Added the reconstruction and approximation errors (#263)

* Added the reconstraction and approximation errors
* Added test for the scaling and possible problem with param scaling

Author: DavideDC95

ezyrb/plugin/scaler.py

@@ -26,7 +26,7 @@ def __init__(self, scaler, mode, target) -> None:
         self.scaler = scaler
         self.mode = mode
         self.target = target
-
+        
     @property
     def target(self):
         """
@@ -141,5 +141,5 @@ def rom_postprocessing(self, rom):
                 db.parameters_matrix,
                 self.scaler.inverse_transform(self._select_matrix(db)),
             )
-
+            
         rom._reduced_database = new_db

ezyrb/reducedordermodel.py

@@ -99,7 +99,12 @@ def predict(self, mu):
         :rtype: Database
         """
         mu = np.atleast_2d(mu)
-
+        
+        for plugin in self.plugins:
+            if plugin.target == 'parameters':
+                mu = plugin.scaler.transform(mu)
+            
+ 
         self._reduced_database = Database(
                 mu, np.atleast_2d(self.approximation.predict(mu)))
 
@@ -312,3 +317,107 @@ def _simplex_volume(self, vertices):
         distance = np.transpose([vertices[0] - vi for vi in vertices[1:]])
         return np.abs(
             np.linalg.det(distance) / math.factorial(vertices.shape[1]))
+
+    def reconstruction_error(self, db=None, relative=True, eps=1e-12):
+        """
+        Calculate the reconstruction error between the original snapshots and
+        the ones reconstructed by the ROM.
+        
+        :param database.Database db: the database to use to compute the error.
+            If None, the error is computed on the training database.
+            Default is None.
+        :param bool relative: True if the error computed is relative. Default is 
+            True.
+        :param float eps: small number to avoid division by zero in relative
+            error computation. Default is 1e-12.
+        :return: the vector containing the reconstruction errors.
+        
+        Esempio:    
+        >>> from ezyrb import ReducedOrderModel as ROM
+        >>> from ezyrb import POD, RBF, Database
+        >>> db = Database(param, snapshots) # param and snapshots are assumed 
+        to be declared
+        >>> db_train = db[:10] # training database
+        >>> db_test = db[10:] # test database
+        >>> pod = POD()
+        >>> rbf = RBF()
+        >>> rom = ROM(db_train, pod, rbf)
+        >>> rom.fit()
+        >>> err_train_reduct = rom.reconstruction_error(relative=True)
+        >>> err_test_reduct = rom.reconstruction_error(db_test, relative=True)
+        """
+        
+        errs = []
+        if db is None:
+            db = self.database   
+        snap = db.snapshots_matrix
+        snap_red = self.reduction.transform(snap.T)
+        snap_full = self.reduction.inverse_transform(snap_red).T
+
+        E = snap - snap_full
+
+        if relative:
+            num = np.linalg.norm(E, axis=1)
+            den = np.linalg.norm(snap, axis=1) + eps
+            
+            err = float(np.mean(num/den))        
+        else:
+            err = float(np.mean(np.linalg.norm(E, axis=1)))
+        errs.append(err)
+        
+        return np.array(errs)
+
+    def approximation_error(self, db=None, relative=True, eps=1e-12):
+        """
+        Calculate the approximation error between the true modal coefficients
+        and the approximated ones.
+        
+        :param database.Database db: the database to use to compute the error.
+            If None, the error is computed on the training database.
+            Default is None.
+        :param bool relative: True if the error computed is relative. Default is 
+            True.
+        :param float eps: small number to avoid division by zero in relative
+            error computation. Default is 1e-12.
+            
+        :return: the vector containing the approximation errors.
+        
+        Esempio:
+        >>> from ezyrb import ReducedOrderModel as ROM
+        >>> from ezyrb import POD, RBF, Database
+        >>> db = Database(param, snapshots) # param and snapshots are assumed 
+        to be declared
+        >>> db_train = db[:10] # training database
+        >>> db_test = db[10:] # test database
+        >>> pod = POD()
+        >>> rbf = RBF()
+        >>> rom = ROM(db_train, pod, rbf)
+        >>> rom.fit()
+        >>> err_train_approx = rom.approximation_error(relative=True)
+        >>> err_test_approx = rom.approximation_error(db_test, relative=True)
+
+        """
+        errs = []
+        if db is None:
+            db = self.database
+
+        snap = db.snapshots_matrix
+        params_true = self.reduction.transform(snap.T).T
+
+        params = db.parameters_matrix
+
+        params_approx = self.approximation.predict(params)
+
+        E = params_true - params_approx
+
+        if relative:
+            num = np.linalg.norm(E, axis=1)
+            den = np.linalg.norm(params_true, axis=1) + eps
+
+            err = float(np.mean(num/den))
+        else:
+            err = float(np.mean(np.linalg.norm(E, axis=1)))
+        errs.append(err)
+
+        return np.array(errs)
+

tests/test_scaler.py

@@ -6,7 +6,7 @@
 from ezyrb import ReducedOrderModel as ROM
 from ezyrb.plugin.scaler import DatabaseScaler
 
-from sklearn.preprocessing import StandardScaler
+from sklearn.preprocessing import StandardScaler, MinMaxScaler
 
 snapshots = np.load('tests/test_datasets/p_snapshots.npy').T
 pred_sol_tst = np.load('tests/test_datasets/p_predsol.npy').T
@@ -18,22 +18,30 @@ def test_constructor():
     pod = POD()
     import torch
     rbf = RBF()
-    rbf = ANN([10, 10], function=torch.nn.Softplus(), stop_training=[1000])
+    #rbf = ANN([10, 10], function=torch.nn.Softplus(), stop_training=[1000])
     db = Database(param, snapshots.T)
     # rom = ROM(db, pod, rbf, plugins=[DatabaseScaler(StandardScaler(), 'full', 'snapshots')])
     rom = ROM(db, pod, rbf, plugins=[
-        DatabaseScaler(StandardScaler(), 'full', 'parameters'),
+        DatabaseScaler(StandardScaler(), 'reduced', 'parameters'),
         DatabaseScaler(StandardScaler(), 'reduced', 'snapshots')
     ])
     rom.fit()
-    print(rom.predict(rom.database.parameters_matrix))
-    print(rom.database.snapshots_matrix)
+   
+    
 
 
-# def test_values():
-#     snap = Snapshot(test_value)
-#     snap.values = test_value
-#     snap = Snapshot(test_value, space=test_space)
-#     with pytest.raises(ValueError):
-#         snap.values = test_value[:-2]
+def test_values():
+    pod = POD()
+    rbf = RBF()
+    db = Database(param, snapshots.T)
+    rom = ROM(db, pod, rbf, plugins=[
+        DatabaseScaler(StandardScaler(), 'reduced', 'snapshots'),
+        DatabaseScaler(StandardScaler(), 'full', 'parameters')
+    ])
+    rom.fit()
+    test_param = param[2]
+    truth_sol = db.snapshots_matrix[2]
+    predicted_sol = rom.predict(test_param).snapshots_matrix[0]
+    np.testing.assert_allclose(predicted_sol, truth_sol, 
+            rtol=1e-5, atol=1e-5)