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639 lines
20 KiB
Python
639 lines
20 KiB
Python
import numpy as np
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import autograd.numpy as anp
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import math
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import scipy.optimize
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from scipy.odr import ODR, Model, RealData
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from scipy.linalg import cholesky
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from scipy.stats import norm
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import pyerrors as pe
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import pytest
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np.random.seed(0)
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def test_fit_lin():
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x = [0, 2]
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y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
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pe.pseudo_Obs(2, 0.1, 'ensemble')]
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res = pe.fits.fit_lin(x, y)
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assert res[0] == y[0]
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assert res[1] == (y[1] - y[0]) / (x[1] - x[0])
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x = y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
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pe.pseudo_Obs(2, 0.1, 'ensemble')]
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res = pe.fits.fit_lin(x, y)
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m = (y[1] - y[0]) / (x[1] - x[0])
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assert res[0] == y[1] - x[1] * m
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assert res[1] == m
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def test_least_squares():
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dim = 10 + int(30 * np.random.rand())
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x = np.arange(dim)
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y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
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yerr = 0.1 + 0.1 * np.random.rand(dim)
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oy = []
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for i, item in enumerate(x):
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oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))
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def f(x, a, b):
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return a * anp.exp(-b * x)
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popt, pcov = scipy.optimize.curve_fit(f, x, y, sigma=[o.dvalue for o in oy], absolute_sigma=True)
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def func(a, x):
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y = a[0] * anp.exp(-a[1] * x)
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return y
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out = pe.least_squares(x, oy, func, expected_chisquare=True, resplot=True, qqplot=True)
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beta = out.fit_parameters
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str(out)
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repr(out)
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len(out)
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for i in range(2):
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beta[i].gamma_method(S=1.0)
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assert math.isclose(beta[i].value, popt[i], abs_tol=1e-5)
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assert math.isclose(pcov[i, i], beta[i].dvalue ** 2, abs_tol=1e-3)
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chi2_pyerrors = np.sum(((f(x, *[o.value for o in beta]) - y) / yerr) ** 2) / (len(x) - 2)
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chi2_scipy = np.sum(((f(x, *popt) - y) / yerr) ** 2) / (len(x) - 2)
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assert math.isclose(chi2_pyerrors, chi2_scipy, abs_tol=1e-10)
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out = pe.least_squares(x, oy, func, const_par=[beta[1]])
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assert((out.fit_parameters[0] - beta[0]).is_zero())
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assert((out.fit_parameters[1] - beta[1]).is_zero())
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oyc = []
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for i, item in enumerate(x):
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oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'cov' + str(i)))
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outc = pe.least_squares(x, oyc, func)
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betac = outc.fit_parameters
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for i in range(2):
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betac[i].gamma_method(S=1.0)
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assert math.isclose(betac[i].value, popt[i], abs_tol=1e-5)
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assert math.isclose(pcov[i, i], betac[i].dvalue ** 2, abs_tol=1e-3)
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def test_alternative_solvers():
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dim = 192
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x = np.arange(dim)
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y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
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yerr = 0.1 + 0.1 * np.random.rand(dim)
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oy = []
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for i, item in enumerate(x):
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oy.append(pe.pseudo_Obs(y[i], yerr[i], 'test'))
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def func(a, x):
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y = a[0] * anp.exp(-a[1] * x)
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return y
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chisquare_values = []
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out = pe.least_squares(x, oy, func, method='migrad')
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chisquare_values.append(out.chisquare)
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out = pe.least_squares(x, oy, func, method='Powell')
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chisquare_values.append(out.chisquare)
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out = pe.least_squares(x, oy, func, method='Nelder-Mead')
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chisquare_values.append(out.chisquare)
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out = pe.least_squares(x, oy, func, method='Levenberg-Marquardt')
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chisquare_values.append(out.chisquare)
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chisquare_values = np.array(chisquare_values)
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assert np.all(np.isclose(chisquare_values, chisquare_values[0]))
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def test_correlated_fit():
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num_samples = 400
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N = 10
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x = norm.rvs(size=(N, num_samples))
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r = np.zeros((N, N))
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for i in range(N):
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for j in range(N):
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r[i, j] = np.exp(-0.8 * np.fabs(i - j))
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errl = np.sqrt([3.4, 2.5, 3.6, 2.8, 4.2, 4.7, 4.9, 5.1, 3.2, 4.2])
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for i in range(N):
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for j in range(N):
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r[i, j] *= errl[i] * errl[j]
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c = cholesky(r, lower=True)
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y = np.dot(c, x)
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x = np.arange(N)
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for linear in [True, False]:
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data = []
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for i in range(N):
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if linear:
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data.append(pe.Obs([[i + 1 + o for o in y[i]]], ['ens']))
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else:
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data.append(pe.Obs([[np.exp(-(i + 1)) + np.exp(-(i + 1)) * o for o in y[i]]], ['ens']))
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[o.gamma_method() for o in data]
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if linear:
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def fitf(p, x):
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return p[1] + p[0] * x
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else:
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def fitf(p, x):
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return p[1] * anp.exp(-p[0] * x)
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fitp = pe.least_squares(x, data, fitf, expected_chisquare=True)
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assert np.isclose(fitp.chisquare / fitp.dof, fitp.chisquare_by_dof, atol=1e-14)
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fitpc = pe.least_squares(x, data, fitf, correlated_fit=True)
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assert np.isclose(fitpc.chisquare / fitpc.dof, fitpc.chisquare_by_dof, atol=1e-14)
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for i in range(2):
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diff = fitp[i] - fitpc[i]
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diff.gamma_method()
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assert(diff.is_zero_within_error(sigma=5))
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def test_fit_corr_independent():
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dim = 50
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x = np.arange(dim)
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y = 0.84 * np.exp(-0.12 * x) + np.random.normal(0.0, 0.1, dim)
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yerr = [0.1] * dim
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oy = []
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for i, item in enumerate(x):
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oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))
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def func(a, x):
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y = a[0] * anp.exp(-a[1] * x)
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return y
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for method in ["Levenberg-Marquardt", "migrad", "Nelder-Mead"]:
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out = pe.least_squares(x, oy, func, method=method)
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out_corr = pe.least_squares(x, oy, func, correlated_fit=True, method=method)
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assert np.isclose(out.chisquare, out_corr.chisquare)
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assert np.isclose(out.dof, out_corr.dof)
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assert np.isclose(out.chisquare_by_dof, out_corr.chisquare_by_dof)
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assert (out[0] - out_corr[0]).is_zero(atol=1e-5)
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assert (out[1] - out_corr[1]).is_zero(atol=1e-5)
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def test_linear_fit_guesses():
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for err in [10, 0.1, 0.001]:
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xvals = []
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yvals = []
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for x in range(1, 8, 2):
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xvals.append(x)
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yvals.append(pe.pseudo_Obs(x + np.random.normal(0.0, err), err, 'test1') + pe.pseudo_Obs(0, err / 100, 'test2', samples=87))
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lin_func = lambda a, x: a[0] + a[1] * x
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with pytest.raises(Exception):
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pe.least_squares(xvals, yvals, lin_func)
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[o.gamma_method() for o in yvals]
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with pytest.raises(Exception):
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pe.least_squares(xvals, yvals, lin_func, initial_guess=[5])
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bad_guess = pe.least_squares(xvals, yvals, lin_func, initial_guess=[999, 999])
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good_guess = pe.least_squares(xvals, yvals, lin_func, initial_guess=[0, 1])
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assert np.isclose(bad_guess.chisquare, good_guess.chisquare, atol=1e-8)
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assert np.all([(go - ba).is_zero(atol=1e-6) for (go, ba) in zip(good_guess, bad_guess)])
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def test_total_least_squares():
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dim = 10 + int(30 * np.random.rand())
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x = np.arange(dim) + np.random.normal(0.0, 0.15, dim)
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xerr = 0.1 + 0.1 * np.random.rand(dim)
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y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
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yerr = 0.1 + 0.1 * np.random.rand(dim)
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ox = []
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for i, item in enumerate(x):
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ox.append(pe.pseudo_Obs(x[i], xerr[i], str(i)))
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oy = []
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for i, item in enumerate(x):
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oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))
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def f(x, a, b):
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return a * anp.exp(-b * x)
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def func(a, x):
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y = a[0] * anp.exp(-a[1] * x)
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return y
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data = RealData([o.value for o in ox], [o.value for o in oy], sx=[o.dvalue for o in ox], sy=[o.dvalue for o in oy])
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model = Model(func)
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odr = ODR(data, model, [0, 0], partol=np.finfo(np.float64).eps)
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odr.set_job(fit_type=0, deriv=1)
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output = odr.run()
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out = pe.total_least_squares(ox, oy, func, expected_chisquare=True)
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beta = out.fit_parameters
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str(out)
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repr(out)
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len(out)
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for i in range(2):
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beta[i].gamma_method(S=1.0)
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assert math.isclose(beta[i].value, output.beta[i], rel_tol=1e-5)
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assert math.isclose(output.cov_beta[i, i], beta[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(beta[i].dvalue ** 2)
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out = pe.total_least_squares(ox, oy, func, const_par=[beta[1]])
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diff = out.fit_parameters[0] - beta[0]
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assert(diff / beta[0] < 1e-3 * beta[0].dvalue)
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assert((out.fit_parameters[1] - beta[1]).is_zero())
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oxc = []
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for i, item in enumerate(x):
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oxc.append(pe.cov_Obs(x[i], xerr[i]**2, 'covx' + str(i)))
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oyc = []
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for i, item in enumerate(x):
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oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'covy' + str(i)))
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outc = pe.total_least_squares(oxc, oyc, func)
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betac = outc.fit_parameters
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for i in range(2):
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betac[i].gamma_method(S=1.0)
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assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
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assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
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outc = pe.total_least_squares(oxc, oyc, func, const_par=[betac[1]])
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diffc = outc.fit_parameters[0] - betac[0]
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assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
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assert((outc.fit_parameters[1] - betac[1]).is_zero())
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outc = pe.total_least_squares(oxc, oy, func)
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betac = outc.fit_parameters
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for i in range(2):
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betac[i].gamma_method(S=1.0)
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assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
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assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
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outc = pe.total_least_squares(oxc, oy, func, const_par=[betac[1]])
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diffc = outc.fit_parameters[0] - betac[0]
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assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
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assert((outc.fit_parameters[1] - betac[1]).is_zero())
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def test_odr_derivatives():
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x = []
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y = []
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x_err = 0.01
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y_err = 0.01
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for n in np.arange(1, 9, 2):
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loc_xvalue = n + np.random.normal(0.0, x_err)
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x.append(pe.pseudo_Obs(loc_xvalue, x_err, str(n)))
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y.append(pe.pseudo_Obs((lambda x: x ** 2 - 1)(loc_xvalue) +
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np.random.normal(0.0, y_err), y_err, str(n)))
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def func(a, x):
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return a[0] + a[1] * x ** 2
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out = pe.total_least_squares(x, y, func)
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fit1 = out.fit_parameters
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tfit = fit_general(x, y, func, base_step=0.1, step_ratio=1.1, num_steps=20)
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assert np.abs(np.max(np.array(list(fit1[1].deltas.values()))
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- np.array(list(tfit[1].deltas.values())))) < 10e-8
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def test_r_value_persistence():
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def f(a, x):
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return a[0] + a[1] * x
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a = pe.pseudo_Obs(1.1, .1, 'a')
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assert np.isclose(a.value, a.r_values['a'])
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a_2 = a ** 2
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assert np.isclose(a_2.value, a_2.r_values['a'])
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b = pe.pseudo_Obs(2.1, .2, 'b')
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y = [a, b]
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[o.gamma_method() for o in y]
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fitp = pe.fits.least_squares([1, 2], y, f)
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assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
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assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
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assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
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assert np.isclose(fitp[1].value, fitp[1].r_values['b'])
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fitp = pe.fits.total_least_squares(y, y, f)
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assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
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assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
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assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
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assert np.isclose(fitp[1].value, fitp[1].r_values['b'])
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fitp = pe.fits.least_squares([1, 2], y, f, priors=y)
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assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
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assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
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assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
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assert np.isclose(fitp[1].value, fitp[1].r_values['b'])
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def test_prior_fit():
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def f(a, x):
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return a[0] + a[1] * x
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a = pe.pseudo_Obs(0.0, 0.1, 'a')
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b = pe.pseudo_Obs(1.0, 0.2, 'a')
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y = [a, b]
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with pytest.raises(Exception):
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fitp = pe.fits.least_squares([0, 1], 1 * np.array(y), f, priors=['0.0(8)', '1.0(8)'])
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[o.gamma_method() for o in y]
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fitp = pe.fits.least_squares([0, 1], y, f, priors=['0.0(8)', '1.0(8)'])
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fitp = pe.fits.least_squares([0, 1], y, f, priors=y, resplot=True, qqplot=True)
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def test_correlated_fit_covobs():
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x1 = pe.cov_Obs(1.01, 0.01 ** 2, 'test1')
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x2 = pe.cov_Obs(2.01, 0.01 ** 2, 'test2')
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x3 = pe.cov_Obs(2.99, 0.01 ** 2, 'test3')
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[o.gamma_method() for o in [x1, x2, x3]]
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def func(a, x):
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return a[0] * x + a[1]
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fit_res = pe.fits.least_squares(np.arange(1, 4), [x1, x2, x3], func, expected_chisquare=True)
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assert np.isclose(fit_res.chisquare_by_dof, fit_res.chisquare_by_expected_chisquare)
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fit_res_corr = pe.fits.least_squares(np.arange(1, 4), [x1, x2, x3], func, correlated_fit=True)
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assert np.isclose(fit_res.chisquare_by_dof, fit_res_corr.chisquare_by_dof)
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def test_error_band():
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def f(a, x):
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return a[0] + a[1] * x
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a = pe.pseudo_Obs(0.0, 0.1, 'a')
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b = pe.pseudo_Obs(1.0, 0.2, 'a')
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x = [0, 1]
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y = [a, b]
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fitp = pe.fits.least_squares(x, y, f)
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with pytest.raises(Exception):
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pe.fits.error_band(x, f, fitp.fit_parameters)
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fitp.gamma_method()
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pe.fits.error_band(x, f, fitp.fit_parameters)
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def test_fit_vs_jackknife():
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od = 0.9999999999
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cov1 = np.array([[1, od, od], [od, 1.0, od], [od, od, 1.0]])
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cov1 *= 0.05
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nod = -0.4
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cov2 = np.array([[1, nod, nod], [nod, 1.0, nod], [nod, nod, 1.0]])
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cov2 *= 0.05
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cov3 = np.identity(3)
|
|
cov3 *= 0.05
|
|
samples = 500
|
|
|
|
for i, cov in enumerate([cov1, cov2, cov3]):
|
|
dat = pe.misc.gen_correlated_data(np.arange(1, 4), cov, 'test', 0.5, samples=samples)
|
|
[o.gamma_method(S=0) for o in dat]
|
|
func = lambda a, x: a[0] + a[1] * x
|
|
fr = pe.least_squares(np.arange(1, 4), dat, func)
|
|
fr.gamma_method(S=0)
|
|
|
|
jd = np.array([o.export_jackknife() for o in dat]).T
|
|
jfr = []
|
|
for jacks in jd:
|
|
|
|
def chisqfunc_residuals(p):
|
|
model = func(p, np.arange(1, 4))
|
|
chisq = ((jacks - model) / [o.dvalue for o in dat])
|
|
return chisq
|
|
|
|
tf = scipy.optimize.least_squares(chisqfunc_residuals, [0.0, 0.0], method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
|
|
jfr.append(tf.x)
|
|
ajfr = np.array(jfr).T
|
|
err = np.array([np.sqrt(np.var(ajfr[j][1:], ddof=0) * (samples - 1)) for j in range(2)])
|
|
assert np.allclose(err, [o.dvalue for o in fr], atol=1e-8)
|
|
|
|
def test_correlated_fit_vs_jackknife():
|
|
od = 0.999999
|
|
cov1 = np.array([[1, od, od], [od, 1.0, od], [od, od, 1.0]])
|
|
cov1 *= 0.1
|
|
nod = -0.44
|
|
cov2 = np.array([[1, nod, nod], [nod, 1.0, nod], [nod, nod, 1.0]])
|
|
cov2 *= 0.1
|
|
cov3 = np.identity(3)
|
|
cov3 *= 0.01
|
|
|
|
samples = 250
|
|
x_val = np.arange(1, 6, 2)
|
|
for i, cov in enumerate([cov1, cov2, cov3]):
|
|
dat = pe.misc.gen_correlated_data(x_val + x_val ** 2 + np.random.normal(0.0, 0.1, 3), cov, 'test', 0.5, samples=samples)
|
|
[o.gamma_method(S=0) for o in dat]
|
|
func = lambda a, x: a[0] * x + a[1] * x ** 2
|
|
fr = pe.least_squares(x_val, dat, func, correlated_fit=True, silent=True)
|
|
[o.gamma_method(S=0) for o in fr]
|
|
|
|
cov = pe.covariance(dat)
|
|
chol = np.linalg.cholesky(cov)
|
|
chol_inv = np.linalg.inv(chol)
|
|
|
|
jd = np.array([o.export_jackknife() for o in dat]).T
|
|
jfr = []
|
|
for jacks in jd:
|
|
|
|
def chisqfunc_residuals(p):
|
|
model = func(p, x_val)
|
|
chisq = np.dot(chol_inv, (jacks - model))
|
|
return chisq
|
|
|
|
tf = scipy.optimize.least_squares(chisqfunc_residuals, [0.0, 0.0], method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
|
|
jfr.append(tf.x)
|
|
ajfr = np.array(jfr).T
|
|
err = np.array([np.sqrt(np.var(ajfr[j][1:], ddof=0) * (samples - 1)) for j in range(2)])
|
|
assert np.allclose(err, [o.dvalue for o in fr], atol=1e-7)
|
|
assert np.allclose(ajfr.T[0], [o.value for o in fr], atol=1e-8)
|
|
|
|
|
|
def test_fit_no_autograd():
|
|
dim = 10
|
|
x = np.arange(dim)
|
|
y = 2 * np.exp(-0.08 * x) + np.random.normal(0.0, 0.15, dim)
|
|
yerr = 0.1 + 0.1 * np.random.rand(dim)
|
|
|
|
oy = []
|
|
for i, item in enumerate(x):
|
|
oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))
|
|
|
|
def func(a, x):
|
|
y = a[0] * np.exp(-a[1] * x)
|
|
return y
|
|
|
|
with pytest.raises(Exception):
|
|
pe.least_squares(x, oy, func)
|
|
|
|
with pytest.raises(Exception):
|
|
pe.total_least_squares(oy, oy, func)
|
|
|
|
|
|
def test_invalid_fit_function():
|
|
def func1(a, x):
|
|
return a[0] + a[1] * x + a[2] * anp.sinh(x) + a[199]
|
|
|
|
def func2(a, x, y):
|
|
return a[0] + a[1] * x
|
|
|
|
def func3(x):
|
|
return x
|
|
|
|
xvals =[]
|
|
yvals =[]
|
|
err = 0.1
|
|
|
|
for x in range(1, 8, 2):
|
|
xvals.append(x)
|
|
yvals.append(pe.pseudo_Obs(x + np.random.normal(0.0, err), err, 'test1') + pe.pseudo_Obs(0, err / 100, 'test2', samples=87))
|
|
[o.gamma_method() for o in yvals]
|
|
for func in [func1, func2, func3]:
|
|
with pytest.raises(Exception):
|
|
pe.least_squares(xvals, yvals, func)
|
|
with pytest.raises(Exception):
|
|
pe.total_least_squares(yvals, yvals, func)
|
|
|
|
|
|
def test_singular_correlated_fit():
|
|
obs1 = pe.pseudo_Obs(1.0, 0.1, 'test')
|
|
with pytest.raises(Exception):
|
|
pe.fits.fit_lin([0, 1], [obs1, obs1], correlated_fit=True)
|
|
|
|
|
|
def test_ks_test():
|
|
def f(a, x):
|
|
y = a[0] + a[1] * x
|
|
return y
|
|
|
|
fit_res = []
|
|
|
|
for i in range(20):
|
|
data = []
|
|
for j in range(10):
|
|
data.append(pe.pseudo_Obs(j + np.random.normal(0.0, 0.25), 0.25, 'test'))
|
|
my_corr = pe.Corr(data)
|
|
|
|
fit_res.append(my_corr.fit(f, silent=True))
|
|
|
|
pe.fits.ks_test()
|
|
pe.fits.ks_test(fit_res)
|
|
|
|
|
|
def fit_general(x, y, func, silent=False, **kwargs):
|
|
"""Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
|
|
|
|
Plausibility of the results should be checked. To control the numerical differentiation
|
|
the kwargs of numdifftools.step_generators.MaxStepGenerator can be used.
|
|
|
|
func has to be of the form
|
|
|
|
def func(a, x):
|
|
y = a[0] + a[1] * x + a[2] * np.sinh(x)
|
|
return y
|
|
|
|
y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.
|
|
x can either be a list of floats in which case no xerror is assumed, or
|
|
a list of Obs, where the dvalues of the Obs are used as xerror for the fit.
|
|
|
|
Keyword arguments
|
|
-----------------
|
|
silent -- If true all output to the console is omitted (default False).
|
|
initial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits
|
|
with many parameters.
|
|
"""
|
|
|
|
if not callable(func):
|
|
raise TypeError('func has to be a function.')
|
|
|
|
for i in range(10):
|
|
try:
|
|
func(np.arange(i), 0)
|
|
except:
|
|
pass
|
|
else:
|
|
break
|
|
n_parms = i
|
|
if not silent:
|
|
print('Fit with', n_parms, 'parameters')
|
|
|
|
global print_output, beta0
|
|
print_output = 1
|
|
if 'initial_guess' in kwargs:
|
|
beta0 = kwargs.get('initial_guess')
|
|
if len(beta0) != n_parms:
|
|
raise Exception('Initial guess does not have the correct length.')
|
|
else:
|
|
beta0 = np.arange(n_parms)
|
|
|
|
if len(x) != len(y):
|
|
raise Exception('x and y have to have the same length')
|
|
|
|
if all(isinstance(n, pe.Obs) for n in x):
|
|
obs = x + y
|
|
x_constants = None
|
|
xerr = [o.dvalue for o in x]
|
|
yerr = [o.dvalue for o in y]
|
|
elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
|
|
obs = y
|
|
x_constants = x
|
|
xerr = None
|
|
yerr = [o.dvalue for o in y]
|
|
else:
|
|
raise Exception('Unsupported types for x')
|
|
|
|
def do_the_fit(obs, **kwargs):
|
|
|
|
global print_output, beta0
|
|
|
|
func = kwargs.get('function')
|
|
yerr = kwargs.get('yerr')
|
|
length = len(yerr)
|
|
|
|
xerr = kwargs.get('xerr')
|
|
|
|
if length == len(obs):
|
|
assert 'x_constants' in kwargs
|
|
data = RealData(kwargs.get('x_constants'), obs, sy=yerr)
|
|
fit_type = 2
|
|
elif length == len(obs) // 2:
|
|
data = RealData(obs[:length], obs[length:], sx=xerr, sy=yerr)
|
|
fit_type = 0
|
|
else:
|
|
raise Exception('x and y do not fit together.')
|
|
|
|
model = Model(func)
|
|
|
|
odr = ODR(data, model, beta0, partol=np.finfo(np.float64).eps)
|
|
odr.set_job(fit_type=fit_type, deriv=1)
|
|
output = odr.run()
|
|
if print_output and not silent:
|
|
print(*output.stopreason)
|
|
print('chisquare/d.o.f.:', output.res_var)
|
|
print_output = 0
|
|
beta0 = output.beta
|
|
return output.beta[kwargs.get('n')]
|
|
res = []
|
|
for n in range(n_parms):
|
|
res.append(pe.derived_observable(do_the_fit, obs, function=func, xerr=xerr, yerr=yerr, x_constants=x_constants, num_grad=True, n=n, **kwargs))
|
|
return res
|