<jupyter_start><jupyter_text>Scalar function $f(x,y) = xy + e^{xy}$ $a = (1, 2)$<jupyter_code>x = rAd_Var(1)
y = rAd_Var(2)

x1 = x * y
x2 = x1.exp()
f = x1 + x2
function_gradient = f.get_ders() # Backward pass
function_value = f.get_val()
print(f"Gradient of the function: {function_gradient}")
print(f"Value of the function: {function_value}")<jupyter_output>Gradient of the function: [16.7781122  8.3890561]
Value of the function: 9.38905609893065<jupyter_text>Full Jacobian for function vectors$f_{1}(x, y, z, a): y + 2^x + z + a$ $f_{2}(x, z): 3x + z$ $f_{3}(x, y): \ln{x^y}$ $a = (1,2,3,4)$<jupyter_code>def f1(x, y, z, a):
    return y + 2*x + z + a
def f2(x, z):
    return 3 * x + z
def f3(x, y):
    return rAd_Var.log(x ** y)
rAd_Var.get_jacobian([f1, f2, f3], ['x', 'y', 'z', 'a'], [1, 2, 3, 4])<jupyter_output><empty_output>
{'fraction_non_alphanumeric': 0.20430107526881722, 'fraction_numerical': 0.07407407407407407, 'mean_word_length': 4.779310344827586, 'pattern_counts': {'":': 0, '<': 8, '<?xml version=': 0, '>': 8, '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': '2', 'dir': 'jupyter-structured-clean-dedup', 'id': '67019', 'license': 'MIT', 'n_tokens_mistral': 425, 'n_tokens_neox': 395, 'n_words': 98, 'path': 'demo/Reverse Demo.ipynb', 'repo_name': 'the-differentiators/cs207-FinalProject', 'size': '837'}