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incorparated (uncorrelated) combined fits in fits.least_squares

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ppetrak 2022-12-16 18:47:25 +01:00
parent 78c7c32f1c
commit 9a05fc916a
3 changed files with 594 additions and 24 deletions
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338
examples/example_combined_fit.ipynb
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File diff suppressed because one or more lines are too long

68
pyerrors/combined_fits.py
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@ -12,7 +12,7 @@ from numdifftools import Hessian as num_hessian
import scipy.optimize
import scipy.stats
def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
def combined_fit(x,y,funcs,silent=False,**kwargs):
r'''Performs a combined non-linear fit.
Parameters
----------
@ -62,10 +62,17 @@ def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
y_all+=y[key]
x_all = np.asarray(x_all)
if len(x_all.shape) > 2:
raise Exception('Unknown format for x values')
# number of fit parameters
n_parms_ls = []
for key in funcs.keys():
if not callable(funcs[key]):
raise TypeError('func (key='+ key + ') is not a function.')
if len(x[key]) != len(y[key]):
raise Exception('x and y input (key='+ key + ') do not have the same length')
for i in range(42):
try:
funcs[key](np.arange(i), x_all.T[0])
@ -76,7 +83,7 @@ def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
else:
break
else:
raise RuntimeError("Fit function is not valid.")
raise RuntimeError("Fit function (key="+ key + ") is not valid.")
n_parms = i
n_parms_ls.append(n_parms)
n_parms = max(n_parms_ls)
@ -102,22 +109,34 @@ def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
chisq += anp.sum((y_f - model)@ C_inv @(y_f - model))
return chisq
if 'tol' in kwargs:
fit_result = iminuit.minimize(chisqfunc, x0,tol=kwargs.get('tol'))
fit_result = iminuit.minimize(chisqfunc, fit_result.x,tol=kwargs.get('tol'))
else:
fit_result = iminuit.minimize(chisqfunc, x0,tol=1e-4)
fit_result = iminuit.minimize(chisqfunc, fit_result.x,tol=1e-4)
output.method = kwargs.get('method', 'Levenberg-Marquardt')
if not silent:
print('Method:', output.method)
if output.method == 'migrad':
tolerance = 1e-4
if 'tol' in kwargs:
tolerance = kwargs.get('tol')
fit_result = iminuit.minimize(chisqfunc, x0, tol=tolerance) # Stopping criterion 0.002 * tol * errordef
output.iterations = fit_result.nfev
else:
tolerance = 1e-12
if 'tol' in kwargs:
tolerance = kwargs.get('tol')
fit_result = scipy.optimize.minimize(chisqfunc, x0, method=kwargs.get('method'), tol=tolerance)
output.iterations = fit_result.nit
chisquare = fit_result.fun
output.method = 'migrad'
output.message = fit_result.message
if not fit_result.success:
raise Exception('The minimization procedure did not converge.')
if x_all.shape[-1] - n_parms > 0:
output.chisquare = chisqfunc(fit_result.x)
output.dof = x_all.shape[-1] - n_parms
output.chisquare_by_dof = output.chisquare/output.dof
output.p_value = 1 - scipy.stats.chi2.cdf(output.chisquare, output.dof)
else:
output.chisquare_by_dof = float('nan')
@ -145,9 +164,22 @@ def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
chisq = anp.sum(list_tmp)
return chisq
def prepare_hat_matrix(): # should be cross-checked again
hat_vector = []
for key in funcs.keys():
x_array = np.asarray(x[key])
if (len(x_array)!= 0):
hat_vector.append(anp.array(jacobian(funcs[key])(fit_result.x, x_array)))
hat_vector = [item for sublist in hat_vector for item in sublist]
return hat_vector
fitp = fit_result.x
y_f = [o.value for o in y_all] # y_f is constructed based on the ordered dictionary if the order is changed then the y values are not allocated to the the correct x and func values in the hessian
dy_f = [o.dvalue for o in y_all] # the same goes for dy_f
if np.any(np.asarray(dy_f) <= 0.0):
raise Exception('No y errors available, run the gamma method first.')
try:
hess = hessian(chisqfunc)(fitp)
except TypeError:
@ -160,6 +192,20 @@ def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms, n_parms:])
except np.linalg.LinAlgError:
raise Exception("Cannot invert hessian matrix.")
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_all)
hat_vector = prepare_hat_matrix()
A = W @ hat_vector #hat_vector = '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)
result = []
for i in range(n_parms):

212
pyerrors/fits.py
View file

@ -70,9 +70,13 @@ class Fit_result(Sequence):
def least_squares(x, y, func, priors=None, silent=False, **kwargs):
r'''Performs a non-linear fit to y = func(x).
```
Parameters
----------
For an uncombined fit:
x : list
list of floats.
y : list
@ -94,9 +98,35 @@ def least_squares(x, y, func, priors=None, silent=False, **kwargs):
(x1, x2) = x
return a[0] * x1 ** 2 + a[1] * x2
```
It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
will not work.
OR For a combined fit:
Do not need to use ordered dictionaries: python version >= 3.7: Dictionary order is guaranteed to be insertion order.
(https://docs.python.org/3/library/stdtypes.html#dict-views) Ensures that x, y and func values are mapped correctly.
x : ordered dict
dict of lists.
y : ordered dict
dict of lists of Obs.
funcs : ordered dict
dict of objects
fit functions have to be of the form (here a[0] is the common fit parameter)
```python
import autograd.numpy as anp
funcs = {"a": func_a,
"b": func_b}
def func_a(a, x):
return a[1] * anp.exp(-a[0] * x)
def func_b(a, x):
return a[2] * anp.exp(-a[0] * x)
It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
will not work.
priors : list, optional
priors has to be a list with an entry for every parameter in the fit. The entries can either be
Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
@ -130,6 +160,10 @@ 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)
else:
return _standard_fit(x, y, func, silent=silent, **kwargs)
@ -462,7 +496,6 @@ def _prior_fit(x, y, func, priors, silent=False, **kwargs):
def _standard_fit(x, y, func, silent=False, **kwargs):
output = Fit_result()
output.fit_function = func
@ -655,6 +688,181 @@ def _standard_fit(x, y, func, silent=False, **kwargs):
return output
def _combined_fit(x,y,func,silent=False,**kwargs):
if kwargs.get('correlated_fit') is True:
raise Exception("Correlated fit has not been implemented yet")
output = Fit_result()
output.fit_function = func
if kwargs.get('num_grad') is True:
jacobian = num_jacobian
hessian = num_hessian
else:
jacobian = auto_jacobian
hessian = auto_hessian
x_all = []
y_all = []
for key in x.keys():
x_all+=x[key]
y_all+=y[key]
x_all = np.asarray(x_all)
if len(x_all.shape) > 2:
raise Exception('Unknown format for x values')
# number of fit parameters
n_parms_ls = []
for key in func.keys():
if not callable(func[key]):
raise TypeError('func (key='+ key + ') is not a function.')
if len(x[key]) != len(y[key]):
raise Exception('x and y input (key='+ key + ') do not have the same length')
for i in range(42):
try:
func[key](np.arange(i), x_all.T[0])
except TypeError:
continue
except IndexError:
continue
else:
break
else:
raise RuntimeError("Fit function (key="+ key + ") is not valid.")
n_parms = i
n_parms_ls.append(n_parms)
n_parms = max(n_parms_ls)
if not silent:
print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
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
def chisqfunc(p):
chisq = 0.0
for key in func.keys():
x_array = np.asarray(x[key])
model = anp.array(func[key](p,x_array))
y_obs = y[key]
y_f = [o.value for o in y_obs]
dy_f = [o.dvalue for o in y_obs]
C_inv = np.diag(np.diag(np.ones((len(x_array),len(x_array)))))/dy_f/dy_f
chisq += anp.sum((y_f - model)@ C_inv @(y_f - model))
return chisq
output.method = kwargs.get('method', 'Levenberg-Marquardt')
if not silent:
print('Method:', output.method)
if output.method == 'migrad':
tolerance = 1e-4
if 'tol' in kwargs:
tolerance = kwargs.get('tol')
fit_result = iminuit.minimize(chisqfunc, x0, tol=tolerance) # Stopping criterion 0.002 * tol * errordef
output.iterations = fit_result.nfev
else:
tolerance = 1e-12
if 'tol' in kwargs:
tolerance = kwargs.get('tol')
fit_result = scipy.optimize.minimize(chisqfunc, x0, method=kwargs.get('method'), tol=tolerance)
output.iterations = fit_result.nit
chisquare = fit_result.fun
output.message = fit_result.message
if not fit_result.success:
raise Exception('The minimization procedure did not converge.')
if x_all.shape[-1] - n_parms > 0:
output.chisquare = chisqfunc(fit_result.x)
output.dof = x_all.shape[-1] - n_parms
output.chisquare_by_dof = output.chisquare/output.dof
output.p_value = 1 - scipy.stats.chi2.cdf(output.chisquare, output.dof)
else:
output.chisquare_by_dof = float('nan')
if not silent:
print(fit_result.message)
print('chisquare/d.o.f.:', output.chisquare_by_dof )
print('fit parameters',fit_result.x)
def chisqfunc_compact(d):
chisq = 0.0
list_tmp = []
c1 = 0
c2 = 0
for key in func.keys():
x_array = np.asarray(x[key])
c2+=len(x_array)
model = anp.array(func[key](d[:n_parms],x_array))
y_obs = y[key]
y_f = [o.value for o in y_obs]
dy_f = [o.dvalue for o in y_obs]
C_inv = np.diag(np.diag(np.ones((len(x_array),len(x_array)))))/dy_f/dy_f
list_tmp.append(anp.sum((d[n_parms+c1:n_parms+c2]- model)@ C_inv @(d[n_parms+c1:n_parms+c2]- model)))
c1+=len(x_array)
chisq = anp.sum(list_tmp)
return chisq
def prepare_hat_matrix():
hat_vector = []
for key in func.keys():
x_array = np.asarray(x[key])
if (len(x_array)!= 0):
hat_vector.append(anp.array(jacobian(func[key])(fit_result.x, x_array)))
hat_vector = [item for sublist in hat_vector for item in sublist]
return hat_vector
fitp = fit_result.x
y_f = [o.value for o in y_all]
dy_f = [o.dvalue for o in y_all]
if np.any(np.asarray(dy_f) <= 0.0):
raise Exception('No y errors available, run the gamma method first.')
try:
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
jac_jac_y = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f)))
# Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv
try:
deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms, n_parms:])
except np.linalg.LinAlgError:
raise Exception("Cannot invert hessian matrix.")
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_all)
hat_vector = prepare_hat_matrix()
A = W @ hat_vector #hat_vector = 'jacobian(func)(fit_result.x, x)'
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 = chisquare / expected_chisquare
if not silent:
print('chisquare/expected_chisquare:', output.chisquare_by_expected_chisquare)
result = []
for i in range(n_parms):
result.append(derived_observable(lambda x_all, **kwargs: (x_all[0] + np.finfo(np.float64).eps) / (y_all[0].value + np.finfo(np.float64).eps) * fitp[i], list(y_all), man_grad=list(deriv_y[i])))
output.fit_parameters = result
return output
def fit_lin(x, y, **kwargs):
"""Performs a linear fit to y = n + m * x and returns two Obs n, m.