Preserve small values in Yeo-Johnson inverse transformation

feature_engine/transformation/yeojohnson.py

@@ -206,15 +206,15 @@ def _inverse_transform_series(self, X: pd.Series, lmbda: float) -> pd.Series:
 
         # when x >= 0
         if lmbda == 0:
-            x_inv[pos] = np.exp(X[pos]) - 1
+            x_inv[pos] = np.expm1(X[pos])
         else:  # lmbda != 0
-            x_inv[pos] = np.power(X[pos] * lmbda + 1, 1 / lmbda) - 1
+            x_inv[pos] = np.expm1(np.log1p(X[pos] * lmbda) / lmbda)
 
         # when x < 0
         if lmbda != 2:
-            x_inv[~pos] = 1 - np.power(-(2 - lmbda) * X[~pos] + 1, 1 / (2 - lmbda))
+            x_inv[~pos] = -np.expm1(np.log1p(-(2 - lmbda) * X[~pos]) / (2 - lmbda))
         else:  # lmbda == 2
-            x_inv[~pos] = 1 - np.exp(-X[~pos])
+            x_inv[~pos] = -np.expm1(-X[~pos])
 
         return x_inv
 

tests/test_transformation/test_yeojohnson_transformer.py

@@ -168,3 +168,44 @@ def test_lambda_equals_lambda_equal_2():
     X_inverse = X_inverse.round(0).astype(int)
 
     pd.testing.assert_frame_equal(X, X_inverse, check_dtype=False)
+
+
+@pytest.mark.parametrize(
+    "training_values",
+    [
+        [-3.0, -1.0, 0.0, 1.0, 3.0],
+        [0.0, 0.25, 1.0, 4.0, 16.0],
+        [-16.0, -4.0, -1.0, -0.25, 0.0],
+    ],
+)
+def test_inverse_preserves_small_values_with_fitted_lambda(training_values):
+    transformer = YeoJohnsonTransformer(variables=["x"]).fit(
+        pd.DataFrame({"x": training_values, "keep": list("abcde")})
+    )
+    X = pd.DataFrame(
+        {"x": [-1e-20, -1e-10, 0.0, 1e-10, 1e-20], "keep": list("abcde")},
+        index=[4, 8, 8, 1, 9],
+    )
+    original = X.copy(deep=True)
+    transformed = transformer.transform(X)
+    transformed_before = transformed.copy(deep=True)
+
+    inverse = transformer.inverse_transform(transformed)
+
+    pd.testing.assert_frame_equal(inverse, X, rtol=3e-14, atol=0)
+    pd.testing.assert_frame_equal(X, original)
+    pd.testing.assert_frame_equal(transformed, transformed_before)
+
+
+@pytest.mark.parametrize("lmbda", [-2.0, 0.0, 0.5, 1.0, 1.5, 2.0, 4.0])
+@pytest.mark.parametrize("magnitude", [1e-20, 0.5])
+def test_inverse_precision_for_lambda_branches(lmbda, magnitude):
+    X = pd.DataFrame({"x": [-magnitude, 0.0, magnitude]}, index=[9, 2, 6])
+    transformer = YeoJohnsonTransformer().fit(
+        pd.DataFrame({"x": [-3.0, -1.0, 0.0, 1.0, 3.0]})
+    )
+    transformer.lambda_dict_["x"] = lmbda
+
+    inverse = transformer.inverse_transform(transformer.transform(X))
+
+    pd.testing.assert_frame_equal(inverse, X, rtol=3e-14, atol=0)