Merge pull request #148 from PiaLJP/feature/correlated_combined_fit

Feature/correlated combined fit

Author: fjosw

pyerrors/fits.py

@@ -705,9 +705,6 @@ def chisqfunc_compact(d):
 
 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
 
@@ -735,6 +732,9 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
     if len(x_all.shape) > 2:
         raise Exception('Unknown format for x values')
 
+    if np.any(np.asarray(dy_f) <= 0.0):
+        raise Exception('No y errors available, run the gamma method first.')
+
     # number of fit parameters
     n_parms_ls = []
     for key in key_ls:
@@ -766,6 +766,22 @@ def _combined_fit(x, y, func, silent=False, **kwargs):
     else:
         x0 = [0.1] * n_parms
 
+    if kwargs.get('correlated_fit') is True:
+        corr = covariance(y_all, 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 = np.concatenate([np.array(func[key](p, np.asarray(x[key]))) 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])
         model = anp.array([func_list[i](p, x_all[i]) for i in range(len(x_all))])
@@ -782,30 +798,46 @@ def chisqfunc(p):
             if 'tol' in kwargs:
                 tolerance = kwargs.get('tol')
             fit_result = iminuit.minimize(chisqfunc, x0, tol=tolerance)  # Stopping criterion 0.002 * tol * errordef
+            if kwargs.get('correlated_fit') is True:
+                fit_result = iminuit.minimize(chisqfunc_corr, fit_result.x, tol=tolerance)
             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)
+            if kwargs.get('correlated_fit') is True:
+                fit_result = scipy.optimize.minimize(chisqfunc_corr, fit_result.x, method=kwargs.get('method'), tol=tolerance)
             output.iterations = fit_result.nit
 
         chisquare = fit_result.fun
 
     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])
+                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])
             chisq = ((y_f - model) / dy_f)
             return chisq
+
         if 'tol' in kwargs:
             print('tol cannot be set for Levenberg-Marquardt')
+
         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)
-        assert np.isclose(chisquare, chisqfunc(fit_result.x), atol=1e-14)
-        output.iterations = fit_result.nfev
+        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.message = fit_result.message
+        output.iterations = fit_result.nfev
 
     if not fit_result.success:
         raise Exception('The minimization procedure did not converge.')
@@ -818,17 +850,12 @@ def chisqfunc_residuals(p):
     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)
         print('fit parameters', fit_result.x)
 
-    def chisqfunc_compact(d):
-        func_list = np.concatenate([[func[k]] * len(x[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
-
     def prepare_hat_matrix():
         hat_vector = []
         for key in key_ls:
@@ -838,16 +865,43 @@ def prepare_hat_matrix():
         hat_vector = [item for sublist in hat_vector for item in sublist]
         return hat_vector
 
-    fitp = fit_result.x
+    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 = output.chisquare / expected_chisquare
+            if not silent:
+                print('chisquare/expected_chisquare:', output.chisquare_by_expected_chisquare)
 
+    fitp = fit_result.x
     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)
+        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):
+            func_list = np.concatenate([[func[k]] * len(x[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])
+            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
+
     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
@@ -856,24 +910,17 @@ def prepare_hat_matrix():
     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 = output.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
 
+    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)
+
     return output
 
 

tests/fits_test.py

@@ -703,6 +703,8 @@ def func_valid(a,x):
         yvals.append(pe.pseudo_Obs(x + np.random.normal(0.0, err), err, 'test1') + pe.pseudo_Obs(0, err / 100, 'test2', samples=87))
     with pytest.raises(Exception):
         pe.least_squares({'a':xvals}, {'b':yvals}, {'a':func_valid})
+    with pytest.raises(Exception):
+        pe.least_squares({'a':xvals}, {'a':yvals}, {'a':func_valid})
 
 def test_combined_fit_no_autograd():
 
@@ -833,6 +835,59 @@ def func_auto_b(a,x):
         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)}
+    y_const = {'a':[pe.Obs([np.random.normal(1, val, 1000)], ['ensemble1']) 
+                for val in [0.25, 0.3, 0.01, 0.2, 0.5, 1.3, 0.26, 0.4, 0.1, 1.0]],
+            'b':[pe.Obs([np.random.normal(1, val, 1000)], ['ensemble1'])
+                for val in [0.5, 1.12, 0.26, 0.25, 0.3, 0.01, 0.2, 1.0, 0.38, 0.1]]}
+    for key in y_const.keys():
+        [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]
+
+    funcs_const = {"a": func_const,"b": func_const}
+    for method_kw in ['Levenberg-Marquardt', 'migrad', 'Powell', 'Nelder-Mead']:
+        res = []
+        res.append(pe.fits.least_squares(x_const, y_const, funcs_const, method = method_kw, correlated_fit=True))
+        res.append(pe.fits.least_squares(x_const_ls, y_const_ls, func_const, method = method_kw, correlated_fit=True))
+        [item.gamma_method for item in res]
+        assert np.isclose(0.0, (res[0].chisquare_by_dof - res[1].chisquare_by_dof), 1e-14, 1e-8)
+        assert np.isclose(0.0, (res[0].p_value - res[1].p_value), 1e-14, 1e-8)
+        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)
+
+    def func_exp1(x):
+        return 0.3*np.exp(0.5*x)
+
+    def func_exp2(x):
+        return 0.3*np.exp(0.8*x)
+
+    def func_a(a,x):
+        return a[0]*anp.exp(a[1]*x)
+
+    def func_b(a,x):
+        return a[0]*anp.exp(a[2]*x)
+
+    funcs = {'a':func_a, 'b':func_b}
+    xs = {'a':xvals_a, 'b':xvals_b}
+    yobs_a = [pe.Obs([np.random.normal(item, item*1.5, 1000)],['ensemble1']) for item in func_exp1(xvals_a)]
+    yobs_b = [pe.Obs([np.random.normal(item, item*1.4, 1000)],['ensemble1']) for item in func_exp2(xvals_b)]
+    ys = {'a': yobs_a, 'b': yobs_b}
+
+    for key in funcs.keys():
+        [item.gamma_method() for item in ys[key]]
+    ft = pe.fits.least_squares(xs, ys, funcs, correlated_fit=True)
+    assert ft.t2_p_value >= ft.p_value
+
 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.