def test_fixed_parameters_2():
"""
Make sure parameter boundaries are respected
"""
x = Parameter('x', min=1)
y = Variable('y')
model = Model({y: x**2})
bounded_minimizers = list(subclasses(BoundedMinimizer))
for minimizer in bounded_minimizers:
if minimizer is MINPACK:
# Not a MINPACKable problem because it only has a param
continue
fit = Fit(model, minimizer=minimizer)
assert isinstance(fit.objective, MinimizeModel)
if minimizer is DifferentialEvolution:
# Also needs a max
x.max = 10
fit_result = fit.execute()
x.max = None
else:
fit_result = fit.execute()
assert fit_result.value(x) >= 1.0
assert fit_result.value(x) <= 2.0
assert fit.minimizer.bounds == [(1, None)]
def test_fixed_parameters():
"""
Make sure fixed parameters don't change on fitting
"""
a, b, c, d = parameters('a, b, c, d')
x, y = variables('x, y')
c.value = 4.0
a.min, a.max = 1.0, 5.0 # Bounds are needed for DifferentialEvolution
b.min, b.max = 1.0, 5.0
c.min, c.max = 1.0, 5.0
d.min, d.max = 1.0, 5.0
c.fixed = True
model = Model({y: a * exp(-(x - b)**2 / (2 * c**2)) + d})
# Generate data
xdata = np.linspace(0, 100)
ydata = model(xdata, a=2, b=3, c=2, d=2).y
for minimizer in subclasses(BaseMinimizer):
if minimizer is ChainedMinimizer:
continue
else:
fit = Fit(model, x=xdata, y=ydata, minimizer=minimizer)
fit_result = fit.execute()
# Should still be 4.0, not 2.0!
assert 4.0 == fit_result.params['c']
def test_constrainedminimizers(self):
"""
Compare the different constrained minimizers, to make sure all support
constraints, and converge to the same answer.
"""
minimizers = list(subclasses(ScipyConstrainedMinimize))
x = Parameter('x', value=-1.0)
y = Parameter('y', value=1.0)
z = Variable('z')
model = Model({z: 2 * x * y + 2 * x - x ** 2 - 2 * y ** 2})
# First we try an unconstrained fit
results = []
for minimizer in minimizers:
fit = Fit(- model, minimizer=minimizer)
fit_result = fit.execute(tol=1e-15)
results.append(fit_result)
# Compare the parameter values.
for r1, r2 in zip(results[:-1], results[1:]):
self.assertAlmostEqual(r1.value(x), r2.value(x), 6)
self.assertAlmostEqual(r1.value(y), r2.value(y), 6)
np.testing.assert_almost_equal(r1.covariance_matrix,
r2.covariance_matrix)
constraints = [
Ge(y - 1, 0), # y - 1 >= 0,
Eq(x ** 3 - y, 0), # x**3 - y == 0,
]
# Constrained fit.
results = []
for minimizer in minimizers:
if minimizer is COBYLA:
# COBYLA only supports inequility.
continue
fit = Fit(- model, constraints=constraints, minimizer=minimizer)
fit_result = fit.execute(tol=1e-15)
results.append(fit_result)
for r1, r2 in zip(results[:-1], results[1:]):
self.assertAlmostEqual(r1.value(x), r2.value(x), 6)
self.assertAlmostEqual(r1.value(y), r2.value(y), 6)
np.testing.assert_almost_equal(r1.covariance_matrix,
r2.covariance_matrix)
def test_constrainedminimizers():
"""
Compare the different constrained minimizers, to make sure all support
constraints, and converge to the same answer.
"""
minimizers = list(subclasses(ScipyConstrainedMinimize))
x = Parameter('x', value=-1.0)
y = Parameter('y', value=1.0)
z = Variable('z')
model = Model({z: 2 * x * y + 2 * x - x**2 - 2 * y**2})
# First we try an unconstrained fit
results = []
for minimizer in minimizers:
fit = Fit(-model, minimizer=minimizer)
assert isinstance(fit.objective, MinimizeModel)
fit_result = fit.execute(tol=1e-15)
results.append(fit_result)
# Compare the parameter values.
for r1, r2 in zip(results[:-1], results[1:]):
assert r1.value(x) == pytest.approx(r2.value(x), 1e-6)
assert r1.value(y) == pytest.approx(r2.value(y), 1e-6)
assert r1.covariance_matrix == pytest.approx(r2.covariance_matrix)
constraints = [
Ge(y - 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
# Constrained fit.
results = []
for minimizer in minimizers:
if minimizer is COBYLA:
# COBYLA only supports inequality.
continue
fit = Fit(-model, constraints=constraints, minimizer=minimizer)
fit_result = fit.execute(tol=1e-15)
results.append(fit_result)
for r1, r2 in zip(results[:-1], results[1:]):
assert r1.value(x) == pytest.approx(r2.value(x), 1e-6)
assert r1.value(y) == pytest.approx(r2.value(y), 1e-6)
assert r1.covariance_matrix == pytest.approx(r2.covariance_matrix)
def test_non_boundaries(self):
"""
Make sure parameter boundaries are not invented
"""
x = Parameter('x')
y = Variable('y')
model = Model({y: x**2})
bounded_minimizers = list(subclasses(BoundedMinimizer))
bounded_minimizers = [minimizer for minimizer in bounded_minimizers
if minimizer is not DifferentialEvolution]
for minimizer in bounded_minimizers:
fit = Fit(model, minimizer=minimizer)
if minimizer is MINPACK:
pass # Not a MINPACKable problem because it only has a param
else:
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(x), 0.0)
self.assertEqual(fit.minimizer.bounds, [(None, None)])
def test_non_boundaries():
"""
Make sure parameter boundaries are not invented
"""
x = Parameter('x')
y = Variable('y')
model = Model({y: x**2})
bounded_minimizers = list(subclasses(BoundedMinimizer))
bounded_minimizers = [
minimizer for minimizer in bounded_minimizers
if minimizer is not DifferentialEvolution
]
for minimizer in bounded_minimizers:
# Not a MINPACKable problem because it only has a param
if minimizer is MINPACK:
continue
fit = Fit(model, minimizer=minimizer)
fit_result = fit.execute()
assert fit_result.value(x) == pytest.approx(0.0)
assert fit.minimizer.bounds == [(None, None)]
def test_boundaries(self):
"""
Make sure parameter boundaries are respected
"""
x = Parameter('x', min=1)
y = Variable('y')
model = Model({y: x**2})
bounded_minimizers = list(subclasses(BoundedMinimizer))
for minimizer in bounded_minimizers:
fit = Fit(model, minimizer=minimizer)
if minimizer is DifferentialEvolution:
# Also needs a max
x.max = 10
fit_result = fit.execute()
x.max = None
elif minimizer is MINPACK:
pass # Not a MINPACKable problem because it only has a param
else:
fit_result = fit.execute()
self.assertGreaterEqual(fit_result.value(x), 1.0)
self.assertLessEqual(fit_result.value(x), 2.0)
self.assertEqual(fit.minimizer.bounds, [(1, None)])