def test_backwards_compatibility(self):
"""
The LinearLeastSquares should give results compatible with the NumericalLeastSquare's
and curve_fit. To do this I test here the simple analytical model also used to calibrate
the definition of absolute_sigma.
"""
N = 1000
sigma = 31.4
xn = np.arange(N, dtype=np.float)
yn = np.zeros_like(xn)
np.random.seed(10)
yn = yn + np.random.normal(size=len(yn), scale=sigma)
a = Parameter()
y = Variable()
model = {y: a}
fit = LinearLeastSquares(model, y=yn, sigma_y=sigma, absolute_sigma=False)
fit_result = fit.execute()
fit = NumericalLeastSquares(model, y=yn, sigma_y=sigma, absolute_sigma=False)
num_result = fit.execute()
popt, pcov = curve_fit(lambda x, a: a * np.ones_like(x), xn, yn, sigma=sigma, absolute_sigma=False)
self.assertAlmostEqual(fit_result.value(a), num_result.value(a))
self.assertAlmostEqual(fit_result.stdev(a), num_result.stdev(a))
self.assertAlmostEqual(fit_result.value(a), popt[0], 5)
self.assertAlmostEqual(fit_result.stdev(a), pcov[0, 0]**0.5, 5)
fit = LinearLeastSquares(model, y=yn, sigma_y=sigma, absolute_sigma=True)
fit_result = fit.execute()
fit = NumericalLeastSquares(model, y=yn, sigma_y=sigma, absolute_sigma=True)
num_result = fit.execute()
popt, pcov = curve_fit(lambda x, a: a * np.ones_like(x), xn, yn, sigma=sigma, absolute_sigma=True)
self.assertAlmostEqual(fit_result.value(a), num_result.value(a))
self.assertAlmostEqual(fit_result.stdev(a), num_result.stdev(a))
self.assertAlmostEqual(fit_result.value(a), popt[0], 5)
self.assertAlmostEqual(fit_result.stdev(a), pcov[0, 0]**0.5, 5)
def test_linear_analytical_fit(self):
a, b = parameters('a, b')
x, y = variables('x, y')
model = {y: a * x + b}
data = [[0, 1], [1, 0], [3, 2], [5, 4]]
xdata, ydata = (np.array(i, dtype='float64') for i in zip(*data))
fit = LinearLeastSquares(model, x=xdata, y=ydata)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(a), 0.694915, 6) # values from Mathematica
self.assertAlmostEqual(fit_result.value(b), 0.186441, 6)
def test_linear_analytical_fit(self):
a, b = parameters('a, b')
x, y = variables('x, y')
model = {y: a * x + b}
data = [[0, 1], [1, 0], [3, 2], [5, 4]]
xdata, ydata = (np.array(i, dtype='float64') for i in zip(*data))
fit = LinearLeastSquares(model, x=xdata, y=ydata)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(a), 0.694915,
6) # values from Mathematica
self.assertAlmostEqual(fit_result.value(b), 0.186441, 6)
def test_backwards_compatibility(self):
"""
The LinearLeastSquares should give results compatible with the NumericalLeastSquare's
and curve_fit. To do this I test here the simple analytical model also used to calibrate
the definition of absolute_sigma.
"""
N = 1000
sigma = 31.4 * np.ones(N)
xn = np.arange(N, dtype=np.float)
yn = np.zeros_like(xn)
np.random.seed(10)
yn = yn + np.random.normal(size=len(yn), scale=sigma)
a = Parameter()
y = Variable()
model = {y: a}
fit = LinearLeastSquares(model,
y=yn,
sigma_y=sigma,
absolute_sigma=False)
fit_result = fit.execute()
fit = NumericalLeastSquares(model,
y=yn,
sigma_y=sigma,
absolute_sigma=False)
num_result = fit.execute()
popt, pcov = curve_fit(lambda x, a: a * np.ones_like(x),
xn,
yn,
sigma=sigma,
absolute_sigma=False)
self.assertAlmostEqual(fit_result.value(a), num_result.value(a))
self.assertAlmostEqual(fit_result.stdev(a), num_result.stdev(a))
self.assertAlmostEqual(fit_result.value(a), popt[0], 5)
self.assertAlmostEqual(fit_result.stdev(a), pcov[0, 0]**0.5, 5)
fit = LinearLeastSquares(model,
y=yn,
sigma_y=sigma,
absolute_sigma=True)
fit_result = fit.execute()
fit = NumericalLeastSquares(model,
y=yn,
sigma_y=sigma,
absolute_sigma=True)
num_result = fit.execute()
popt, pcov = curve_fit(lambda x, a: a * np.ones_like(x),
xn,
yn,
sigma=sigma,
absolute_sigma=True)
self.assertAlmostEqual(fit_result.value(a), num_result.value(a))
self.assertAlmostEqual(fit_result.stdev(a), num_result.stdev(a))
self.assertAlmostEqual(fit_result.value(a), popt[0], 5)
self.assertAlmostEqual(fit_result.stdev(a), pcov[0, 0]**0.5, 5)
