refactor: _standard_fit method made redundant. (#154)

* refactor: _standard_fit method made redundant.

* fix: xs and yz in Corr.fit promoted to arrays.

* fix: x promoted to array in _combined_fit if input is just a list.

* feat: residual_plot and qqplot now work with combined fits with
dictionary inputs.

* tests: test for combined fit resplot and qqplot added.

* docs: docstring of fits.residual_plot extended.
This commit is contained in:
Fabian Joswig 2023-03-01 10:00:35 +00:00 committed by GitHub
parent de35332a80
commit dc7033e51f
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3 changed files with 75 additions and 225 deletions

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@ -734,8 +734,8 @@ class Corr:
if len(fitrange) != 2:
raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
result = least_squares(xs, ys, function, silent=silent, **kwargs)
return result

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@ -168,13 +168,8 @@ def least_squares(x, y, func, priors=None, silent=False, **kwargs):
'''
if priors is not None:
return _prior_fit(x, y, func, priors, silent=silent, **kwargs)
elif (type(x) == dict and type(y) == dict and type(func) == dict):
return _combined_fit(x, y, func, silent=silent, **kwargs)
elif (type(x) == dict or type(y) == dict or type(func) == dict):
raise TypeError("All arguments have to be dictionaries in order to perform a combined fit.")
else:
return _standard_fit(x, y, func, silent=silent, **kwargs)
return _combined_fit(x, y, func, silent=silent, **kwargs)
def total_least_squares(x, y, func, silent=False, **kwargs):
@ -509,204 +504,23 @@ def _prior_fit(x, y, func, priors, silent=False, **kwargs):
return output
def _standard_fit(x, y, func, silent=False, **kwargs):
output = Fit_result()
output.fit_function = func
x = np.asarray(x)
if kwargs.get('num_grad') is True:
jacobian = num_jacobian
hessian = num_hessian
else:
jacobian = auto_jacobian
hessian = auto_hessian
if x.shape[-1] != len(y):
raise Exception('x and y input have to have the same length')
if len(x.shape) > 2:
raise Exception('Unknown format for x values')
if not callable(func):
raise TypeError('func has to be a function.')
for i in range(42):
try:
func(np.arange(i), x.T[0])
except TypeError:
continue
except IndexError:
continue
else:
break
else:
raise RuntimeError("Fit function is not valid.")
n_parms = i
if not silent:
print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
y_f = [o.value for o in y]
dy_f = [o.dvalue for o in y]
if np.any(np.asarray(dy_f) <= 0.0):
raise Exception('No y errors available, run the gamma method first.')
if 'initial_guess' in kwargs:
x0 = kwargs.get('initial_guess')
if len(x0) != n_parms:
raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
else:
x0 = [0.1] * n_parms
if kwargs.get('correlated_fit') is True:
corr = covariance(y, correlation=True, **kwargs)
covdiag = np.diag(1 / np.asarray(dy_f))
condn = np.linalg.cond(corr)
if condn > 0.1 / np.finfo(float).eps:
raise Exception(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
if condn > 1e13:
warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
chol = np.linalg.cholesky(corr)
chol_inv = scipy.linalg.solve_triangular(chol, covdiag, lower=True)
def chisqfunc_corr(p):
model = func(p, x)
chisq = anp.sum(anp.dot(chol_inv, (y_f - model)) ** 2)
return chisq
def chisqfunc(p):
model = func(p, x)
chisq = anp.sum(((y_f - model) / dy_f) ** 2)
return chisq
output.method = kwargs.get('method', 'Levenberg-Marquardt')
if not silent:
print('Method:', output.method)
if output.method != 'Levenberg-Marquardt':
if output.method == 'migrad':
fit_result = iminuit.minimize(chisqfunc, x0, tol=1e-4) # Stopping criterion 0.002 * tol * errordef
if kwargs.get('correlated_fit') is True:
fit_result = iminuit.minimize(chisqfunc_corr, fit_result.x, tol=1e-4) # Stopping criterion 0.002 * tol * errordef
output.iterations = fit_result.nfev
else:
fit_result = scipy.optimize.minimize(chisqfunc, x0, method=kwargs.get('method'), tol=1e-12)
if kwargs.get('correlated_fit') is True:
fit_result = scipy.optimize.minimize(chisqfunc_corr, fit_result.x, method=kwargs.get('method'), tol=1e-12)
output.iterations = fit_result.nit
chisquare = fit_result.fun
else:
if kwargs.get('correlated_fit') is True:
def chisqfunc_residuals_corr(p):
model = func(p, x)
chisq = anp.dot(chol_inv, (y_f - model))
return chisq
def chisqfunc_residuals(p):
model = func(p, x)
chisq = ((y_f - model) / dy_f)
return chisq
fit_result = scipy.optimize.least_squares(chisqfunc_residuals, x0, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
if kwargs.get('correlated_fit') is True:
fit_result = scipy.optimize.least_squares(chisqfunc_residuals_corr, fit_result.x, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
chisquare = np.sum(fit_result.fun ** 2)
if kwargs.get('correlated_fit') is True:
assert np.isclose(chisquare, chisqfunc_corr(fit_result.x), atol=1e-14)
else:
assert np.isclose(chisquare, chisqfunc(fit_result.x), atol=1e-14)
output.iterations = fit_result.nfev
if not fit_result.success:
raise Exception('The minimization procedure did not converge.')
if x.shape[-1] - n_parms > 0:
output.chisquare_by_dof = chisquare / (x.shape[-1] - n_parms)
else:
output.chisquare_by_dof = float('nan')
output.message = fit_result.message
if not silent:
print(fit_result.message)
print('chisquare/d.o.f.:', output.chisquare_by_dof)
if kwargs.get('expected_chisquare') is True:
if kwargs.get('correlated_fit') is not True:
W = np.diag(1 / np.asarray(dy_f))
cov = covariance(y)
A = W @ jacobian(func)(fit_result.x, x)
P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
expected_chisquare = np.trace((np.identity(x.shape[-1]) - P_phi) @ W @ cov @ W)
output.chisquare_by_expected_chisquare = chisquare / expected_chisquare
if not silent:
print('chisquare/expected_chisquare:',
output.chisquare_by_expected_chisquare)
fitp = fit_result.x
try:
if kwargs.get('correlated_fit') is True:
hess = hessian(chisqfunc_corr)(fitp)
else:
hess = hessian(chisqfunc)(fitp)
except TypeError:
raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
if kwargs.get('correlated_fit') is True:
def chisqfunc_compact(d):
model = func(d[:n_parms], x)
chisq = anp.sum(anp.dot(chol_inv, (d[n_parms:] - model)) ** 2)
return chisq
else:
def chisqfunc_compact(d):
model = func(d[:n_parms], x)
chisq = anp.sum(((d[n_parms:] - model) / dy_f) ** 2)
return chisq
jac_jac = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f)))
# Compute hess^{-1} @ jac_jac[:n_parms, n_parms:] using LAPACK dgesv
try:
deriv = -scipy.linalg.solve(hess, jac_jac[:n_parms, n_parms:])
except np.linalg.LinAlgError:
raise Exception("Cannot invert hessian matrix.")
result = []
for i in range(n_parms):
result.append(derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (y[0].value + np.finfo(np.float64).eps) * fit_result.x[i], list(y), man_grad=list(deriv[i])))
output.fit_parameters = result
output.chisquare = chisquare
output.dof = x.shape[-1] - n_parms
output.p_value = 1 - scipy.stats.chi2.cdf(output.chisquare, output.dof)
# Hotelling t-squared p-value for correlated fits.
if kwargs.get('correlated_fit') is True:
n_cov = np.min(np.vectorize(lambda x: x.N)(y))
output.t2_p_value = 1 - scipy.stats.f.cdf((n_cov - output.dof) / (output.dof * (n_cov - 1)) * output.chisquare,
output.dof, n_cov - output.dof)
if kwargs.get('resplot') is True:
residual_plot(x, y, func, result)
if kwargs.get('qqplot') is True:
qqplot(x, y, func, result)
return output
def _combined_fit(x, y, func, silent=False, **kwargs):
output = Fit_result()
output.fit_function = func
if (type(x) == dict and type(y) == dict and type(func) == dict):
xd = x
yd = y
funcd = func
output.fit_function = func
elif (type(x) == dict or type(y) == dict or type(func) == dict):
raise TypeError("All arguments have to be dictionaries in order to perform a combined fit.")
else:
x = np.asarray(x)
xd = {"": x}
yd = {"": y}
funcd = {"": func}
output.fit_function = func
if kwargs.get('num_grad') is True:
jacobian = num_jacobian
@ -715,16 +529,16 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
jacobian = auto_jacobian
hessian = auto_hessian
key_ls = sorted(list(x.keys()))
key_ls = sorted(list(xd.keys()))
if sorted(list(y.keys())) != key_ls:
if sorted(list(yd.keys())) != key_ls:
raise Exception('x and y dictionaries do not contain the same keys.')
if sorted(list(func.keys())) != key_ls:
if sorted(list(funcd.keys())) != key_ls:
raise Exception('x and func dictionaries do not contain the same keys.')
x_all = np.concatenate([np.array(x[key]) for key in key_ls])
y_all = np.concatenate([np.array(y[key]) for key in key_ls])
x_all = np.concatenate([np.array(xd[key]) for key in key_ls])
y_all = np.concatenate([np.array(yd[key]) for key in key_ls])
y_f = [o.value for o in y_all]
dy_f = [o.dvalue for o in y_all]
@ -738,13 +552,13 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
# number of fit parameters
n_parms_ls = []
for key in key_ls:
if not callable(func[key]):
if not callable(funcd[key]):
raise TypeError('func (key=' + key + ') is not a function.')
if len(x[key]) != len(y[key]):
if len(xd[key]) != len(yd[key]):
raise Exception('x and y input (key=' + key + ') do not have the same length')
for i in range(100):
try:
func[key](np.arange(i), x_all.T[0])
funcd[key](np.arange(i), x_all.T[0])
except TypeError:
continue
except IndexError:
@ -778,12 +592,12 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
chol_inv = scipy.linalg.solve_triangular(chol, covdiag, lower=True)
def chisqfunc_corr(p):
model = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) for key in key_ls])
model = np.concatenate([np.array(funcd[key](p, np.asarray(xd[key]))).reshape(-1) for key in key_ls])
chisq = anp.sum(anp.dot(chol_inv, (y_f - model)) ** 2)
return chisq
def chisqfunc(p):
func_list = np.concatenate([[func[k]] * len(x[k]) for k in key_ls])
func_list = np.concatenate([[funcd[k]] * len(xd[k]) for k in key_ls])
model = anp.array([func_list[i](p, x_all[i]) for i in range(len(x_all))])
chisq = anp.sum(((y_f - model) / dy_f) ** 2)
return chisq
@ -815,12 +629,12 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
else:
if kwargs.get('correlated_fit') is True:
def chisqfunc_residuals_corr(p):
model = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) for key in key_ls])
model = np.concatenate([np.array(funcd[key](p, np.asarray(xd[key]))).reshape(-1) for key in key_ls])
chisq = anp.dot(chol_inv, (y_f - model))
return chisq
def chisqfunc_residuals(p):
model = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) for key in key_ls])
model = np.concatenate([np.array(funcd[key](p, np.asarray(xd[key]))).reshape(-1) for key in key_ls])
chisq = ((y_f - model) / dy_f)
return chisq
@ -859,9 +673,9 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
def prepare_hat_matrix():
hat_vector = []
for key in key_ls:
x_array = np.asarray(x[key])
x_array = np.asarray(xd[key])
if (len(x_array) != 0):
hat_vector.append(jacobian(func[key])(fit_result.x, x_array))
hat_vector.append(jacobian(funcd[key])(fit_result.x, x_array))
hat_vector = [item for sublist in hat_vector for item in sublist]
return hat_vector
@ -870,7 +684,7 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
W = np.diag(1 / np.asarray(dy_f))
cov = covariance(y_all)
hat_vector = prepare_hat_matrix()
A = W @ hat_vector # hat_vector = 'jacobian(func)(fit_result.x, x)'
A = W @ hat_vector
P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
expected_chisquare = np.trace((np.identity(x_all.shape[-1]) - P_phi) @ W @ cov @ W)
output.chisquare_by_expected_chisquare = output.chisquare / expected_chisquare
@ -891,13 +705,13 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
if kwargs.get('correlated_fit') is True:
def chisqfunc_compact(d):
func_list = np.concatenate([[func[k]] * len(x[k]) for k in key_ls])
func_list = np.concatenate([[funcd[k]] * len(xd[k]) for k in key_ls])
model = anp.array([func_list[i](d[:n_parms], x_all[i]) for i in range(len(x_all))])
chisq = anp.sum(anp.dot(chol_inv, (d[n_parms:] - model)) ** 2)
return chisq
else:
def chisqfunc_compact(d):
func_list = np.concatenate([[func[k]] * len(x[k]) for k in key_ls])
func_list = np.concatenate([[funcd[k]] * len(xd[k]) for k in key_ls])
model = anp.array([func_list[i](d[:n_parms], x_all[i]) for i in range(len(x_all))])
chisq = anp.sum(((d[n_parms:] - model) / dy_f) ** 2)
return chisq
@ -916,11 +730,20 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
output.fit_parameters = result
# Hotelling t-squared p-value for correlated fits.
if kwargs.get('correlated_fit') is True:
n_cov = np.min(np.vectorize(lambda x_all: x_all.N)(y_all))
output.t2_p_value = 1 - scipy.stats.f.cdf((n_cov - output.dof) / (output.dof * (n_cov - 1)) * output.chisquare,
output.dof, n_cov - output.dof)
if kwargs.get('resplot') is True:
for key in key_ls:
residual_plot(xd[key], yd[key], funcd[key], result, title=key)
if kwargs.get('qqplot') is True:
for key in key_ls:
qqplot(xd[key], yd[key], funcd[key], result, title=key)
return output
@ -955,7 +778,7 @@ def fit_lin(x, y, **kwargs):
raise Exception('Unsupported types for x')
def qqplot(x, o_y, func, p):
def qqplot(x, o_y, func, p, title=""):
"""Generates a quantile-quantile plot of the fit result which can be used to
check if the residuals of the fit are gaussian distributed.
@ -981,13 +804,15 @@ def qqplot(x, o_y, func, p):
plt.xlabel('Theoretical quantiles')
plt.ylabel('Ordered Values')
plt.legend()
plt.legend(title=title)
plt.draw()
def residual_plot(x, y, func, fit_res):
def residual_plot(x, y, func, fit_res, title=""):
"""Generates a plot which compares the fit to the data and displays the corresponding residuals
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
Returns
-------
None
@ -1005,7 +830,7 @@ def residual_plot(x, y, func, fit_res):
ax0.set_xticklabels([])
ax0.set_xlim([xstart, xstop])
ax0.set_xticklabels([])
ax0.legend()
ax0.legend(title=title)
residuals = (np.asarray([o.value for o in y]) - func([o.value for o in fit_res], x)) / np.asarray([o.dvalue for o in y])
ax1 = plt.subplot(gs[1])

View file

@ -1,5 +1,6 @@
import numpy as np
import autograd.numpy as anp
import matplotlib.pyplot as plt
import math
import scipy.optimize
from scipy.odr import ODR, Model, RealData
@ -618,7 +619,7 @@ def test_combined_fit_vs_standard_fit():
[item.gamma_method() for item in y_const[key]]
y_const_ls = np.concatenate([np.array(o) for o in y_const.values()])
x_const_ls = np.arange(0, 20)
def func_const(a,x):
return 0 * x + a[0]
@ -633,6 +634,7 @@ def test_combined_fit_vs_standard_fit():
assert np.isclose(0.0, (res[0].p_value - res[1].p_value), 1e-14, 1e-8)
assert (res[0][0] - res[1][0]).is_zero(atol=1e-8)
def test_combined_fit_no_autograd():
def func_exp1(x):
@ -663,6 +665,7 @@ def test_combined_fit_no_autograd():
pe.least_squares(xs, ys, funcs, num_grad=True)
def test_combined_fit_invalid_fit_functions():
def func1(a, x):
return a[0] + a[1] * x + a[2] * anp.sinh(x) + a[199]
@ -692,6 +695,7 @@ def test_combined_fit_invalid_fit_functions():
with pytest.raises(Exception):
pe.least_squares({'a':xvals, 'b':xvals}, {'a':yvals, 'b':yvals}, {'a':func_valid, 'b':func})
def test_combined_fit_invalid_input():
xvals =[]
yvals =[]
@ -706,6 +710,7 @@ def test_combined_fit_invalid_input():
with pytest.raises(Exception):
pe.least_squares({'a':xvals}, {'a':yvals}, {'a':func_valid})
def test_combined_fit_no_autograd():
def func_exp1(x):
@ -774,6 +779,7 @@ def test_combined_fit_num_grad():
assert(num[0] == auto[0])
assert(num[1] == auto[1])
def test_combined_fit_dictkeys_no_order():
def func_exp1(x):
return 0.3*np.exp(0.5*x)
@ -835,6 +841,7 @@ def test_combined_fit_dictkeys_no_order():
assert(no_order_x_y[0] == order[0])
assert(no_order_x_y[1] == order[1])
def test_correlated_combined_fit_vs_correlated_standard_fit():
x_const = {'a':[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'b':np.arange(10, 20)}
@ -861,6 +868,7 @@ def test_correlated_combined_fit_vs_correlated_standard_fit():
assert np.isclose(0.0, (res[0].t2_p_value - res[1].t2_p_value), 1e-14, 1e-8)
assert (res[0][0] - res[1][0]).is_zero(atol=1e-8)
def test_combined_fit_hotelling_t():
xvals_b = np.arange(0,6)
xvals_a = np.arange(0,8)
@ -888,6 +896,23 @@ def test_combined_fit_hotelling_t():
ft = pe.fits.least_squares(xs, ys, funcs, correlated_fit=True)
assert ft.t2_p_value >= ft.p_value
def test_combined_resplot_qqplot():
x = np.arange(3)
y1 = [pe.pseudo_Obs(2 * o + np.random.normal(0, 0.1), 0.1, "test") for o in x]
y2 = [pe.pseudo_Obs(3 * o ** 2 + np.random.normal(0, 0.1), 0.1, "test") for o in x]
fr = pe.least_squares(x, y1, lambda a, x: a[0] + a[1] * x, resplot=True, qqplot=True)
xd = {"1": x,
"2": x}
yd = {"1": y1,
"2": y2}
fd = {"1": lambda a, x: a[0] + a[1] * x,
"2": lambda a, x: a[0] + a[2] * x ** 2}
fr = pe.least_squares(xd, yd, fd, resplot=True, qqplot=True)
plt.close('all')
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.