pyerrors/tests/fits_test.py

639 lines
20 KiB
Python

import numpy as np
import autograd.numpy as anp
import math
import scipy.optimize
from scipy.odr import ODR, Model, RealData
from scipy.linalg import cholesky
from scipy.stats import norm
import pyerrors as pe
import pytest
np.random.seed(0)
def test_fit_lin():
x = [0, 2]
y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
pe.pseudo_Obs(2, 0.1, 'ensemble')]
res = pe.fits.fit_lin(x, y)
assert res[0] == y[0]
assert res[1] == (y[1] - y[0]) / (x[1] - x[0])
x = y = [pe.pseudo_Obs(0, 0.1, 'ensemble'),
pe.pseudo_Obs(2, 0.1, 'ensemble')]
res = pe.fits.fit_lin(x, y)
m = (y[1] - y[0]) / (x[1] - x[0])
assert res[0] == y[1] - x[1] * m
assert res[1] == m
def test_least_squares():
dim = 10 + int(30 * np.random.rand())
x = np.arange(dim)
y = 2 * np.exp(-0.06 * 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 f(x, a, b):
return a * anp.exp(-b * x)
popt, pcov = scipy.optimize.curve_fit(f, x, y, sigma=[o.dvalue for o in oy], absolute_sigma=True)
def func(a, x):
y = a[0] * anp.exp(-a[1] * x)
return y
out = pe.least_squares(x, oy, func, expected_chisquare=True, resplot=True, qqplot=True)
beta = out.fit_parameters
str(out)
repr(out)
len(out)
for i in range(2):
beta[i].gamma_method(S=1.0)
assert math.isclose(beta[i].value, popt[i], abs_tol=1e-5)
assert math.isclose(pcov[i, i], beta[i].dvalue ** 2, abs_tol=1e-3)
chi2_pyerrors = np.sum(((f(x, *[o.value for o in beta]) - y) / yerr) ** 2) / (len(x) - 2)
chi2_scipy = np.sum(((f(x, *popt) - y) / yerr) ** 2) / (len(x) - 2)
assert math.isclose(chi2_pyerrors, chi2_scipy, abs_tol=1e-10)
out = pe.least_squares(x, oy, func, const_par=[beta[1]])
assert((out.fit_parameters[0] - beta[0]).is_zero())
assert((out.fit_parameters[1] - beta[1]).is_zero())
oyc = []
for i, item in enumerate(x):
oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'cov' + str(i)))
outc = pe.least_squares(x, oyc, func)
betac = outc.fit_parameters
for i in range(2):
betac[i].gamma_method(S=1.0)
assert math.isclose(betac[i].value, popt[i], abs_tol=1e-5)
assert math.isclose(pcov[i, i], betac[i].dvalue ** 2, abs_tol=1e-3)
def test_alternative_solvers():
dim = 192
x = np.arange(dim)
y = 2 * np.exp(-0.06 * 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], 'test'))
def func(a, x):
y = a[0] * anp.exp(-a[1] * x)
return y
chisquare_values = []
out = pe.least_squares(x, oy, func, method='migrad')
chisquare_values.append(out.chisquare)
out = pe.least_squares(x, oy, func, method='Powell')
chisquare_values.append(out.chisquare)
out = pe.least_squares(x, oy, func, method='Nelder-Mead')
chisquare_values.append(out.chisquare)
out = pe.least_squares(x, oy, func, method='Levenberg-Marquardt')
chisquare_values.append(out.chisquare)
chisquare_values = np.array(chisquare_values)
assert np.all(np.isclose(chisquare_values, chisquare_values[0]))
def test_correlated_fit():
num_samples = 400
N = 10
x = norm.rvs(size=(N, num_samples))
r = np.zeros((N, N))
for i in range(N):
for j in range(N):
r[i, j] = np.exp(-0.8 * np.fabs(i - j))
errl = np.sqrt([3.4, 2.5, 3.6, 2.8, 4.2, 4.7, 4.9, 5.1, 3.2, 4.2])
for i in range(N):
for j in range(N):
r[i, j] *= errl[i] * errl[j]
c = cholesky(r, lower=True)
y = np.dot(c, x)
x = np.arange(N)
for linear in [True, False]:
data = []
for i in range(N):
if linear:
data.append(pe.Obs([[i + 1 + o for o in y[i]]], ['ens']))
else:
data.append(pe.Obs([[np.exp(-(i + 1)) + np.exp(-(i + 1)) * o for o in y[i]]], ['ens']))
[o.gamma_method() for o in data]
if linear:
def fitf(p, x):
return p[1] + p[0] * x
else:
def fitf(p, x):
return p[1] * anp.exp(-p[0] * x)
fitp = pe.least_squares(x, data, fitf, expected_chisquare=True)
assert np.isclose(fitp.chisquare / fitp.dof, fitp.chisquare_by_dof, atol=1e-14)
fitpc = pe.least_squares(x, data, fitf, correlated_fit=True)
assert np.isclose(fitpc.chisquare / fitpc.dof, fitpc.chisquare_by_dof, atol=1e-14)
for i in range(2):
diff = fitp[i] - fitpc[i]
diff.gamma_method()
assert(diff.is_zero_within_error(sigma=5))
def test_fit_corr_independent():
dim = 50
x = np.arange(dim)
y = 0.84 * np.exp(-0.12 * x) + np.random.normal(0.0, 0.1, dim)
yerr = [0.1] * 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] * anp.exp(-a[1] * x)
return y
for method in ["Levenberg-Marquardt", "migrad", "Nelder-Mead"]:
out = pe.least_squares(x, oy, func, method=method)
out_corr = pe.least_squares(x, oy, func, correlated_fit=True, method=method)
assert np.isclose(out.chisquare, out_corr.chisquare)
assert np.isclose(out.dof, out_corr.dof)
assert np.isclose(out.chisquare_by_dof, out_corr.chisquare_by_dof)
assert (out[0] - out_corr[0]).is_zero(atol=1e-5)
assert (out[1] - out_corr[1]).is_zero(atol=1e-5)
def test_linear_fit_guesses():
for err in [10, 0.1, 0.001]:
xvals = []
yvals = []
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))
lin_func = lambda a, x: a[0] + a[1] * x
with pytest.raises(Exception):
pe.least_squares(xvals, yvals, lin_func)
[o.gamma_method() for o in yvals]
with pytest.raises(Exception):
pe.least_squares(xvals, yvals, lin_func, initial_guess=[5])
bad_guess = pe.least_squares(xvals, yvals, lin_func, initial_guess=[999, 999])
good_guess = pe.least_squares(xvals, yvals, lin_func, initial_guess=[0, 1])
assert np.isclose(bad_guess.chisquare, good_guess.chisquare, atol=1e-8)
assert np.all([(go - ba).is_zero(atol=1e-6) for (go, ba) in zip(good_guess, bad_guess)])
def test_total_least_squares():
dim = 10 + int(30 * np.random.rand())
x = np.arange(dim) + np.random.normal(0.0, 0.15, dim)
xerr = 0.1 + 0.1 * np.random.rand(dim)
y = 2 * np.exp(-0.06 * x) + np.random.normal(0.0, 0.15, dim)
yerr = 0.1 + 0.1 * np.random.rand(dim)
ox = []
for i, item in enumerate(x):
ox.append(pe.pseudo_Obs(x[i], xerr[i], str(i)))
oy = []
for i, item in enumerate(x):
oy.append(pe.pseudo_Obs(y[i], yerr[i], str(i)))
def f(x, a, b):
return a * anp.exp(-b * x)
def func(a, x):
y = a[0] * anp.exp(-a[1] * x)
return y
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])
model = Model(func)
odr = ODR(data, model, [0, 0], partol=np.finfo(np.float64).eps)
odr.set_job(fit_type=0, deriv=1)
output = odr.run()
out = pe.total_least_squares(ox, oy, func, expected_chisquare=True)
beta = out.fit_parameters
str(out)
repr(out)
len(out)
for i in range(2):
beta[i].gamma_method(S=1.0)
assert math.isclose(beta[i].value, output.beta[i], rel_tol=1e-5)
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)
out = pe.total_least_squares(ox, oy, func, const_par=[beta[1]])
diff = out.fit_parameters[0] - beta[0]
assert(diff / beta[0] < 1e-3 * beta[0].dvalue)
assert((out.fit_parameters[1] - beta[1]).is_zero())
oxc = []
for i, item in enumerate(x):
oxc.append(pe.cov_Obs(x[i], xerr[i]**2, 'covx' + str(i)))
oyc = []
for i, item in enumerate(x):
oyc.append(pe.cov_Obs(y[i], yerr[i]**2, 'covy' + str(i)))
outc = pe.total_least_squares(oxc, oyc, func)
betac = outc.fit_parameters
for i in range(2):
betac[i].gamma_method(S=1.0)
assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
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)
outc = pe.total_least_squares(oxc, oyc, func, const_par=[betac[1]])
diffc = outc.fit_parameters[0] - betac[0]
assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
assert((outc.fit_parameters[1] - betac[1]).is_zero())
outc = pe.total_least_squares(oxc, oy, func)
betac = outc.fit_parameters
for i in range(2):
betac[i].gamma_method(S=1.0)
assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
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)
outc = pe.total_least_squares(oxc, oy, func, const_par=[betac[1]])
diffc = outc.fit_parameters[0] - betac[0]
assert(diffc / betac[0] < 1e-3 * betac[0].dvalue)
assert((outc.fit_parameters[1] - betac[1]).is_zero())
def test_odr_derivatives():
x = []
y = []
x_err = 0.01
y_err = 0.01
for n in np.arange(1, 9, 2):
loc_xvalue = n + np.random.normal(0.0, x_err)
x.append(pe.pseudo_Obs(loc_xvalue, x_err, str(n)))
y.append(pe.pseudo_Obs((lambda x: x ** 2 - 1)(loc_xvalue) +
np.random.normal(0.0, y_err), y_err, str(n)))
def func(a, x):
return a[0] + a[1] * x ** 2
out = pe.total_least_squares(x, y, func)
fit1 = out.fit_parameters
tfit = fit_general(x, y, func, base_step=0.1, step_ratio=1.1, num_steps=20)
assert np.abs(np.max(np.array(list(fit1[1].deltas.values()))
- np.array(list(tfit[1].deltas.values())))) < 10e-8
def test_r_value_persistence():
def f(a, x):
return a[0] + a[1] * x
a = pe.pseudo_Obs(1.1, .1, 'a')
assert np.isclose(a.value, a.r_values['a'])
a_2 = a ** 2
assert np.isclose(a_2.value, a_2.r_values['a'])
b = pe.pseudo_Obs(2.1, .2, 'b')
y = [a, b]
[o.gamma_method() for o in y]
fitp = pe.fits.least_squares([1, 2], y, f)
assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
assert np.isclose(fitp[1].value, fitp[1].r_values['b'])
fitp = pe.fits.total_least_squares(y, y, f)
assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
assert np.isclose(fitp[1].value, fitp[1].r_values['b'])
fitp = pe.fits.least_squares([1, 2], y, f, priors=y)
assert np.isclose(fitp[0].value, fitp[0].r_values['a'])
assert np.isclose(fitp[0].value, fitp[0].r_values['b'])
assert np.isclose(fitp[1].value, fitp[1].r_values['a'])
assert np.isclose(fitp[1].value, fitp[1].r_values['b'])
def test_prior_fit():
def f(a, x):
return a[0] + a[1] * x
a = pe.pseudo_Obs(0.0, 0.1, 'a')
b = pe.pseudo_Obs(1.0, 0.2, 'a')
y = [a, b]
with pytest.raises(Exception):
fitp = pe.fits.least_squares([0, 1], 1 * np.array(y), f, priors=['0.0(8)', '1.0(8)'])
[o.gamma_method() for o in y]
fitp = pe.fits.least_squares([0, 1], y, f, priors=['0.0(8)', '1.0(8)'])
fitp = pe.fits.least_squares([0, 1], y, f, priors=y, resplot=True, qqplot=True)
def test_correlated_fit_covobs():
x1 = pe.cov_Obs(1.01, 0.01 ** 2, 'test1')
x2 = pe.cov_Obs(2.01, 0.01 ** 2, 'test2')
x3 = pe.cov_Obs(2.99, 0.01 ** 2, 'test3')
[o.gamma_method() for o in [x1, x2, x3]]
def func(a, x):
return a[0] * x + a[1]
fit_res = pe.fits.least_squares(np.arange(1, 4), [x1, x2, x3], func, expected_chisquare=True)
assert np.isclose(fit_res.chisquare_by_dof, fit_res.chisquare_by_expected_chisquare)
fit_res_corr = pe.fits.least_squares(np.arange(1, 4), [x1, x2, x3], func, correlated_fit=True)
assert np.isclose(fit_res.chisquare_by_dof, fit_res_corr.chisquare_by_dof)
def test_error_band():
def f(a, x):
return a[0] + a[1] * x
a = pe.pseudo_Obs(0.0, 0.1, 'a')
b = pe.pseudo_Obs(1.0, 0.2, 'a')
x = [0, 1]
y = [a, b]
fitp = pe.fits.least_squares(x, y, f)
with pytest.raises(Exception):
pe.fits.error_band(x, f, fitp.fit_parameters)
fitp.gamma_method()
pe.fits.error_band(x, f, fitp.fit_parameters)
def test_fit_vs_jackknife():
od = 0.9999999999
cov1 = np.array([[1, od, od], [od, 1.0, od], [od, od, 1.0]])
cov1 *= 0.05
nod = -0.4
cov2 = np.array([[1, nod, nod], [nod, 1.0, nod], [nod, nod, 1.0]])
cov2 *= 0.05
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