(x[1])
errors = leave_one_out(self.fitter)
npreds, nstr = errors.shape
prediction = errors[ arange(errors.shape[0]), arange(errors.shape[0]) ]
return sqrt(average(prediction*prediction))
def callable_lmo(x):
from math import sqrt, log as ln, fabs, exp
if self.nfun > EvalFitPairs.max_nfuncs: raise StopIteration
if fabs(x[0]) > EvalFitPairs.max_pow: raise ValueError
if fabs(x[1]) > EvalFitPairs.max_pow: raise ValueError
self.nfun += 1
self.fitter.alpha = x[0]
self.fitter.tcoef = 100*exp(x[1])
errors = leave_many_out(self.fitter, self._sets)
npred, prediction = 0, 0e0
for i in xrange(errors.shape[0]):
for j in xrange(errors.shape[1]):
if j not in self._sets[i]: continue
prediction += errors[i,j] * errors[i,j]
npred += 1
return sqrt(prediction / float(npred))
which_callable = callable_lmo
if len(self._sets) == 0: which_callable = callable_loo
# creates pair values.
pairs = [ self.pairs[0] ]
while pairs[-1] < self.pairs[1]:
pairs.append( pairs[-1] + self.pairs[2] )
if pairs[-1] != self.pairs[1]: pairs.append( self.pairs[1] )
x0 = array([1.1,1.0])
minvals = None
for p in pairs:
onoffs = zeros((len(self._mlclasses),), dtype=bool)
for i, index in enumerate(self._pairindex[:-1]):
nbpairs = min(i+p, self._pairindex[index+1])
onoffs[i:nbpairs] = True
onoffs[self._pairindex[-1]:self._fixed] = True
onoffs[self._fixed:] = indiv.genes
self.fitter.extinguish_cluster(onoffs, mask=True)
# x0, fopt, dummy, dummy, dummy, dummy = \
fopt, iter, = 0,0
try:
x0, fopt, iter, dummy, dummy = \
simplex(which_callable, x0, ftol=0.1, xtol=0.1, full_output=True,
disp=False, maxfun=20, maxiter=20)
except StopIteration:
fopt = 1e12; x0 = array([1.1,1.0])
except ValueError:
fopt = 1e12; x0 = array([1.1,1.0])
if minvals is None or minvals[0] > fopt: minvals = (fopt, iter)
return minvals[0]
# Define the objective function to be minimised by Simplex.
# params ... array holding the values of the fit parameters.
# X ... array holding x-positions of observed data.
# Y ... array holding y-values of observed data.
# Err ... array holding errors of observed data.
def func(params, X, Y, Err):
# extract current values of fit parameters from input array
a = params[0]
b = params[1]
c = params[2]
# compute chi-square
chi2 = 0.0
for n in range(len(X)):
x = X[n]
# The function y(x)=a+b*x+c*x^2 is a polynomial
# in this example.
y = a + b*x + c*x*x
chi2 = chi2 + (Y[n] - y)*(Y[n] - y)/(Err[n]*Err[n])
return chi2
xdata = [0.0,1.0,2.0,3.0,4.0,5.0]
ydata = [0.1,0.9,2.2,2.8,3.9,5.1]
sigma = [1.0,1.0,1.0,1.0,1.0,1.0]
#Initial guess.
x0 = [0.0, 0.0, 0.0]
# Apply downhill Simplex algorithm.
print simplex(func, x0, args=(xdata, ydata, sigma), full_output=0)
def solve_branch_cut(weights, values, max_w):
values = np.asarray(values)
best_solution = None
best_value = -np.inf
subproblems = deque([(np.asarray(weights).reshape(1, 3),
np.asarray(max_w).reshape(1, 1))])
nodes_opened = 0
while subproblems:
A_parent, b_parent = subproblems.popleft()
nodes_opened += 1
# if nodes_opened % 5 == 0:
# print(nodes_opened)
# Solve relaxed subproblem
res = simplex(-values, A_parent, b_parent)
if not res.success:
if res.status == 1:
print("Iteration limit reached... mby cycles?")
elif res.status == 2:
continue # Infeasible subproblem
else:
print(
"Subproblem appears to be unbounded... mby bad initial problem?"
)
# Filter relaxed solution for zeros
res.x[np.isclose(res.x, 0)] = 0
# Check if subspace's relaxed optimal value is above current best value
if -res.fun <= best_value:
continue # skip branching on this subproblem
# Find basic fractional elements
fracts = []
for i in range(len(res.x)):
if not res.x[i].is_integer():
fracts.append(i)
# Check if solution is in integer space
if not fracts:
best_solution = res.x.astype('int')
best_value = int(-res.fun)
continue
# Select a fractional element to branch from
branch_i = fracts[0]
# Create new constrains
down = np.floor(res.x[branch_i])
constrain_1 = np.zeros((1, len(values)))
constrain_1[0, branch_i] = 1
A_child_1 = np.concatenate([A_parent, constrain_1])
b_child_1 = np.concatenate([b_parent, np.array([[down]])])
subproblems.append((A_child_1, b_child_1))
up = np.ceil(res.x[branch_i])
constrain_2 = np.zeros((1, len(values)))
constrain_2[0, branch_i] = -1
A_child_2 = np.concatenate([A_parent, constrain_2])
b_child_2 = np.concatenate([b_parent, np.array([[-up]])])
subproblems.append((A_child_2, b_child_2))
return best_solution, best_value, nodes_opened
def read_atom_locations(path, file, n0, n1, n2, n3, n4, n5, ax, f1):
x, y, z = [], [], []
xi, yi, zi = [], [], []
label = []
f = open(path + file, "r")
data = f.readlines()
for line in data:
words = line.split()
label.append(words[0])
xi.append(words[1])
yi.append(words[2])
zi.append(words[3])
f.close()
xmi, ymi, zmi = [], [], []
xm, ym, zm = [], [], []
labelm = []
f = open(path + "methyl.xyz", "r")
data = f.readlines()
for line in data:
words = line.split()
labelm.append(words[0])
xmi.append(words[1])
ymi.append(words[2])
zmi.append(words[3])
f.close()
S0 = define_central_octa(xi, yi, zi, n0, n1, n2, n3, n4, n5)
#Rotate into conveniant orientation : (at_3-at_4 axis) = (001)
ux = float(S0[3][0]) - float(S0[4][0])
uy = float(S0[3][1]) - float(S0[4][1])
uz = float(S0[3][2]) - float(S0[4][2])
norm = np.sqrt(ux * ux + uy * uy + uz * uz)
ux = ux / norm
uy = uy / norm
uz = uz / norm
G = barycenter(S0)
xinit = [0, 0, 0]
opt = simplex(func3, xinit, args=(0, 0, 1, ux, uy, uz), full_output=0)
# Rotate & move the atoms of the residu without any terminating CH3 fragments
for i in range(len(xi)):
vect1 = [[float(xi[i]) - float(G[0])], [float(yi[i]) - float(G[1])],
[float(zi[i]) - float(G[2])]]
vect2 = move3(opt[0], opt[1], opt[2], vect1)
x.append(vect2[0])
y.append(vect2[1])
z.append(vect2[2])
for i in range(54):
ax.scatter(float(x[i]), float(y[i]), float(z[i]), c='blue', s=30)
f = open("./" + "monomer_0.xyz", "w")
for i in range(len(x)):
line = label[i] + " " + str(float(x[i])) + " " + str(float(
y[i])) + " " + str(float(z[i])) + "\n"
f1.write(line)
f.write(line)
f.close()
# Operate the same displacement for the terminating CH3 fragments
for i in range(len(xmi)):
vect1 = [[float(xmi[i]) - float(G[0])], [float(ymi[i]) - float(G[1])],
[float(zmi[i]) - float(G[2])]]
vect2 = move3(opt[0], opt[1], opt[2], vect1)
xm.append(vect2[0])
ym.append(vect2[1])
zm.append(vect2[2])
# Do the same for the central octahedra
S = []
S = define_central_octa(x, y, z, n0, n1, n2, n3, n4, n5)
return S, label, x, y, z, labelm, xm, ym, zm
def pload(C3_target, lus = lusrl):
return simplex(c3, 27000, args=(lus, C3_target))[0]
def findMin(self, x, y, numIters=100):
meanfunc = self.model.meanfunc
covfunc = self.model.covfunc
likfunc = self.model.likfunc
inffunc = self.model.inffunc
hypInArray = self._convert_to_array()
try:
opt = simplex(self._nlml,
hypInArray,
maxiter=numIters,
disp=False,
full_output=True)
optimalHyp = deepcopy(opt[0])
funcValue = opt[1]
warnFlag = opt[4]
if warnFlag == 1:
self.logger.warning(
"Maximum number of function evaluations made")
elif warnFlag == 2:
self.logger.warning("Maximum number of iterations exceeded.")
except:
self.errorCounter += 1
if not self.searchConfig:
raise Exception(
"Can not learn hyperparamters using Nelder-Mead.")
self.trailsCounter += 1
if self.searchConfig:
searchRange = self.searchConfig.meanRange + self.searchConfig.covRange + self.searchConfig.likRange
if not (self.searchConfig.num_restarts
or self.searchConfig.min_threshold):
raise Exception('Specify at least one of the stop conditions')
while True:
self.trailsCounter += 1 # increase counter
for i in range(hypInArray.shape[0]): # random init of hyp
hypInArray[i] = np.random.uniform(low=searchRange[i][0],
high=searchRange[i][1])
# value this time is better than optiaml min value
try:
thisopt = simplex(self._nlml,
hypInArray,
maxiter=numIters,
disp=False,
full_output=True)
if thisopt[1] < funcValue:
funcValue = thisopt[1]
optimalHyp = thisopt[0]
except:
self.errorCounter += 1
if self.searchConfig.num_restarts and self.errorCounter > old_div(
self.searchConfig.num_restarts, 2):
self.logger.warning(
"[Simplex] %d out of %d trails failed during optimization",
self.errorCounter, self.trailsCounter)
raise Exception(
"Over half of the trails failed for Nelder-Mead")
if self.searchConfig.num_restarts and self.trailsCounter > self.searchConfig.num_restarts - 1: # if exceed num_restarts
self.logger.warning(
"[Simplex] %d out of %d trails failed during optimization",
self.errorCounter, self.trailsCounter)
return optimalHyp, funcValue
if self.searchConfig.min_threshold and funcValue <= self.searchConfig.min_threshold: # reach provided mininal
self.logger.warning(
"[Simplex] %d out of %d trails failed during optimization",
self.errorCounter, self.trailsCounter)
return optimalHyp, funcValue
return optimalHyp, funcValue
from scipy.optimize import fmin as simplex def func(params, X, Y): # extract current values of fit parameters from input array a = params[0] b = params[1] c = params[2] # compute chi-square chi2 = 0.0 for n in range(len(X)): x = X[n] # The function y(x) is a polynomial in this example. y = a + b*x + c*x*x chi2 = chi2 + (Y[n] - y)*(Y[n] - y) return chi2 xdata = [0.0,1.0,2.0,3.0,4.0,5.0] ydata = [0.1,0.9,2.2,2.8,3.9,5.1] sigma = [1.0,1.0,1.0,1.0,1.0,1.0] #Initial guess. x0 = [0.0, 0.0, 0.0] # Apply downhill Simplex algorithm. print simplex(func, x0, args=(xdata, ydata), xtol=0.0001, ftol=0.0001, maxiter=None, full_output=0)
#######################################################################
# Branch & Cut Solution #
#######################################################################
best_solution = None
opt_value = -np.inf
subproblems = deque([(A, b)])
nodes_opened = 0
while subproblems:
A_parent, b_parent = subproblems.popleft()
nodes_opened += 1
# Solve relaxed subproblem
res = simplex(-profit, A_parent, b_parent)
if not res.success:
if res.status == 1:
print("Iteration limit reached... mby cycles?")
elif res.status == 2:
continue # Infeasible subproblem
else:
print("Subproblem appears to be unbounded... mby bad initial problem?")
# Filter relaxed solution for zeros
res.x[np.isclose(res.x, 0)] = 0
# Check if subspace's relaxed optimal value is above current best value
if -res.fun <= opt_value:
continue # skip branching on this subproblem
# Find basic fractional elements