def test_crystalball():
'''
Test the "Crystal-Ball" PDF.
'''
m = minkit.Parameter('m', bounds=(460, 540))
c = minkit.Parameter('c', 500)
s = minkit.Parameter('s', 5)
a = minkit.Parameter('a', 10000)
n = minkit.Parameter('n', 2)
cb = minkit.CrystalBall('crystal-ball', m, c, s, a, n)
data = np.random.normal(500, 5, 100000)
# For a very large value of "a", it behaves as a Gaussian
compare_with_numpy(cb, data, m)
# The same stands if the tail is flipped
a.value = -a.value
compare_with_numpy(cb, data, m)
# Test the normalization
assert np.allclose(cb.integral(), 1)
a.value = +1
assert np.allclose(cb.numerical_normalization(), cb.norm())
a.value = -1
assert np.allclose(cb.numerical_normalization(), cb.norm())
def test_range():
'''
Test the "Range" class.
'''
# Simple constructor
v = [(1, 2), (5, 6)]
r = minkit.Range(v)
assert np.allclose(r.bounds, v)
# Do calculations in a range
m = minkit.Parameter('m', bounds=(0, 10))
k = minkit.Parameter('k', -0.5, bounds=(-0.8, -0.3))
e = minkit.Exponential('exponential', m, k)
m.set_range('sides', [(0, 4), (6, 10)])
assert np.allclose(e.norm(range='sides'),
e.numerical_normalization(range='sides'))
data = e.generate(10000)
with helpers.fit_test(e) as test:
with minkit.minimizer('uml', e, data, minimizer='minuit', range='sides') as minuit:
test.result = minuit.migrad()
# Test generation of data only in the range
data = e.generate(10000, range='sides')
with helpers.fit_test(e) as test:
with minkit.minimizer('uml', e, data, minimizer='minuit', range='sides') as minuit:
test.result = minuit.migrad()
def test_simultaneous_minimizer():
'''
Test the "simultaneous_minimizer" function.
'''
m = minkit.Parameter('m', bounds=(10, 20))
# Common mean
s = minkit.Parameter('s', 1, bounds=(0.1, +3))
# First Gaussian
c1 = minkit.Parameter('c1', 15, bounds=(10, 20))
g1 = minkit.Gaussian('g1', m, c1, s)
data1 = g1.generate(size=1000)
# Second Gaussian
c2 = minkit.Parameter('c2', 15, bounds=(10, 20))
g2 = minkit.Gaussian('g2', m, c2, s)
data2 = g2.generate(size=10000)
categories = [
minkit.Category('uml', g1, data1),
minkit.Category('uml', g2, data2)
]
with helpers.fit_test(categories, simultaneous=True) as test:
with minkit.simultaneous_minimizer(categories,
minimizer='minuit') as minuit:
test.result = minuit.migrad()
def test_unbinned_maximum_likelihood():
'''
Test the "unbinned_maximum_likelihood" FCN.
'''
# Simple fit to a Gaussian
m = minkit.Parameter('m', bounds=(5, 15))
c = minkit.Parameter('c', 10., bounds=(5, 15))
s = minkit.Parameter('s', 1., bounds=(0.5, 2))
g = minkit.Gaussian('gaussian', m, c, s)
data = g.generate(10000)
with helpers.fit_test(g) as test:
with minkit.minimizer('uml', g, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
# Add constraints
cc = minkit.Parameter('cc', 10)
sc = minkit.Parameter('sc', 0.1)
gc = minkit.Gaussian('constraint', c, cc, sc)
with helpers.fit_test(g) as test:
with minkit.minimizer('uml',
g,
data,
minimizer='minuit',
constraints=[gc]) as minuit:
test.result = minuit.migrad()
def test_range():
'''
Test for disjointed ranges.
'''
# Do calculations in a range
m = minkit.Parameter('m', bounds=(0, 10))
k = minkit.Parameter('k', -0.5, bounds=(-0.8, -0.3))
e = minkit.Exponential('exponential', m, k)
m.set_range('sides', [(0, 4), (6, 10)])
helpers.check_numerical_normalization(e, range='sides')
data = e.generate(10000)
with helpers.fit_test(e) as test:
with minkit.minimizer('uml',
e,
data,
minimizer='minuit',
range='sides') as minuit:
test.result = minuit.migrad()
# Test generation of data only in the range
data = e.generate(10000, range='sides')
with helpers.fit_test(e) as test:
with minkit.minimizer('uml',
e,
data,
minimizer='minuit',
range='sides') as minuit:
test.result = minuit.migrad()
def default_gaussian(pdf_name='g', data_par='x', center='c', sigma='s'):
'''
Create a Gaussian function.
'''
x = minkit.Parameter(data_par, bounds=(-4, +4))
c = minkit.Parameter(center, 0, bounds=(-4, +4))
s = minkit.Parameter(sigma, 1, bounds=(0.1, 2.))
return minkit.Gaussian(pdf_name, x, c, s)
def basic():
'''
Basic model.
'''
x = minkit.Parameter('x', bounds=(-5, +5))
c = minkit.Parameter('c', 0, bounds=(-5, +5))
s = minkit.Parameter('s', 1, bounds=(0.1, 5))
g = minkit.Gaussian('g', x, c, s)
return g
def intermediate():
'''
Model composed by a single narrow Gaussian function.
'''
x = minkit.Parameter('x', bounds=(-5, +5))
c = minkit.Parameter('c', 0, bounds=(-5, +5))
s = minkit.Parameter('s', 0.5, bounds=(1e-3, 5))
g = minkit.Gaussian('g', x, c, s)
return g
def basic():
'''
Basic Gaussian model.
'''
m = minkit.Parameter('m', bounds=(10, 20))
c = minkit.Parameter('c', 15, bounds=(10, 20))
s = minkit.Parameter('s', 2, bounds=(0.1, 5))
g = minkit.Gaussian('g', m, c, s)
return g
def numeric(backend):
'''
Model where numerical integration is needed (Argus).
'''
m = minkit.Parameter('m', bounds=(0, 1))
mu = minkit.Parameter('mu', 0.9, bounds=(0.5, 1))
c = minkit.Parameter('c', 0.2, bounds=(0.01, 2))
p = minkit.Parameter('p', 0.6, bounds=(0.1, 1))
pdf = minkit.Argus('argus', m, mu, c, p)
return pdf
def test_convpdfs(tmpdir):
'''
Test the "ConvPDFs" class.
'''
m = minkit.Parameter('m', bounds=(-20, +20))
# Create two Gaussians
c1 = minkit.Parameter('c1', 0, bounds=(-2, +2))
s1 = minkit.Parameter('s1', 3, bounds=(0.5, +10))
g1 = minkit.Gaussian('g1', m, c1, s1)
c2 = minkit.Parameter('c2', 0, bounds=(-2, +2))
s2 = minkit.Parameter('s2', 4, bounds=(0.5, +10))
g2 = minkit.Gaussian('g2', m, c2, s2)
pdf = minkit.ConvPDFs('convolution', g1, g2)
data = pdf.generate(10000)
# Check that the output is another Gaussian with bigger standard deviation
mean = minkit.core.aop.sum(data[m.name]) / len(data)
var = minkit.core.aop.sum((data[m.name] - mean)**2) / len(data)
assert np.allclose(var, s1.value**2 + s2.value**2, rtol=0.1)
# Check that the normalization is correct
with pdf.bind() as proxy:
assert np.allclose(proxy.integral(), 1.)
assert np.allclose(proxy.norm(), 1.)
assert np.allclose(proxy.numerical_normalization(), 1.)
# Ordinary check for PDFs
values, edges = np.histogram(minkit.as_ndarray(data[m.name]),
bins=100,
range=m.bounds)
centers = minkit.DataSet.from_array(0.5 * (edges[1:] + edges[:-1]), m)
pdf_values = minkit.plotting.scaled_pdf_values(pdf, centers, values, edges)
assert np.allclose(np.sum(pdf_values), np.sum(values), rtol=0.01)
# Test a fit
with fit_test(pdf) as test:
with minkit.minimizer('uml', pdf, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
# Test the JSON conversion
with open(os.path.join(tmpdir, 'pdf.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(pdf), fi)
with open(os.path.join(tmpdir, 'pdf.json'), 'rt') as fi:
s = minkit.pdf_from_json(json.load(fi))
check_multi_pdfs(s, pdf)
def test_landau():
'''
Test the "Landau" PDF.
'''
m = minkit.Parameter('m', bounds=(-5, +5))
c = minkit.Parameter('c', 0., bounds=(-2, +2))
s = minkit.Parameter('s', 1., bounds=(-3, +3))
l = minkit.Landau('landau', m, c, s)
assert np.allclose(l.integral(), 1)
helpers.check_numerical_normalization(l)
def test_exppoly():
'''
Test the "ExpPoly" PDF
'''
m = minkit.Parameter('m', bounds=(-5, +5))
k = minkit.Parameter('k', -0.05, bounds=(-0.1, 0))
p = minkit.Parameter('p1', 1, bounds=(0, 2))
pdf = minkit.ExpPoly('exp_poly', m, k, p)
assert np.allclose(pdf.integral(), 1)
helpers.check_numerical_normalization(pdf)
def test_addpdfs(tmpdir):
'''
Test the "AddPDFs" class.
'''
m = minkit.Parameter('m', bounds=(-5, +5))
# Create an Exponential PDF
k = minkit.Parameter('k', -0.05, bounds=(-0.1, 0))
e = minkit.Exponential('exponential', m, k)
# Create a Gaussian PDF
c = minkit.Parameter('c', 0., bounds=(-2, +2))
s = minkit.Parameter('s', 1., bounds=(-3, +3))
g = minkit.Gaussian('gaussian', m, c, s)
# Add them together
g2e = minkit.Parameter('g2e', 0.5, bounds=(0, 1))
pdf = minkit.AddPDFs.two_components('model', g, e, g2e)
assert len(pdf.all_args) == (1 + len(g.args) + len(e.args))
gdata = helpers.rndm_gen.normal(c.value, s.value, 100000)
edata = helpers.rndm_gen.exponential(-1. / k.value, 100000)
data = np.concatenate([gdata, edata])
values, edges = np.histogram(data, bins=100, range=m.bounds)
centers = minkit.DataSet.from_ndarray(0.5 * (edges[1:] + edges[:-1]), m)
pdf_values = minkit.utils.core.scaled_pdf_values(pdf, centers, values,
edges)
assert np.allclose(np.sum(pdf_values), np.sum(values))
# Test consteness of the PDFs
k.constant = True
assert e.constant and not pdf.constant
g2e.constant = True
assert not pdf.constant
for p in pdf.all_args:
p.constant = True
assert pdf.constant
# Test the JSON conversion
with open(os.path.join(tmpdir, 'pdf.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(pdf), fi)
with open(os.path.join(tmpdir, 'pdf.json'), 'rt') as fi:
s = minkit.pdf_from_json(json.load(fi))
check_multi_pdfs(s, pdf)
# Check copying the PDF
pdf.copy()
def test_powerlaw():
'''
Test the "PowerLaw" PDF.
'''
m = minkit.Parameter('m', bounds=(460, 540))
c = minkit.Parameter('c', 400)
n = minkit.Parameter('n', 2)
pl = minkit.PowerLaw('power-law', m, c, n)
# Test the normalization
assert np.allclose(pl.integral(), 1)
assert np.allclose(pl.numerical_normalization(), pl.norm())
def test_exponential():
'''
Test the "Exponential" PDF
'''
m = minkit.Parameter('m', bounds=(-5, +5))
k = minkit.Parameter('k', -0.05, bounds=(-0.1, 0))
e = minkit.Exponential('exponential', m, k)
data = helpers.rndm_gen.exponential(-1. / k.value, 100000)
compare_with_numpy(e, data, m)
helpers.check_numerical_normalization(e)
def test_exponential():
'''
Test the "Exponential" PDF
'''
m = minkit.Parameter('m', bounds=(-5, +5))
k = minkit.Parameter('k', -0.05, bounds=(-0.1, 0))
e = minkit.Exponential('exponential', m, k)
data = np.random.exponential(-1. / k.value, 100000)
compare_with_numpy(e, data, m)
assert np.allclose(e.numerical_normalization(), e.norm())
def test_unbinned_extended_maximum_likelihood():
'''
Test the "unbinned_extended_maximum_likelihood" FCN.
'''
m = minkit.Parameter('m', bounds=(-5, +15))
# Create an Exponential PDF
k = minkit.Parameter('k', -0.1, bounds=(-0.2, 0))
e = minkit.Exponential('exponential', m, k)
# Create a Gaussian PDF
c = minkit.Parameter('c', 10., bounds=(8, 12))
s = minkit.Parameter('s', 1., bounds=(0.5, 2))
g = minkit.Gaussian('gaussian', m, c, s)
# Add them together
ng = minkit.Parameter('ng', 10000, bounds=(0, 100000))
ne = minkit.Parameter('ne', 1000, bounds=(0, 100000))
pdf = minkit.AddPDFs.two_components('model', g, e, ng, ne)
data = pdf.generate(int(ng.value + ne.value))
with helpers.fit_test(pdf) as test:
with minkit.minimizer('ueml', pdf, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
# Add constraints
cc = minkit.Parameter('cc', 10)
sc = minkit.Parameter('sc', 1)
gc = minkit.Gaussian('constraint', c, cc, sc)
with helpers.fit_test(pdf) as test:
with minkit.minimizer('ueml', pdf, data, minimizer='minuit', constraints=[gc]) as minuit:
test.result = minuit.migrad()
def test_gaussian():
'''
Test the "Gaussian" PDF.
'''
m = minkit.Parameter('m', bounds=(-5, +5))
c = minkit.Parameter('c', 0., bounds=(-2, +2))
s = minkit.Parameter('s', 1., bounds=(-3, +3))
g = minkit.Gaussian('gaussian', m, c, s)
data = np.random.normal(c.value, s.value, 100000)
compare_with_numpy(g, data, m)
assert np.allclose(g.numerical_normalization(), g.norm())
def test_gaussian():
'''
Test the "Gaussian" PDF.
'''
m = minkit.Parameter('m', bounds=(-5, +5))
c = minkit.Parameter('c', 0., bounds=(-2, +2))
s = minkit.Parameter('s', 1., bounds=(-3, +3))
g = minkit.Gaussian('gaussian', m, c, s)
data = helpers.rndm_gen.normal(c.value, s.value, 100000)
compare_with_numpy(g, data, m)
helpers.check_numerical_normalization(g)
def test_interppdf(tmpdir):
'''
Test the InterpPDF class.
'''
m = minkit.Parameter('m', bounds=(-3, +3))
centers = np.linspace(*m.bounds, 100)
values = np.exp(-0.5 * centers**2)
ip = minkit.InterpPDF.from_ndarray('ip', m, centers, values)
ip.max() # check that we can calculate the maximum
# Test the JSON conversion
with open(os.path.join(tmpdir, 'ip.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(ip), fi)
with open(os.path.join(tmpdir, 'ip.json'), 'rt') as fi:
p = minkit.pdf_from_json(json.load(fi))
check_pdfs(p, ip)
# Check copying the PDF
ip.copy()
# Combine the PDF with another
k = minkit.Parameter('k', -0.1, bounds=(-1, +1))
e = minkit.Exponential('exp', m, k)
y = minkit.Parameter('y', 0.5, bounds=(0, 1))
pdf = minkit.AddPDFs.two_components('pdf', ip, e, y)
data = pdf.generate(10000)
with fit_test(pdf) as test:
with minkit.minimizer('uml', pdf, data,
minimizer='minuit') as minimizer:
test.result = minimizer.migrad()
bdata = data.make_binned(20)
with fit_test(pdf) as test:
with minkit.minimizer('bml', pdf, bdata,
minimizer='minuit') as minimizer:
test.result = minimizer.migrad()
# Test the construction from a binned data set
minkit.InterpPDF.from_binned_dataset('pdf', bdata)
def test_pdf():
'''
General tests for the PDF class.
'''
# Create a Polynomial PDF
m = minkit.Parameter('m', bounds=(0, 10))
p1 = minkit.Parameter('p1', 0.)
p2 = minkit.Parameter('p2', 0.)
p = minkit.Polynomial('polynomial', m, p1, p2)
m.set_range('sides', [(0, 4), (6, 10)])
# integral
assert np.allclose(p.integral(integral_range='full', range='full'), 1.)
assert np.allclose(p.integral(integral_range='sides', range='full'), 0.8)
assert np.allclose(p.integral(integral_range='sides', range='sides'), 1.)
def test_argus():
'''
Test the "Argus" PDF.
'''
# This is actually the chi-square distribution with one degree of freedom
m = minkit.Parameter('m', bounds=(0, 1))
mu = minkit.Parameter('mu', 0.9, bounds=(0.5, 1))
c = minkit.Parameter('c', 0.2, bounds=(0.01, 2))
p = minkit.Parameter('p', 0.5, bounds=(0.1, 1))
pdf = minkit.Argus('argus', m, mu, c, p)
assert np.allclose(pdf.integral(), 1)
m.set_range('reduced', (0, mu.value))
assert np.allclose(pdf.integral('reduced'), 1)
def test_backend():
'''
Test the construction of the backend.
'''
with pytest.raises(AttributeError):
minkit.Backend.DataSet
bk = minkit.Backend(minkit.backends.core.CPU)
x = minkit.Parameter('x', bounds=(-1, +1))
data = helpers.rndm_gen.uniform(0, 1, 1000)
# Test initialization and constructor methods
bk.DataSet(minkit.darray.from_ndarray(data, bk), [x])
dataset = bk.DataSet.from_ndarray(data, x)
new_bk = minkit.Backend(minkit.backends.core.CPU)
m = bk.Parameter('m')
c = bk.Parameter('c')
s = bk.Parameter('s')
k = bk.Parameter('k')
y = bk.Parameter('y')
g = bk.Gaussian('gauss', m, c, s)
e = bk.Exponential('exponential', m, k)
bk.AddPDFs.two_components('pdf', g, e, y)
# Test the adaption of objects to new backends
dataset.to_backend(new_bk)
def test_evaluation_grid():
'''
Test the "evaluation_grid" function.
'''
x = minkit.Parameter('x', bounds=(0, 20))
y = minkit.Parameter('y', bounds=(0, 20))
n = 100
# Test single range
g = dataset.evaluation_grid(minkit.Registry([x]), x.bounds, n)
assert len(g) == n
# Test multi-range
g = dataset.evaluation_grid(minkit.Registry(
[x, y]), np.concatenate([x.bounds, y.bounds]), n)
assert len(g) == n**2
def test_dataset():
'''
Test for the "DataSet" class.
'''
numpy_data = helpers.rndm_gen.normal(0, 1, 10000)
m = minkit.Parameter('m', bounds=(-5, +5))
m.set_range('reduced', (-2, +2))
data = minkit.DataSet.from_ndarray(numpy_data, m)
new_data = data.subset('reduced')
assert np.allclose(aop.count_nonzero(aop.le(new_data[m.name], -2.1)), 0)
assert np.allclose(aop.count_nonzero(aop.ge(new_data[m.name], +2.1)), 0)
binned_data = data.make_binned(bins=100)
values, _ = np.histogram(numpy_data, range=m.bounds, bins=100)
assert np.allclose(binned_data.values.as_ndarray(), values)
# Multidimensional case
x = minkit.Parameter('x', bounds=(-5, +5))
y = minkit.Parameter('y', bounds=(-5, +5))
nps = np.empty(10000, dtype=[('x', np.float64), ('y', np.float64)])
nps['x'] = helpers.rndm_gen.normal(0, 0.1, 10000)
nps['y'] = helpers.rndm_gen.normal(0, 0.2, 10000)
data = minkit.DataSet.from_records(nps, [x, y])
assert len(data) == len(nps)
x.set_range('reduced', (-2, 2))
y.set_range('reduced', (-3, 3))
data.subset('reduced')
data.make_binned(bins=100)
data.make_binned(bins=(100, 100))
r = data.to_records()
data = minkit.DataSet.from_records(r, data.data_pars)
assert len(r) == len(data)
def gaussian_model(backend):
'''
Return a gaussian model that can be in the minkit or RooFit backends.
'''
if backend == 'minkit':
m = minkit.Parameter('m', bounds=(30, 50))
c = minkit.Parameter('c', 40, bounds=(30, 50))
s = minkit.Parameter('s', 5, bounds=(0.1, 10))
return minkit.Gaussian('g', m, c, s)
elif backend == 'roofit':
m = rt.RooRealVar('m', 'm', 30, 50)
c = rt.RooRealVar('c', 'c', 40, 30, 50)
s = rt.RooRealVar('s', 's', 5, 0.1, 10)
g = rt.RooGaussian('g', 'g', m, c, s)
return RooFitModel(g, m, [c, s])
else:
raise ValueError(f'Unknown backend "{backend}"')
def test_add_pdf_src(tmpdir):
'''
Test for the "add_pdf_src" function.
'''
@minkit.register_pdf
class NonExistingPDF(minkit.SourcePDF):
def __init__(self, name, x):
super(NonExistingPDF, self).__init__(name, [x])
x = minkit.Parameter('x', bounds=(0, 10))
with pytest.raises(RuntimeError):
NonExistingPDF('non-existing', x)
with open(os.path.join(tmpdir, 'ExistingPDF.xml'), 'wt') as fi:
fi.write('''
<PDF>
<parameters a="a"/>
<function>
<data x="x"/>
<code>
return a * x;
</code>
</function>
<integral>
<bounds xmin="xmin" xmax="xmax"/>
<code>
return 0.5 * a * (xmax * xmax - xmin * xmin);
</code>
</integral>
</PDF>
''')
# Add the temporary directory to the places where to look for PDFs
minkit.add_pdf_src(tmpdir)
@minkit.register_pdf
class ExistingPDF(minkit.SourcePDF):
def __init__(self, name, x, a):
super(ExistingPDF, self).__init__(name, [x], [a])
a = minkit.Parameter('a', 1.)
pdf = ExistingPDF('existing', x, a)
assert np.allclose(pdf.integral(), 1)
assert np.allclose(pdf.numerical_normalization(), pdf.norm())
def test_minimizer():
'''
Test the "minimizer" function
'''
m = minkit.Parameter('m', bounds=(20, 80))
c = minkit.Parameter('c', 50, bounds=(30, 70))
s = minkit.Parameter('s', 5, bounds=(1, 10))
g = minkit.Gaussian('gaussian', m, c, s)
initials = g.get_values()
arr = np.random.normal(c.value, s.value, 10000)
data = minkit.DataSet.from_array(arr, m)
with helpers.fit_test(g) as test:
with minkit.minimizer('uml', g, data, minimizer='minuit') as minuit:
test.result = pytest.shared_result = minuit.migrad()
pytest.shared_names = [p.name for p in g.all_args]
# Unweighted fit to uniform distribution fails
arr = np.random.uniform(*m.bounds, 100000)
data = minkit.DataSet.from_array(arr, m)
with minkit.minimizer('uml', g, data, minimizer='minuit') as minuit:
r = minuit.migrad()
print(r)
reg = minkit.minuit_to_registry(r.params)
assert not np.allclose(reg.get(s.name).value, initials[s.name])
# With weights fits correctly
data.weights = minkit.as_ndarray(g(data))
with helpers.fit_test(g) as test:
with minkit.minimizer('uml', g, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
# Test the binned case
data = data.make_binned(bins=100)
with helpers.fit_test(g) as test:
with minkit.minimizer('bml', g, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
def test_amoroso():
'''
Test the "Amoroso" PDF.
'''
# This is actually the chi-square distribution with one degree of freedom
m = minkit.Parameter('m', bounds=(0, 10))
a = minkit.Parameter('a', 0)
theta = minkit.Parameter('theta', 2)
alpha = minkit.Parameter('alpha', 0.5)
beta = minkit.Parameter('beta', 2)
pdf = minkit.Amoroso('amoroso', m, a, theta, alpha, beta)
assert np.allclose(pdf.integral(), 1)
data = np.random.chisquare(2, 100000)
compare_with_numpy(pdf, data, m)