def generate(self, x: np.ndarray, y: np.ndarray | None = None, **kwargs) -> np.ndarray:
        """
        Generate adversarial samples and return them in an array.

        :param x: An array with the original inputs.
        :param y: Target values (class labels) one-hot-encoded of shape `(nb_samples, nb_classes)` or indices of shape
                  (nb_samples,). Only provide this parameter if you'd like to use true labels when crafting adversarial
                  samples. Otherwise, model predictions are used as labels to avoid the "label leaking" effect
                  (explained in this paper: https://arxiv.org/abs/1611.01236). Default is `None`.
        :return: An array holding the adversarial examples.
        """
        if x.ndim != 4:  # pragma: no cover
            raise ValueError("Unrecognized input dimension. Attack can only be applied to image data.")

        x_adv = x.astype(ART_NUMPY_DTYPE)

        if isinstance(self.estimator, ClassifierMixin):
            if y is not None:
                y = check_and_transform_label_format(y, nb_classes=self.estimator.nb_classes)

        if y is None:
            # Use model predictions as true labels
            logger.info("Using model predictions as true labels.")
            y = self.estimator.predict(x, batch_size=self.batch_size)
            if isinstance(self.estimator, ClassifierMixin):
                y = get_labels_np_array(y)

        if isinstance(self.estimator, ClassifierMixin):
            if self.estimator.nb_classes == 2 and y.shape[1] == 1:  # pragma: no cover
                raise ValueError(
                    "This attack has not yet been tested for binary classification with a single output classifier."
                )

        if self.estimator.channels_first:
            channels = x.shape[1]
            height = x.shape[2]
            width = x.shape[3]
        else:
            height = x.shape[1]
            width = x.shape[2]
            channels = x.shape[3]

        for _ in trange(self.nb_restarts, desc="SquareAttack - restarts", disable=not self.verbose):

            # Determine correctly predicted samples
            y_pred = self.estimator.predict(x_adv, batch_size=self.batch_size)
            sample_is_robust = np.logical_not(self.adv_criterion(y_pred, y))

            if np.sum(sample_is_robust) == 0:  # pragma: no cover
                break

            # x_robust = x_adv[sample_is_robust]
            x_robust = x[sample_is_robust]
            y_robust = y[sample_is_robust]
            sample_loss_init = self.loss(x_robust, y_robust)

            if self.norm in [np.inf, "inf"]:

                if self.estimator.channels_first:
                    size = (x_robust.shape[0], channels, 1, width)
                else:
                    size = (x_robust.shape[0], 1, width, channels)

                # Add vertical stripe perturbations
                x_robust_new = np.clip(
                    x_robust + self.eps * np.random.choice([-1, 1], size=size),
                    a_min=self.estimator.clip_values[0],
                    a_max=self.estimator.clip_values[1],
                ).astype(ART_NUMPY_DTYPE)

                sample_loss_new = self.loss(x_robust_new, y_robust)
                loss_improved = (sample_loss_new - sample_loss_init) < 0.0

                x_robust[loss_improved] = x_robust_new[loss_improved]

                x_adv[sample_is_robust] = x_robust

                for i_iter in trange(
                    self.max_iter, desc="SquareAttack - iterations", leave=False, disable=not self.verbose
                ):

                    percentage_of_elements = self._get_percentage_of_elements(i_iter)

                    # Determine correctly predicted samples
                    y_pred = self.estimator.predict(x_adv, batch_size=self.batch_size)
                    sample_is_robust = np.logical_not(self.adv_criterion(y_pred, y))

                    if np.sum(sample_is_robust) == 0:  # pragma: no cover
                        break

                    x_robust = x_adv[sample_is_robust]
                    x_init = x[sample_is_robust]
                    y_robust = y[sample_is_robust]

                    sample_loss_init = self.loss(x_robust, y_robust)

                    height_tile = max(int(round(math.sqrt(percentage_of_elements * height * width))), 1)

                    height_mid = np.random.randint(0, height - height_tile)
                    width_start = np.random.randint(0, width - height_tile)

                    delta_new = np.zeros(self.estimator.input_shape)

                    if self.estimator.channels_first:
                        delta_new[:, height_mid : height_mid + height_tile, width_start : width_start + height_tile] = (
                            np.random.choice([-2 * self.eps, 2 * self.eps], size=[channels, 1, 1])
                        )
                    else:
                        delta_new[height_mid : height_mid + height_tile, width_start : width_start + height_tile, :] = (
                            np.random.choice([-2 * self.eps, 2 * self.eps], size=[1, 1, channels])
                        )

                    x_robust_new = x_robust + delta_new

                    x_robust_new = np.minimum(np.maximum(x_robust_new, x_init - self.eps), x_init + self.eps)

                    x_robust_new = np.clip(
                        x_robust_new, a_min=self.estimator.clip_values[0], a_max=self.estimator.clip_values[1]
                    ).astype(ART_NUMPY_DTYPE)

                    sample_loss_new = self.loss(x_robust_new, y_robust)
                    loss_improved = (sample_loss_new - sample_loss_init) < 0.0

                    x_robust[loss_improved] = x_robust_new[loss_improved]

                    x_adv[sample_is_robust] = x_robust

            elif self.norm == 2:

                n_tiles = 5

                height_tile = height // n_tiles

                def _get_perturbation(height):
                    delta = np.zeros([height, height])
                    gaussian_perturbation = np.zeros([height // 2, height])

                    x_c = height // 4
                    y_c = height // 2

                    for i_y in range(y_c):
                        gaussian_perturbation[
                            max(x_c, 0) : min(x_c + (2 * i_y + 1), height // 2),
                            max(0, y_c) : min(y_c + (2 * i_y + 1), height),
                        ] += 1.0 / ((i_y + 1) ** 2)
                        x_c -= 1
                        y_c -= 1

                    gaussian_perturbation /= np.sqrt(np.sum(gaussian_perturbation**2))

                    delta[: height // 2] = gaussian_perturbation
                    delta[height // 2 : height // 2 + gaussian_perturbation.shape[0]] = -gaussian_perturbation

                    delta /= np.sqrt(np.sum(delta**2))

                    if random.random() > 0.5:
                        delta = np.transpose(delta)

                    if random.random() > 0.5:
                        delta = -delta

                    return delta

                delta_init = np.zeros(x_robust.shape, dtype=ART_NUMPY_DTYPE)

                height_start = 0
                for _ in range(n_tiles):
                    width_start = 0
                    for _ in range(n_tiles):
                        if self.estimator.channels_first:
                            perturbation_size = (1, 1, height_tile, height_tile)
                            random_size = (x_robust.shape[0], channels, 1, 1)
                        else:
                            perturbation_size = (1, height_tile, height_tile, 1)
                            random_size = (x_robust.shape[0], 1, 1, channels)

                        perturbation = _get_perturbation(height_tile).reshape(perturbation_size) * np.random.choice(
                            [-1, 1], size=random_size
                        )

                        if self.estimator.channels_first:
                            delta_init[
                                :, :, height_start : height_start + height_tile, width_start : width_start + height_tile
                            ] += perturbation
                        else:
                            delta_init[
                                :, height_start : height_start + height_tile, width_start : width_start + height_tile, :
                            ] += perturbation
                        width_start += height_tile
                    height_start += height_tile

                x_robust_new = np.clip(
                    x_robust + delta_init / np.sqrt(np.sum(delta_init**2, axis=(1, 2, 3), keepdims=True)) * self.eps,
                    self.estimator.clip_values[0],
                    self.estimator.clip_values[1],
                )

                sample_loss_new = self.loss(x_robust_new, y_robust)
                loss_improved = (sample_loss_new - sample_loss_init) < 0.0

                x_robust[loss_improved] = x_robust_new[loss_improved]

                x_adv[sample_is_robust] = x_robust

                for i_iter in trange(
                    self.max_iter, desc="SquareAttack - iterations", leave=False, disable=not self.verbose
                ):

                    percentage_of_elements = self._get_percentage_of_elements(i_iter)

                    # Determine correctly predicted samples
                    y_pred = self.estimator.predict(x_adv, batch_size=self.batch_size)
                    sample_is_robust = np.logical_not(self.adv_criterion(y_pred, y))

                    if np.sum(sample_is_robust) == 0:  # pragma: no cover
                        break

                    x_robust = x_adv[sample_is_robust]
                    x_init = x[sample_is_robust]
                    y_robust = y[sample_is_robust]

                    sample_loss_init = self.loss(x_robust, y_robust)

                    delta_x_robust_init = x_robust - x_init

                    height_tile = max(int(round(math.sqrt(percentage_of_elements * height * width))), 3)

                    if height_tile % 2 == 0:
                        height_tile += 1
                    height_tile_2 = height_tile

                    height_start = np.random.randint(0, height - height_tile)
                    width_start = np.random.randint(0, width - height_tile)

                    new_deltas_mask = np.zeros(x_init.shape)
                    if self.estimator.channels_first:
                        new_deltas_mask[
                            :, :, height_start : height_start + height_tile, width_start : width_start + height_tile
                        ] = 1.0
                        w_1_norm = np.sqrt(
                            np.sum(
                                delta_x_robust_init[
                                    :,
                                    :,
                                    height_start : height_start + height_tile,
                                    width_start : width_start + height_tile,
                                ]
                                ** 2,
                                axis=(2, 3),
                                keepdims=True,
                            )
                        )
                    else:
                        new_deltas_mask[
                            :, height_start : height_start + height_tile, width_start : width_start + height_tile, :
                        ] = 1.0
                        w_1_norm = np.sqrt(
                            np.sum(
                                delta_x_robust_init[
                                    :,
                                    height_start : height_start + height_tile,
                                    width_start : width_start + height_tile,
                                    :,
                                ]
                                ** 2,
                                axis=(1, 2),
                                keepdims=True,
                            )
                        )

                    height_2_start = np.random.randint(0, height - height_tile_2)
                    width_2_start = np.random.randint(0, width - height_tile_2)

                    new_deltas_mask_2 = np.zeros(x_init.shape)
                    if self.estimator.channels_first:
                        new_deltas_mask_2[
                            :,
                            :,
                            height_2_start : height_2_start + height_tile_2,
                            width_2_start : width_2_start + height_tile_2,
                        ] = 1.0
                    else:
                        new_deltas_mask_2[
                            :,
                            height_2_start : height_2_start + height_tile_2,
                            width_2_start : width_2_start + height_tile_2,
                            :,
                        ] = 1.0

                    norms_x_robust = np.sqrt(np.sum((x_robust - x_init) ** 2, axis=(1, 2, 3), keepdims=True))
                    w_norm = np.sqrt(
                        np.sum(
                            (delta_x_robust_init * np.maximum(new_deltas_mask, new_deltas_mask_2)) ** 2,
                            axis=(1, 2, 3),
                            keepdims=True,
                        )
                    )

                    if self.estimator.channels_first:
                        new_deltas_size = [x_init.shape[0], channels, height_tile, height_tile]
                        random_choice_size = [x_init.shape[0], channels, 1, 1]
                        perturbation_size = (1, 1, height_tile, height_tile)
                    else:
                        new_deltas_size = [x_init.shape[0], height_tile, height_tile, channels]
                        random_choice_size = [x_init.shape[0], 1, 1, channels]
                        perturbation_size = (1, height_tile, height_tile, 1)

                    delta_new = (
                        np.ones(new_deltas_size)
                        * _get_perturbation(height_tile).reshape(perturbation_size)
                        * np.random.choice([-1, 1], size=random_choice_size)
                    )

                    if self.estimator.channels_first:
                        delta_new += delta_x_robust_init[
                            :, :, height_start : height_start + height_tile, width_start : width_start + height_tile
                        ] / (np.maximum(1e-9, w_1_norm))
                    else:
                        delta_new += delta_x_robust_init[
                            :, height_start : height_start + height_tile, width_start : width_start + height_tile, :
                        ] / (np.maximum(1e-9, w_1_norm))

                    diff_norm = (self.eps * np.ones(delta_new.shape)) ** 2 - norms_x_robust**2
                    diff_norm[diff_norm < 0.0] = 0.0

                    if self.estimator.channels_first:
                        delta_new /= np.sqrt(np.sum(delta_new**2, axis=(2, 3), keepdims=True)) * np.sqrt(
                            diff_norm / channels + w_norm**2
                        )
                        delta_x_robust_init[
                            :,
                            :,
                            height_2_start : height_2_start + height_tile_2,
                            width_2_start : width_2_start + height_tile_2,
                        ] = 0.0
                        delta_x_robust_init[
                            :, :, height_start : height_start + height_tile, width_start : width_start + height_tile
                        ] = delta_new
                    else:
                        delta_new /= np.sqrt(np.sum(delta_new**2, axis=(1, 2), keepdims=True)) * np.sqrt(
                            diff_norm / channels + w_norm**2
                        )
                        delta_x_robust_init[
                            :,
                            height_2_start : height_2_start + height_tile_2,
                            width_2_start : width_2_start + height_tile_2,
                            :,
                        ] = 0.0
                        delta_x_robust_init[
                            :, height_start : height_start + height_tile, width_start : width_start + height_tile, :
                        ] = delta_new

                    x_robust_new = np.clip(
                        x_init
                        + self.eps
                        * delta_x_robust_init
                        / np.sqrt(np.sum(delta_x_robust_init**2, axis=(1, 2, 3), keepdims=True)),
                        self.estimator.clip_values[0],
                        self.estimator.clip_values[1],
                    )

                    sample_loss_new = self.loss(x_robust_new, y_robust)
                    loss_improved = (sample_loss_new - sample_loss_init) < 0.0

                    x_robust[loss_improved] = x_robust_new[loss_improved]

                    x_adv[sample_is_robust] = x_robust

        return x_adv

        Generate adversarial samples and return them in an array.

        :param x: An array with the original inputs.
        :param y: Target values (class labels) one-hot-encoded of shape `(nb_samples, nb_classes)` or indices of shape
                  (nb_samples,). Only provide this parameter if you'd like to use true labels when crafting adversarial
                  samples. Otherwise, model predictions are used as labels to avoid the "label leaking" effect
                  (explained in this paper: https://arxiv.org/abs/1611.01236). Default is `None`.
        :return: An array holding the adversarial examples.
        
art/attacks/evasion/square_attack.py