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refactor: _standard_fit method made redundant.
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@fjosw
fjosw committed Feb 23, 2023
1 parent a2ed265 commit 4b2aa62
Showing 1 changed file with 38 additions and 218 deletions.
256 changes: 38 additions & 218 deletions pyerrors/fits.py
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Expand Up @@ -168,13 +168,8 @@ def func_b(a, x):
'''
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):
Expand Down Expand Up @@ -509,204 +504,22 @@ def chisqfunc_compact(d):
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:
xd = {"a": x}
yd = {"a": y}
funcd = {"a": func}
output.fit_function = func

if kwargs.get('num_grad') is True:
jacobian = num_jacobian
Expand All @@ -715,16 +528,16 @@ 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]
Expand All @@ -738,13 +551,13 @@ 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:
Expand Down Expand Up @@ -778,12 +591,12 @@ 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
Expand Down Expand Up @@ -815,12 +628,12 @@ def chisqfunc(p):
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

Expand Down Expand Up @@ -859,9 +672,9 @@ def chisqfunc_residuals(p):
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

Expand All @@ -870,7 +683,7 @@ def prepare_hat_matrix():
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
Expand All @@ -891,13 +704,13 @@ def prepare_hat_matrix():

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
Expand All @@ -916,11 +729,18 @@ def chisqfunc_compact(d):

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:
residual_plot(x, y, func, result)

if kwargs.get('qqplot') is True:
qqplot(x, y, func, result)

return output


Expand Down

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