diff --git a/cellcommunicationpf2/cc_pf2.py b/cellcommunicationpf2/cc_pf2.py
index 92a9872..c3921d4 100644
--- a/cellcommunicationpf2/cc_pf2.py
+++ b/cellcommunicationpf2/cc_pf2.py
@@ -1,5 +1,4 @@
 import numpy as np
-import tensorly as tl
 from pymanopt.manifolds import Stiefel
 from pymanopt import Problem
 from pymanopt.optimizers import ConjugateGradient
@@ -37,13 +36,13 @@ def solve_projections(
 
         @pymanopt.function.autograd(manifold)
         def objective_function(proj):
-            a_mat_recon = anp.einsum("ab,cd,acg->bdg", proj.T, proj.T, a_lhs)
+            a_mat_recon = anp.einsum("ba,dc,acg->bdg", proj, proj, a_lhs)
             return anp.sum(anp.square(a_mat - a_mat_recon))
 
         problem = Problem(manifold=manifold, cost=objective_function)
 
         # Solve the problem
-        solver = ConjugateGradient(verbosity=1)
+        solver = ConjugateGradient(verbosity=1, min_gradient_norm=1e-9, min_step_size=1e-12)
         proj = solver.run(problem).point
 
         U, _, Vt = np.linalg.svd(proj, full_matrices=False)
diff --git a/cellcommunicationpf2/tests/test_OP.py b/cellcommunicationpf2/tests/test_OP.py
index b67b923..29a0ea6 100644
--- a/cellcommunicationpf2/tests/test_OP.py
+++ b/cellcommunicationpf2/tests/test_OP.py
@@ -1,6 +1,5 @@
 import numpy as np
 from ..cc_pf2 import project_data, solve_projections
-import pytest
 
 
 def test_project_data():
@@ -26,44 +25,6 @@ def test_project_data():
     assert projected_X.shape == (rank, rank, LR)
 
 
-def test_project_data_output_proj_data():
-    """
-    Tests that the project data method is actually able to solve for the correct optimal projection matrix.
-    Asserts that the projected data through the solved matrices is the same as the input projectedX.
-    """
-    # Define dimensions
-    num_tensors = 3
-    cells = 20
-    LR = 10
-    obs = 5
-    rank = 5
-    # Generate a random projected tensor
-    projected_X = np.random.rand(obs, rank, rank, LR)
-
-    # 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 projected tensors are the same
-    for i in range(num_tensors):
-        assert np.allclose(project_data(recreated_tensors[i], projections_recreated[i]), projected_X[i])
-
-
 def test_project_data_output_proj_matrix():
     """
     Tests that the project data method is actually able to solve for the correct optimal projection matrix.
@@ -72,11 +33,11 @@ def test_project_data_output_proj_matrix():
     # Define dimensions
     num_tensors = 3
     cells = 20
-    LR = 10
-    obs = 5
+    variables = 10
+    obs = 20
     rank = 5
     # Generate a random projected tensor
-    projected_X = np.random.rand(obs, rank, rank, LR)
+    projected_X = np.random.rand(obs, rank, rank, variables)
 
     # Generate a random set of projection matrices
     projections = [
@@ -99,5 +60,6 @@ def test_project_data_output_proj_matrix():
 
     # Assert that the projections are the same
     for i in range(num_tensors):
-        assert np.allclose(projections[i], projections_recreated[i]) or np.allclose(projections[i], -projections_recreated[i])
+        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)