Finished initialization method first draft

cellcommunicationpf2/cc_pf2.py

@@ -4,6 +4,38 @@
 from pymanopt import Problem
 from pymanopt.manifolds import Stiefel
 from pymanopt.optimizers import TrustRegions
+from typing import Optional
+from sklearn.utils.extmath import randomized_svd
+
+
+def flatten_tensor_list(tensor_list: list):
+    """
+    Flatten a list of 3D tensors from A x B x B x C to a matrix of (A*B*B) x C
+    """
+
+    # Reshape each tensor to a 2D matrix
+    # This will stack rows of each B x B tensor into a single row
+    reshaped_tensors = [tensor.reshape(-1, tensor.shape[-1]) for tensor in tensor_list]
+
+    # Vertically stack these matrices
+    flattened_matrix = np.vstack(reshaped_tensors)
+
+    return flattened_matrix
+
+
+def init(
+    X_list: list,
+    rank: int,
+    random_state: Optional[int] = None,
+) -> list[np.ndarray]:
+    """
+    Initializes the factors for the CP decomposition of a list of 3D tensors
+    """
+    data_matrix = flatten_tensor_list(X_list)
+
+    _, _, C = randomized_svd(data_matrix, rank, random_state=random_state)
+    factors = [np.ones((X_list[0].shape[0], rank)), np.eye(rank), np.eye(rank), C.T]
+    return factors
 
 
 def project_data(tensor: np.ndarray, proj_matrix: np.ndarray) -> np.ndarray: