<jupyter_start><jupyter_text>"""Test your code before submissionTo test the code you've written above, run the cell (select the cell above, then press the play button [ ▶| ] or press shift-enter). You can then use the code below to test out your function. You don't need to submit this cell; you can edit and run it as much as you like.Try out your code on tricky test cases!"""<jupyter_code>V = np.array([[1,0,2,6],
              [0,1,8,2],
              [2,8,3,1],
              [1,-6,2,3]], dtype=np.float_)
gsBasis4(V)
# Once you've done Gram-Schmidt once,
# doing it again should give you the same result. Test this:
U = gsBasis4(V)
gsBasis4(U)
# Try the general function too.
gsBasis(V)
# See what happens for non-square matrices
A = np.array([[3,2,3],
              [2,5,-1],
              [2,4,8],
              [12,2,1]], dtype=np.float_)
gsBasis(A)
dimensions(A)
B = np.array([[6,2,1,7,5],
              [2,8,5,-4,1],
              [1,-6,3,2,8]], dtype=np.float_)
gsBasis(B)
dimensions(B)
# Now let's see what happens when we have one vector that is a linear combination of the others.
C = np.array([[1,0,2],
              [0,1,-3],
              [1,0,2]], dtype=np.float_)
gsBasis(C)
dimensions(C)<jupyter_output><empty_output>
{'fraction_non_alphanumeric': 0.14862681744749595, 'fraction_numerical': 0.045234248788368334, 'mean_word_length': 2.933333333333333, 'pattern_counts': {'":': 0, '<': 5, '<?xml version=': 0, '>': 5, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '1', 'dir': 'jupyter-structured-clean-dedup', 'id': '310441', 'license': 'MIT', 'n_tokens_mistral': 455, 'n_tokens_neox': 447, 'n_words': 141, 'path': 'ipynb/GramSchmidtProcess.ipynb', 'repo_name': 'abhishekkumaribt/Grey_Atom', 'size': '1238'}