Fix bad initial value for Yamamoto method

Change initial value from the automatic middle of the boundary space (500 & 500) to (1, 1), as an initial value of 500 can lead to numerical errors.

Also adapted yamamoto.py to PEP8

CADETProcess/tools/yamamoto.py

@@ -7,7 +7,6 @@
 from CADETProcess import CADETProcessError
 from CADETProcess.processModel import TubularReactorBase, StericMassAction
 
-
 __all__ = ['GradientExperiment', 'plot_experiments', 'YamamotoResults', 'fit_parameters']
 
 
@@ -66,7 +65,7 @@ def calculate_normalized_gradient_slope(self, column_volume, total_porosity):
 
         """
         slope = (self.c_salt_end - self.c_salt_start) / self.gradient_volume
-        vol_factor = column_volume - total_porosity*column_volume
+        vol_factor = column_volume - total_porosity * column_volume
         return slope * vol_factor
 
     def plot(self, fig=None, ax=None, sec_ax=None):
@@ -118,9 +117,9 @@ def yamamoto_equation(log_c_salt_at_max_M, lambda_, nu, k_eq):
         DESCRIPTION.
 
     """
-    lambda_M = lambda_/1000
+    lambda_M = lambda_ / 1000
 
-    return np.multiply((nu + 1), log_c_salt_at_max_M) - np.log10(k_eq * lambda_M**nu * (nu + 1))
+    return np.multiply((nu + 1), log_c_salt_at_max_M) - np.log10(k_eq * lambda_M ** nu * (nu + 1))
 
 
 class YamamotoResults:
@@ -154,8 +153,8 @@ def plot(self, fig=None, ax=None):
             nu = self.characteristic_charge[i_p]
 
             x = [
-                min(self.log_c_salt_at_max_M[:, i_p])*1.05,
-                max(self.log_c_salt_at_max_M[:, i_p])*0.95
+                min(self.log_c_salt_at_max_M[:, i_p]) * 1.05,
+                max(self.log_c_salt_at_max_M[:, i_p]) * 0.95
             ]
 
             y = yamamoto_equation(
@@ -212,7 +211,7 @@ def fit_parameters(experiments, column):
 
     for i_p in range(experiments[0].n_proteins):
         c_salt_at_max = [exp.c_salt_at_max[i_p] for exp in experiments]
-        log_c_salt_at_max_M[:, i_p] = np.log10(np.array(c_salt_at_max)/1000)
+        log_c_salt_at_max_M[:, i_p] = np.log10(np.array(c_salt_at_max) / 1000)
 
         nu[i_p], k_eq[i_p] = _fit_yamamoto(
             log_c_salt_at_max_M[:, i_p], log_gradient_slope, column.binding_model.capacity
@@ -224,7 +223,7 @@ def fit_parameters(experiments, column):
     yamamoto_results = YamamotoResults(
         column, experiments,
         log_gradient_slope, log_c_salt_at_max_M
-        )
+    )
 
     return yamamoto_results
 
@@ -254,8 +253,7 @@ def _fit_yamamoto(log_c_salt_at_max_M, log_gradient_slope, lambda_):
     def yamamoto_wrapper(c_s, nu, k_eq):
         return yamamoto_equation(c_s, lambda_, nu, k_eq)
 
-    results, pcov = curve_fit(
-        yamamoto_wrapper, log_c_salt_at_max_M, log_gradient_slope, bounds=bounds
-    )
+    results, pcov = curve_fit(f=yamamoto_wrapper, xdata=log_c_salt_at_max_M, ydata=log_gradient_slope, bounds=bounds,
+                              p0=(1, 1))
 
     return results