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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
GitHub
parent
de35332a80
commit
dc7033e51f
3 changed files with 75 additions and 225 deletions
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@ -734,8 +734,8 @@ class Corr:
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if len(fitrange) != 2:
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raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
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xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
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ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
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xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
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ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
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result = least_squares(xs, ys, function, silent=silent, **kwargs)
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return result
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269
pyerrors/fits.py
269
pyerrors/fits.py
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@ -168,13 +168,8 @@ def least_squares(x, y, func, priors=None, silent=False, **kwargs):
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'''
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if priors is not None:
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return _prior_fit(x, y, func, priors, silent=silent, **kwargs)
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elif (type(x) == dict and type(y) == dict and type(func) == dict):
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return _combined_fit(x, y, func, silent=silent, **kwargs)
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elif (type(x) == dict or type(y) == dict or type(func) == dict):
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raise TypeError("All arguments have to be dictionaries in order to perform a combined fit.")
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else:
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return _standard_fit(x, y, func, silent=silent, **kwargs)
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return _combined_fit(x, y, func, silent=silent, **kwargs)
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def total_least_squares(x, y, func, silent=False, **kwargs):
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@ -509,204 +504,23 @@ def _prior_fit(x, y, func, priors, silent=False, **kwargs):
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return output
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def _standard_fit(x, y, func, silent=False, **kwargs):
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output = Fit_result()
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output.fit_function = func
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x = np.asarray(x)
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if kwargs.get('num_grad') is True:
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jacobian = num_jacobian
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hessian = num_hessian
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else:
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jacobian = auto_jacobian
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hessian = auto_hessian
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if x.shape[-1] != len(y):
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raise Exception('x and y input have to have the same length')
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if len(x.shape) > 2:
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raise Exception('Unknown format for x values')
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if not callable(func):
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raise TypeError('func has to be a function.')
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for i in range(42):
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try:
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func(np.arange(i), x.T[0])
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except TypeError:
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continue
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except IndexError:
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continue
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else:
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break
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else:
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raise RuntimeError("Fit function is not valid.")
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n_parms = i
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if not silent:
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print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
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y_f = [o.value for o in y]
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dy_f = [o.dvalue for o in y]
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if np.any(np.asarray(dy_f) <= 0.0):
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raise Exception('No y errors available, run the gamma method first.')
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if 'initial_guess' in kwargs:
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x0 = kwargs.get('initial_guess')
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if len(x0) != n_parms:
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raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
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else:
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x0 = [0.1] * n_parms
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if kwargs.get('correlated_fit') is True:
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corr = covariance(y, correlation=True, **kwargs)
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covdiag = np.diag(1 / np.asarray(dy_f))
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condn = np.linalg.cond(corr)
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if condn > 0.1 / np.finfo(float).eps:
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raise Exception(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
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if condn > 1e13:
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warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
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chol = np.linalg.cholesky(corr)
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chol_inv = scipy.linalg.solve_triangular(chol, covdiag, lower=True)
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def chisqfunc_corr(p):
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model = func(p, x)
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chisq = anp.sum(anp.dot(chol_inv, (y_f - model)) ** 2)
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return chisq
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def chisqfunc(p):
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model = func(p, x)
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chisq = anp.sum(((y_f - model) / dy_f) ** 2)
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return chisq
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output.method = kwargs.get('method', 'Levenberg-Marquardt')
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if not silent:
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print('Method:', output.method)
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if output.method != 'Levenberg-Marquardt':
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if output.method == 'migrad':
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fit_result = iminuit.minimize(chisqfunc, x0, tol=1e-4) # Stopping criterion 0.002 * tol * errordef
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if kwargs.get('correlated_fit') is True:
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fit_result = iminuit.minimize(chisqfunc_corr, fit_result.x, tol=1e-4) # Stopping criterion 0.002 * tol * errordef
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output.iterations = fit_result.nfev
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else:
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fit_result = scipy.optimize.minimize(chisqfunc, x0, method=kwargs.get('method'), tol=1e-12)
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if kwargs.get('correlated_fit') is True:
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fit_result = scipy.optimize.minimize(chisqfunc_corr, fit_result.x, method=kwargs.get('method'), tol=1e-12)
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output.iterations = fit_result.nit
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chisquare = fit_result.fun
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else:
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if kwargs.get('correlated_fit') is True:
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def chisqfunc_residuals_corr(p):
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model = func(p, x)
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chisq = anp.dot(chol_inv, (y_f - model))
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return chisq
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def chisqfunc_residuals(p):
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model = func(p, x)
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chisq = ((y_f - model) / dy_f)
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return chisq
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fit_result = scipy.optimize.least_squares(chisqfunc_residuals, x0, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
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if kwargs.get('correlated_fit') is True:
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fit_result = scipy.optimize.least_squares(chisqfunc_residuals_corr, fit_result.x, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
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chisquare = np.sum(fit_result.fun ** 2)
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if kwargs.get('correlated_fit') is True:
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assert np.isclose(chisquare, chisqfunc_corr(fit_result.x), atol=1e-14)
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else:
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assert np.isclose(chisquare, chisqfunc(fit_result.x), atol=1e-14)
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output.iterations = fit_result.nfev
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if not fit_result.success:
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raise Exception('The minimization procedure did not converge.')
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if x.shape[-1] - n_parms > 0:
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output.chisquare_by_dof = chisquare / (x.shape[-1] - n_parms)
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else:
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output.chisquare_by_dof = float('nan')
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output.message = fit_result.message
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if not silent:
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print(fit_result.message)
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print('chisquare/d.o.f.:', output.chisquare_by_dof)
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if kwargs.get('expected_chisquare') is True:
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if kwargs.get('correlated_fit') is not True:
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W = np.diag(1 / np.asarray(dy_f))
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cov = covariance(y)
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A = W @ jacobian(func)(fit_result.x, x)
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P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
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expected_chisquare = np.trace((np.identity(x.shape[-1]) - P_phi) @ W @ cov @ W)
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output.chisquare_by_expected_chisquare = chisquare / expected_chisquare
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if not silent:
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print('chisquare/expected_chisquare:',
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output.chisquare_by_expected_chisquare)
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fitp = fit_result.x
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try:
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if kwargs.get('correlated_fit') is True:
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hess = hessian(chisqfunc_corr)(fitp)
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else:
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hess = hessian(chisqfunc)(fitp)
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except TypeError:
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raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
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if kwargs.get('correlated_fit') is True:
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def chisqfunc_compact(d):
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model = func(d[:n_parms], x)
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chisq = anp.sum(anp.dot(chol_inv, (d[n_parms:] - model)) ** 2)
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return chisq
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else:
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def chisqfunc_compact(d):
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model = func(d[:n_parms], x)
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chisq = anp.sum(((d[n_parms:] - model) / dy_f) ** 2)
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return chisq
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jac_jac = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f)))
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# Compute hess^{-1} @ jac_jac[:n_parms, n_parms:] using LAPACK dgesv
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try:
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deriv = -scipy.linalg.solve(hess, jac_jac[:n_parms, n_parms:])
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except np.linalg.LinAlgError:
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raise Exception("Cannot invert hessian matrix.")
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result = []
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for i in range(n_parms):
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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])))
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output.fit_parameters = result
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output.chisquare = chisquare
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output.dof = x.shape[-1] - n_parms
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output.p_value = 1 - scipy.stats.chi2.cdf(output.chisquare, output.dof)
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# Hotelling t-squared p-value for correlated fits.
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if kwargs.get('correlated_fit') is True:
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n_cov = np.min(np.vectorize(lambda x: x.N)(y))
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output.t2_p_value = 1 - scipy.stats.f.cdf((n_cov - output.dof) / (output.dof * (n_cov - 1)) * output.chisquare,
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output.dof, n_cov - output.dof)
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if kwargs.get('resplot') is True:
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residual_plot(x, y, func, result)
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if kwargs.get('qqplot') is True:
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qqplot(x, y, func, result)
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return output
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def _combined_fit(x, y, func, silent=False, **kwargs):
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output = Fit_result()
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output.fit_function = func
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if (type(x) == dict and type(y) == dict and type(func) == dict):
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xd = x
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yd = y
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funcd = func
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output.fit_function = func
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elif (type(x) == dict or type(y) == dict or type(func) == dict):
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raise TypeError("All arguments have to be dictionaries in order to perform a combined fit.")
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else:
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x = np.asarray(x)
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xd = {"": x}
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yd = {"": y}
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funcd = {"": func}
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output.fit_function = func
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if kwargs.get('num_grad') is True:
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jacobian = num_jacobian
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@ -715,16 +529,16 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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jacobian = auto_jacobian
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hessian = auto_hessian
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key_ls = sorted(list(x.keys()))
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key_ls = sorted(list(xd.keys()))
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if sorted(list(y.keys())) != key_ls:
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if sorted(list(yd.keys())) != key_ls:
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raise Exception('x and y dictionaries do not contain the same keys.')
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if sorted(list(func.keys())) != key_ls:
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if sorted(list(funcd.keys())) != key_ls:
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raise Exception('x and func dictionaries do not contain the same keys.')
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x_all = np.concatenate([np.array(x[key]) for key in key_ls])
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y_all = np.concatenate([np.array(y[key]) for key in key_ls])
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x_all = np.concatenate([np.array(xd[key]) for key in key_ls])
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y_all = np.concatenate([np.array(yd[key]) for key in key_ls])
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y_f = [o.value for o in y_all]
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dy_f = [o.dvalue for o in y_all]
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@ -738,13 +552,13 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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# number of fit parameters
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n_parms_ls = []
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for key in key_ls:
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if not callable(func[key]):
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if not callable(funcd[key]):
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raise TypeError('func (key=' + key + ') is not a function.')
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if len(x[key]) != len(y[key]):
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if len(xd[key]) != len(yd[key]):
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raise Exception('x and y input (key=' + key + ') do not have the same length')
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for i in range(100):
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try:
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func[key](np.arange(i), x_all.T[0])
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funcd[key](np.arange(i), x_all.T[0])
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except TypeError:
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continue
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except IndexError:
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@ -778,12 +592,12 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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chol_inv = scipy.linalg.solve_triangular(chol, covdiag, lower=True)
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def chisqfunc_corr(p):
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model = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) for key in key_ls])
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model = np.concatenate([np.array(funcd[key](p, np.asarray(xd[key]))).reshape(-1) for key in key_ls])
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chisq = anp.sum(anp.dot(chol_inv, (y_f - model)) ** 2)
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return chisq
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def chisqfunc(p):
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func_list = np.concatenate([[func[k]] * len(x[k]) for k in key_ls])
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func_list = np.concatenate([[funcd[k]] * len(xd[k]) for k in key_ls])
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model = anp.array([func_list[i](p, x_all[i]) for i in range(len(x_all))])
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chisq = anp.sum(((y_f - model) / dy_f) ** 2)
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return chisq
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@ -815,12 +629,12 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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else:
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if kwargs.get('correlated_fit') is True:
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def chisqfunc_residuals_corr(p):
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model = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) for key in key_ls])
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model = np.concatenate([np.array(funcd[key](p, np.asarray(xd[key]))).reshape(-1) for key in key_ls])
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chisq = anp.dot(chol_inv, (y_f - model))
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return chisq
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def chisqfunc_residuals(p):
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model = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) for key in key_ls])
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model = np.concatenate([np.array(funcd[key](p, np.asarray(xd[key]))).reshape(-1) for key in key_ls])
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chisq = ((y_f - model) / dy_f)
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return chisq
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@ -859,9 +673,9 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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def prepare_hat_matrix():
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hat_vector = []
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for key in key_ls:
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x_array = np.asarray(x[key])
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x_array = np.asarray(xd[key])
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if (len(x_array) != 0):
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hat_vector.append(jacobian(func[key])(fit_result.x, x_array))
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hat_vector.append(jacobian(funcd[key])(fit_result.x, x_array))
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hat_vector = [item for sublist in hat_vector for item in sublist]
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return hat_vector
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@ -870,7 +684,7 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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W = np.diag(1 / np.asarray(dy_f))
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cov = covariance(y_all)
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hat_vector = prepare_hat_matrix()
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A = W @ hat_vector # hat_vector = 'jacobian(func)(fit_result.x, x)'
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A = W @ hat_vector
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P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
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expected_chisquare = np.trace((np.identity(x_all.shape[-1]) - P_phi) @ W @ cov @ W)
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output.chisquare_by_expected_chisquare = output.chisquare / expected_chisquare
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@ -891,13 +705,13 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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if kwargs.get('correlated_fit') is True:
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def chisqfunc_compact(d):
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func_list = np.concatenate([[func[k]] * len(x[k]) for k in key_ls])
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func_list = np.concatenate([[funcd[k]] * len(xd[k]) for k in key_ls])
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model = anp.array([func_list[i](d[:n_parms], x_all[i]) for i in range(len(x_all))])
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chisq = anp.sum(anp.dot(chol_inv, (d[n_parms:] - model)) ** 2)
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return chisq
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else:
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def chisqfunc_compact(d):
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func_list = np.concatenate([[func[k]] * len(x[k]) for k in key_ls])
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func_list = np.concatenate([[funcd[k]] * len(xd[k]) for k in key_ls])
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model = anp.array([func_list[i](d[:n_parms], x_all[i]) for i in range(len(x_all))])
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chisq = anp.sum(((d[n_parms:] - model) / dy_f) ** 2)
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return chisq
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@ -916,11 +730,20 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
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output.fit_parameters = result
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# Hotelling t-squared p-value for correlated fits.
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if kwargs.get('correlated_fit') is True:
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n_cov = np.min(np.vectorize(lambda x_all: x_all.N)(y_all))
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output.t2_p_value = 1 - scipy.stats.f.cdf((n_cov - output.dof) / (output.dof * (n_cov - 1)) * output.chisquare,
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output.dof, n_cov - output.dof)
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||||
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])
|
||||
|
|
|
|||
|
|
@ -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.
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue