Fix the issue facebook#1814

I did as PyStanBackend. And now when we use the method fit of Prophet, we can do like in the documentation:

https://facebook.github.io/prophet/docs/additional_topics.html#updating-fitted-models

def stan_init(m):
    """Retrieve parameters from a trained model.

    Retrieve parameters from a trained model in the format
    used to initialize a new Stan model.

    Parameters
    ----------
    m: A trained model of the Prophet class.

    Returns
    -------
    A Dictionary containing retrieved parameters of m.

    """
    res = {}
    for pname in ['k', 'm', 'sigma_obs']:
        res[pname] = m.params[pname][0][0]
    for pname in ['delta', 'beta']:
        res[pname] = m.params[pname][0]
    return res

df = pd.read_csv('../examples/example_wp_log_peyton_manning.csv')
df1 = df.loc[df['ds'] < '2016-01-19', :]  # All data except the last day
m1 = Prophet().fit(df1) # A model fit to all data except the last day

%timeit m2 = Prophet().fit(df)  # Adding the last day, fitting from scratch
%timeit m2 = Prophet().fit(df, init=stan_init(m1))  # Adding the last day, warm-starting from m1

Update models.py

Update models.py

Update models.py

Update models.py

Update models.py

Update models.py

Update models.py

Test

Test2

Test4

Test4

Test are fixed

python/fbprophet/models.py

@@ -87,25 +87,30 @@ def load_model(self):
 
     def fit(self, stan_init, stan_data, **kwargs):
         (stan_init, stan_data) = self.prepare_data(stan_init, stan_data)
-        if 'algorithm' not in kwargs:
-            kwargs['algorithm'] = 'Newton' if stan_data['T'] < 100 else 'LBFGS'
-        iterations = int(1e4)
+        if 'init' in kwargs:
+            kwargs['init'] = self.prepare_data(kwargs['init'], stan_data)[0]
+
+        args = dict(
+            data=stan_data,
+            init=stan_init,
+            algorithm='Newton' if stan_data['T'] < 100 else 'LBFGS',
+            iter=int(1e4),
+        )
+        args.update(kwargs)
+
+        args['inits'] = args['init']
+        del args['init']
+
         try:
-            self.stan_fit = self.model.optimize(data=stan_data,
-                                                inits=stan_init,
-                                                iter=iterations,
-                                                **kwargs)
+            self.stan_fit = self.model.optimize(**args)
         except RuntimeError as e:
             # Fall back on Newton
-            if self.newton_fallback and kwargs['algorithm'] != 'Newton':
+            if self.newton_fallback and args['algorithm'] != 'Newton':
                 logger.warning(
                     'Optimization terminated abnormally. Falling back to Newton.'
                 )
-                kwargs['algorithm'] = 'Newton'
-                self.stan_fit = self.model.optimize(data=stan_data,
-                                                    inits=stan_init,
-                                                    iter=iterations,
-                                                    **kwargs)
+                args['algorithm'] = 'Newton'
+                self.stan_fit = self.model.optimize(**args)
             else:
                 raise e
 
@@ -117,17 +122,28 @@ def fit(self, stan_init, stan_data, **kwargs):
 
     def sampling(self, stan_init, stan_data, samples, **kwargs) -> dict:
         (stan_init, stan_data) = self.prepare_data(stan_init, stan_data)
+        if 'init' in kwargs:
+            kwargs['init'] = self.prepare_data(kwargs['init'], stan_data)[0]
+
+        args = dict(
+            data=stan_data,
+            init=stan_init,
+            algorithm='Newton' if stan_data['T'] < 100 else 'LBFGS',
+        )
 
         if 'chains' not in kwargs:
             kwargs['chains'] = 4
         iter_half = samples // 2
+        kwargs['iter_sampling'] = iter_half
         if 'iter_warmup' not in kwargs:
             kwargs['iter_warmup'] = iter_half
+
+        args.update(kwargs)
 
-        self.stan_fit = self.model.sample(data=stan_data,
-                                          inits=stan_init,
-                                          iter_sampling=iter_half,
-                                          **kwargs)
+        args['inits'] = args['init']
+        del args['init']
+
+        self.stan_fit = self.model.sample(**args)
         res = self.stan_fit.sample
         (samples, c, columns) = res.shape
         res = res.reshape((samples * c, columns))
@@ -166,10 +182,10 @@ def prepare_data(init, data) -> Tuple[dict, dict]:
             'm': init['m'],
             'delta': init['delta'].tolist(),
             'beta': init['beta'].tolist(),
-            'sigma_obs': 1
+            'sigma_obs': init['sigma_obs']
         }
         return (cmdstanpy_init, cmdstanpy_data)
-
+    
     @staticmethod
     def stan_to_dict_numpy(column_names: Tuple[str, ...], data: 'np.array'):
         import numpy as np