Add modulus-weighted fit option (#185)

* Add modulus-weighted fit option

* add test on modulus-weighted option

impedance/models/circuits/circuits.py

@@ -57,7 +57,8 @@ def __eq__(self, other):
         else:
             raise TypeError('Comparing object is not of the same type.')
 
-    def fit(self, frequencies, impedance, bounds=None, **kwargs):
+    def fit(self, frequencies, impedance, bounds=None,
+            weight_by_modulus=False, **kwargs):
         """ Fit the circuit model
 
         Parameters
@@ -73,6 +74,11 @@ def fit(self, frequencies, impedance, bounds=None, **kwargs):
             parameters of 0 and np.inf, except the CPE alpha
             which has an upper bound of 1
 
+        weight_by_modulus : bool, optional
+            Uses the modulus of each data (|Z|) as the weighting factor.
+            Standard weighting scheme when experimental variances are
+            unavailable. Only applicable when global_opt = False
+
         kwargs :
             Keyword arguments passed to
             impedance.models.circuits.fitting.circuit_fit,
@@ -108,7 +114,9 @@ def fit(self, frequencies, impedance, bounds=None, **kwargs):
             parameters, conf = circuit_fit(frequencies, impedance,
                                            self.circuit, self.initial_guess,
                                            constants=self.constants,
-                                           bounds=bounds, **kwargs)
+                                           bounds=bounds,
+                                           weight_by_modulus=weight_by_modulus,
+                                           **kwargs)
             self.parameters_ = parameters
             if conf is not None:
                 self.conf_ = conf

impedance/models/circuits/fitting.py

@@ -67,7 +67,8 @@ def set_default_bounds(circuit, constants={}):
 
 
 def circuit_fit(frequencies, impedances, circuit, initial_guess, constants={},
-                bounds=None, global_opt=False, **kwargs):
+                bounds=None, weight_by_modulus=False, global_opt=False,
+                **kwargs):
 
     """ Main function for fitting an equivalent circuit to data.
 
@@ -103,6 +104,11 @@ def circuit_fit(frequencies, impedances, circuit, initial_guess, constants={},
         parameters of 0 and np.inf, except the CPE alpha
         which has an upper bound of 1
 
+    weight_by_modulus : bool, optional
+        Uses the modulus of each data (|Z|) as the weighting factor.
+        Standard weighting scheme when experimental variances are unavailable.
+        Only applicable when global_opt = False
+
     global_opt : bool, optional
         If global optimization should be used (uses the basinhopping
         algorithm). Defaults to False
@@ -137,6 +143,11 @@ def circuit_fit(frequencies, impedances, circuit, initial_guess, constants={},
         if 'ftol' not in kwargs:
             kwargs['ftol'] = 1e-13
 
+        # weighting scheme for fitting
+        if weight_by_modulus:
+            abs_Z = np.abs(Z)
+            kwargs['sigma'] = np.hstack([abs_Z, abs_Z])
+
         popt, pcov = curve_fit(wrapCircuit(circuit, constants), frequencies,
                                np.hstack([Z.real, Z.imag]),
                                p0=initial_guess, bounds=bounds, **kwargs)

impedance/tests/test_fitting.py

@@ -105,6 +105,13 @@ def test_circuit_fit():
                                    constants={})[0],
                        results_local_weighted, rtol=1e-2)
 
+    # Test if using weight_by_modulus=True produces the same results
+    assert np.allclose(circuit_fit(example_frequencies_filtered,
+                                   Z_correct_filtered, circuit,
+                                   initial_guess, weight_by_modulus=True,
+                                   constants={})[0],
+                       results_local_weighted, rtol=1e-2)
+
     # Test global fitting on multiple seeds
     # All seeds should converge to the same parameter values
     # seed = 0 (default)