Comment by credit_guy

"Here’s how you can create a test case to compare the performance of the for-loop method and the vectorized method using numpy.linalg.solve. I will provide the Python code for you to test this."

    import numpy as np
    import time

    # Create random test data
    np.random.seed(42)  # For reproducibility
    A = np.random.rand(100, 5, 5)  # 100 random 5x5 matrices
    x = np.random.rand(100, 5)     # 100 random vectors of length 5

    # Method 1: For-loop approach
    start_time = time.time()
    y_loop = np.empty_like(x)
    for i in range(100):
        y_loop[i, :] = np.linalg.solve(A[i, :, :], x[i, :])
    loop_time = time.time() - start_time

    # Method 2: Vectorized approach
    start_time = time.time()
    y_vectorized = np.linalg.solve(A, x)
    vectorized_time = time.time() - start_time

    # Verify correctness
    correctness = np.allclose(y_loop, y_vectorized)

    # Print results
    print(f"For-loop method time: {loop_time:.6f} seconds")
    print(f"Vectorized method time: {vectorized_time:.6f} seconds")
    print(f"Results are {'correct' if correctness else 'incorrect'}")

For-loop method time: 0.001004 seconds Vectorized method time: 0.000000 seconds Results are correct