diff --git a/cellcommunicationpf2/tests/test_ccpf2.py b/cellcommunicationpf2/tests/test_ccpf2.py
new file mode 100644
index 0000000..a52594e
--- /dev/null
+++ b/cellcommunicationpf2/tests/test_ccpf2.py
@@ -0,0 +1,89 @@
+import numpy as np
+
+from ..cc_pf2 import project_data, solve_projections, init
+
+
+def test_init():
+    """
+    Tests that the dimensions are correct and that the method is able to run without errors.
+    """
+
+    # Define dimensions
+    cells = 20
+    LR = 10
+    rank = 5
+
+    # Generate random X_list
+    X_list = [np.random.rand(cells, cells, LR) for _ in range(3)]
+
+    # Call the init method
+    factors = init(X_list, rank)
+
+    assert factors[0].shape == (cells, rank)
+    assert factors[1].shape == (rank, rank)
+    assert factors[2].shape == (rank, rank)
+    assert factors[3].shape == (LR, rank)
+
+
+def test_project_data():
+    """
+    Tests that the dimensions are correct and that the method is able to run without errors.
+    """
+
+    # Define dimensions
+    cells = 20
+    LR = 10
+    rank = 5
+
+    # Generate random X_list
+    X_mat = np.random.rand(cells, cells, LR)
+
+    # Projection matrix
+    proj_matrix = np.linalg.qr(np.random.rand(cells, rank))[0]
+
+    # Call the project_data method
+    print(proj_matrix.shape)
+    projected_X = project_data(X_mat, proj_matrix)
+
+    assert projected_X.shape == (rank, rank, LR)
+
+
+def test_project_data_output_proj_matrix():
+    """
+    Tests that the project data method is actually able to solve for the correct optimal projection matrix.
+    Asserts that the projection matrices solved are the same.
+    """
+    # Define dimensions
+    num_tensors = 3
+    cells = 20
+    variables = 10
+    obs = 20
+    rank = 5
+    # Generate a random projected tensor
+    projected_X = np.random.rand(obs, rank, rank, variables)
+
+    # Generate a random set of projection matrices
+    projections = [
+        np.linalg.qr(np.random.rand(cells, rank))[0] for _ in range(num_tensors)
+    ]
+
+    # Recreate the original tensor using the projection matrices and projected tensor
+    recreated_tensors = []
+    for i in range(num_tensors):
+        Q = projections[i]
+        A = projected_X[i, :, :, :]
+        B = project_data(A, Q.T)
+        recreated_tensors.append(B)
+
+    # Call the project_data method using the recreated tensors to get the projected_X that gets solved by our method
+    projections_recreated = solve_projections(
+        recreated_tensors,
+        projected_X,
+    )
+
+    # Assert that the projections are the same
+    for i in range(num_tensors):
+        sign_correct = np.sign(projections[i][0, 0] * projections_recreated[i][0, 0])
+        np.testing.assert_allclose(
+            projections[i], projections_recreated[i] * sign_correct, atol=1e-9
+        )