def test_vector_fitting(self):
"""
Test the behavior in the presence of bounds or constraints: `Fit` should
select `ConstrainedNumericalLeastSquares` when bounds or constraints are
provided, or for vector models in general. For scalar models, use
`NumericalLeastSquares`.
"""
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = {a_i: a, b_i: b, c_i: c}
xdata = np.array([
[10.1, 9., 10.5, 11.2, 9.5, 9.6, 10.],
[102.1, 101., 100.4, 100.8, 99.2, 100., 100.8],
[71.6, 73.2, 69.5, 70.2, 70.8, 70.6, 70.1],
])
# Make a new scalar model.
scalar_model = {a_i: a + b}
simple_fit = Fit(
model=scalar_model,
a_i=xdata[0],
)
self.assertIsInstance(simple_fit.fit, NumericalLeastSquares)
constrained_fit = Fit(model=scalar_model,
a_i=xdata[0],
constraints=[Equality(a + b, 110)])
self.assertIsInstance(constrained_fit.fit,
ConstrainedNumericalLeastSquares)
a.min = 0
a.max = 25
a.value = 10
b.min = 80
b.max = 120
b.value = 100
bound_fit = Fit(
model=scalar_model,
a_i=xdata[0],
)
self.assertIsInstance(bound_fit.fit, ConstrainedNumericalLeastSquares)
# Repeat all of the above for the Vector model
simple_fit = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
self.assertIsInstance(simple_fit.fit, ConstrainedNumericalLeastSquares)
constrained_fit = Fit(model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
constraints=[Equality(a + b + c, 180)])
self.assertIsInstance(constrained_fit.fit,
ConstrainedNumericalLeastSquares)
a.min = 0
a.max = 25
a.value = 10
b.min = 80
b.max = 120
b.value = 100
bound_fit = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
self.assertIsInstance(bound_fit.fit, ConstrainedNumericalLeastSquares)
fit_result = bound_fit.execute()
self.assertAlmostEqual(fit_result.value(a), np.mean(xdata[0]), 6)
self.assertAlmostEqual(fit_result.value(b), np.mean(xdata[1]), 6)
self.assertAlmostEqual(fit_result.value(c), np.mean(xdata[2]), 6)
def test_vector_fitting():
"""
Test the behavior in the presence of bounds or constraints: `Fit` should
select `ConstrainedNumericalLeastSquares` when bounds or constraints are
provided, or for vector models in general. For scalar models, use
`NumericalLeastSquares`.
"""
a, b = parameters('a, b')
a_i, = variables('a_i')
xdata = np.array([
[10.1, 9., 10.5, 11.2, 9.5, 9.6, 10.],
[102.1, 101., 100.4, 100.8, 99.2, 100., 100.8],
[71.6, 73.2, 69.5, 70.2, 70.8, 70.6, 70.1],
])
# Make a new scalar model.
scalar_model = {a_i: a + b}
simple_fit = Fit(model=scalar_model, a_i=xdata[0], minimizer=MINPACK)
assert isinstance(simple_fit.minimizer, MINPACK)
constrained_fit = Fit(model=scalar_model,
a_i=xdata[0],
constraints=[Equality(a + b, 110)])
assert isinstance(constrained_fit.minimizer, SLSQP)
a.min = 0
a.max = 25
a.value = 10
b.min = 80
b.max = 120
b.value = 100
bound_fit = Fit(
model=scalar_model,
a_i=xdata[0],
)
assert isinstance(bound_fit.minimizer, LBFGSB)
# Repeat all of the above for the Vector model
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = {a_i: a, b_i: b, c_i: c}
simple_fit = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
assert isinstance(simple_fit.minimizer, BFGS)
constrained_fit = Fit(model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
constraints=[Equality(a + b + c, 180)])
assert isinstance(constrained_fit.minimizer, SLSQP)
a.min = 0
a.max = 25
a.value = 10
b.min = 80
b.max = 120
b.value = 100
bound_fit = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
assert isinstance(bound_fit.minimizer, LBFGSB)
fit_result = bound_fit.execute()
assert fit_result.value(a) == pytest.approx(np.mean(xdata[0]), rel=1e-6)
assert fit_result.value(b) == pytest.approx(np.mean(xdata[1]), rel=1e-6)
assert fit_result.value(c) == pytest.approx(np.mean(xdata[2]), rel=1e-6)
def test_vector_constrained_fitting(self):
"""
Tests `Fit` with vector models. The
classical example of fitting measurements of the angles of a triangle is
taken. In this case we know they should add up to 180 degrees, so this
can be added as a constraint. Additionally, not even all three angles
have to be provided with measurement data since the constrained means
the angles are not independent.
"""
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = {a_i: a, b_i: b, c_i: c}
xdata = np.array([
[10.1, 9., 10.5, 11.2, 9.5, 9.6, 10.],
[102.1, 101., 100.4, 100.8, 99.2, 100., 100.8],
[71.6, 73.2, 69.5, 70.2, 70.8, 70.6, 70.1],
])
fit_none = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=None,
)
fit = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
fit_std = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
minimizer = MINPACK
)
fit_constrained = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
constraints=[Equality(a + b + c, 180)]
)
fit_none_result = fit_none.execute()
fit_new_result = fit.execute()
std_result = fit_std.execute()
constr_result = fit_constrained.execute()
# The total of averages should equal the total of the params by definition
mean_total = np.mean(np.sum(xdata, axis=0))
params_tot = std_result.value(a) + std_result.value(b) + std_result.value(c)
self.assertAlmostEqual(mean_total / params_tot, 1.0, 4)
# The total after constraining to 180 should be exactly 180.
params_tot = constr_result.value(a) + constr_result.value(b) + constr_result.value(c)
self.assertIsInstance(fit_constrained.minimizer, SLSQP)
self.assertAlmostEqual(180.0, params_tot, 4)
# The standard method and the Constrained object called without constraints
# should behave roughly the same.
self.assertAlmostEqual(fit_new_result.value(a), std_result.value(a), 4)
self.assertAlmostEqual(fit_new_result.value(b), std_result.value(b), 4)
self.assertAlmostEqual(fit_new_result.value(c), std_result.value(c), 4)
# When fitting with a dataset set to None, for this example the value of c
# should be unaffected.
self.assertAlmostEqual(fit_none_result.value(a), std_result.value(a), 4)
self.assertAlmostEqual(fit_none_result.value(b), std_result.value(b), 4)
self.assertAlmostEqual(fit_none_result.value(c), c.value)
fit_none_constr = Fit(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=None,
constraints=[Equality(a + b + c, 180)]
)
none_constr_result = fit_none_constr.execute()
params_tot = none_constr_result.value(a) + none_constr_result.value(b) + none_constr_result.value(c)
self.assertAlmostEqual(180.0, params_tot, 4)