"""Tests for backend module """

# Author: Remi Flamary <remi.flamary@polytechnique.edu>
#         Nicolas Courty <ncourty@irisa.fr>
#
# License: MIT License

import ot
import ot.backend
from ot.backend import torch, jax, tf

import pytest

import numpy as np
from numpy.testing import assert_array_almost_equal_nulp

from ot.backend import get_backend, get_backend_list, to_numpy


def test_get_backend_list():

    lst = get_backend_list()

    assert len(lst) > 0
    assert isinstance(lst[0], ot.backend.NumpyBackend)


def test_to_numpy(nx):

    v = nx.zeros(10)
    M = nx.ones((10, 10))

    v2 = to_numpy(v)
    assert isinstance(v2, np.ndarray)

    v2, M2 = to_numpy(v, M)
    assert isinstance(M2, np.ndarray)


def test_get_backend_invalid():
    # error if no parameters
    with pytest.raises(ValueError):
        get_backend()

    # error if unknown types
    with pytest.raises(ValueError):
        get_backend(1, 2.0)


def test_get_backend(nx):

    A = np.zeros((3, 2))
    B = np.zeros((3, 1))

    nx_np = get_backend(A)
    assert nx_np.__name__ == 'numpy'

    A2, B2 = nx.from_numpy(A, B)

    effective_nx = get_backend(A2)
    assert effective_nx.__name__ == nx.__name__

    effective_nx = get_backend(A2, B2)
    assert effective_nx.__name__ == nx.__name__

    if nx.__name__ != "numpy":
        # test that types mathcing different backends in input raise an error
        with pytest.raises(ValueError):
            get_backend(A, B2)
    else:
        # Check that subclassing a numpy array does not break get_backend
        # note: This is only tested for numpy as this is hard to be consistent
        # with other backends
        class nx_subclass(nx.__type__):
            pass

        A3 = nx_subclass(0)

        effective_nx = get_backend(A3, B2)
        assert effective_nx.__name__ == nx.__name__


def test_convert_between_backends(nx):

    A = np.zeros((3, 2))
    B = np.zeros((3, 1))

    A2 = nx.from_numpy(A)
    B2 = nx.from_numpy(B)

    assert isinstance(A2, nx.__type__)
    assert isinstance(B2, nx.__type__)

    nx2 = get_backend(A2, B2)

    assert nx2.__name__ == nx.__name__

    assert_array_almost_equal_nulp(nx.to_numpy(A2), A)
    assert_array_almost_equal_nulp(nx.to_numpy(B2), B)


def test_empty_backend():

    rnd = np.random.RandomState(0)
    M = rnd.randn(10, 3)
    v = rnd.randn(3)

    nx = ot.backend.Backend()

    with pytest.raises(NotImplementedError):
        nx.from_numpy(M)
    with pytest.raises(NotImplementedError):
        nx.to_numpy(M)
    with pytest.raises(NotImplementedError):
        nx.set_gradients(0, 0, 0)
    with pytest.raises(NotImplementedError):
        nx.zeros((10, 3))
    with pytest.raises(NotImplementedError):
        nx.ones((10, 3))
    with pytest.raises(NotImplementedError):
        nx.arange(10, 1, 2)
    with pytest.raises(NotImplementedError):
        nx.full((10, 3), 3.14)
    with pytest.raises(NotImplementedError):
        nx.eye((10, 3))
    with pytest.raises(NotImplementedError):
        nx.sum(M)
    with pytest.raises(NotImplementedError):
        nx.cumsum(M)
    with pytest.raises(NotImplementedError):
        nx.max(M)
    with pytest.raises(NotImplementedError):
        nx.min(M)
    with pytest.raises(NotImplementedError):
        nx.maximum(v, v)
    with pytest.raises(NotImplementedError):
        nx.minimum(v, v)
    with pytest.raises(NotImplementedError):
        nx.abs(M)
    with pytest.raises(NotImplementedError):
        nx.log(M)
    with pytest.raises(NotImplementedError):
        nx.exp(M)
    with pytest.raises(NotImplementedError):
        nx.sqrt(M)
    with pytest.raises(NotImplementedError):
        nx.power(v, 2)
    with pytest.raises(NotImplementedError):
        nx.dot(v, v)
    with pytest.raises(NotImplementedError):
        nx.norm(M)
    with pytest.raises(NotImplementedError):
        nx.exp(M)
    with pytest.raises(NotImplementedError):
        nx.any(M)
    with pytest.raises(NotImplementedError):
        nx.isnan(M)
    with pytest.raises(NotImplementedError):
        nx.isinf(M)
    with pytest.raises(NotImplementedError):
        nx.einsum('ij->i', M)
    with pytest.raises(NotImplementedError):
        nx.sort(M)
    with pytest.raises(NotImplementedError):
        nx.argsort(M)
    with pytest.raises(NotImplementedError):
        nx.searchsorted(v, v)
    with pytest.raises(NotImplementedError):
        nx.flip(M)
    with pytest.raises(NotImplementedError):
        nx.outer(v, v)
    with pytest.raises(NotImplementedError):
        nx.clip(M, -1, 1)
    with pytest.raises(NotImplementedError):
        nx.repeat(M, 0, 1)
    with pytest.raises(NotImplementedError):
        nx.take_along_axis(M, v, 0)
    with pytest.raises(NotImplementedError):
        nx.concatenate([v, v])
    with pytest.raises(NotImplementedError):
        nx.zero_pad(M, v)
    with pytest.raises(NotImplementedError):
        nx.argmax(M)
    with pytest.raises(NotImplementedError):
        nx.argmin(M)
    with pytest.raises(NotImplementedError):
        nx.mean(M)
    with pytest.raises(NotImplementedError):
        nx.median(M)
    with pytest.raises(NotImplementedError):
        nx.std(M)
    with pytest.raises(NotImplementedError):
        nx.linspace(0, 1, 50)
    with pytest.raises(NotImplementedError):
        nx.meshgrid(v, v)
    with pytest.raises(NotImplementedError):
        nx.diag(M)
    with pytest.raises(NotImplementedError):
        nx.unique([M, M])
    with pytest.raises(NotImplementedError):
        nx.logsumexp(M)
    with pytest.raises(NotImplementedError):
        nx.stack([M, M])
    with pytest.raises(NotImplementedError):
        nx.reshape(M, (5, 3, 2))
    with pytest.raises(NotImplementedError):
        nx.seed(42)
    with pytest.raises(NotImplementedError):
        nx.rand()
    with pytest.raises(NotImplementedError):
        nx.randn()
        nx.coo_matrix(M, M, M)
    with pytest.raises(NotImplementedError):
        nx.issparse(M)
    with pytest.raises(NotImplementedError):
        nx.tocsr(M)
    with pytest.raises(NotImplementedError):
        nx.eliminate_zeros(M)
    with pytest.raises(NotImplementedError):
        nx.todense(M)
    with pytest.raises(NotImplementedError):
        nx.where(M, M, M)
    with pytest.raises(NotImplementedError):
        nx.copy(M)
    with pytest.raises(NotImplementedError):
        nx.allclose(M, M)
    with pytest.raises(NotImplementedError):
        nx.squeeze(M)
    with pytest.raises(NotImplementedError):
        nx.bitsize(M)
    with pytest.raises(NotImplementedError):
        nx.device_type(M)
    with pytest.raises(NotImplementedError):
        nx._bench(lambda x: x, M, n_runs=1)
    with pytest.raises(NotImplementedError):
        nx.solve(M, v)
    with pytest.raises(NotImplementedError):
        nx.trace(M)
    with pytest.raises(NotImplementedError):
        nx.inv(M)
    with pytest.raises(NotImplementedError):
        nx.sqrtm(M)
    with pytest.raises(NotImplementedError):
        nx.kl_div(M, M)
    with pytest.raises(NotImplementedError):
        nx.isfinite(M)
    with pytest.raises(NotImplementedError):
        nx.array_equal(M, M)
    with pytest.raises(NotImplementedError):
        nx.is_floating_point(M)
    with pytest.raises(NotImplementedError):
        nx.tile(M, (10, 1))
    with pytest.raises(NotImplementedError):
        nx.floor(M)
    with pytest.raises(NotImplementedError):
        nx.prod(M)
    with pytest.raises(NotImplementedError):
        nx.sort2(M)
    with pytest.raises(NotImplementedError):
        nx.qr(M)
    with pytest.raises(NotImplementedError):
        nx.atan2(v, v)
    with pytest.raises(NotImplementedError):
        nx.transpose(M)
    with pytest.raises(NotImplementedError):
        nx.detach(M)
    with pytest.raises(NotImplementedError):
        nx.matmul(M, M.T)


def test_func_backends(nx):

    rnd = np.random.RandomState(0)
    M = rnd.randn(10, 3)
    SquareM = rnd.randn(10, 10)
    v = rnd.randn(3)
    val = np.array([1.0])

    M1 = rnd.randn(1, 2, 10, 10)
    M2 = rnd.randn(3, 1, 10, 10)

    # Sparse tensors test
    sp_row = np.array([0, 3, 1, 0, 3])
    sp_col = np.array([0, 3, 1, 2, 2])
    sp_data = np.array([4, 5, 7, 9, 0], dtype=np.float64)

    lst_tot = []

    for nx in [ot.backend.NumpyBackend(), nx]:

        print('Backend: ', nx.__name__)

        lst_b = []
        lst_name = []

        Mb = nx.from_numpy(M)
        SquareMb = nx.from_numpy(SquareM)
        vb = nx.from_numpy(v)

        M1b = nx.from_numpy(M1)
        M2b = nx.from_numpy(M2)

        val = nx.from_numpy(val)

        sp_rowb = nx.from_numpy(sp_row)
        sp_colb = nx.from_numpy(sp_col)
        sp_datab = nx.from_numpy(sp_data)

        A = nx.set_gradients(val, v, v)

        lst_b.append(nx.to_numpy(A))
        lst_name.append('set_gradients')

        A = nx.zeros((10, 3))
        A = nx.zeros((10, 3), type_as=Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('zeros')

        A = nx.ones((10, 3))
        A = nx.ones((10, 3), type_as=Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('ones')

        A = nx.arange(10, 1, 2)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('arange')

        A = nx.full((10, 3), 3.14)
        A = nx.full((10, 3), 3.14, type_as=Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('full')

        A = nx.eye(10, 3)
        A = nx.eye(10, 3, type_as=Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('eye')

        A = nx.sum(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('sum')

        A = nx.sum(Mb, axis=1, keepdims=True)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('sum(axis)')

        A = nx.cumsum(Mb, 0)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('cumsum(axis)')

        A = nx.max(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('max')

        A = nx.max(Mb, axis=1, keepdims=True)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('max(axis)')

        A = nx.min(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('min')

        A = nx.min(Mb, axis=1, keepdims=True)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('min(axis)')

        A = nx.maximum(vb, 0)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('maximum')

        A = nx.minimum(vb, 0)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('minimum')

        A = nx.sign(vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('sign')

        A = nx.abs(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('abs')

        A = nx.log(A)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('log')

        A = nx.exp(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('exp')

        A = nx.sqrt(nx.abs(Mb))
        lst_b.append(nx.to_numpy(A))
        lst_name.append('sqrt')

        A = nx.power(Mb, 2)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('power')

        A = nx.dot(vb, vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('dot(v,v)')

        A = nx.dot(Mb, vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('dot(M,v)')

        A = nx.dot(Mb, Mb.T)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('dot(M,M)')

        A = nx.norm(vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('norm')

        A = nx.any(vb > 0)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('any')

        A = nx.isnan(vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('isnan')

        A = nx.isinf(vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('isinf')

        A = nx.einsum('ij->i', Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('einsum(ij->i)')

        A = nx.einsum('ij,j->i', Mb, vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('nx.einsum(ij,j->i)')

        A = nx.einsum('ij->i', Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('nx.einsum(ij->i)')

        A = nx.sort(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('sort')

        A = nx.argsort(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('argsort')

        tmp = nx.sort(Mb)
        A = nx.searchsorted(tmp, tmp, 'right')
        lst_b.append(nx.to_numpy(A))
        lst_name.append('searchsorted')

        A = nx.flip(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('flip')

        A = nx.outer(vb, vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('outer')

        A = nx.clip(vb, 0, 1)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('clip')

        A = nx.repeat(Mb, 0)
        A = nx.repeat(Mb, 2, -1)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('repeat')

        A = nx.take_along_axis(vb, nx.arange(3), -1)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('take_along_axis')

        A = nx.concatenate((Mb, Mb), -1)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('concatenate')

        A = nx.zero_pad(Mb, len(Mb.shape) * [(3, 3)])
        lst_b.append(nx.to_numpy(A))
        lst_name.append('zero_pad')

        A = nx.argmax(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('argmax')

        A = nx.argmin(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('argmin')

        A = nx.mean(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('mean')

        A = nx.median(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('median')

        A = nx.std(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('std')

        A = nx.linspace(0, 1, 50)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('linspace')

        X, Y = nx.meshgrid(vb, vb)
        lst_b.append(np.stack([nx.to_numpy(X), nx.to_numpy(Y)]))
        lst_name.append('meshgrid')

        A = nx.diag(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('diag2D')

        A = nx.diag(vb, 1)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('diag1D')

        A = nx.unique(nx.from_numpy(np.stack([M, M])))
        lst_b.append(nx.to_numpy(A))
        lst_name.append('unique')

        A = nx.logsumexp(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('logsumexp')

        A = nx.stack([Mb, Mb])
        lst_b.append(nx.to_numpy(A))
        lst_name.append('stack')

        A = nx.reshape(Mb, (5, 3, 2))
        lst_b.append(nx.to_numpy(A))
        lst_name.append('reshape')

        sp_Mb = nx.coo_matrix(sp_datab, sp_rowb, sp_colb, shape=(4, 4))
        nx.todense(Mb)
        lst_b.append(nx.to_numpy(nx.todense(sp_Mb)))
        lst_name.append('coo_matrix')

        assert not nx.issparse(Mb), 'Assert fail on: issparse (expected False)'
        assert nx.issparse(sp_Mb) or nx.__name__ in ("jax", "tf"), 'Assert fail on: issparse (expected True)'

        A = nx.tocsr(sp_Mb)
        lst_b.append(nx.to_numpy(nx.todense(A)))
        lst_name.append('tocsr')

        A = nx.eliminate_zeros(nx.copy(sp_datab), threshold=5.)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('eliminate_zeros (dense)')

        A = nx.eliminate_zeros(sp_Mb)
        lst_b.append(nx.to_numpy(nx.todense(A)))
        lst_name.append('eliminate_zeros (sparse)')

        A = nx.where(Mb >= nx.stack([nx.linspace(0, 1, 10)] * 3, axis=1), Mb, 0.0)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('where (cond, x, y)')

        A = nx.where(nx.from_numpy(np.array([True, False])))
        lst_b.append(nx.to_numpy(nx.stack(A)))
        lst_name.append('where (cond)')

        A = nx.copy(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('copy')

        assert nx.allclose(Mb, Mb), 'Assert fail on: allclose (expected True)'
        assert not nx.allclose(2 * Mb, Mb), 'Assert fail on: allclose (expected False)'

        A = nx.squeeze(nx.zeros((3, 1, 4, 1)))
        assert tuple(A.shape) == (3, 4), 'Assert fail on: squeeze'

        A = nx.bitsize(Mb)
        lst_b.append(float(A))
        lst_name.append("bitsize")

        A = nx.device_type(Mb)
        assert A in ("CPU", "GPU")

        nx._bench(lambda x: x, M, n_runs=1)

        A = nx.solve(SquareMb, Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('solve')

        A = nx.trace(SquareMb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('trace')

        A = nx.inv(SquareMb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append('matrix inverse')

        A = nx.sqrtm(SquareMb.T @ SquareMb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("matrix square root")

        D, U = nx.eigh(SquareMb.T @ SquareMb)
        lst_b.append(nx.to_numpy(nx.dot(U, nx.dot(nx.diag(D), U.T))))
        lst_name.append("eigh ")

        A = nx.kl_div(nx.abs(Mb), nx.abs(Mb) + 1)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("Kullback-Leibler divergence")

        A = nx.concatenate([vb, nx.from_numpy(np.array([np.inf, np.nan]))], axis=0)
        A = nx.isfinite(A)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("isfinite")

        A = nx.tile(vb, (10, 1))
        lst_b.append(nx.to_numpy(A))
        lst_name.append("tile")

        A = nx.floor(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("floor")

        A = nx.prod(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("prod")

        A, B = nx.sort2(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("sort2 sort")
        lst_b.append(nx.to_numpy(B))
        lst_name.append("sort2 argsort")

        A, B = nx.qr(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("QR Q")
        lst_b.append(nx.to_numpy(B))
        lst_name.append("QR R")

        A = nx.atan2(vb, vb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("atan2")

        A = nx.transpose(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("transpose")

        A = nx.detach(Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("detach")

        A, B = nx.detach(Mb, Mb)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("detach A")
        lst_b.append(nx.to_numpy(B))
        lst_name.append("detach B")

        A = nx.matmul(Mb, Mb.T)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("matmul")
        A = nx.matmul(M1b, M2b)
        lst_b.append(nx.to_numpy(A))
        lst_name.append("matmul broadcast")

        assert not nx.array_equal(Mb, vb), "array_equal (shape)"
        assert nx.array_equal(Mb, Mb), "array_equal (elements) - expected true"
        assert not nx.array_equal(
            Mb, Mb + nx.eye(*list(Mb.shape))
        ), "array_equal (elements) - expected false"

        assert nx.is_floating_point(Mb), "is_floating_point - expected true"
        assert not nx.is_floating_point(
            nx.from_numpy(np.array([0, 1, 2], dtype=int))
        ), "is_floating_point - expected false"

        lst_tot.append(lst_b)

    lst_np = lst_tot[0]
    lst_b = lst_tot[1]

    for a1, a2, name in zip(lst_np, lst_b, lst_name):
        np.testing.assert_allclose(
            a2, a1, atol=1e-7, err_msg=f'ASSERT FAILED ON: {name}'
        )


def test_random_backends(nx):

    tmp_u = nx.rand()

    assert tmp_u < 1

    tmp_n = nx.randn()

    nx.seed(0)
    M1 = nx.to_numpy(nx.rand(5, 2))
    nx.seed(0)
    M2 = nx.to_numpy(nx.rand(5, 2, type_as=tmp_n))

    assert np.all(M1 >= 0)
    assert np.all(M1 < 1)
    assert M1.shape == (5, 2)
    assert np.allclose(M1, M2)

    nx.seed(0)
    M1 = nx.to_numpy(nx.randn(5, 2))
    nx.seed(0)
    M2 = nx.to_numpy(nx.randn(5, 2, type_as=tmp_u))

    nx.seed(42)
    v1 = nx.randn()
    v2 = nx.randn()
    assert v1 != v2


def test_gradients_backends():

    rnd = np.random.RandomState(0)
    v = rnd.randn(10)
    c = rnd.randn()
    e = rnd.randn()

    if torch:

        nx = ot.backend.TorchBackend()

        v2 = torch.tensor(v, requires_grad=True)
        c2 = torch.tensor(c, requires_grad=True)

        val = c2 * torch.sum(v2 * v2)

        val2 = nx.set_gradients(val, (v2, c2), (v2, c2))

        val2.backward()

        assert torch.equal(v2.grad, v2)
        assert torch.equal(c2.grad, c2)

    if jax:
        nx = ot.backend.JaxBackend()
        with jax.checking_leaks():
            def fun(a, b, d):
                val = b * nx.sum(a ** 4) + d
                return nx.set_gradients(val, (a, b, d), (a, b, 2 * d))
            grad_val = jax.grad(fun, argnums=(0, 1, 2))(v, c, e)

        np.testing.assert_almost_equal(fun(v, c, e), c * np.sum(v ** 4) + e, decimal=4)
        np.testing.assert_allclose(grad_val[0], v, atol=1e-4)
        np.testing.assert_allclose(grad_val[2], 2 * e, atol=1e-4)

    if tf:
        nx = ot.backend.TensorflowBackend()
        w = tf.Variable(tf.random.normal((3, 2)), name='w')
        b = tf.Variable(tf.random.normal((2,), dtype=tf.float32), name='b')
        x = tf.random.normal((1, 3), dtype=tf.float32)

        with tf.GradientTape() as tape:
            y = x @ w + b
            loss = tf.reduce_mean(y ** 2)
            manipulated_loss = nx.set_gradients(loss, (w, b), (w, b))
            [dl_dw, dl_db] = tape.gradient(manipulated_loss, [w, b])
            assert nx.allclose(dl_dw, w)
            assert nx.allclose(dl_db, b)
