def test_UnbinnedLH(self):
f = gaussian
assert list(describe(f)) == ['x', 'mean', 'sigma']
lh = UnbinnedLH(gaussian, self.data, )
assert list(describe(lh)) == ['mean', 'sigma']
assert_allclose(lh(0, 1), 28188.201229348757)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 0.5)
def test_BinnedChi2(self):
f = gaussian
assert list(describe(f)) == ['x', 'mean', 'sigma']
lh = BinnedChi2(gaussian, self.data, bound=[-3, 3])
assert list(describe(lh)) == ['mean', 'sigma']
assert_allclose(lh(0, 1), 19951.005399882044, atol=1)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 1.0)
def test_BinnedChi2(self):
f = gaussian
assert_equal(list(describe(f)), ['x', 'mean', 'sigma'])
lh = BinnedChi2(gaussian, self.data, bound=[-3, 3])
assert_equal(list(describe(lh)), ['mean', 'sigma'])
assert_almost_equal(lh(0, 1), 19951.005399882044, 1)
minuit = iminuit.Minuit(lh)
assert_equal(minuit.errordef, 1.0)
def test_BinnedChi2(self):
f = gaussian
assert list(describe(f)) == ['x', 'mean', 'sigma']
lh = BinnedChi2(gaussian, self.data, bound=[-3, 3])
assert list(describe(lh)) == ['mean', 'sigma']
assert_allclose(lh(0, 1), 19951.005399882044, atol=1)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 1.0)
def test_BinnedChi2(self):
f = gaussian
assert_equal(list(describe(f)), ['x', 'mean', 'sigma'])
lh = BinnedChi2(gaussian, self.data, bound=[-3, 3])
assert_equal(list(describe(lh)), ['mean', 'sigma'])
assert_almost_equal(lh(0, 1), 19951.005399882044, 1)
minuit = iminuit.Minuit(lh)
assert_equal(minuit.errordef, 1.0)
def test_UnbinnedLH(self):
f = gaussian
assert_equal(list(describe(f)), ['x', 'mean', 'sigma'])
lh = UnbinnedLH(gaussian, self.data,)
assert_equal(list(describe(lh)), ['mean', 'sigma'])
assert_almost_equal(lh(0, 1), 28188.201229348757)
minuit = iminuit.Minuit(lh)
assert_equal(minuit.errordef, 0.5)
def test_BinnedLH(self):
# write a better test... this depends on subtraction
f = gaussian
assert list(describe(f)) == ["x", "mean", "sigma"]
lh = BinnedLH(gaussian, self.data, bound=[-3, 3])
assert list(describe(lh)) == ["mean", "sigma"]
assert_allclose(lh(0, 1), 20.446130781601543, atol=1)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 0.5)
def test_BinnedLH(self):
# write a better test... this depends on subtraction
f = gaussian
assert list(describe(f)) == ['x', 'mean', 'sigma']
lh = BinnedLH(gaussian, self.data, bound=[-3, 3])
assert list(describe(lh)) == ['mean', 'sigma']
assert_allclose(lh(0, 1), 20.446130781601543, atol=1)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 0.5)
def test_BinnedLH(self):
# write a better test... this depends on subtraction
f = gaussian
assert_equal(list(describe(f)), ['x', 'mean', 'sigma'])
lh = BinnedLH(gaussian, self.data, bound=[-3, 3])
assert_equal(list(describe(lh)), ['mean', 'sigma'])
assert_almost_equal(lh(0, 1), 20.446130781601543, 1)
minuit = iminuit.Minuit(lh)
assert_equal(minuit.errordef, 0.5)
def test_UnbinnedLH(self):
f = gaussian
assert_equal(list(describe(f)), ['x', 'mean', 'sigma'])
lh = UnbinnedLH(
gaussian,
self.data,
)
assert_equal(list(describe(lh)), ['mean', 'sigma'])
assert_almost_equal(lh(0, 1), 28188.201229348757)
minuit = iminuit.Minuit(lh)
assert_equal(minuit.errordef, 0.5)
def test_UnbinnedLH(self):
f = gaussian
assert list(describe(f)) == ['x', 'mean', 'sigma']
lh = UnbinnedLH(
gaussian,
self.data,
)
assert list(describe(lh)) == ['mean', 'sigma']
assert_allclose(lh(0, 1), 28188.201229348757)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 0.5)
def test_polynomial():
p = pdf.Polynomial(1)
assert describe(p) == ['x', 'c_0', 'c_1']
assert_allclose(p(2, 2, 1), 4)
integral = p.integrate((0, 1), 1, 2, 1)
assert_allclose(integral, 2.5)
p = pdf.Polynomial(2)
assert describe(p) == ['x', 'c_0', 'c_1', 'c_2']
assert_allclose(p(2, 3, 4, 5), 31)
integral = p.integrate((2, 10), 10, 1, 2, 3)
analytical = 8 + 2 / 2. * (10 ** 2 - 2 ** 2) + 3 / 3. * (10 ** 3 - 2 ** 3)
assert_allclose(integral, analytical)
def test_polynomial():
p = pdf.Polynomial(1)
assert_equal(describe(p), ['x', 'c_0', 'c_1'])
assert_equal(p(2, 2, 1), 4)
integral = p.integrate((0, 1), 1, 2, 1)
assert_equal(integral, 2.5)
p = pdf.Polynomial(2)
assert_equal(describe(p), ['x', 'c_0', 'c_1', 'c_2'])
assert_equal(p(2, 3, 4, 5), 31)
integral = p.integrate((2, 10), 10, 1, 2, 3)
analytical = 8 + 2 / 2.*(10 ** 2 - 2 ** 2) + 3 / 3.*(10 ** 3 - 2 ** 3)
assert_equal(integral, analytical)
def test_Chi2Regression(self):
x = np.linspace(1, 10, 10)
y = 10 * x + 1
f = linear
assert list(describe(f)) == ["x", "m", "c"]
lh = Chi2Regression(f, x, y)
assert list(describe(lh)) == ["m", "c"]
assert_allclose(lh(10, 1), 0)
assert_allclose(lh(10, 0), 10.0)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 1.0)
def test_Chi2Regression(self):
x = np.linspace(1, 10, 10)
y = 10 * x + 1
f = linear
assert_equal(list(describe(f)), ['x', 'm', 'c'])
lh = Chi2Regression(f, x, y)
assert_equal(list(describe(lh)), ['m', 'c'])
assert_almost_equal(lh(10, 1), 0)
assert_almost_equal(lh(10, 0), 10.)
minuit = iminuit.Minuit(lh)
assert_equal(minuit.errordef, 1.0)
def test_Chi2Regression(self):
x = np.linspace(1, 10, 10)
y = 10 * x + 1
f = linear
assert list(describe(f)) == ['x', 'm', 'c']
lh = Chi2Regression(f, x, y)
assert list(describe(lh)) == ['m', 'c']
assert_allclose(lh(10, 1), 0)
assert_allclose(lh(10, 0), 10.)
minuit = iminuit.Minuit(lh)
assert_allclose(minuit.errordef, 1.0)
def merge_func_code(*arg):
"""
merge function arguments.::
def f(x,y,z): return do_something(x,y,z)
def g(x,z,p): return do_something(x,y,z)
fc, pos = merge_func_code(f,g)
#fc is now ('x','y','z','p')
"""
all_arg = []
for i, f in enumerate(arg):
tmp = []
first = False
for vn in describe(f):
newv = vn
first = False
tmp.append(newv)
all_arg.append(tmp)
#FIXME: do something smarter
merge_arg = []
for a in all_arg:
for v in a:
if v not in merge_arg:
merge_arg.append(v)
#build the map list of numpy int array
pos = []
for a in all_arg:
tmp = []
for v in a:
tmp.append(merge_arg.index(v))
pos.append(np.array(tmp, dtype=np.int))
return MinimalFuncCode(merge_arg), pos
def __init__(self, model, x, y, dx, dy):
self.model = model # model predicts y value for given x value
self.x = np.array(x) # the x values
self.y = np.array(y) # the y values
self.dx = np.array(dx) # the x-axis uncertainties
self.dy = np.array(dy) # the y-axis uncertainties
self.func_code = make_func_code(describe(self.model)[1:])
def __init__(self,
f,
data,
weights=None,
bound=None,
badvalue=-100000,
extended=False,
extended_bound=None,
extended_nint=100):
if bound is not None:
data = np.array(data)
mask = (data >= bound[0]) & (data <= bound[1])
data = data[mask]
if (weights is not None):
weights = weights[mask]
self.f = f # model predicts PDF for given x
self.data = np.array(data)
self.weights = set_var_if_None(weights, self.data)
self.bad_value = badvalue
self.extended = extended
self.extended_bound = extended_bound
self.extended_nint = extended_nint
if extended and extended_bound is None:
self.extended_bound = (np.min(data), np.max(data))
self.func_code = make_func_code(describe(self.f)[1:])
def _validate_minuit_args(cost_func: Union[cost_function.CostFunctionBase, cost_function.SimultaneousFit],
minuit_args: T_FitArguments) -> None:
""" Validate the arguments provided for Minuit.
Checks that there are sufficient and valid arguments for each parameter in the fit function.
Args:
cost_func: Cost function to be used with Minuit.
minuit_args: Arguments for minuit. Need to set the initial value, limits, and error (step)
of each parameter.
Returns:
None. An exception is raised if there's a problem with any of the arguments.
"""
# Need the parameters in the function to check the arguments. Recall that "x" is skipped because it's a cost
# function (which is useful, because we want to skip x since it's not a parameter).
parameters = iminuit.describe(cost_func)
# Loop over the available parameters because each one needs to be specified in the Minuit args.
for p in parameters:
if p in minuit_args:
if f"limit_{p}" not in minuit_args:
raise ValueError(f"Limits on parameter '{p}' must be specified.")
if f"error_{p}" not in minuit_args:
raise ValueError(f"Initial error on parameter '{p}' must be specified.")
# If p and limit_p and error_p were specified, then the parameter is fully specified.
elif p.replace("fix", "") in minuit_args:
# The parameter is fixed and therefore needs no further specification.
pass
else:
# The parameter wasn't specified.
raise ValueError(f"Parameter '{p}' must be specified in the fit arguments.")
def test_doublecrystalball():
assert describe(pdf.doublecrystalball) == [
"x",
"alpha",
"alpha2",
"n",
"n2",
"mean",
"sigma",
]
assert_allclose(pdf.doublecrystalball(10, 1, 1, 2, 2, 10, 2), 1.0)
assert_allclose(pdf.doublecrystalball(11, 1, 1, 2, 2, 10, 2),
0.8824969025845955)
assert_allclose(pdf.doublecrystalball(12, 1, 1, 2, 2, 10, 2),
0.6065306597126334)
assert_allclose(pdf.doublecrystalball(14, 1, 1, 2, 2, 10, 2),
0.26956918209450376)
assert_allclose(pdf.doublecrystalball(6, 1, 1, 2, 2, 10, 2),
0.26956918209450376)
assert_allclose(pdf.doublecrystalball(-10, 1, 5, 3, 4, 10, 2),
0.00947704155801)
assert_allclose(pdf.doublecrystalball(0, 1, 5, 3, 4, 10, 2),
0.047744395954055)
assert_allclose(pdf.doublecrystalball(11, 1, 5, 3, 4, 10, 2),
0.8824969025846)
assert_allclose(pdf.doublecrystalball(20, 1, 5, 3, 4, 10, 2),
0.0000037266531720786)
assert_allclose(pdf.doublecrystalball(25, 1, 5, 3, 4, 10, 2),
0.00000001287132228271)
def fit_fmpe(x, y, y_err, init_params, limit_params):
chi2 = Chi2Regression(fmpe_pdf_10, x=x, y=y, error=y_err)
bin_width = np.diff(x)
bin_width = np.mean(bin_width)
params = describe(fmpe_pdf_10, verbose=False)[1:]
fixed_params = {}
for param in params:
if param not in init_params.keys():
fixed_params['fix_{}'.format(param)] = True
m = Minuit(
chi2,
**init_params,
**limit_params,
**fixed_params,
bin_width=bin_width,
print_level=0,
pedantic=False,
)
m.migrad()
return m
def test_crystalball():
assert describe(pdf.crystalball) == ['x', 'alpha', 'n', 'mean', 'sigma']
assert_allclose(pdf.crystalball(10, 1, 2, 10, 2), 1.)
assert_allclose(pdf.crystalball(11, 1, 2, 10, 2), 0.8824969025845955)
assert_allclose(pdf.crystalball(12, 1, 2, 10, 2), 0.6065306597126334)
assert_allclose(pdf.crystalball(14, 1, 2, 10, 2), 0.1353352832366127)
assert_allclose(pdf.crystalball(6, 1, 2, 10, 2), 0.26956918209450376)
def test_crystalball():
assert describe(pdf.crystalball) == ["x", "alpha", "n", "mean", "sigma"]
assert_allclose(pdf.crystalball(10, 1, 2, 10, 2), 1.0)
assert_allclose(pdf.crystalball(11, 1, 2, 10, 2), 0.8824969025845955)
assert_allclose(pdf.crystalball(12, 1, 2, 10, 2), 0.6065306597126334)
assert_allclose(pdf.crystalball(14, 1, 2, 10, 2), 0.1353352832366127)
assert_allclose(pdf.crystalball(6, 1, 2, 10, 2), 0.26956918209450376)
def test_doublegaussian():
assert_equal(tuple(describe(pdf.doublegaussian)),
('x', 'mean', 'sigma_L', 'sigma_R'))
assert_almost_equal(pdf.doublegaussian(0., 0., 1., 2.), 1.)
assert_almost_equal(pdf.doublegaussian(-1., 0., 1., 2.),
0.6065306597126334)
assert_almost_equal(pdf.doublegaussian(1., 0., 1., 2.), 0.8824969025845955)
def __init__(self, f, data):
self.f = f
self.data = data
f_sig = describe(f)
# this is how you fake function
# signature dynamically
self.func_code = make_func_code(f_sig[1:]) # docking off independent variable
self.func_defaults = None # this keeps np.vectorize happy
def __init__(self, model, x, y, cov_inv, regulator=0, regulator_val=1):
self.model = model
self.regulator = regulator
self.regulator_val = regulator_val
self.x = np.array(x)
self.y = np.array(y)
self.cov_inv = np.array(cov_inv)
self.func_code = make_func_code(describe(self.model)[1:])
def test_crystalball():
assert_equal(tuple(describe(pdf.crystalball)),
('x', 'alpha', 'n', 'mean', 'sigma'))
assert_almost_equal(pdf.crystalball(10, 1, 2, 10, 2), 1.)
assert_almost_equal(pdf.crystalball(11, 1, 2, 10, 2), 0.8824969025845955)
assert_almost_equal(pdf.crystalball(12, 1, 2, 10, 2), 0.6065306597126334)
assert_almost_equal(pdf.crystalball(14, 1, 2, 10, 2), 0.1353352832366127)
assert_almost_equal(pdf.crystalball(6, 1, 2, 10, 2), 0.26956918209450376)
def test_crystalball():
assert_equal(tuple(describe(pdf.crystalball)),
('x', 'alpha', 'n', 'mean', 'sigma'))
assert_almost_equal(pdf.crystalball(10, 1, 2, 10, 2), 1.)
assert_almost_equal(pdf.crystalball(11, 1, 2, 10, 2), 0.8824969025845955)
assert_almost_equal(pdf.crystalball(12, 1, 2, 10, 2), 0.6065306597126334)
assert_almost_equal(pdf.crystalball(14, 1, 2, 10, 2), 0.1353352832366127)
assert_almost_equal(pdf.crystalball(6, 1, 2, 10, 2), 0.26956918209450376)
def __init__(self, f, x, y, y_err):
self.x = x
self.y = y
self.y_err = y_err
self.f = f
args = describe(f) # extract function signature
self.func_code = Struct(
co_varnames=args[1:], # dock off independent param
co_argcount=len(args) - 1)
def test_cruijff():
assert describe(pdf.cruijff) == ['x', 'm_0', 'sigma_L', 'sigma_R', 'alpha_L', 'alpha_R']
val = pdf.cruijff(0, 0, 1., 2., 1., 2.)
assert_allclose(val, 1.)
vl = pdf.cruijff(0, 1, 1., 1., 2., 2.)
vr = pdf.cruijff(2, 1, 1., 1., 2., 2.)
assert_allclose(vl, vr)
assert_allclose(vl, 0.7788007830714)
assert_allclose(vr, 0.7788007830714)
def __init__(self, f, x, y, sy=None, weights=None):
self.f = f # model predicts y for given x
self.x = np.array(x)
self.y = np.array(y)
self.sy = set_var_if_None(sy, self.x)
self.weights = set_var_if_None(weights, self.x)
self.func_code = make_func_code(describe(self.f)[1:])
def __init__(self, data1D, func):
self.data = data1D
self.pdf = func
# take function signature
func_signature = iminuit.describe(func)
# overwrite func_code to provide func signature
self.func_code = iminuit.util.make_func_code(func_signature[1:])
def __init__(self,
f,
data,
bins=40,
weights=None,
weighterrors=None,
bound=None,
badvalue=1000000,
extended=False,
use_w2=False,
nint_subdiv=1):
if bound is not None:
data = np.array(data)
mask = (data >= bound[0]) & (data <= bound[1])
data = data[mask]
if (weights is not None):
weights = weights[mask]
if (weighterrors is not None):
weighterrors = weighterrors[mask]
self.weights = set_var_if_None(weights, data)
self.f = f
self.use_w2 = use_w2
self.extended = extended
if bound is None:
bound = (np.min(data), np.max(data))
self.mymin, self.mymax = bound
h, self.edges = np.histogram(data, bins, range=bound, weights=weights)
self.bins = bins
self.h = h
self.N = np.sum(self.h)
if weights is not None:
if weighterrors is None:
self.w2, _ = np.histogram(data,
bins,
range=bound,
weights=weights**2)
else:
self.w2, _ = np.histogram(data,
bins,
range=bound,
weights=weighterrors**2)
else:
self.w2, _ = np.histogram(data, bins, range=bound, weights=None)
self.badvalue = badvalue
self.nint_subdiv = nint_subdiv
self.func_code = make_func_code(describe(self.f)[1:])
self.ndof = np.sum(self.h > 0) - (self.func_code.co_argcount - 1)
def __init__(self,f,x,y):
self.f = f
self.x = x
self.y = y
f_sig = describe(f)
#this is how you fake function
#signature dynamically
self.func_code = make_func_code(f_sig[1:])#docking off independent variable
self.func_defaults = None #this keeps np.vectorize happy
def test_cruijff():
iterable_equal(tuple(describe(pdf.cruijff)),
('x', 'm_0', 'sigma_L', 'sigma_R', 'alpha_L', 'alpha_R'))
val = pdf.cruijff(0, 0, 1., 2., 1., 2.)
assert_almost_equal(val, 1.)
vl = pdf.cruijff(0, 1, 1., 1., 2., 2.)
vr = pdf.cruijff(2, 1, 1., 1., 2., 2.)
assert_almost_equal(vl, vr, msg='symmetric test')
assert_almost_equal(vl, 0.7788007830714)
assert_almost_equal(vr, 0.7788007830714)
def test_cruijff():
iterable_equal(tuple(describe(pdf.cruijff)),
('x', 'm_0', 'sigma_L', 'sigma_R', 'alpha_L', 'alpha_R'))
val = pdf.cruijff(0, 0, 1., 2., 1., 2.)
assert_almost_equal(val, 1.)
vl = pdf.cruijff(0, 1, 1., 1., 2., 2.)
vr = pdf.cruijff(2, 1, 1., 1., 2., 2.)
assert_almost_equal(vl, vr, msg='symmetric test')
assert_almost_equal(vl, 0.7788007830714)
assert_almost_equal(vr, 0.7788007830714)
def __init__(self, model, x, y, dx, dy):
self.model = model # model predicts y value for given x value
self.x = np.array(x) # the x values
self.y = np.array(y) # the y values
self.dx = np.array(dx) # the x-axis uncertainties
self.dy = np.array(dy) # the y-axis uncertainties
self.func_code = make_func_code(describe(self.model)[1:])
self.h = (
x[-1] - x[0]
) / 10000 # this is the step size for the numerical calculation of the df/dx = last value in x (x[-1]) - first value in x (x[0])/10000
def PerformFitToBKG():
print 'About to start MINUIT '
stepSigma = 0.01
m = Minuit(Chi2_BKG,
v2_t=0.20,
limit_v2_t=(0, 0.50),
error_v2_t=0.01,
v2_a=0.10,
limit_v2_a=(0, 0.50),
error_v2_a=0.01,
v4_t=0.05,
limit_v4_t=(0, 0.10),
error_v4_t=0.01,
v4_a=0.05,
limit_v4_a=(0, 0.10),
error_v4_a=0.01,
V3=0,
limit_V3=(0, 0.1),
error_V3=0.01,
B=2.0,
limit_B=(0.1, 10.0),
error_B=0.01)
m.migrad()
print ' Describe ', describe(m)
#m.minos()
#print ' values'
#print(m.values) # {'x': 2,'y': 3,'z': 4}
#print ' errors'
#print(m.errors) # {'x': 1,'y': 1,'z': 1}
#print('covariance', m.covariance)
#print('matrix()', m.matrix()) #covariance
#print('matrix(correlation=True)', m.matrix(correlation=True)) #correlation
#m.print_matrix() #correlation
axes = {}
f, (axes["Inplane"], axes["Midplane"], axes["Outplane"],
axes["AllAngles"]) = plt.subplots(1, 4, sharex=True, sharey=True)
for key in data.keys():
x = data[key]["Bkg"]["x_center"] #
y = data[key]["Bkg"]["y"]
dy = data[key]["Bkg"]["dy"]
axes[key].errorbar(x, y, yerr=dy, fmt='o')
xfit = np.linspace(-0.5, 1.5, num=50, endpoint=True)
model = Background(xfit, m.values, phi_s[key], c[key])
axes[key].plot(xfit, model, '-r') ##plot fit function
x = data[key]["All"]["x_center"]
y = data[key]["All"]["y"]
dy = data[key]["All"]["dy"]
axes[key].errorbar(x, y, yerr=dy, fmt='o')
plt.show()
def test_johnsonSU():
assert describe(pdf.johnsonSU), ["x", "mean", "sigma", "nu", "tau"]
assert_allclose(pdf.johnsonSU(1.0, 1.0, 1.0, 1.0, 1.0), 0.5212726124342)
assert_allclose(pdf.johnsonSU(1.0, 2.0, 1.0, 1.0, 1.0), 0.1100533373219)
assert_allclose(pdf.johnsonSU(1.0, 2.0, 2.0, 1.0, 1.0), 0.4758433826682)
j = pdf.johnsonSU
assert hasattr(j, "integrate")
integral = j.integrate((-100, 100), 0, 1.0, 1.0, 1.0, 1.0)
assert_allclose(integral, 1.0)
integral = j.integrate((0, 2), 0, 1.0, 1.0, 1.0, 1.0)
assert_allclose(integral, 0.8837311663857358)
def __init__(self,f,x,y):
self.f = f
self.x = x
self.y = y
f_sig = describe(f)
#this is how you fake function
#signature dynamically
self.func_code = Struct(
co_varnames = f_sig[1:], #dock off independent variable
co_argcount = len(f_sig)-1
)
self.func_defaults = None #this keeps np.vectorize happy
def __init__(self, chi2, q_bins, dG, m_P, m_D, m_Pr, t0, num_var):
self.chi2 = chi2
self.q_bins = q_bins
self.dG = dG
self.m_P = m_P
self.m_D = m_D
self.m_Pr = m_Pr
self.t0 = t0
self.num_var = num_var
args = minuit.describe(chi2)
self.func_code = minuit.Struct(
co_varnames = args[len(args)-self.num_var:],
co_argcount = len(args)-self.num_var
)
def test_simultaneous(self):
np.random.seed(0)
data = np.random.randn(10000)
shifted = data + 3.
g1 = rename(gaussian, ['x', 'lmu', 'sigma'])
g2 = rename(gaussian, ['x', 'rmu', 'sigma'])
ulh1 = UnbinnedLH(g1, data)
ulh2 = UnbinnedLH(g2, shifted)
sim = SimultaneousFit(ulh1, ulh2)
assert describe(sim) == ['lmu', 'sigma', 'rmu']
minuit = iminuit.Minuit(sim, sigma=1.2, pedantic=False, print_level=0)
minuit.migrad()
assert minuit.migrad_ok()
assert_allclose(minuit.values['lmu'], 0., atol=2 * minuit.errors['lmu'])
assert_allclose(minuit.values['rmu'], 3., atol=2 * minuit.errors['rmu'])
assert_allclose(minuit.values['sigma'], 1., atol=2 * minuit.errors['sigma'])
def _setup_fitter_kwargs(self, fitarg, kwargs=None):
"""Setup initial fitter kwargs
Use this to pass default fitargs and parameter names to Minuit.
This allows to initialize a Model class with only a fitfunc and no
boilerplate chi2 function.
"""
# This gurantees correct oder and names of fitparameters
# we start at 1 because running value (x or t) must be skipped
self.parameter_names = describe(self.fit_func)[1:]
# The oder of parameters is important
fitarg['forced_parameters'] = self.parameter_names
if not kwargs:
kwargs = {}
if not kwargs.get('fitarg'):
kwargs['fitarg'] = {}
kwargs['fitarg'] = {**fitarg, **kwargs['fitarg']}
# DODO add check that fitargs and parameter_names fit together
return kwargs
def fit_dist(self,data,pinit = {}, error = {}, fix = {}, limit = {}):
self.data = data
pars = iminuit.describe(self.func)
if not len(fix.keys()):
for k in pars:
fix[k] = 0
if not len(pinit.keys()):
for k in pars:
pinit[k] = 1.
if not len(error.keys()):
for k in pars:
error[k] = pinit[k] * self.int_steps
if not len(limit.keys()):
for k in pars:
limit[k] = [pinit[k] / 1e5, pinit[k] * 1e5]
fitarg = {}
for k in pars:
fitarg[k] = pinit[k]
fitarg['error_{0:s}'.format(k)] = error[k]
fitarg['fix_{0:s}'.format(k)] = fix[k]
fitarg['limit_{0:s}'.format(k)] = limit[k]
m = iminuit.Minuit(self.func,
errordef = self.errordef, pedantic = self.pedantic, print_level = self.print_level,
**fitarg
)
m.tol = self.tol
m.strategy = self.strategy
m.migrad(ncall = self.ncall)
return (kstest(self.data,self.distr,args = m.values.values(), mode = self.ksmode)), m.values, m.errors
def test_poly2():
assert_equal(describe(pdf.poly2), ['x', 'a', 'b', 'c'])
assert_almost_equal(pdf.poly2(2, 3, 4, 5), 25)
def test_linear():
assert_equal(describe(pdf.linear), ['x', 'm', 'c'])
assert_almost_equal(pdf.linear(1, 2, 3), 5)
assert(hasattr(pdf.linear, 'integrate'))
integral = pdf.linear.integrate((0., 1.), 1, 1, 1)
assert_equal(integral, 1.5)
def test_argus():
assert_equal(tuple(describe(pdf.argus)), ('x', 'c', 'chi', 'p'))
assert_almost_equal(pdf.argus(6., 10, 2, 3), 0.004373148605400128)
assert_almost_equal(pdf.argus(10., 10, 2, 3), 0.)
assert_almost_equal(pdf.argus(8., 10, 2, 3), 0.0018167930603254737)
def test_poly2():
assert describe(pdf.poly2) == ['x', 'a', 'b', 'c']
assert_allclose(pdf.poly2(2, 3, 4, 5), 25)
def test_doublegaussian():
assert_equal(
tuple(describe(pdf.doublegaussian)), ('x', 'mean', 'sigma_L', 'sigma_R'))
assert_almost_equal(pdf.doublegaussian(0., 0., 1., 2.), 1.)
assert_almost_equal(pdf.doublegaussian(-1., 0., 1., 2.), 0.6065306597126334)
assert_almost_equal(pdf.doublegaussian(1., 0., 1., 2.), 0.8824969025845955)
def test_cauchy():
assert_equal(describe(pdf.cauchy), ['x', 'm', 'gamma'])
assert_almost_equal(pdf.cauchy(1, 1, 1.), 0.3183098861837907)
assert_almost_equal(pdf.cauchy(1, 1, 2.), 0.15915494309189535)
assert_almost_equal(pdf.cauchy(1, 2, 4.), 0.07489644380795074)
def test_rtv_breitwigner():
assert_equal(describe(pdf.rtv_breitwigner), ['x', 'm', 'gamma'])
assert_almost_equal(pdf.rtv_breitwigner(1, 1, 1.), 0.8194496535636714)
assert_almost_equal(pdf.rtv_breitwigner(1, 1, 2.), 0.5595531041435416)
assert_almost_equal(pdf.rtv_breitwigner(1, 2, 3.), 0.2585302502852219)
def test_novosibirsk():
assert_equal(describe(pdf.novosibirsk), ['x', 'width', 'peak', 'tail'])
assert_almost_equal(pdf.novosibirsk(3, 2, 3, 4), 1.1253517471925912e-07)
def test_poly3():
assert_equal(describe(pdf.poly3), ['x', 'a', 'b', 'c', 'd'])
assert_almost_equal(pdf.poly3(2, 3, 4, 5, 6), 56.)
#
# We know easily that the answer has is
# $x=1$, $y=2$, $z=3$ and the minimum value should be $-1$
# <codecell>
def f(x,y,z):
return (x-1.)**2 + (y-2*x)**2 + (z-3.*x)**2 -1.
# <markdowncell>
# iminuit relies on Python introspection. If you wonder what kind of function iminuit sees, you can use
# <codecell>
describe(f)
# <markdowncell>
# ###Contruct Minuit Object
# To minimize we need to construct a Minuit object
# <codecell>
m=Minuit(f, x=2, error_x=0.2, limit_x=(-10.,10.), y=3., fix_y=True, print_level=1)
# <markdowncell>
# The initial value/error are optional but it's nice to do it
# and here is how to use it
#
def test_ugaussian():
assert_equal(tuple(describe(pdf.ugaussian)), ('x', 'mean', 'sigma'))
assert_almost_equal(pdf.ugaussian(0, 0, 1), 1.)
assert_almost_equal(pdf.ugaussian(-1, 0, 1), 0.6065306597126334)
assert_almost_equal(pdf.ugaussian(1, 0, 1), 0.6065306597126334)
def test_gaussian():
assert_equal(tuple(describe(pdf.gaussian)), ('x', 'mean', 'sigma'))
assert_almost_equal(pdf.gaussian(0, 0, 1), 0.3989422804014327)
assert_almost_equal(pdf.gaussian(-1, 0, 1), 0.24197072451914337)
assert_almost_equal(pdf.gaussian(1, 0, 1), 0.24197072451914337)
from iminuit import Minuit, describe
# <codecell>
%load_ext inumpy
# <codecell>
#define a functino to minimize
def f(x,y,z):
return (x-2)**2 + (y-3)**2 + (z-4)**2
# <codecell>
#iminuit relies on python introspection to read function signature
describe(f) # one of the most useful function from iminuit
# <codecell>
#notice here that it automatically knows about x,y,z
#no RooRealVar etc. needed here
m = Minuit(f)
#it warns about every little thing that might go wrong
# <codecell>
#the most frequently asked question is Does my fit converge
#also look at your console it print progress if you use print_level=2
m.migrad();
# <markdowncell>
