def test_constpdf(tmpdir):
'''
Test a fit with a constant PDF.
'''
pdf = helpers.default_add_pdfs(extended=False)
# Check for "get_values" and "set_values"
p = pdf.norm()
pdf.set_values(**pdf.get_values())
assert np.allclose(p, pdf.norm())
# Test a simple fit
data = pdf.generate(10000)
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_sourcepdf(tmpdir):
'''
Test the "SourcePDF" class.
'''
# Test the construction of a normal 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)
# Test the construction of a PDF with variable number of arguments
m = minkit.Parameter('m', bounds=(-5, +5))
p1 = minkit.Parameter('p1', 1.)
p2 = minkit.Parameter('p2', 2.)
pol0 = minkit.Polynomial('pol0', m)
pol1 = minkit.Polynomial('pol1', m, p1)
pol2 = minkit.Polynomial('pol2', m, p1, p2)
# Test the JSON conversion
with open(os.path.join(tmpdir, 'pdf.json'), 'wt') as fi:
json.dump(minkit.pdf_to_json(pol0), fi)
with open(os.path.join(tmpdir, 'pdf.json'), 'rt') as fi:
s = minkit.pdf_from_json(json.load(fi))
check_pdfs(s, pol0)
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_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_formulapdf(tmpdir):
'''
Test the "FormulaPDF" class.
'''
x = minkit.Parameter('x', bounds=(-2. * np.pi, +2 * np.pi))
a = minkit.Parameter('a', 1., bounds=(0.9, 1.1))
b = minkit.Parameter('b', 0., bounds=(-0.1, 0.1))
pdf = minkit.FormulaPDF.unidimensional('pdf', 'pow(sin(a * x + b), 2)', x,
[a, b])
norm = pdf.norm()
data = pdf.generate(10000)
with helpers.fit_test(pdf) as test:
with minkit.minimizer('uml', pdf, data) as minimizer:
test.result = minimizer.migrad()
# Include the integral
pdf = minkit.FormulaPDF.unidimensional(
'pdf',
'pow(sin(a * x + b), 2)',
x, [a, b],
primitive='- sin(2 * (a * x + b)) -2 * (a * x + b) / (4 * a)')
assert np.allclose(norm, pdf.norm())
with helpers.fit_test(pdf) as test:
with minkit.minimizer('uml', pdf, data) as minimizer:
test.result = minimizer.migrad()
# In two dimensions
x = minkit.Parameter('x', bounds=(0, 10))
y = minkit.Parameter('y', bounds=(0, 10))
ax = minkit.Parameter('ax', -0.01, bounds=(-1, 0))
ay = minkit.Parameter('ay', -0.01, bounds=(-1, 0))
pdf = minkit.FormulaPDF('pdf', 'exp(ax * x) * exp(ay * y)', [x, y],
[ax, ay])
data = pdf.generate(10000)
with helpers.fit_test(pdf) as test:
with minkit.minimizer('uml', pdf, data) as minimizer:
test.result = minimizer.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:
p = minkit.pdf_from_json(json.load(fi))
check_pdfs(p, pdf)
def test_prodpdfs(tmpdir):
'''
Test the "ProdPDFs" class.
'''
# Create two Gaussians
mx = minkit.Parameter('mx', bounds=(-5, +5))
cx = minkit.Parameter('cx', 0., bounds=(-2, +2))
sx = minkit.Parameter('sx', 1., bounds=(0.1, +3))
gx = minkit.Gaussian('gx', mx, cx, sx)
my = minkit.Parameter('my', bounds=(-5, +5))
cy = minkit.Parameter('cy', 0., bounds=(-2, +2))
sy = minkit.Parameter('sy', 2., bounds=(0.5, +3))
gy = minkit.Gaussian('gy', my, cy, sy)
pdf = minkit.ProdPDFs('pdf', [gx, gy])
# Test integration
helpers.check_numerical_normalization(pdf)
# Test consteness of the PDFs
for p in gx.all_args:
p.constant = True
assert gx.constant and not pdf.constant
for p in gy.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()
# Do a simple fit
for p in pdf.all_real_args:
p.constant = False
data = pdf.generate(10000)
with fit_test(pdf) as test:
with minkit.minimizer('uml', pdf, data) as minimizer:
test.result = minimizer.migrad()
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_constpdf(tmpdir):
'''
Test a fit with a constant PDF.
'''
m = minkit.Parameter('m', bounds=(0, 10))
# Create an Exponential PDF
k = minkit.Parameter('k', -0.05)
e = minkit.Exponential('exponential', m, k)
# Create a Gaussian PDF
c = minkit.Parameter('c', 5., bounds=(0, 10))
s = minkit.Parameter('s', 1., bounds=(0.5, 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)
# Check for "get_values" and "set_values"
p = pdf.norm()
pdf.set_values(**pdf.get_values())
assert np.allclose(p, pdf.norm())
# Test a simple fit
data = pdf.generate(10000)
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_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_prodpdfs(tmpdir):
'''
Test the "ProdPDFs" class.
'''
# Create two Gaussians
mx = minkit.Parameter('mx', bounds=(-5, +5))
cx = minkit.Parameter('cx', 0., bounds=(-2, +2))
sx = minkit.Parameter('sx', 1., bounds=(-3, +3))
gx = minkit.Gaussian('gx', mx, cx, sx)
my = minkit.Parameter('my', bounds=(-5, +5))
cy = minkit.Parameter('cy', 0., bounds=(-2, +2))
sy = minkit.Parameter('sy', 1., bounds=(-3, +3))
gy = minkit.Gaussian('gy', my, cy, sy)
pdf = minkit.ProdPDFs('pdf', [gx, gy])
# Test integration
assert np.allclose(pdf.norm(), pdf.numerical_normalization())
# Test consteness of the PDFs
for p in gx.all_args:
p.constant = True
assert gx.constant and not pdf.constant
for p in gy.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)
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))
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 = aop.sum(data[m.name]) / len(data)
var = aop.sum((data[m.name] - mean)**2) / len(data)
assert np.allclose(var, s1.value**2 + s2.value**2, rtol=0.1)
# Ordinary check for PDFs
values, edges = np.histogram(data[m.name].as_ndarray(),
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), rtol=0.01)
# Test a fit
s2.constant = True # otherwise the minimization is undefined
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)
# Check copying the PDF
pdf.copy()
# Test for binned data samples
bdata = data.make_binned(20)
with fit_test(pdf) as test:
with minkit.minimizer('bml', pdf, bdata, minimizer='minuit') as minuit:
test.result = minuit.migrad()
