tests/python/testing/test_testing.py

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import numpy as np
import tvm
from tvm import te
import tvm.testing


def test_check_numerical_grads():
    # Functions and their derivatives
    functions = [
        lambda x: (x * x * x, 3 * x * x),
        lambda x: (x * x, 2 * x),
        lambda x: (np.abs(x), np.sign(x)),
        lambda x: (np.log(np.abs(x)), 1 / x),
        lambda x: (np.sqrt(np.abs(x)), np.sign(x) / (2 * np.sqrt(np.abs(x)))),
        lambda x: (1 / x, -1 / (x * x)),
        lambda x: (np.sign(np.sin(1 / x)), np.zeros_like(x)),
        lambda x: (x * np.sin(1 / x), np.sin(1 / x) - np.cos(1 / x) / x),
        lambda x: (np.sin(1 / x), -np.cos(1 / x) / (x * x)),
        lambda x: (np.tan(x), 1.0 / (np.cos(x) * np.cos(x))),
    ]

    np.random.seed(0)

    # Avoid values too close to 0 since singularities of our functions are there
    min_x = 0.5

    for func in functions:
        x_input = np.random.uniform(min_x, 10, size=(3, 4))

        # We need a function returning a scalar, so sum the results
        func_forw = lambda x: np.sum(func(x)[0])
        grads = [func(x_input)[1]]

        tvm.testing.check_numerical_grads(func_forw, [x_input], grads)

    # Check functions with multiple arguments
    for f1 in functions:
        for f2 in functions:
            x_input = np.random.uniform(min_x, 10, size=(3, 4))
            y_input = np.random.uniform(min_x, 10, size=(3, 4))

            func_forw = lambda x, y: np.sum(f1(x)[0] + f2(y)[0])
            grads = [f1(x_input)[1], f2(y_input)[1]]

            tvm.testing.check_numerical_grads(func_forw, [x_input, y_input], grads)

            # Same thing but with keyword arguments
            func_forw = lambda x, y: np.sum(f1(x)[0] + f2(y)[0])
            grads = {"x": f1(x_input)[1], "y": f2(y_input)[1]}

            tvm.testing.check_numerical_grads(func_forw, {"x": x_input, "y": y_input}, grads)

    def _noise1(x, atol=1e-2, rtol=0.1):
        # We go in random direction using twice the original tolerance to be sure this
        # results in an error
        sqrt_n = np.sqrt(float(np.prod(x.shape)))
        tol = 2 * (np.linalg.norm(x) * rtol + atol * sqrt_n)
        noise = np.random.normal(size=x.shape)
        noise = tol * noise / np.linalg.norm(noise)
        return x + noise

    def _noise2(x, atol=1e-2, rtol=0.1):
        # This noise affects just a single component
        sqrt_n = np.sqrt(float(np.prod(x.shape)))
        tol = 2 * (np.linalg.norm(x) * rtol + atol * sqrt_n)
        n = np.random.randint(np.prod(x.shape))
        noise = np.zeros_like(x)
        noise.reshape(-1)[n] = tol
        return x + noise

    # Add noise to gradients and check that the function throws
    for f1 in functions:
        for f2 in functions:
            x_input = np.random.uniform(min_x, 10, size=(3, 4))
            y_input = np.random.uniform(min_x, 10, size=(3, 4))

            func_forw = lambda x, y: np.sum(f1(x)[0] + f2(y)[0])
            grads = [_noise1(f1(x_input)[1]), _noise1(f2(y_input)[1])]

            try:
                tvm.testing.check_numerical_grads(func_forw, [x_input, y_input], grads)
            except AssertionError as e:
                pass
            else:
                raise AssertionError("tvm.testing.check_numerical_grads didn't raise an exception")

            func_forw = lambda x, y: np.sum(f1(x)[0] + f2(y)[0])
            grads = {"x": _noise2(f1(x_input)[1]), "y": _noise2(f2(y_input)[1])}

            try:
                tvm.testing.check_numerical_grads(func_forw, {"x": x_input, "y": y_input}, grads)
            except AssertionError as e:
                pass
            else:
                raise AssertionError("tvm.testing.check_numerical_grads didn't raise an exception")


if __name__ == "__main__":
    test_tvm.testing.check_numerical_grads()