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_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_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_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_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)
def test_formula(tmpdir):
'''
Test the "Formula" class.
'''
a = minkit.Parameter('a', 1)
b = minkit.Parameter('b', 2)
c = minkit.Formula('c', 'a * b', [a, b])
assert np.allclose(c.value, a.value * b.value)
# Test its use on a PDF
m = minkit.Parameter('m', bounds=(10, 20))
c = minkit.Parameter('c', 15, bounds=(10, 20))
s = minkit.Formula('s', '0.1 + c / 10', [c])
g = minkit.Gaussian('gaussian', m, c, s)
data = g.generate(10000)
nd = np.random.normal(c.value, s.value, 10000)
compare_with_numpy(g, nd, m)
with helpers.fit_test(g) as test:
with minkit.minimizer('uml', g, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
# Test the JSON (only for formula)
with open(os.path.join(tmpdir, 'r.json'), 'wt') as fi:
json.dump(s.to_json_object(), fi)
with open(os.path.join(tmpdir, 'r.json'), 'rt') as fi:
s = minkit.Formula.from_json_object(json.load(fi), g.all_real_args)
# Test the JSON (whole PDF)
with open(os.path.join(tmpdir, 'pdf.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(g), fi)
with open(os.path.join(tmpdir, 'pdf.json'), 'rt') as fi:
s = minkit.pdf_from_json(json.load(fi))
def test_polynomial():
'''
Test the "Polynomial" PDF.
'''
m = minkit.Parameter('m', bounds=(-5, +5))
p1 = minkit.Parameter('p1', 1.)
p2 = minkit.Parameter('p2', 2.)
p3 = minkit.Parameter('p3', 3.)
# Test constant PDF
pol0 = minkit.Polynomial('pol0', m)
data = np.random.uniform(-5, 5, 100000)
compare_with_numpy(pol0, data, m)
rndm = pol0.generate(1000)
assert np.allclose(pol0.integral(), 1)
assert np.allclose(pol0.numerical_normalization(), pol0.norm())
# Test straight line
pol1 = minkit.Polynomial('pol1', m, p1)
assert np.allclose(pol1.integral(), 1)
assert np.allclose(pol1.numerical_normalization(), pol1.norm())
# Test a parabola
pol2 = minkit.Polynomial('pol2', m, p1, p2)
assert np.allclose(pol2.integral(), 1)
assert np.allclose(pol2.numerical_normalization(), pol2.norm())
# Test a three-degree polynomial
pol3 = minkit.Polynomial('pol3', m, p1, p2, p3)
assert np.allclose(pol3.integral(), 1)
assert np.allclose(pol3.numerical_normalization(), pol3.norm())
def test_chebyshev():
'''
Test the "Chebyshev" PDF.
'''
m = minkit.Parameter('m', bounds=(-5, +5))
p1 = minkit.Parameter('p1', 1.)
p2 = minkit.Parameter('p2', 2.)
p3 = minkit.Parameter('p3', 3.)
# Test constant PDF
pol0 = minkit.Chebyshev('pol0', m)
data = np.random.uniform(-5, 5, 100000)
compare_with_numpy(pol0, data, m)
# Test straight line
pol1 = minkit.Chebyshev('pol1', m, p1)
# Test a parabola
pol2 = minkit.Chebyshev('pol2', m, p1, p2)
# Test a three-degree polynomial
pol2 = minkit.Chebyshev('pol2', m, p1, p2, p3)
def test_formula(tmpdir):
'''
Test the "Formula" class.
'''
a = minkit.Parameter('a', 1)
b = minkit.Parameter('b', 2)
c = minkit.Formula('c', '{a} * {b}', [a, b])
assert np.allclose(c.value, a.value * b.value)
# Test its use on a PDF
m = minkit.Parameter('m', bounds=(10, 20))
c = minkit.Parameter('c', 15, bounds=(10, 20))
s = minkit.Formula('s', '0.1 + {c} / 10', [c])
g = minkit.Gaussian('gaussian', m, c, s)
data = g.generate(10000)
nd = rndm_gen.normal(c.value, s.value, 10000)
compare_with_numpy(g, nd, m)
with helpers.fit_test(g) as test:
with minkit.minimizer('uml', g, data, minimizer='minuit') as minuit:
test.result = minuit.migrad()
# Test the JSON (only for formula)
with open(os.path.join(tmpdir, 'r.json'), 'wt') as fi:
json.dump(s.to_json_object(), fi)
with open(os.path.join(tmpdir, 'r.json'), 'rt') as fi:
s = minkit.Formula.from_json_object(json.load(fi), g.all_real_args)
# Test the JSON (whole PDF)
with open(os.path.join(tmpdir, 'pdf.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(g), fi)
with open(os.path.join(tmpdir, 'pdf.json'), 'rt') as fi:
minkit.pdf_from_json(json.load(fi))
# Test the copy of a formula
new_args = s.args.copy()
assert all(not o is p for o, p in zip(s.args, s.copy(new_args).args))
# Test for a formula depending on another formula
m = minkit.Parameter('m', bounds=(10, 20))
c = minkit.Parameter('c', 15, bounds=(10, 20))
d = minkit.Formula('d', '0.1 + {c} / 10', [c])
s = minkit.Formula('s', '2 * {d}', [d])
g = minkit.Gaussian('gaussian', m, c, s)
assert s.value == 3.2
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()
# Test the JSON (only for formula)
with open(os.path.join(tmpdir, 'r.json'), 'wt') as fi:
json.dump(s.to_json_object(), fi)
with open(os.path.join(tmpdir, 'r.json'), 'rt') as fi:
s = minkit.Formula.from_json_object(json.load(fi), g.all_args)
# Test the copy of a formula depending on another formula
new_args = s.args.copy()
assert all(not o is p for o, p in zip(s.args, s.copy(new_args).args))
# Test the JSON (whole PDF)
with open(os.path.join(tmpdir, 'pdf.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(g), fi)
with open(os.path.join(tmpdir, 'pdf.json'), 'rt') as fi:
minkit.pdf_from_json(json.load(fi))