feat: support setting the backend engine with environment variable

Author: gavincyi

docs/source/engine.md

@@ -10,6 +10,8 @@ CPU and GPU runtime.
 
 - [TensorFlow](https://www.tensorflow.org/guide/tf_numpy)
 
+- [PyTorch](https://pytorch.org/)
+
 The backend engine can be switched in the following ways.
 
 ## Local
@@ -48,6 +50,17 @@ from fpm_risk_model.engine import set_backend
 set_backend("tensorflow")
 ```
 
+## Environment variable
+
+Set the environment variable `FPM_BACKEND_ENGINE` before starting the process.
+
+For example, to start the IPython with setting the default backend engine to `torch`, launch the
+terminal as below
+
+```
+FPM_BACKEND_ENGINE=torch ipython
+```
+
 ## Reference
 
 For further details, please find the following notebook [example](https://colab.research.google.com/github/factorpricingmodel/factor-pricing-model-risk-model/blob/main/examples/notebook/numpy_backend_engine.ipynb).

src/fpm_risk_model/engine.py

@@ -1,4 +1,5 @@
 from contextlib import contextmanager
+from os import environ
 from typing import Any
 
 _BACKEND_ENGINE = "numpy"
@@ -86,6 +87,7 @@ def __getattribute__(self, __name: str) -> Any:
 
                 anp.array = anp.tensor
                 anp.ndarray = anp.Tensor
+                anp.newaxis = None
             else:
                 raise ValueError(f"Cannot recognize backend {_BACKEND_ENGINE}")
         except ImportError:
@@ -145,5 +147,6 @@ def __getattribute__(self, __name: str) -> Any:
             )
 
 
+set_backend(environ.get("FPM_BACKEND_ENGINE", "numpy"))
 numpy = NumpyEngine()
 linalg = LinAlgEngine()

src/fpm_risk_model/risk_model.py

@@ -112,9 +112,9 @@ def _to_numpy(values: Union[ndarray, DataFrame]) -> ndarray:
         if values is None:
             return values
         elif isinstance(values, (DataFrame, Series)):
-            return values.values
+            return np.array(values.values)
         elif isinstance(values, ndarray):
-            return values
+            return np.array(values)
         else:
             raise TypeError(
                 "Expect either pandas DataFrame or numpy array, "

src/fpm_risk_model/statistical/pca.py

@@ -91,7 +91,7 @@ def fit(
 
         # Normalize the instrument return by full history mean
         if self._config.demean:
-            X_mean = np.array(np.mean(X, axis=0))[np.newaxis, :]
+            X_mean = np.array(X.mean(axis=0))[np.newaxis, :]
             X_fit = np.subtract(X_fit, X_mean)
 
         # Remove the instruments without any returns always
@@ -109,11 +109,11 @@ def fit(
         N = X.shape[1]
         # Dimension (n, N) where n is the number of instruments
         # Eigenvectors
-        U_m = self._model.components_
+        U_m = np.array(self._model.components_)
         # Exposure matrix (n, N)
         B = np.multiply(
             U_m,
-            np.array(self._model.singular_values_ * np.sqrt(T))[:, np.newaxis],
+            np.array(self._model.singular_values_ * (T**0.5))[:, np.newaxis],
         )
         # Factor matrix (T, n)
         wls = WLS()