def fmin_minuit(func, x0, names=None, verbose=False):
inits = dict()
if verbose:
print_level = 2
else:
print_level = 0
if names is None:
names = map(lambda x: 'param' + str(x), range(len(x0)))
else:
assert(len(x0) == len(names))
for n, x in zip(names, x0):
inits[n] = x
# TODO use a method to set this correctly
inits['error_' + n] = 1
m = Minuit(Min_Func(func, names), print_level=print_level, errordef=1, **inits)
a, b = m.migrad()
return OptimizeResult(
x=m.values,
fun=a['fval'],
edm=a['edm'],
nfev=a['nfcn'],
is_valid=a['is_valid'],
has_valid_parameters=a['has_valid_parameters'],
)
def _fit_amplitude_minuit(counts, background, model, flux):
"""Fit amplitude using minuit.
Parameters
----------
counts : `~numpy.ndarray`
Slice of count map.
background : `~numpy.ndarray`
Slice of background map.
model : `~numpy.ndarray`
Model template to fit.
flux : float
Starting value for the fit.
Returns
-------
amplitude : float
Fitted flux amplitude.
niter : int
Number of function evaluations needed for the fit.
"""
from iminuit import Minuit
def stat(x):
return f_cash(x, counts, background, model)
minuit = Minuit(f_cash, x=flux, pedantic=False, print_level=0)
minuit.migrad()
return minuit.values['x'], minuit.ncalls
def optimise_minuit(target_time):
from iminuit import Minuit
def minimizer(on1, on2, on3, on4, on5, on6, on7, on8, on9, on10, on11, on12, delta1, delta2, delta3, delta4, delta5, delta6, delta7, delta8, delta9, delta10, delta11, delta12):
ontimes = np.array([on1, on2, on3, on4, on5, on6, on7, on8, on9, on10, on11, on12])
offtimes = np.array([on1 + delta1, on2 + delta2, on3 + delta3, on4 + delta4, on5 + delta5, on6 + delta6, on7 + delta7, on8 + delta8, on9 + delta9, on10 + delta10, on11 + delta11, on12 + delta12])
#currents = [c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12]
currents = [243.]*12
flyer.prop.overwriteCoils(ontimes.ctypes.data_as(c_double_p), offtimes.ctypes.data_as(c_double_p))
flyer.preparePropagation(currents)
flyer.propagate(0)
pos = flyer.finalPositions[0]
vel = flyer.finalVelocities[0]
ind = np.where((pos[:, 2] > 268.) & (vel[:, 2] < 1.1*target_speed) & (vel[:, 2] > 0.9*target_speed))[0] # all particles that reach the end
print 'good particles:', ind.shape[0]
return -1.*ind.shape[0]
initvals = {}
for i in np.arange(12) + 1:
initvals['on' + str(i)] = flyer.ontimes[i - 1]
initvals['limit_on' + str(i)] = (0, 600)
initvals['error_on' + str(i)] = 50
initvals['delta' + str(i)] = flyer.offtimes[i - 1] - flyer.ontimes[i - 1]
initvals['limit_delta' + str(i)] = (0, 85)
initvals['error_delta' + str(i)] = 5
#initvals['c' + str(i)] = 243.
#initvals['limit_c' + str(i)] = (0, 300)
#initvals['error_c' + str(i)] = 50
m = Minuit(minimizer, **initvals)
m.set_strategy(2)
m.migrad(ncall=20)
print m.values
def test_minos_single_fixed_raising():
m = Minuit(func3, pedantic=False, print_level=0, fix_x=True)
m.migrad()
with warnings.catch_warnings():
warnings.simplefilter('error')
ret = m.minos('x')
def test_minos_all():
m = Minuit(func3, pedantic=False, print_level=0)
m.migrad()
m.minos()
assert_almost_equal(m.merrors[('x', -1.0)], -sqrt(5))
assert_almost_equal(m.merrors[('x', 1.0)], sqrt(5))
assert_almost_equal(m.merrors[('y', 1.0)], 1.)
def test_minos_single_fixed_result():
m = Minuit(func3, pedantic=False, print_level=0, fix_x=True)
m.migrad()
with warnings.catch_warnings():
warnings.simplefilter('ignore')
ret = m.minos('x')
assert_equal(ret, None)
def test_reverse_limit():
# issue 94
def f(x, y, z):
return (x - 2) ** 2 + (y - 3) ** 2 + (z - 4) ** 2
m = Minuit(f, limit_x=(3., 2.), pedantic=False)
m.migrad()
def test_fix_param(self):
m = Minuit(func4,print_level=0)
m.migrad()
m.minos()
val = m.values
self.assertAlmostEqual(val['x'],2.)
self.assertAlmostEqual(val['y'],5.)
self.assertAlmostEqual(val['z'],7.)
err = m.errors#second derivative
# self.assertAlmostEqual(err['x'],5.)
# self.assertAlmostEqual(err['y'],10.)
# self.assertAlmostEqual(err['z'],4.)
#now fix z = 10
m = Minuit(func4,print_level=-1,y=10.,fix_y=True)
m.migrad()
val = m.values
self.assertAlmostEqual(val['x'],2.)
self.assertAlmostEqual(val['y'],10.)
self.assertAlmostEqual(val['z'],7.)
self.assertAlmostEqual(m.fval,10.+2.5)
free_param = m.list_of_vary_param()
fix_param = m.list_of_fixed_param()
self.assertIn('x', free_param)
self.assertNotIn('x', fix_param)
self.assertIn('y', fix_param)
self.assertNotIn('y', free_param)
self.assertNotIn('z', fix_param)
def functesthelper(self,f):
m = Minuit(f,print_level=0)
m.migrad()
val = m.values
self.assertAlmostEqual(val['x'],2.)
self.assertAlmostEqual(val['y'],5.)
self.assertAlmostEqual(m.fval,10.)
def test_rosenbrock():
random.seed(0.258)
m = Minuit(rosenbrock, x=0, y=0, pedantic=False, print_level=1)
m.tol = 1e-4
m.migrad()
assert_less(m.fval, 1e-6)
assert_almost_equal(m.values['x'], 1., places=3)
assert_almost_equal(m.values['y'], 1., places=3)
def fit_spectrum(f, m, w):
def chi2(a0):
return numpy.sum(numpy.power(f - a0 * m, 2) * w)
minuit = Minuit(chi2, a0=1.0, error_a0=1.0, print_level=-1, errordef=0.01)
minuit.migrad()
return minuit.values["a0"]
def test_extended_ulh(self):
eg = Extended(gaussian)
lh = UnbinnedLH(eg, self.data, extended=True, extended_bound=(-20, 20))
minuit = Minuit(lh, mean=4.5, sigma=1.5, N=19000.,
pedantic=False, print_level=0)
minuit.migrad()
assert_allclose(minuit.values['N'], 20000, atol=sqrt(20000.))
assert minuit.migrad_ok()
def test_printfmin_uninitialized():
# issue 85
def f(x):
return 2 + 3 * x
fitter = Minuit(f, pedantic=False)
with pytest.raises(RuntimeError):
fitter.print_fmin()
def test_rosenbrock():
random.seed(0.258)
m = Minuit(rosenbrock, x=0, y=0, pedantic=False, print_level=1)
m.tol = 1e-4
m.migrad()
assert_allclose(m.fval, 0, atol=1e-6)
assert_allclose(m.values['x'], 1., atol=1e-3)
assert_allclose(m.values['y'], 1., atol=1e-3)
def test_matyas():
random.seed(0.258)
m = Minuit(matyas, x=random.random(), y=random.random(),
pedantic=False, print_level=0)
m.migrad()
assert m.fval < 1e-26
assert_array_almost_equal(m.args, [0, 0], decimal=12)
def m():
m = Minuit(f1, x=0, y=0, pedantic=False, print_level=1)
m.tol = 1e-4
m.migrad()
assert_allclose(m.fval, 0, atol=1e-6)
assert_allclose(m.values['x'], 1, atol=1e-3)
assert_allclose(m.values['y'], 1, atol=1e-3)
return m
def test_extended_ulh_2(self):
eg = Extended(gaussian)
lh = UnbinnedLH(eg, self.data, extended=True)
minuit = Minuit(lh, mean=4.5, sigma=1.5, N=19000.,
pedantic=False, print_level=0)
minuit.migrad()
assert(minuit.migrad_ok())
assert_almost_equal(minuit.values['N'], 20000, delta=sqrt(20000.))
def test_reverse_limit():
# issue 94
def f(x, y, z):
return (x - 2) ** 2 + (y - 3) ** 2 + (z - 4) ** 2
m = Minuit(f, limit_x=(3., 2.), pedantic=False)
with pytest.raises(ValueError):
m.migrad()
def fit_spectrum(f,m,w,l): def chi2(a0,a1): return numpy.sum( numpy.power(f-(a0+a1*l)*m,2)*w ) minuit = Minuit(chi2,a0=1.,error_a0=1.,a1=0.001,error_a1=1.,print_level=-1, errordef=0.01) minuit.migrad() return minuit.values['a0'], minuit.values['a1']
def test_matyas_oneside():
'''One-side limit when the minimum is in the forbidden region'''
random.seed(0.258)
m = Minuit(matyas, x=2 + random.random(), y=random.random(),
limit_x=(1, None),
pedantic=False, print_level=0)
m.migrad()
assert_array_almost_equal(m.args, [1, 0.923], decimal=3)
def functesthelper(f):
m = Minuit(f, print_level=0, pedantic=False)
m.migrad()
val = m.values
assert_almost_equal(val['x'], 2.)
assert_almost_equal(val['y'], 5.)
assert_almost_equal(m.fval, 10.)
assert(m.matrix_accurate())
assert(m.migrad_ok())
def test_beale():
random.seed(0.258)
m = Minuit(beale, x=random.random(), y=0.5 * random.random(),
pedantic=False, print_level=0)
m.migrad()
assert_array_almost_equal(m.args, [3, 0.5], decimal=3)
assert m.fval < 1e-6
def test_matyas():
random.seed(0.258)
m = Minuit(matyas, x=random.random(), y=random.random(),
pedantic=False, print_level=0)
m.tol = 1e-4
m.migrad()
assert m.fval < 1e-26
assert_allclose(m.args, [0, 0], atol=1e-12)
def test_matyas_oneside():
"""One-sided limit when the minimum is in the forbidden region"""
random.seed(0.258)
m = Minuit(matyas, x=2 + random.random(), y=random.random(),
limit_x=(1, None),
pedantic=False, print_level=0)
m.tol = 1e-4
m.migrad()
assert_allclose(m.args, [1, 0.923], atol=1e-3)
def test_beale():
random.seed(0.258)
m = Minuit(beale, x=random.random(), y=0.5 * random.random(),
pedantic=False, print_level=0)
m.tol = 1e-4
m.migrad()
assert_allclose(m.fval, 0, atol=1e-6)
assert_allclose(m.args, [3, 0.5], atol=1e-3)
assert m.fval < 1e-6
def test_ackleys():
random.seed(0.258)
m = Minuit(ackleys, x=1.5 * random.random(), y=1.5 * random.random(),
error_x=1.7, error_y=1.7,
pedantic=False, print_level=0)
m.migrad()
assert m.fval < 1e-5
assert_array_almost_equal(m.args, [0, 0], decimal=3)
def _create_new_minuit_object(self, args):
# Now create the new minimizer
_contour_minuit = Minuit(self._function, **args)
_contour_minuit.tol = 100
return _contour_minuit
def test_chi2_fit():
"""Fit a curve to data."""
m = Minuit(chi2, s=2., error_A=0.1, errordef=0.01,
print_level=0, pedantic=False)
m.migrad()
output = [round(10 * m.values['A']), round(100 * m.values['s']),
round(100 * m.values['m'])]
expected = [round(10 * 64.375993), round(100 * 4.267970),
round(100 * 9.839172)]
assert_array_almost_equal(output, expected)
def functesthelper(f):
m = Minuit(f, print_level=0, pedantic=False)
m.migrad()
val = m.values
assert_allclose(val['x'], 2.)
assert_allclose(val['y'], 5.)
assert_allclose(m.fval, 10.)
assert m.matrix_accurate()
assert m.migrad_ok()
return m
def fit_power_lawab(x, y, ey, **kwargs):
'''
Use chisq regression to fit for y = b * x^a
Return two dictionaries: one for the values of a and b.
and the second for the errors.
'''
x2reg= Chi2Regression(powerlaw, x, y, ey)
m = Minuit(x2reg, print_level=0, a= -0.5, error_a= 0.1, b=10, error_b=1)
m.migrad()
m.hesse()
return m.values, m.errors
def SecondIteration(values):
ant1_pxb = values[0]
ant1_pyb = values[1]
ant1_pzb = values[2]
ant1_pxt = values[0]
ant1_pyt = values[1]
ant1_pzt = values[3]
ant2_pxb = values[4]
ant2_pyb = values[5]
ant2_pzb = values[6]
ant2_pxt = values[4]
ant2_pyt = values[5]
ant2_pzt = values[7]
ant3_pxb = values[8]
ant3_pyb = values[9]
ant3_pzb = values[10]
ant3_pxt = values[8]
ant3_pyt = values[9]
ant3_pzt = values[11]
ant4_pxb = values[12]
ant4_pyb = values[13]
ant4_pzb = values[14]
ant4_pxt = values[12]
ant4_pyt = values[13]
ant4_pzt = values[15]
cal_pz = values[16]
SPICE_x_guess = values[17]
SPICE_y_guess = values[18]
c0p = values[19]
c1p = values[20]
c8p = values[21]
c9p = values[22]
c16p = values[23]
c17p = values[24]
c24p = values[25]
c25p = values[26]
initial_step = 0.1 #m
m = Minuit( f2,\
ant1_xb=ant1_pxb,\
ant1_yb=ant1_pyb,\
ant1_zb=ant1_pzb,\
ant1_xt=ant1_pxt,\
ant1_yt=ant1_pyt,\
ant1_zt=ant1_pzt,\
ant2_xb=ant2_pxb,\
ant2_yb=ant2_pyb,\
ant2_zb=ant2_pzb,\
ant2_xt=ant2_pxt,\
ant2_yt=ant2_pyt,\
ant2_zt=ant2_pzt,\
ant3_xb=ant3_pxb,\
ant3_yb=ant3_pyb,\
ant3_zb=ant3_pzb,\
ant3_xt=ant3_pxt,\
ant3_yt=ant3_pyt,\
ant3_zt=ant3_pzt,\
ant4_xb=ant4_pxb,\
ant4_yb=ant4_pyb,\
ant4_zb=ant4_pzb,\
ant4_xt=ant4_pxt,\
ant4_yt=ant4_pyt,\
ant4_zt=ant4_pzt,\
cal_z = cal_pz,\
SPICE_x=SPICE_x_guess,\
SPICE_y=SPICE_y_guess,\
c0 = c0p,\
c1 = c1p,\
c8 = c8p,\
c9 = c9p,\
c16 = c16p,\
c17 = c17p,\
c24 = c24p,\
c25 = c25p,\
error_ant1_xb=initial_step,\
error_ant1_yb=initial_step,\
error_ant1_zb=initial_step,\
error_ant1_xt=initial_step,\
error_ant1_yt=initial_step,\
error_ant1_zt=initial_step,\
error_ant2_xb=initial_step,\
error_ant2_yb=initial_step,\
error_ant2_zb=initial_step,\
error_ant2_xt=initial_step,\
error_ant2_yt=initial_step,\
error_ant2_zt=initial_step,\
error_ant3_xb=initial_step,\
error_ant3_yb=initial_step,\
error_ant3_zb=initial_step,\
error_ant3_xt=initial_step,\
error_ant3_yt=initial_step,\
error_ant3_zt=initial_step,\
error_ant4_xb=initial_step,\
error_ant4_yb=initial_step,\
error_ant4_zb=initial_step,\
error_ant4_xt=initial_step,\
error_ant4_yt=initial_step,\
error_ant4_zt=initial_step,\
error_cal_z=initial_step,\
error_SPICE_x=initial_step,\
error_SPICE_y=initial_step,\
error_c0 = initial_step,\
error_c1 = initial_step,\
error_c8 = initial_step,\
error_c9 = initial_step,\
error_c16 = initial_step,\
error_c17 = initial_step,\
error_c24 = initial_step,\
error_c25 = initial_step,\
errordef = 1.0,\
limit_ant1_xb=(ant1_pxb-10,ant1_pxb+10),\
limit_ant1_yb=(ant1_pyb-10,ant1_pyb+10),\
limit_ant1_zb=(ant1_pzb-1,ant1_pzb+2),\
limit_ant1_xt=(ant1_pxt-10,ant1_pxt+10),\
limit_ant1_yt=(ant1_pyt-10,ant1_pyt+10),\
limit_ant1_zt=(ant1_pzt-1,ant1_pzt+2),\
limit_ant2_xb=(ant2_pxb-10,ant2_pxb+10),\
limit_ant2_yb=(ant2_pyb-10,ant2_pyb+10),\
limit_ant2_zb=(ant2_pzb-1,ant2_pzb+2),\
limit_ant2_xt=(ant2_pxt-10,ant2_pxt+10),\
limit_ant2_yt=(ant2_pyt-10,ant2_pyt+10),\
limit_ant2_zt=(ant2_pzt-1,ant2_pzt+2),\
limit_ant3_xb=(ant3_pxb-10,ant3_pxb+10),\
limit_ant3_yb=(ant3_pyb-10,ant3_pyb+10),\
limit_ant3_zb=(ant3_pzb-1,ant3_pzb+2),\
limit_ant3_xt=(ant3_pxt-10,ant3_pxt+10),\
limit_ant3_yt=(ant3_pyt-10,ant3_pyt+10),\
limit_ant3_zt=(ant3_pzt-1,ant3_pzt+2),\
limit_ant4_xb=(ant4_pxb-10,ant4_pxb+10),\
limit_ant4_yb=(ant4_pyb-10,ant4_pyb+10),\
limit_ant4_zb=(ant4_pzb-1,ant4_pzb+2),\
limit_ant4_xt=(ant4_pxt-10,ant4_pxt+10),\
limit_ant4_yt=(ant4_pyt-10,ant4_pyt+10),\
limit_ant4_zt=(ant4_pzt-1,ant4_pzt+2),\
limit_SPICE_x=(SPICE_x_guess-5.0,SPICE_x_guess+5.0),\
limit_SPICE_y=(SPICE_y_guess-5.0,SPICE_y_guess+5.0),\
limit_c0 = (c0p-15.0,c0p+15.0),\
limit_c1 = (c1p-15.0,c1p+15.0),\
limit_c8 = (c8p-15.0,c8p+15.0),\
limit_c9 = (c9p-15.0,c9p+15.0),\
limit_c16 = (c16p-15.0,c16p+15.0),\
limit_c17 = (c17p-15.0,c17p+15.0),\
limit_c24 = (c24p-15.0,c24p+15.0),\
limit_c25 = (c25p-15.0,c25p+15.0),\
limit_cal_z = (-175.0,-170.0)
)
result = m.migrad()
print(result)
print(m.values)
#m.hesse()
#m.minos()
#print(m.get_fmin())
print(result)
np.save('best_ARA_values.npy',m.values)
return(m.values)
from ROOT import *
from iminuit import Minuit
import numpy as np
from math import *
def flogl(tau):
val = 0
# Definisco logl
return val
#Main
h = TH1D("h", "", 20, 0, 10)
for line in open("exp.dat"):
h.Fill(float(line))
m = Minuit(flogl, tau=2, norm=1000)
# Istruisco fir di logl
# m.migrad()
# tau = m.values[0]
h.Draw("E")
# Disegno del fit
f = TF1("f", "[0]*1/[1]*exp(-x/[1])", 0, 20)
gApplication.Run(True)
def fit_muon(self, centre_x, centre_y, radius, pixel_x, pixel_y, image):
"""
Parameters
----------
centre_x: float
Centre of muon ring in the field of view from circle fitting
centre_y: float
Centre of muon ring in the field of view from circle fitting
radius: float
Radius of muon ring from circle fitting
pixel_x: ndarray
X position of pixels in image from circle fitting
pixel_y: ndarray
Y position of pixel in image from circle fitting
image: ndarray
Amplitude of image pixels
Returns
-------
MuonIntensityParameters
"""
# First store these parameters in the class so we can use them in minimisation
self.image = image
self.pixel_x = pixel_x.to(u.deg)
self.pixel_y = pixel_y.to(u.deg)
self.unit = pixel_x.unit
radius.to(u.deg)
centre_x.to(u.deg)
centre_y.to(u.deg)
# Return interesting stuff
fitoutput = MuonIntensityParameter()
init_params = {}
init_errs = {}
init_constrain = {}
init_params['impact_parameter'] = 4.
init_params['phi'] = 0.
init_params['radius'] = radius.value
init_params['centre_x'] = centre_x.value
init_params['centre_y'] = centre_y.value
init_params['ring_width'] = 0.1
init_params['optical_efficiency_muon'] = 0.1
init_errs['error_impact_parameter'] = 2.
init_constrain['limit_impact_parameter'] = (0., 25.)
init_errs['error_phi'] = 0.1
init_errs['error_ring_width'] = 0.001 * radius.value
init_errs['error_optical_efficiency_muon'] = 0.05
init_constrain['limit_phi'] = (-np.pi, np.pi)
init_constrain['fix_radius'] = True
init_constrain['fix_centre_x'] = True
init_constrain['fix_centre_y'] = True
init_constrain['limit_ring_width'] = (0., 1.)
init_constrain['limit_optical_efficiency_muon'] = (0., 1.)
print("radius =", radius, " pre migrad")
parameter_names = init_params.keys()
# Create Minuit object with first guesses at parameters
# strip away the units as Minuit doesnt like them
minuit = Minuit(
self.likelihood,
#forced_parameters=parameter_names,
**init_params,
**init_errs,
**init_constrain,
errordef=1.,
print_level=1
#pedantic=False
)
# Perform minimisation
minuit.migrad()
# Get fitted values
fit_params = minuit.values
fitoutput.impact_parameter = fit_params['impact_parameter'] * u.m
#fitoutput.phi = fit_params['phi']*u.rad
fitoutput.impact_parameter_pos_x = fit_params[
'impact_parameter'] * np.cos(fit_params['phi'] * u.rad) * u.m
fitoutput.impact_parameter_pos_y = fit_params[
'impact_parameter'] * np.sin(fit_params['phi'] * u.rad) * u.m
fitoutput.ring_width = fit_params['ring_width'] * self.unit
fitoutput.optical_efficiency_muon = fit_params[
'optical_efficiency_muon']
fitoutput.prediction = self.prediction
return fitoutput
def Chi2_Gauss(x_data, N, mu, sigma, N_bins, plot=False, title=False):
"""
IMPORTANT: It is not possible to give estimations for the Chi2 fit.
INPUT:
x = x-data, array-like
N = number of experiments:
mu = mean
sigma = uncertainty of y-data, integer
plots = whether to plot (True or False)
title = title of plot in string: ex. 'title'
"""
def Gauss(x, N, mu, sigma):
return N * binwidth * stats.norm.pdf(x, mu, sigma)
counts, bin_edges = np.histogram(x_data, bins=N_bins)
bin_centers = 0.5 * (bin_edges[1:] + bin_edges[:-1])
bin_width = bin_edges[1] - bin_edges[0]
s_counts = np.sqrt(counts)
x = bin_centers[counts > 0]
y = counts[counts > 0]
sy = s_counts[counts > 0]
chi2_gaussian = Chi2Regression(Gauss, x, y, sy)
minuit_gaussian = Minuit(chi2_gaussian,
pedantic=False,
N=N_bins,
mu=mu,
sigma=sigma)
minuit_gaussian.migrad()
print(minuit_gaussian.values['N'])
Chi2 = minuit_gaussian.fval
Ndof = len(x) - 3
p = stats.chi2.sf(Chi2, Ndof)
xmin = mu - 4 * sigma
xmax = mu + 4 * sigma
xaxis = np.linspace(xmin, xmax, 1000)
if plot:
fig, ax = plt.subplots(figsize=(12, 8))
ax.hist(x_data, bins=N_bins, color='r', alpha=0.3)
ax.hist(x_data, bins=N_bins, histtype='step', color='r')
ax.errorbar(x,
y,
yerr=sy,
fmt='ko',
ecolor='k',
elinewidth=1,
capsize=1,
capthick=1,
label='Measurements')
ax.plot(xaxis,
Gauss(xaxis, *minuit_gaussian.args),
color='k',
linewidth=2)
d = {
'Mean': [minuit_gaussian.args[1], minuit_gaussian.args[2]],
'N': minuit_gaussian.args[0],
'Chi2': Chi2,
'Ndof': Ndof,
'Prob': p,
}
text = nice_string_output(d, extra_spacing=2, decimals=3)
add_text_to_ax(0.02, 0.95, text, ax, fontsize=18)
fig.suptitle(title, fontsize=25)
"""
OUTPUT:
Chi2 = Chi2 value
p = Probabillity of this fit or worse
minuit_fit.args = fitted value of Chi2
Plot of the function, along with the Chi2 fit
"""
return mean, sigma, Chi2, p
def linearFitFunction(x, a, b):
return a * x + b
for data in dataListDf:
#We want to find the best fit using rms, since we don't know the errors (yet)
#This is equvialent to using χ² with σᵢ= 1 ∀i.
np.ones_like(data.values[:, 0])
lsLinearTimeReg = Chi2Regression(linearFitFunction, data.values[:, 0],
data.values[:, 1],
np.ones_like(data.values[:, 0]))
a_start = 7.0
miniutFit = Minuit(lsLinearTimeReg, pedantic=False, a=a_start, b=0)
miniutFit.migrad()
ls_a = miniutFit.args[0]
ls_b = miniutFit.args[1]
fittedLinear = partial(linearFitFunction, a=ls_a, b=ls_b)
residuals = list(map((lambda x: fittedLinear(x[0]) - x[1]), data.values))
y, x_edges = np.histogram(residuals, bins=10)
x_center = x_edges[:-1] + (x_edges[1] - x_edges[0]) / 2
plt.plot(x_center, y)
plt.show()
#Notice it has no offset.
#FIXME: Trying with offset
def linearFitFunction(x, a, b):
return a * x + b
#We want to find the best fit using rms, since we don't know the errors (yet)
#This is equvialent to using χ² with σᵢ= 1 ∀i.
np.ones_like(data.values[:, 0])
lsLinearTimeReg = Chi2Regression(linearFitFunction, data.values[:, 0],
data.values[:, 1],
np.ones_like(data.values[:, 0]))
a_start = 7.0
miniutFit = Minuit(lsLinearTimeReg, pedantic=False, a=a_start, b=0)
miniutFit.migrad()
ls_a = miniutFit.args[0]
ls_b = miniutFit.args[1]
fittedLinear = partial(linearFitFunction, a=ls_a, b=ls_b)
residuals = list(map((lambda x: fittedLinear(x[0]) - x[1]), dataMatrix))
ndfData = np.transpose([range(0, len(residuals)), residuals])
ndf = pd.DataFrame(data=ndfData, columns=["x-val", "Residuals"])
#newDataPlot = sns.relplot(x = "x-val",y = "Residuals",data = ndf,kind = "scatter")
#plt.show()
def test_NormalConstraint_2():
lsq1 = NormalConstraint(("a", "b"), (1, 2), (2, 2))
lsq2 = lsq1 + NormalConstraint("b", 2, 0.1) + NormalConstraint("a", 1, 0.01)
sa = 0.1
sb = 0.02
rho = 0.5
cov = ((sa ** 2, rho * sa * sb), (rho * sa * sb, sb ** 2))
lsq3 = lsq1 + NormalConstraint(("a", "b"), (1, 2), cov)
assert lsq1.func_code.co_varnames == ("a", "b")
assert lsq2.func_code.co_varnames == ("a", "b")
assert lsq3.func_code.co_varnames == ("a", "b")
m = Minuit(lsq1, 0, 0)
m.migrad()
assert_allclose(m.values, (1, 2), atol=1e-3)
assert_allclose(m.errors, (2, 2), rtol=1e-3)
m = Minuit(lsq2, 0, 0)
m.migrad()
assert_allclose(m.values, (1, 2), atol=1e-3)
assert_allclose(m.errors, (0.01, 0.1), rtol=1e-2)
m = Minuit(lsq3, 0, 0)
m.migrad()
assert_allclose(m.values, (1, 2), atol=1e-3)
assert_allclose(m.errors, (sa, sb), rtol=1e-2)
assert_allclose(m.covariance, cov, rtol=1e-2)
# -*- coding: utf-8 -*-
from iminuit import Minuit
from matplotlib import pyplot as plt
from numpy.random import randn, seed
from probfit import BinnedChi2, Extended, gaussian
seed(0)
data = randn(1000) * 2 + 1
ext_gauss = Extended(gaussian)
ulh = BinnedChi2(ext_gauss, data)
m = Minuit(ulh, mean=0.0, sigma=0.5, N=800)
plt.figure(figsize=(8, 3))
plt.subplot(121)
ulh.draw(m)
plt.title("Before")
m.migrad() # fit
plt.subplot(122)
ulh.draw(m)
plt.title("After")
######################################################################
print "***** initializating *****"
# Initialize a Lilith object
lilithcalc = lilith.Lilith(verbose, timer)
# Read experimental data
lilithcalc.readexpinput(myexpinput)
# Initialize the fit; parameter starting values and limits
m = Minuit(getL,
CGa=1,
limit_CGa=(0, 3),
Cg=1,
limit_Cg=(0, 3),
BRinv=0.2,
limit_BRinv=(0, 0.9),
errordef=1,
error_CGa=0.1,
error_Cg=0.1,
error_BRinv=0.1)
print "\n***** performing model fit with iminuit *****"
# Minimization and error estimation
m.migrad()
m.minos()
print "\n***** fit summary *****"
print "\nbest-fit point:", m.values
# ax1 = P_DBACK.plot(kind='scatter', y ='gammaxpos', x='Back_Counts', label = 'phot',color='b')
# elif whatDetector == 'Difference':
# ax1 = P_DDIFF.plot(kind='scatter', y ='gammaxpos', x='Difference_Counts', label = 'phot',color='b')
# elif whatDetector == 'Aug':
# ax1 = P_DAUG.plot(kind='scatter', y ='gammaxpos', x='Augmented_Difference_Counts', label = 'phot',color='b')
P_DDIFF = P_DDIFF.dropna()
doiListPhot = P_DDIFF.gammaxpos.tolist()
differenceCountsPhot = P_DDIFF.Difference_Counts.tolist()
DATA_DIFFERENCE = DATA_DIFFERENCE.dropna()
doiList = DATA_DIFFERENCE.gammaxpos.tolist()
differenceCounts = DATA_DIFFERENCE.Difference_Counts.tolist()
m = Minuit(LeastSquares(differenceCountsPhot, doiListPhot, 10.0, Line),
m=-500,
b=3000)
m.migrad()
m.hesse()
# print(m.values)
# x = range(int(min(differenceCounts)), int(max(differenceCounts)))
# y = [Line(k, *m.values[0:2]) for k in x]
# ax1.plot(x, y, color = 'k')
# C = pd.DataFrame(eid_c)
# if not C.empty:
# C.columns = ['EventID']
# C_DFRONT = pd.merge(C,DATA_FRONT, on='EventID')
# C_DBACK = pd.merge(C,DATA_BACK, on='EventID')
# C_DDIFF = pd.merge(C,DATA_DIFFERENCE, on='EventID')
# C_DDIFF = pd.merge(C,DATA_DIFFERENCE, on='EventID')
# C_DAUG = pd.merge(C,DATA_AUG, on='EventID')
def test_draw_ulh_with_minuit():
np.random.seed(0)
data = np.random.randn(1000)
ulh = UnbinnedLH(gaussian, data)
minuit = Minuit(ulh, mean=0, sigma=1)
ulh.draw(minuit)
def fitPhysicalModel(self, frame, tabs, args, direction, lo, hi, offset):
# initial parameter guesses
loGuess = lo
hiGuess = hi
t0Guess = offset
DGuess = 1.7
LGuess = 1020.
dthetaGuess = 4.66
# initialize model prediction
global prediction
prediction = numpy.zeros_like(frame.samples)
# define chi-square function to use
def chiSquare(t0, lo, hi, D, L, dtheta):
global prediction
prediction = physicalModel(t0,
direction,
lo,
hi,
tabs,
D,
L,
dtheta,
nsamples=args.nsamples,
adcTick=args.adc_tick)
residuals = frame.samples - prediction
return numpy.dot(residuals, residuals)
# initialize fitter
print_level = 1 if args.verbose else 0
engine = Minuit(chiSquare,
errordef=1.0,
print_level=print_level,
t0=t0Guess,
error_t0=1.,
lo=loGuess,
error_lo=1.,
hi=hiGuess,
error_hi=1.,
D=DGuess,
error_D=0.1,
fix_D=False,
L=LGuess,
error_L=10.,
fix_L=True,
dtheta=dthetaGuess,
error_dtheta=0.5,
fix_dtheta=False)
engine.tol = 10.
# do the fit
minimum = engine.migrad()
if not minimum[0]['has_valid_parameters']:
raise RuntimeError('Fit failed!')
# calculate the best fit model
chiSquare(*engine.args)
# return best-fit parameter values and best-fit model prediction
return engine.args, prediction
def test_matyas():
m = Minuit(matyas, x=0.5, y=0.5, pedantic=False)
m.tol = 1e-4
m.migrad()
assert_allclose(m.fval, 0, atol=1e-14)
assert_allclose(m.args, [0, 0], atol=1e-14)
def FirstIteration():
print('done')
#SPICE_delays = np.load('all_SPICE_delays_int.npy',allow_pickle=True)
#SPICE_depths = np.load('all_SPICE_depths_int.npy',allow_pickle=True)
#print('SPICE is', SPICE_delays,SPICE_depths)
ant2_pxb = 19.79
ant2_pyb = 64.73
ant2_pzb = -195.31
ant2_pxt = 19.79
ant2_pyt = 64.73
ant2_pzt = -165.46
ant1_pxb = 44.89
ant1_pyb = 49.59
ant1_pzb = -194.52
ant1_pxt = 44.89
ant1_pyt = 49.59
ant1_pzt = -164.67
ant3_pxb = 27.06
ant3_pyb = 21.85
ant3_pzb = -191.28
ant3_pxt = 27.06
ant3_pyt = 21.85
ant3_pzt = -161.34
ant4_pxb = 5.27
ant4_pyb = 38.95
ant4_pzb = -177.72
ant4_pxt = 5.27
ant4_pyt = 38.95
ant4_pzt = -145.01
cal_pz = -171.278558
SPICE_x_guess = +3072.295822
SPICE_y_guess = +2861.7688200
c0p = +138.485012
c1p = +17.547130
c8p = +133.911865
c9p = +18.789163
c16p = +131.291872
c17p = +13.460643
c24p = +132.996322
c25p = +16.938025
rvals = np.linspace(4100.0,4190.0,90)
zs_vals = np.linspace(-1450,-1050,20)
zd_vals = np.linspace(-200.0,-140.0,120)
initial_step = 0.1 #m
print('trying minimization now')
#-12 ft on pulser locations relative to antennas to account for additional mast elevation.
m = Minuit( f1,\
ant1_xb=ant1_pxb,\
ant1_yb=ant1_pyb,\
ant1_zb=ant1_pzb,\
ant1_zt=ant1_pzt,\
ant2_xb=ant2_pxb,\
ant2_yb=ant2_pyb,\
ant2_zb=ant2_pzb,\
ant2_zt=ant2_pzt,\
ant3_xb=ant3_pxb,\
ant3_yb=ant3_pyb,\
ant3_zb=ant3_pzb,\
ant3_zt=ant3_pzt,\
ant4_xb=ant4_pxb,\
ant4_yb=ant4_pyb,\
ant4_zb=ant4_pzb,\
ant4_zt=ant4_pzt,\
cal_z = cal_pz,\
SPICE_x=SPICE_x_guess,\
SPICE_y=SPICE_y_guess,\
c0 = c0p,\
c1 = c1p,\
c8 = c8p,\
c9 = c9p,\
c16 = c16p,\
c17 = c17p,\
c24 = c24p,\
c25 = c25p,\
error_ant1_xb=initial_step,\
error_ant1_yb=initial_step,\
error_ant1_zb=initial_step,\
error_ant1_zt=initial_step,\
error_ant2_xb=initial_step,\
error_ant2_yb=initial_step,\
error_ant2_zb=initial_step,\
error_ant2_zt=initial_step,\
error_ant3_xb=initial_step,\
error_ant3_yb=initial_step,\
error_ant3_zb=initial_step,\
error_ant3_zt=initial_step,\
error_ant4_xb=initial_step,\
error_ant4_yb=initial_step,\
error_ant4_zb=initial_step,\
error_ant4_zt=initial_step,\
error_cal_z=initial_step,\
error_SPICE_x=initial_step,\
error_SPICE_y=initial_step,\
error_c0 = initial_step,\
error_c1 = initial_step,\
error_c8 = initial_step,\
error_c9 = initial_step,\
error_c16 = initial_step,\
error_c17 = initial_step,\
error_c24 = initial_step,\
error_c25 = initial_step,\
errordef = 1.0,\
limit_ant1_xb=(ant1_pxb-10,ant1_pxb+10),\
limit_ant1_yb=(ant1_pyb-10,ant1_pyb+10),\
limit_ant1_zb=(ant1_pzb-1,ant1_pzb+2),\
limit_ant1_zt=(ant1_pzt-1,ant1_pzt+2),\
limit_ant2_xb=(ant2_pxb-10,ant2_pxb+10),\
limit_ant2_yb=(ant2_pyb-10,ant2_pyb+10),\
limit_ant2_zb=(ant2_pzb-1,ant2_pzb+2),\
limit_ant2_zt=(ant2_pzt-1,ant2_pzt+2),\
limit_ant3_xb=(ant3_pxb-10,ant3_pxb+10),\
limit_ant3_yb=(ant3_pyb-10,ant3_pyb+10),\
limit_ant3_zb=(ant3_pzb-1,ant3_pzb+2),\
limit_ant3_zt=(ant3_pzt-1,ant3_pzt+2),\
limit_ant4_xb=(ant4_pxb-10,ant4_pxb+10),\
limit_ant4_yb=(ant4_pyb-10,ant4_pyb+10),\
limit_ant4_zb=(ant4_pzb-1,ant4_pzb+2),\
limit_ant4_zt=(ant4_pzt-1,ant4_pzt+2),\
limit_SPICE_x=(SPICE_x_guess-5.0,SPICE_x_guess+5.0),\
limit_SPICE_y=(SPICE_y_guess-5.0,SPICE_y_guess+5.0),\
limit_c0 = (c0p-15.0,c0p+15.0),\
limit_c1 = (c1p-15.0,c1p+15.0),\
limit_c8 = (c8p-15.0,c8p+15.0),\
limit_c9 = (c9p-15.0,c9p+15.0),\
limit_c16 = (c16p-15.0,c16p+15.0),\
limit_c17 = (c17p-15.0,c17p+15.0),\
limit_c24 = (c24p-15.0,c24p+15.0),\
limit_c25 = (c25p-15.0,c25p+15.0),\
limit_cal_z = (-175.0,-170.0)
)
result = m.migrad()
values = m.values
print(result)
print(m.values)
#m.hesse()
#m.minos()
#print(m.get_fmin())
print(result)
#print(m.values['ant1_xb'])
print(m.values[0])
np.save('first_iteration.npy',m.values)
return(values)
from iminuit import Minuit
def f(x, y, z):
return (x - 1) ** 2 + (y - x) ** 2 + (z - 2) ** 2
m = Minuit(f, print_level=0, pedantic=False)
m.migrad()
m.draw_mncontour('x', 'y')
def LLwrapper(params):
"""Need this for scipy.optimize. There might be a better way of doing it."""
NLL = LogLikelihood(gauss, s)
return NLL(params[0], params[1])
def gauss(x, mu, sigma):
return 1. / (np.sqrt(2 * np.pi * sigma**2)) * np.exp(-(x - mu)**2 /
(2 * sigma**2))
NLL = LogLikelihood(gauss, time_diff.values)
m = Minuit(NLL,
mu=-14.,
sigma=1.,
limit_mu=(-16., -10.),
limit_sigma=(0.05, 2.),
print_level=1,
errordef=0.5)
result = m.migrad() # hesse called at the end of migrad
print m.values
print m.errors
max_time = -10.
min_time = -20.
nbins = 50
width = float(max_time - min_time) / nbins
fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(6, 6))
time_diff.plot(kind='hist', bins=np.arange(min_time, max_time, width), ax=axes)
axes.set_xlabel("Time difference [ns]")
axes.set_ylabel("Entries / (%0.2f ns)" % width)
# -*- coding: utf-8 -*- import numpy as np from iminuit import Minuit from probfit import AddPdf, BinnedLH, Extended, gen_toy from probfit.pdf import HistogramPdf bound = (0, 10) np.random.seed(0) bkg = gen_toy(lambda x: x**2, 100000, bound=bound) # a parabola background sig = np.random.randn(50000) + 5 # a Gaussian signal data = np.concatenate([sig, bkg]) # fill histograms with large statistics hsig, be = np.histogram(sig, bins=40, range=bound) hbkg, be = np.histogram(bkg, bins=be, range=bound) # randomize data data = np.random.permutation(data) fitdata = data[:1000] psig = HistogramPdf(hsig, be) pbkg = HistogramPdf(hbkg, be) epsig = Extended(psig, extname="N1") epbkg = Extended(pbkg, extname="N2") pdf = AddPdf(epbkg, epsig) blh = BinnedLH(pdf, fitdata, bins=40, bound=bound, extended=True) m = Minuit(blh, N1=330, N2=670, error_N1=20, error_N2=30) # m.migrad() blh.draw(m, parts=True)
def minimise(self, params, step, limits, minimiser_name="minuit"):
"""
Parameters
----------
params
step
limits
minimiser_name
Returns
-------
"""
if minimiser_name == "minuit":
min = Minuit(self.get_likelihood,
print_level=1,
source_x=params[0],
error_source_x=step[0],
limit_source_x=limits[0],
source_y=params[1],
error_source_y=step[1],
limit_source_y=limits[1],
core_x=params[2],
error_core_x=step[2],
limit_core_x=limits[2],
core_y=params[3],
error_core_y=step[3],
limit_core_y=limits[3],
energy=params[4],
error_energy=step[4],
limit_energy=limits[4],
x_max_scale=params[5], error_x_max_scale=step[5],
limit_x_max_scale=limits[5],
fix_x_max_scale=False,
errordef=1)
min.migrad()
min.tol *= 1000
min.set_strategy(0)
# Perform minimisation
fit_params = min.values
errors = min.errors
return (fit_params["source_x"], fit_params["source_y"], fit_params["core_x"],
fit_params["core_y"], fit_params["energy"], fit_params[
"x_max_scale"]),\
(errors["source_x"], errors["source_y"], errors["core_x"],
errors["core_x"], errors["energy"], errors["x_max_scale"])
elif minimiser_name in ("lm", "trf", "dogleg"):
self.array_return = True
limits = np.array(limits)
min = least_squares(self.get_likelihood_min, params,
method=minimiser_name,
x_scale=step,
xtol=1e-10,
ftol=1e-10
)
return min.x, (0, 0, 0, 0, 0, 0)
else:
min = minimize(self.get_likelihood_min, params,
method=minimiser_name,
bounds=limits
)
return min.x, (0, 0, 0, 0, 0, 0)
# initilize model
model = Quarks(boundary_type=boundary_type)
chi_squared_threshold = 10.
N = 100 # number of trials
x = np.array([None])
# 2-step optimization process
# fit masses then fit full
for i in tqdm(range(N)):
# Step 1: fitting the masses only
params = model.generate_random_inputs(c_min=1., c_max=5.)
least_squares = LeastSquares(x, model.output_values[:, :6],
model.output_errors[:, :6],
model.get_output_masses)
optimizer = Minuit(least_squares, params, name=model.input_names)
optimizer.limits = model.input_limits
optimizer.fixed[:36] = True
try:
optimizer.migrad()
optimizer.hesse()
except ValueError:
pass
# Step 2: fitting all at once
# Only run if step 1 is error-free
if optimizer.fval:
params_2 = np.array(optimizer.values) # feed forward
y_2 = model.get_output_full(x, params_2)
chi_squared_2 = get_chi_squared(y_2, model.output_values,
model.output_errors)
dppLg = np.zeros_like(dppHg)
pedestalLg = np.zeros_like(pedestalHg)
if GUI:
fig, ax = plt.subplots()
for r in range(row):
for c in range(col):
channelHgPe = matrixHg[r, c, :]
channelLgADC = matrixLg[r, c, :]
x = channelHgPe[(channelHgPe > INF) & (channelHgPe < SUP)]
y = channelLgADC[(channelHgPe > INF) & (channelHgPe < SUP)]
lsq = LeastSquares(x, y, np.ones_like(y), line)
fit = Minuit(lsq, m=1, q=60)
fit.migrad()
fit.hesse()
dppLg[r, c] = fit.values["m"]
pedestalLg[r, c] = fit.values["q"]
print(
f"Channel {r} - {c} ADC/pe: {fit.values[0]:.2f} +/- {fit.errors[0]:.2f} Pedestal: {fit.values[1]:.2f} +/- {fit.errors[1]:.2f}"
)
if GUI:
xFit = np.arange(channelHgPe.min(), channelHgPe.max(), 0.1)
yFit = line(xFit, *fit.values)
par_b = np.random.multivariate_normal(fit.values,
fit.covariance,
size=100)
initialValues = (1.89278, 0.0291215, 0.273023, 8.96853, 353.824, 2.50639,
-5.92725, 0., 0.) ### NNPDF
#initialValues=(1.54728, 0.04678,0.1982, 26.49689,2727.9766, 3.00668, -23.54749, 0.,0.) ##MMHT14
#initialValues=(2.34665, 0.022735,0.27706, 24.8883, 1241.34, 2.66869, -23.7589, 0., 0.) ##CT14
#initialValues=(1.92659, 0.036548,0.218079, 17.9138, 926.078, 2.5431, -15.5469, 0. ,0.) ##PDF4LHC
initialErrors = (0.1, 0.01, 0.05, 0.1, 10., 0.05, 0.05, 0.1, 0.1)
searchLimits = ((1.4, 4.5), (0.001, 5.0), (0.0, 4.0), (8., 25.0), (0.0, 400),
(0., 5), None, None, None)
parametersToMinimize = (False, False, False, False, False, False, False, True,
True)
m = Minuit.from_array_func(chi_2,
initialValues,
error=initialErrors,
limit=searchLimits,
fix=parametersToMinimize,
errordef=1)
#m.get_param_states()
m.tol = 0.0001 * totalN * 10000 ### the last 0.0001 is to compensate MINUIT def
m.strategy = 1
SaveToLog("MINIMIZATION STARTED", str(m.params))
#%%
m.tol = 0.0001 * totalN * 10000 ### the last 0.0001 is to compensate MINUIT def
m.strategy = 1
m.migrad()
def fit_template(events,
pulse_width=(4, 5),
rise_time=12,
template=PULSE_TEMPLATE):
for event in events:
adc_samples = event.data.adc_samples.copy()
time = np.arange(adc_samples.shape[-1]) * 4
pulse_indices = event.data.pulse_mask
pulse_indices = np.argwhere(pulse_indices)
pulse_indices = [tuple(arr) for arr in pulse_indices]
amplitudes = np.zeros(adc_samples.shape) * np.nan
times = np.zeros(adc_samples.shape) * np.nan
plt.figure()
for pulse_index in pulse_indices:
left = pulse_index[-1] - int(pulse_width[0])
left = max(0, left)
right = pulse_index[-1] + int(pulse_width[1]) + 1
right = min(adc_samples.shape[-1] - 1, right)
y = adc_samples[pulse_index[0], left:right]
t = time[left:right]
where_baseline = np.arange(adc_samples.shape[-1])
where_baseline = (where_baseline < left) + \
(where_baseline >= right)
where_baseline = adc_samples[pulse_index[0]][where_baseline]
baseline_0 = np.mean(where_baseline)
baseline_std = np.std(where_baseline)
limit_baseline = (baseline_0 - baseline_std,
baseline_0 + baseline_std)
t_0 = time[pulse_index[-1]] - rise_time
limit_t = (t_0 - 2 * 4, t_0 + 2 * 4)
amplitude_0 = np.max(y)
limit_amplitude = (max(np.min(y), 0), amplitude_0 * 1.2)
chi2 = Chi2Regression(template, t, y)
m = Minuit(chi2,
t_0=t_0,
amplitude=amplitude_0,
limit_t=limit_t,
limit_amplitude=limit_amplitude,
baseline=baseline_0,
limit_baseline=limit_baseline,
print_level=0,
pedantic=False)
m.migrad()
adc_samples[pulse_index[0]] -= template(time, **m.values)
amplitudes[pulse_index] = m.values['amplitude']
times[pulse_index] = m.values['t']
event.data.reconstructed_amplitude = amplitudes
event.data.reconstructed_time = times
yield event
import random as rnd
from iminuit import Minuit
# Will overwrite the values passed from param.py
# if (sys.argv[1].isnumeric()): loc = int(sys.argv[1])
# if (sys.argv[2].isnumeric()): bin_min = int(sys.argv[2])
# if (sys.argv[3].isnumeric()): num_of_bins = int(sys.argv[3])
# Other variable assosiated with the run
rnd_seed = int( sys.argv[1])
directory = sys.argv[2]
job_id = os.environ.get('SLURM_JOB_ID')
# First run is assgned the default choice of profiles i.e., "rnd_seed = -1"
bins, Y_exp, V_inv = experimental_input_all_a(bin_min_all_a, num_of_bins_all_a)
chi = set_chi_all_a(Q, bins, Y_exp, V_inv, rnd_seed)
print("Minuit: " )
m = Minuit(chi, 0.11, 0.4)
m.migrad() # run optimiser
fit = np.append(np.array(m.values), rnd_seed )
out_name = directory + "fits_"+ job_id +".txt"
np.savetxt(out_name, fit , delimiter='\t') # export data
def minimize(fun,
x0,
args=(),
method=None,
jac=None,
hess=None,
hessp=None,
bounds=None,
constraints=None,
tol=None,
callback=None,
options=None):
"""An interface to MIGRAD using the ``scipy.optimize.minimize`` API.
For a general description of the arguments, see ``scipy.optimize.minimize``.
The ``method`` argument is ignored. The optimisation is always done using MIGRAD.
The `options` argument can be used to pass special settings to Minuit.
All are optional.
**Options:**
- *disp* (bool): Set to true to print convergence messages. Default: False.
- *maxfev* (int): Maximum allowed number of iterations. Default: 10000.
- *eps* (sequence): Initial step size to numerical compute derivative.
Minuit automatically refines this in subsequent iterations and is very
insensitive to the initial choice. Default: 1.
**Returns: OptimizeResult** (dict with attribute access)
- *x* (ndarray): Solution of optimization.
- *fun* (float): Value of objective function at minimum.
- *message* (str): Description of cause of termination.
- *hess_inv* (ndarray): Inverse of Hesse matrix at minimum (may not be exact).
- nfev (int): Number of function evaluations.
- njev (int): Number of jacobian evaluations.
- minuit (object): Minuit object internally used to do the minimization.
Use this to extract more information about the parameter errors.
"""
from scipy.optimize import OptimizeResult
if method not in {None, 'migrad'}:
warnings.warn("method argument is ignored")
if constraints is not None:
raise ValueError(
"Constraints are not supported by Minuit, only bounds")
if hess or hessp:
warnings.warn(
"hess and hessp arguments cannot be handled and are ignored")
if tol:
warnings.warn("tol argument has no effect on Minuit")
def wrapped(func, args, callback=None):
if callback is None:
return lambda x: func(x, *args)
else:
def f(x):
callback(x)
return func(x, *args)
return f
wrapped_fun = wrapped(fun, args, callback)
maxfev = 10000
error = None
kwargs = {'print_level': 0, 'errordef': 1}
if options:
if "disp" in options:
kwargs['print_level'] = 1
if "maxiter" in options:
warnings.warn("maxiter not supported, acts like maxfev instead")
maxfev = options["maxiter"]
if "maxfev" in options:
maxfev = options["maxfev"]
if "eps" in options:
error = options["eps"]
# prevent warnings from Minuit about missing initial step
if error is None:
error = np.ones_like(x0)
if bool(jac):
if jac is True:
raise ValueError("jac=True is not supported, only jac=callable")
assert hasattr(jac, "__call__")
wrapped_grad = wrapped(jac, args)
else:
wrapped_grad = None
m = Minuit.from_array_func(wrapped_fun,
x0,
error=error,
limit=bounds,
grad=wrapped_grad,
**kwargs)
m.migrad(ncall=maxfev)
message = "Optimization terminated successfully."
success = m.migrad_ok()
if not success:
message = "Optimization failed."
fmin = m.get_fmin()
if fmin.has_reached_call_limit:
message += " Call limit was reached."
if fmin.is_above_max_edm:
message += " Estimated distance to minimum too large."
return OptimizeResult(
x=m.np_values(),
success=success,
fun=m.fval,
hess_inv=m.np_covariance(),
message=message,
nfev=m.get_num_call_fcn(),
njev=m.get_num_call_grad(),
minuit=m,
)
def test_matyas_oneside():
"""One-sided limit when the minimum is in the forbidden region."""
m = Minuit(matyas, x=2 + 0.5, y=0.5, limit_x=(1, None), pedantic=False)
m.tol = 1e-4
m.migrad()
assert_allclose(m.args, [1, 0.923], atol=1e-3)
m1,m2 = 100,200
############# FIT num. 1 ##########################<3
print('Fit number 1:\nExponential')
#background pdf #1: exponential, copying formula from the question
def B_1(x,alpha):
pdf = alpha*np.exp(-alpha*x)/(np.exp(-alpha*m1)-np.exp(-alpha*m2))
return pdf
#define the NLL corresponding to B_1
def NLL_1(S,B,alpha):
temp = np.log(S*S_pdf(mass)+B*B_1(mass,alpha))
return S + B -temp.sum()
#start to fit
m_fit_1 = Minuit(NLL_1,S=30.,B = 170., alpha = 1., print_level = 1,
errordef=0.5,error_S=1.0,error_B=1.0,error_alpha = 1.0)
m_fit_1.migrad()
m_fit_1.minos()
m_fit_1.print_param()
fittedB1 = m_fit_1.values['B']
fittedS1 = m_fit_1.values['S']
fitteda = m_fit_1.values['alpha']
####################################### end of fit 1
print('end of fit 1')
############# FIT num. 2 ##########################<3
print('Fit number 2:\nLinear')
#background pdf #2: linear, y = -kx+b. By normalization,
#b = 1/(m2-m1)+1/2*k*(m2+m1)
return lilithcalc.l
######################################################################
# Calculations
######################################################################
# Initialize a Lilith object
lilithcalc = lilith.Lilith(verbose, timer)
# Read experimental data
lilithcalc.readexpinput(myexpinput)
print "\n***** performing model fit: migrad, hesse, minos *****"
# Initialize the fit; parameter starting values and limits
m = Minuit(getL, CV=1, limit_CV=(0,3), CF=1, limit_CF=(0,3), print_level=0, errordef=1, error_CV=0.2, error_CF=0.2)
# Minimization and error estimation
m.migrad()
m.hesse() # run covariance estimator
m.minos()
print "\nbest-fit point:", m.values
print "\nHesse errors:", m.errors
print "\nMinos errors:"
for key, value in m.merrors.items():
print key, value
print "\nCorrelation matrix:\n", m.matrix(correlation=True)
print "\nCovariance matrix:\n", m.matrix()
def xyzResolution(errorPosIN, uninteractedEvents):
guess = [[0, 100], [0, 50], [0, 50]]
displayBinsMM = np.array([0.5, 0.5, 5]) #*0.25
axes = ["X(Depth/Width) ", "Y(Height) ", "Z(Length) "]
# fig, axs = plt.subplots(3)
# for i in range(3):
# axs[i].hist(errorPosIN[:,i],bins=200)
# plt.savefig(Options.plotDIR+"test.png")
# plt.close()
fig, axs = plt.subplots(3)
for i in range(3):
errorPosI = errorPosIN[:, i]
errorPosI = errorPosI[np.isfinite(errorPosI)]
print("-------------------\n", i, "- axis events: ", len(errorPosI),
" NaN events: ", (Options.nEvents - len(errorPosI)))
xmin, xmax = -U[i], U[i] #np.min(errorPosI),np.max(errorPosI)
axs[i].set_xlim(xmin / 2, xmax / 2)
nbins = len(errorPosI)
dbins = int(L[i] / displayBinsMM[i]) #8*int(2*U[i]/10)
axs[i].hist(errorPosI, bins=dbins, range=(xmin, xmax), density=False)
hist, bin_edges = np.histogram(errorPosI,
bins=np.arange(xmin, xmax,
L[i] / nbins))
###hist = hist*nbins/(len(errorPosI)*(xmax-xmin)) #- enable if density=true
hist = (nbins / dbins) * len(errorPosI) * hist / np.sum(hist)
print(np.sum(hist) * (L[i] / nbins))
bins = bin_edges[0:(len(bin_edges) - 1)] + 0.5 * (L[i] / nbins)
lnspc = np.linspace(xmin, xmax, len(hist))
def pdf(x, m, s):
###return (1/(math.sqrt(2*math.pi)*s))*np.exp(-0.5*((x-m)**2)/(s**2)) #- enable if density=true
return (nbins / dbins) * len(errorPosI) * (L[i] / nbins) * (
1 / (math.sqrt(2 * math.pi) * s)) * np.exp(-0.5 *
((x - m)**2) /
(s**2))
def spdf(x, df, scale):
return (len(errorPosI) *
(L[i] / dbins)) * stats.t.pdf(x, df, 0, scale)
def fcn(m, s):
return np.sum(np.power((hist - pdf(bins, m, s)), 2))
def sfcn(df, scale):
return np.sum(np.power((hist - spdf(bins, df, scale)), 2))
fcn.errordef = Minuit.LEAST_SQUARES
sfcn.errordef = Minuit.LEAST_SQUARES
param = guess[i]
m = Minuit(fcn, param[0], param[1])
m.migrad()
param = m.values
pdf_g = pdf(lnspc, param[0], param[1])
axs[i].plot(lnspc, pdf_g, label='Norm')
axs[i].text(0.01,
0.99,
"Total Events = %1.0f " % (Options.nEvents),
verticalalignment='top',
horizontalalignment='left',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.01,
0.79,
"Interacted Events = %1.0f " %
(Options.nEvents - uninteractedEvents),
verticalalignment='top',
horizontalalignment='left',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.01,
0.59,
"Usable Events = %1.0f " % (len(errorPosI)),
verticalalignment='top',
horizontalalignment='left',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.01,
0.39,
"NaN Events = %1.0f " %
(Options.nEvents - len(errorPosI) - uninteractedEvents),
verticalalignment='top',
horizontalalignment='left',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.01,
0.19,
"Bin Size = %1.2f mm" % (displayBinsMM[i]),
verticalalignment='top',
horizontalalignment='left',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.99,
0.99,
"Mean = %4.2f mm" % (param[0]),
verticalalignment='top',
horizontalalignment='right',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.99,
0.79,
"STD = %4.2f mm" % (param[1]),
verticalalignment='top',
horizontalalignment='right',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.99,
0.59,
"FWHM = %4.2f mm" % (FWHM * param[1]),
verticalalignment='top',
horizontalalignment='right',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.99,
0.39,
"Error = +-%4.2f mm" % (0.5 * FWHM * param[1]),
verticalalignment='top',
horizontalalignment='right',
transform=axs[i].transAxes,
fontsize=12)
axs[i].text(0.99,
0.19,
"RSQ = %1.2f" % (RSQ(hist, pdf_g)),
verticalalignment='top',
horizontalalignment='right',
transform=axs[i].transAxes,
fontsize=12)
axs[i].set_title(axes[i] +
"predicted/expected difference histogram in mm")
#axs[i].margins(2, 2)
print("MU =", param[0])
print("STD =", param[1])
print("FWHM =", FWHM * param[1], " mm")
print("Error = +-", 0.5 * FWHM * param[1], " mm")
plt.tight_layout()
if Options.Strip_Based_Reconstruction:
plt.savefig(Options.plotDIR + 'PositionResolution_StripCounts_AR' +
str(Options.ArrayNumber) + '.png')
else:
if Options.SiPM_Based_Reconstruction:
plt.savefig(Options.plotDIR +
'PositionResolution_SiPMCounts_True_AR' +
str(Options.ArrayNumber) + '.png')
else:
plt.savefig(Options.plotDIR +
'PositionResolution_Strip_Endcounts_AR' +
str(Options.ArrayNumber) + '.png')
plt.show()
def fit_muon(self, centre_x, centre_y, radius, pixel_x, pixel_y, image):
"""
Parameters
----------
centre_x: float
Centre of muon ring in the field of view from circle fitting
centre_y: float
Centre of muon ring in the field of view from circle fitting
radius: float
Radius of muon ring from circle fitting
pixel_x: ndarray
X position of pixels in image from circle fitting
pixel_y: ndarray
Y position of pixel in image from circle fitting
image: ndarray
Amplitude of image pixels
Returns
-------
MuonIntensityParameters
"""
# First store these parameters in the class so we can use them in minimisation
self.image = image
self.pixel_x = pixel_x.to(u.deg)
self.pixel_y = pixel_y.to(u.deg)
self.unit = pixel_x.unit
radius.to(u.deg)
centre_x.to(u.deg)
centre_y.to(u.deg)
# Return interesting stuff
fitoutput = MuonIntensityParameter()
# Create Minuit object with first guesses at parameters
# strip away the units as Minuit doesnt like them
minuit = Minuit(
self.likelihood,
impact_parameter=4,
limit_impact_parameter=(0, 25),
error_impact_parameter=5,
phi=0,
limit_phi=(-np.pi, np.pi),
error_phi=0.1,
radius=radius.value,
fix_radius=True,
error_radius=0.,
centre_x=centre_x.value,
fix_centre_x=True,
error_centre_x=0.,
centre_y=centre_y.value,
fix_centre_y=True,
error_centre_y=0.,
ring_width=0.1,
error_ring_width=0.001 * radius.value,
limit_ring_width=(0, 1),
optical_efficiency_muon=0.1,
error_optical_efficiency_muon=0.05,
limit_optical_efficiency_muon=(0, 1),
throw_nan=False,
print_level=0,
pedantic=False,
errordef=1,
)
# Perform minimisation
minuit.migrad()
# Get fitted values
fit_params = minuit.values
fitoutput.impact_parameter = fit_params['impact_parameter'] * u.m
#fitoutput.phi = fit_params['phi']*u.rad
fitoutput.ring_width = fit_params['ring_width'] * self.unit
fitoutput.optical_efficiency_muon = fit_params[
'optical_efficiency_muon']
#embed()
#
fitoutput.prediction = self.prediction
return fitoutput
# -*- coding: utf-8 -*-
from iminuit import Minuit
from matplotlib import pyplot as plt
from numpy.random import randn
from probfit import BinnedLH, Extended, gaussian
data = randn(1000) * 2 + 1
# Unextended
blh = BinnedLH(gaussian, data)
# if you wonder what it looks like call describe(blh)
m = Minuit(blh, mean=0.0, sigma=0.5)
plt.figure(figsize=(8, 6))
plt.subplot(221)
blh.draw(m)
plt.title("Unextended Before")
m.migrad() # fit
plt.subplot(222)
blh.draw(m)
plt.title("Unextended After")
# Extended
ext_gauss = Extended(gaussian)
blh = BinnedLH(ext_gauss, data, extended=True)