def test_error_advanced(self):
"""
Compare the error propagation of ConstrainedNumericalLeastSquares against
NumericalLeastSquares.
Models an example from the mathematica docs and try's to replicate it:
http://reference.wolfram.com/language/howto/FitModelsWithMeasurementErrors.html
"""
data = [[0.9, 6.1, 9.5], [3.9, 6., 9.7], [0.3, 2.8,
6.6], [1., 2.2, 5.9],
[1.8, 2.4, 7.2], [9., 1.7, 7.], [7.9, 8., 10.4],
[4.9, 3.9, 9.], [2.3, 2.6, 7.4], [4.7, 8.4, 10.]]
xdata, ydata, zdata = [np.array(data) for data in zip(*data)]
# errors = np.array([.4, .4, .2, .4, .1, .3, .1, .2, .2, .2])
a = Parameter(3.0)
b = Parameter(0.9)
c = Parameter(5.0)
x = Variable()
y = Variable()
z = Variable()
model = {z: a * log(b * x + c * y)}
const_fit = ConstrainedNumericalLeastSquares(model,
xdata,
ydata,
zdata,
absolute_sigma=False)
const_result = const_fit.execute()
fit = NumericalLeastSquares(model,
xdata,
ydata,
zdata,
absolute_sigma=False)
std_result = fit.execute()
self.assertEqual(const_fit.absolute_sigma, fit.absolute_sigma)
self.assertAlmostEqual(const_result.value(a), std_result.value(a), 4)
self.assertAlmostEqual(const_result.value(b), std_result.value(b), 4)
self.assertAlmostEqual(const_result.value(c), std_result.value(c), 4)
self.assertAlmostEqual(const_result.stdev(a), std_result.stdev(a), 4)
self.assertAlmostEqual(const_result.stdev(b), std_result.stdev(b), 4)
self.assertAlmostEqual(const_result.stdev(c), std_result.stdev(c), 4)
def test_error_advanced(self):
"""
Compare the error propagation of ConstrainedNumericalLeastSquares against
NumericalLeastSquares.
Models an example from the mathematica docs and try's to replicate it:
http://reference.wolfram.com/language/howto/FitModelsWithMeasurementErrors.html
"""
data = [
[0.9, 6.1, 9.5], [3.9, 6., 9.7], [0.3, 2.8, 6.6],
[1., 2.2, 5.9], [1.8, 2.4, 7.2], [9., 1.7, 7.],
[7.9, 8., 10.4], [4.9, 3.9, 9.], [2.3, 2.6, 7.4],
[4.7, 8.4, 10.]
]
xdata, ydata, zdata = [np.array(data) for data in zip(*data)]
# errors = np.array([.4, .4, .2, .4, .1, .3, .1, .2, .2, .2])
a = Parameter(3.0)
b = Parameter(0.9)
c = Parameter(5.0)
x = Variable()
y = Variable()
z = Variable()
model = {z: a * log(b * x + c * y)}
const_fit = ConstrainedNumericalLeastSquares(model, xdata, ydata, zdata, absolute_sigma=False)
const_result = const_fit.execute()
fit = NumericalLeastSquares(model, xdata, ydata, zdata, absolute_sigma=False)
std_result = fit.execute()
self.assertEqual(const_fit.absolute_sigma, fit.absolute_sigma)
self.assertAlmostEqual(const_result.value(a), std_result.value(a), 4)
self.assertAlmostEqual(const_result.value(b), std_result.value(b), 4)
self.assertAlmostEqual(const_result.value(c), std_result.value(c), 4)
self.assertAlmostEqual(const_result.stdev(a), std_result.stdev(a), 4)
self.assertAlmostEqual(const_result.stdev(b), std_result.stdev(b), 4)
self.assertAlmostEqual(const_result.stdev(c), std_result.stdev(c), 4)
def test_error_advanced(self):
"""
Models an example from the mathematica docs and try's to replicate it
using both symfit and scipy's curve_fit.
http://reference.wolfram.com/language/howto/FitModelsWithMeasurementErrors.html
"""
data = [
[0.9, 6.1, 9.5], [3.9, 6., 9.7], [0.3, 2.8, 6.6],
[1., 2.2, 5.9], [1.8, 2.4, 7.2], [9., 1.7, 7.],
[7.9, 8., 10.4], [4.9, 3.9, 9.], [2.3, 2.6, 7.4],
[4.7, 8.4, 10.]
]
xdata, ydata, zdata = [np.array(data) for data in zip(*data)]
xy = np.vstack((xdata, ydata))
# z = np.array(z)
errors = np.array([.4, .4, .2, .4, .1, .3, .1, .2, .2, .2])
# raise Exception(xy, z)
a = Parameter(value=3.0)
b = Parameter(value=0.9)
c = Parameter(value=5)
x = Variable('x')
y = Variable('y')
z = Variable('z')
model = {z: a * log(b * x + c * y)}
# fit = Fit(model, xy, z, absolute_sigma=False)
fit = Fit(model, xdata, ydata, zdata, absolute_sigma=False)
# fit = Fit(model, x=xdata, y=ydata, z=zdata, absolute_sigma=False)
fit_result = fit.execute()
# Same as Mathematica default behavior.
self.assertAlmostEqual(fit_result.value(a), 2.9956, 4)
self.assertAlmostEqual(fit_result.value(b), 0.563212, 4)
self.assertAlmostEqual(fit_result.value(c), 3.59732, 4)
self.assertAlmostEqual(fit_result.stdev(a), 0.278304, 4)
self.assertAlmostEqual(fit_result.stdev(b), 0.224107, 4)
self.assertAlmostEqual(fit_result.stdev(c), 0.980352, 4)
fit = Fit(model, xdata, ydata, zdata, absolute_sigma=True)
fit_result = fit.execute()
# Same as Mathematica in Measurement error mode, but without suplying
# any errors.
self.assertAlmostEqual(fit_result.value(a), 2.9956, 4)
self.assertAlmostEqual(fit_result.value(b), 0.563212, 4)
self.assertAlmostEqual(fit_result.value(c), 3.59732, 4)
self.assertAlmostEqual(fit_result.stdev(a), 0.643259, 4)
self.assertAlmostEqual(fit_result.stdev(b), 0.517992, 4)
self.assertAlmostEqual(fit_result.stdev(c), 2.26594, 4)
fit = Fit(model, xdata, ydata, zdata, sigma_z=errors)
fit_result = fit.execute()
popt, pcov, infodict, errmsg, ier = curve_fit(lambda x_vec, a, b, c: a * np.log(b * x_vec[0] + c * x_vec[1]), xy, zdata, sigma=errors, absolute_sigma=True, full_output=True)
# Same as curve_fit?
self.assertAlmostEqual(fit_result.value(a), popt[0], 4)
self.assertAlmostEqual(fit_result.value(b), popt[1], 4)
self.assertAlmostEqual(fit_result.value(c), popt[2], 4)
self.assertAlmostEqual(fit_result.stdev(a), np.sqrt(pcov[0,0]), 4)
self.assertAlmostEqual(fit_result.stdev(b), np.sqrt(pcov[1,1]), 4)
self.assertAlmostEqual(fit_result.stdev(c), np.sqrt(pcov[2,2]), 4)
# Same as Mathematica with MEASUREMENT ERROR
self.assertAlmostEqual(fit_result.value(a), 2.68807, 4)
self.assertAlmostEqual(fit_result.value(b), 0.941344, 4)
self.assertAlmostEqual(fit_result.value(c), 5.01541, 4)
self.assertAlmostEqual(fit_result.stdev(a), 0.0974628, 4)
self.assertAlmostEqual(fit_result.stdev(b), 0.247018, 4)
self.assertAlmostEqual(fit_result.stdev(c), 0.597661, 4)
def test_LogLikelihood():
"""
Tests if the LeastSquares objective gives the right shapes of output by
comparing with its analytical equivalent.
"""
# TODO: update these tests to use indexed variables in the future
a, b = parameters('a, b')
i = Idx('i', 100)
x, y = variables('x, y')
pdf = Exp(x, 1 / a) * Exp(x, b)
np.random.seed(10)
xdata = np.random.exponential(3.5, 100)
# We use minus loglikelihood for the model, because the objective was
# designed to find the maximum when used with a *minimizer*, so it has
# opposite sign. Also test MinimizeModel at the same time.
logL_model = Model({y: pdf})
logL_exact = Model({y: -FlattenSum(log(pdf), i)})
logL_numerical = LogLikelihood(logL_model, {x: xdata, y: None})
logL_minmodel = MinimizeModel(logL_exact, data={x: xdata, y: None})
# Test model jacobian and hessian shape
eval_exact = logL_exact(x=xdata, a=2, b=3)
jac_exact = logL_exact.eval_jacobian(x=xdata, a=2, b=3)
hess_exact = logL_exact.eval_hessian(x=xdata, a=2, b=3)
eval_minimizemodel = logL_minmodel(a=2, b=3)
jac_minimizemodel = logL_minmodel.eval_jacobian(a=2, b=3)
hess_minimizemodel = logL_minmodel.eval_hessian(a=2, b=3)
eval_numerical = logL_numerical(a=2, b=3)
jac_numerical = logL_numerical.eval_jacobian(a=2, b=3)
hess_numerical = logL_numerical.eval_hessian(a=2, b=3)
# TODO: These shapes should not have the ones! This is due to the current
# convention that scalars should be returned as a 1d array by Model's.
assert eval_exact[0].shape == (1, )
assert jac_exact[0].shape == (2, 1)
assert hess_exact[0].shape == (2, 2, 1)
# Test if identical to MinimizeModel
assert eval_exact[0] == pytest.approx(eval_minimizemodel)
assert jac_exact[0] == pytest.approx(jac_minimizemodel)
assert hess_exact[0] == pytest.approx(hess_minimizemodel)
# Test if these two models have the same call, jacobian, and hessian.
# Since models always have components as their first dimension, we have
# to slice that away.
assert eval_exact.y == pytest.approx(eval_numerical)
assert isinstance(eval_numerical, float)
assert isinstance(eval_exact.y[0], float)
assert np.squeeze(jac_exact[0], axis=-1) == pytest.approx(jac_numerical)
assert isinstance(jac_numerical, np.ndarray)
assert np.squeeze(hess_exact[0], axis=-1) == pytest.approx(hess_numerical)
assert isinstance(hess_numerical, np.ndarray)
fit = Fit(logL_exact, x=xdata, objective=MinimizeModel)
fit_exact_result = fit.execute()
fit = Fit(logL_model, x=xdata, objective=LogLikelihood)
fit_num_result = fit.execute()
assert fit_exact_result.value(a) == pytest.approx(fit_num_result.value(a))
assert fit_exact_result.value(b) == pytest.approx(fit_num_result.value(b))
assert fit_exact_result.stdev(a) == pytest.approx(fit_num_result.stdev(a))
assert fit_exact_result.stdev(b) == pytest.approx(fit_num_result.stdev(b))
def test_error_advanced(self):
"""
Models an example from the mathematica docs and try's to replicate it
using both symfit and scipy's curve_fit.
http://reference.wolfram.com/language/howto/FitModelsWithMeasurementErrors.html
"""
data = [
[0.9, 6.1, 9.5], [3.9, 6., 9.7], [0.3, 2.8, 6.6],
[1., 2.2, 5.9], [1.8, 2.4, 7.2], [9., 1.7, 7.],
[7.9, 8., 10.4], [4.9, 3.9, 9.], [2.3, 2.6, 7.4],
[4.7, 8.4, 10.]
]
xdata, ydata, zdata = [np.array(data) for data in zip(*data)]
xy = np.vstack((xdata, ydata))
# z = np.array(z)
errors = np.array([.4, .4, .2, .4, .1, .3, .1, .2, .2, .2])
# raise Exception(xy, z)
a = Parameter(3.0)
b = Parameter(0.9)
c = Parameter(5)
x = Variable()
y = Variable()
z = Variable()
model = {z: a * log(b * x + c * y)}
# fit = Fit(model, xy, z, absolute_sigma=False)
fit = Fit(model, xdata, ydata, zdata, absolute_sigma=False)
# fit = Fit(model, x=xdata, y=ydata, z=zdata, absolute_sigma=False)
fit_result = fit.execute()
# Same as Mathematica default behavior.
self.assertAlmostEqual(fit_result.value(a), 2.9956, 4)
self.assertAlmostEqual(fit_result.value(b), 0.563212, 4)
self.assertAlmostEqual(fit_result.value(c), 3.59732, 4)
self.assertAlmostEqual(fit_result.stdev(a), 0.278304, 4)
self.assertAlmostEqual(fit_result.stdev(b), 0.224107, 4)
self.assertAlmostEqual(fit_result.stdev(c), 0.980352, 4)
fit = Fit(model, xdata, ydata, zdata, absolute_sigma=True)
fit_result = fit.execute()
# Same as Mathematica in Measurement error mode, but without suplying
# any errors.
self.assertAlmostEqual(fit_result.value(a), 2.9956, 4)
self.assertAlmostEqual(fit_result.value(b), 0.563212, 4)
self.assertAlmostEqual(fit_result.value(c), 3.59732, 4)
self.assertAlmostEqual(fit_result.stdev(a), 0.643259, 4)
self.assertAlmostEqual(fit_result.stdev(b), 0.517992, 4)
self.assertAlmostEqual(fit_result.stdev(c), 2.26594, 4)
fit = Fit(model, xdata, ydata, zdata, sigma_z=errors)
fit_result = fit.execute()
popt, pcov, infodict, errmsg, ier = curve_fit(lambda x_vec, a, b, c: a * np.log(b * x_vec[0] + c * x_vec[1]), xy, zdata, sigma=errors, absolute_sigma=True, full_output=True)
# Same as curve_fit?
self.assertAlmostEqual(fit_result.value(a), popt[0], 4)
self.assertAlmostEqual(fit_result.value(b), popt[1], 4)
self.assertAlmostEqual(fit_result.value(c), popt[2], 4)
self.assertAlmostEqual(fit_result.stdev(a), np.sqrt(pcov[0,0]), 4)
self.assertAlmostEqual(fit_result.stdev(b), np.sqrt(pcov[1,1]), 4)
self.assertAlmostEqual(fit_result.stdev(c), np.sqrt(pcov[2,2]), 4)
# Same as Mathematica with MEASUREMENT ERROR
self.assertAlmostEqual(fit_result.value(a), 2.68807, 4)
self.assertAlmostEqual(fit_result.value(b), 0.941344, 4)
self.assertAlmostEqual(fit_result.value(c), 5.01541, 4)
self.assertAlmostEqual(fit_result.stdev(a), 0.0974628, 4)
self.assertAlmostEqual(fit_result.stdev(b), 0.247018, 4)
self.assertAlmostEqual(fit_result.stdev(c), 0.597661, 4)
def test_error_advanced(self):
"""
Compare the error propagation of Fit against
NumericalLeastSquares.
Models an example from the mathematica docs and try's to replicate it:
http://reference.wolfram.com/language/howto/FitModelsWithMeasurementErrors.html
"""
data = [
[0.9, 6.1, 9.5], [3.9, 6., 9.7], [0.3, 2.8, 6.6],
[1., 2.2, 5.9], [1.8, 2.4, 7.2], [9., 1.7, 7.],
[7.9, 8., 10.4], [4.9, 3.9, 9.], [2.3, 2.6, 7.4],
[4.7, 8.4, 10.]
]
xdata, ydata, zdata = [np.array(data) for data in zip(*data)]
# errors = np.array([.4, .4, .2, .4, .1, .3, .1, .2, .2, .2])
a = Parameter('a', 3.0)
b = Parameter('b', 0.9)
c = Parameter('c', 5.0)
x = Variable('x')
y = Variable('y')
z = Variable('z')
model = {z: a * log(b * x + c * y)}
const_fit = Fit(model, xdata, ydata, zdata, absolute_sigma=False)
self.assertEqual(len(const_fit.model(x=xdata, y=ydata, a=2, b=2, c=5)), 1)
self.assertEqual(
const_fit.model(x=xdata, y=ydata, a=2, b=2, c=5)[0].shape,
(10,)
)
self.assertEqual(len(const_fit.model.eval_jacobian(x=xdata, y=ydata, a=2, b=2, c=5)), 1)
self.assertEqual(
const_fit.model.eval_jacobian(x=xdata, y=ydata, a=2, b=2, c=5)[0].shape,
(3, 10)
)
self.assertEqual(len(const_fit.model.eval_hessian(x=xdata, y=ydata, a=2, b=2, c=5)), 1)
self.assertEqual(
const_fit.model.eval_hessian(x=xdata, y=ydata, a=2, b=2, c=5)[0].shape,
(3, 3, 10)
)
self.assertEqual(const_fit.objective(a=2, b=2, c=5).shape,
tuple())
self.assertEqual(
const_fit.objective.eval_jacobian(a=2, b=2, c=5).shape,
(3,)
)
self.assertEqual(
const_fit.objective.eval_hessian(a=2, b=2, c=5).shape,
(3, 3)
)
self.assertNotEqual(
const_fit.objective.eval_hessian(a=2, b=2, c=5).dtype,
object
)
const_result = const_fit.execute()
fit = Fit(model, xdata, ydata, zdata, absolute_sigma=False, minimizer=MINPACK)
std_result = fit.execute()
self.assertEqual(const_fit.absolute_sigma, fit.absolute_sigma)
self.assertAlmostEqual(const_result.value(a), std_result.value(a), 4)
self.assertAlmostEqual(const_result.value(b), std_result.value(b), 4)
self.assertAlmostEqual(const_result.value(c), std_result.value(c), 4)
# This used to be a tighter equality test, but since we now use the
# Hessian we actually get a more accurate value from the standard fit
# then for MINPACK. Hence we check if it is roughly equal, and if our
# stdev is greater than that of minpack.
self.assertAlmostEqual(const_result.stdev(a) / std_result.stdev(a), 1, 2)
self.assertAlmostEqual(const_result.stdev(b) / std_result.stdev(b), 1, 1)
self.assertAlmostEqual(const_result.stdev(c) / std_result.stdev(c), 1, 2)
self.assertGreaterEqual(const_result.stdev(a), std_result.stdev(a))
self.assertGreaterEqual(const_result.stdev(b), std_result.stdev(b))
self.assertGreaterEqual(const_result.stdev(c), std_result.stdev(c))
def test_error_advanced():
"""
Compare the error propagation of Fit against
NumericalLeastSquares.
Models an example from the mathematica docs and tries to replicate it:
http://reference.wolfram.com/language/howto/FitModelsWithMeasurementErrors.html
"""
data = [[0.9, 6.1, 9.5], [3.9, 6., 9.7], [0.3, 2.8, 6.6], [1., 2.2, 5.9],
[1.8, 2.4, 7.2], [9., 1.7, 7.], [7.9, 8., 10.4], [4.9, 3.9, 9.],
[2.3, 2.6, 7.4], [4.7, 8.4, 10.]]
xdata, ydata, zdata = [np.array(data) for data in zip(*data)]
# errors = np.array([.4, .4, .2, .4, .1, .3, .1, .2, .2, .2])
a = Parameter('a', 3.0)
b = Parameter('b', 0.9)
c = Parameter('c', 5.0)
x = Variable('x')
y = Variable('y')
z = Variable('z')
model = {z: a * log(b * x + c * y)}
const_fit = Fit(model, xdata, ydata, zdata, absolute_sigma=False)
assert len(const_fit.model(x=xdata, y=ydata, a=2, b=2, c=5)) == 1
assert const_fit.model(x=xdata, y=ydata, a=2, b=2, c=5)[0].shape == (10, )
assert len(const_fit.model.eval_jacobian(x=xdata, y=ydata, a=2, b=2,
c=5)) == 1
assert const_fit.model.eval_jacobian(x=xdata, y=ydata, a=2, b=2,
c=5)[0].shape == (3, 10)
assert len(const_fit.model.eval_hessian(x=xdata, y=ydata, a=2, b=2,
c=5)) == 1
assert const_fit.model.eval_hessian(x=xdata, y=ydata, a=2, b=2,
c=5)[0].shape == (3, 3, 10)
assert const_fit.objective(a=2, b=2, c=5).shape == tuple()
assert const_fit.objective.eval_jacobian(a=2, b=2, c=5).shape == (3, )
assert const_fit.objective.eval_hessian(a=2, b=2, c=5).shape == (3, 3)
assert const_fit.objective.eval_hessian(a=2, b=2, c=5).dtype != object
const_result = const_fit.execute()
fit = Fit(model,
xdata,
ydata,
zdata,
absolute_sigma=False,
minimizer=MINPACK)
std_result = fit.execute()
assert const_fit.absolute_sigma == fit.absolute_sigma
assert const_result.value(a) == pytest.approx(std_result.value(a), 1e-4)
assert const_result.value(b) == pytest.approx(std_result.value(b), 1e-4)
assert const_result.value(c) == pytest.approx(std_result.value(c), 1e-4)
# This used to be a tighter equality test, but since we now use the
# Hessian we actually get a more accurate value from the standard fit
# then for MINPACK. Hence we check if it is roughly equal, and if our
# stdev is greater than that of minpack.
assert const_result.stdev(a) / std_result.stdev(a) == pytest.approx(
1, 1e-2)
assert const_result.stdev(b) / std_result.stdev(b) == pytest.approx(
1, 1e-1)
assert const_result.stdev(c) / std_result.stdev(c) == pytest.approx(
1, 1e-2)
assert const_result.stdev(a) >= std_result.stdev(a)
assert const_result.stdev(b) >= std_result.stdev(b)
assert const_result.stdev(c) >= std_result.stdev(c)
