import math

import numpy as np

import torch

import torch.nn.functional as F

from torch_scatter import scatter_add, scatter_mean

import utils

from equivariant_diffusion.en_diffusion import EnVariationalDiffusion

class ConditionalDDPM(EnVariationalDiffusion):

    """

    Conditional Diffusion Module.

    """

    def __init__(self, *args, **kwargs):

        super().__init__(*args, **kwargs)

        assert not self.dynamics.update_pocket_coords

    def kl_prior(self, xh_lig, mask_lig, num_nodes):

        """Computes the KL between q(z1 | x) and the prior p(z1) = Normal(0, 1).

        This is essentially a lot of work for something that is in practice

        negligible in the loss. However, you compute it so that you see it when

        you've made a mistake in your noise schedule.

        """

        batch_size = len(num_nodes)

        # Compute the last alpha value, alpha_T.

        ones = torch.ones((batch_size, 1), device=xh_lig.device)

        gamma_T = self.gamma(ones)

        alpha_T = self.alpha(gamma_T, xh_lig)

        # Compute means.

        mu_T_lig = alpha_T[mask_lig] * xh_lig

        mu_T_lig_x, mu_T_lig_h = \

            mu_T_lig[:, :self.n_dims], mu_T_lig[:, self.n_dims:]

        # Compute standard deviations (only batch axis for x-part, inflated for h-part).

        sigma_T_x = self.sigma(gamma_T, mu_T_lig_x).squeeze()

        sigma_T_h = self.sigma(gamma_T, mu_T_lig_h).squeeze()

        # Compute KL for h-part.

        zeros = torch.zeros_like(mu_T_lig_h)

        ones = torch.ones_like(sigma_T_h)

        mu_norm2 = self.sum_except_batch((mu_T_lig_h - zeros) ** 2, mask_lig)

        kl_distance_h = self.gaussian_KL(mu_norm2, sigma_T_h, ones, d=1)

        # Compute KL for x-part.

        zeros = torch.zeros_like(mu_T_lig_x)

        ones = torch.ones_like(sigma_T_x)

        mu_norm2 = self.sum_except_batch((mu_T_lig_x - zeros) ** 2, mask_lig)

        subspace_d = self.subspace_dimensionality(num_nodes)

        kl_distance_x = self.gaussian_KL(mu_norm2, sigma_T_x, ones, subspace_d)

        return kl_distance_x + kl_distance_h

    def log_pxh_given_z0_without_constants(self, ligand, z_0_lig, eps_lig,

                                           net_out_lig, gamma_0, epsilon=1e-10):

        # Discrete properties are predicted directly from z_t.

        z_h_lig = z_0_lig[:, self.n_dims:]

        # Take only part over x.

        eps_lig_x = eps_lig[:, :self.n_dims]

        net_lig_x = net_out_lig[:, :self.n_dims]

        # Compute sigma_0 and rescale to the integer scale of the data.

        sigma_0 = self.sigma(gamma_0, target_tensor=z_0_lig)

        sigma_0_cat = sigma_0 * self.norm_values[1]

        # Computes the error for the distribution

        # N(x | 1 / alpha_0 z_0 + sigma_0/alpha_0 eps_0, sigma_0 / alpha_0),

        # the weighting in the epsilon parametrization is exactly '1'.

        squared_error = (eps_lig_x - net_lig_x) ** 2

        if self.vnode_idx is not None:

            # coordinates of virtual atoms should not contribute to the error

            squared_error[ligand['one_hot'][:, self.vnode_idx].bool(), :self.n_dims] = 0

        log_p_x_given_z0_without_constants_ligand = -0.5 * (

            self.sum_except_batch(squared_error, ligand['mask'])

        )

        # Compute delta indicator masks.

        # un-normalize

        ligand_onehot = ligand['one_hot'] * self.norm_values[1] + self.norm_biases[1]

        estimated_ligand_onehot = z_h_lig * self.norm_values[1] + self.norm_biases[1]

        # Centered h_cat around 1, since onehot encoded.

        centered_ligand_onehot = estimated_ligand_onehot - 1

        # Compute integrals from 0.5 to 1.5 of the normal distribution

        # N(mean=z_h_cat, stdev=sigma_0_cat)

        log_ph_cat_proportional_ligand = torch.log(

            self.cdf_standard_gaussian((centered_ligand_onehot + 0.5) / sigma_0_cat[ligand['mask']])

            - self.cdf_standard_gaussian((centered_ligand_onehot - 0.5) / sigma_0_cat[ligand['mask']])

            + epsilon

        )

        # Normalize the distribution over the categories.

        log_Z = torch.logsumexp(log_ph_cat_proportional_ligand, dim=1,

                                keepdim=True)

        log_probabilities_ligand = log_ph_cat_proportional_ligand - log_Z

        # Select the log_prob of the current category using the onehot

        # representation.

        log_ph_given_z0_ligand = self.sum_except_batch(

            log_probabilities_ligand * ligand_onehot, ligand['mask'])

        return log_p_x_given_z0_without_constants_ligand, log_ph_given_z0_ligand

    def sample_p_xh_given_z0(self, z0_lig, xh0_pocket, lig_mask, pocket_mask,

                             batch_size, fix_noise=False):

        """Samples x ~ p(x|z0)."""

        t_zeros = torch.zeros(size=(batch_size, 1), device=z0_lig.device)

        gamma_0 = self.gamma(t_zeros)

        # Computes sqrt(sigma_0^2 / alpha_0^2)

        sigma_x = self.SNR(-0.5 * gamma_0)

        net_out_lig, _ = self.dynamics(

            z0_lig, xh0_pocket, t_zeros, lig_mask, pocket_mask)

        # Compute mu for p(zs | zt).

        mu_x_lig = self.compute_x_pred(net_out_lig, z0_lig, gamma_0, lig_mask)

        xh_lig, xh0_pocket = self.sample_normal_zero_com(

            mu_x_lig, xh0_pocket, sigma_x, lig_mask, pocket_mask, fix_noise)

        x_lig, h_lig = self.unnormalize(

            xh_lig[:, :self.n_dims], z0_lig[:, self.n_dims:])

        x_pocket, h_pocket = self.unnormalize(

            xh0_pocket[:, :self.n_dims], xh0_pocket[:, self.n_dims:])

        h_lig = F.one_hot(torch.argmax(h_lig, dim=1), self.atom_nf)

        # h_pocket = F.one_hot(torch.argmax(h_pocket, dim=1), self.residue_nf)

        return x_lig, h_lig, x_pocket, h_pocket

    def sample_normal(self, *args):

        raise NotImplementedError("Has been replaced by sample_normal_zero_com()")

    def sample_normal_zero_com(self, mu_lig, xh0_pocket, sigma, lig_mask,

                               pocket_mask, fix_noise=False):

        """Samples from a Normal distribution."""

        if fix_noise:

            # bs = 1 if fix_noise else mu.size(0)

            raise NotImplementedError("fix_noise option isn't implemented yet")

        eps_lig = self.sample_gaussian(

            size=(len(lig_mask), self.n_dims + self.atom_nf),

            device=lig_mask.device)

        out_lig = mu_lig + sigma[lig_mask] * eps_lig

        # project to COM-free subspace

        xh_pocket = xh0_pocket.detach().clone()

        out_lig[:, :self.n_dims], xh_pocket[:, :self.n_dims] = \

            self.remove_mean_batch(out_lig[:, :self.n_dims],

                                   xh0_pocket[:, :self.n_dims],

                                   lig_mask, pocket_mask)

        return out_lig, xh_pocket

    def noised_representation(self, xh_lig, xh0_pocket, lig_mask, pocket_mask,

                              gamma_t):

        # Compute alpha_t and sigma_t from gamma.

        alpha_t = self.alpha(gamma_t, xh_lig)

        sigma_t = self.sigma(gamma_t, xh_lig)

        # Sample zt ~ Normal(alpha_t x, sigma_t)

        eps_lig = self.sample_gaussian(

            size=(len(lig_mask), self.n_dims + self.atom_nf),

            device=lig_mask.device)

        # Sample z_t given x, h for timestep t, from q(z_t | x, h)

        z_t_lig = alpha_t[lig_mask] * xh_lig + sigma_t[lig_mask] * eps_lig

        # project to COM-free subspace

        xh_pocket = xh0_pocket.detach().clone()

        z_t_lig[:, :self.n_dims], xh_pocket[:, :self.n_dims] = \

            self.remove_mean_batch(z_t_lig[:, :self.n_dims],

                                   xh_pocket[:, :self.n_dims],

                                   lig_mask, pocket_mask)

        return z_t_lig, xh_pocket, eps_lig

    def log_pN(self, N_lig, N_pocket):

        """

        Prior on the sample size for computing

        log p(x,h,N) = log p(x,h|N) + log p(N), where log p(x,h|N) is the

        model's output

        Args:

            N: array of sample sizes

        Returns:

            log p(N)

        """

        log_pN = self.size_distribution.log_prob_n1_given_n2(N_lig, N_pocket)

        return log_pN

    def delta_log_px(self, num_nodes):

        return -self.subspace_dimensionality(num_nodes) * \

               np.log(self.norm_values[0])

    def forward(self, ligand, pocket, return_info=False):

        """

        Computes the loss and NLL terms

        """

        # Normalize data, take into account volume change in x.

        ligand, pocket = self.normalize(ligand, pocket)

        # Likelihood change due to normalization

        # if self.vnode_idx is not None:

        #     delta_log_px = self.delta_log_px(ligand['size'] - ligand['num_virtual_atoms'] + pocket['size'])

        # else:

        delta_log_px = self.delta_log_px(ligand['size'])

        # Sample a timestep t for each example in batch

        # At evaluation time, loss_0 will be computed separately to decrease

        # variance in the estimator (costs two forward passes)

        lowest_t = 0 if self.training else 1

        t_int = torch.randint(

            lowest_t, self.T + 1, size=(ligand['size'].size(0), 1),

            device=ligand['x'].device).float()

        s_int = t_int - 1  # previous timestep

        # Masks: important to compute log p(x | z0).

        t_is_zero = (t_int == 0).float()

        t_is_not_zero = 1 - t_is_zero

        # Normalize t to [0, 1]. Note that the negative

        # step of s will never be used, since then p(x | z0) is computed.

        s = s_int / self.T

        t = t_int / self.T

        # Compute gamma_s and gamma_t via the network.

        gamma_s = self.inflate_batch_array(self.gamma(s), ligand['x'])

        gamma_t = self.inflate_batch_array(self.gamma(t), ligand['x'])

        # Concatenate x, and h[categorical].

        xh0_lig = torch.cat([ligand['x'], ligand['one_hot']], dim=1)

        xh0_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)

        # Center the input nodes

        xh0_lig[:, :self.n_dims], xh0_pocket[:, :self.n_dims] = \

            self.remove_mean_batch(xh0_lig[:, :self.n_dims],

                                   xh0_pocket[:, :self.n_dims],

                                   ligand['mask'], pocket['mask'])

        # Find noised representation

        z_t_lig, xh_pocket, eps_t_lig = \

            self.noised_representation(xh0_lig, xh0_pocket, ligand['mask'],

                                       pocket['mask'], gamma_t)

        # Neural net prediction.

        net_out_lig, _ = self.dynamics(

            z_t_lig, xh_pocket, t, ligand['mask'], pocket['mask'])

        # For LJ loss term

        # xh_lig_hat does not need to be zero-centered as it is only used for

        # computing relative distances

        xh_lig_hat = self.xh_given_zt_and_epsilon(z_t_lig, net_out_lig, gamma_t,

                                                  ligand['mask'])

        # Compute the L2 error.

        squared_error = (eps_t_lig - net_out_lig) ** 2

        if self.vnode_idx is not None:

            # coordinates of virtual atoms should not contribute to the error

            squared_error[ligand['one_hot'][:, self.vnode_idx].bool(), :self.n_dims] = 0

        error_t_lig = self.sum_except_batch(squared_error, ligand['mask'])

        # Compute weighting with SNR: (1 - SNR(s-t)) for epsilon parametrization

        SNR_weight = (1 - self.SNR(gamma_s - gamma_t)).squeeze(1)

        assert error_t_lig.size() == SNR_weight.size()

        # The _constants_ depending on sigma_0 from the

        # cross entropy term E_q(z0 | x) [log p(x | z0)].

        neg_log_constants = -self.log_constants_p_x_given_z0(

            n_nodes=ligand['size'], device=error_t_lig.device)

        # The KL between q(zT | x) and p(zT) = Normal(0, 1).

        # Should be close to zero.

        kl_prior = self.kl_prior(xh0_lig, ligand['mask'], ligand['size'])

        if self.training:

            # Computes the L_0 term (even if gamma_t is not actually gamma_0)

            # and this will later be selected via masking.

            log_p_x_given_z0_without_constants_ligand, log_ph_given_z0 = \

                self.log_pxh_given_z0_without_constants(

                    ligand, z_t_lig, eps_t_lig, net_out_lig, gamma_t)

            loss_0_x_ligand = -log_p_x_given_z0_without_constants_ligand * \

                              t_is_zero.squeeze()

            loss_0_h = -log_ph_given_z0 * t_is_zero.squeeze()

            # apply t_is_zero mask

            error_t_lig = error_t_lig * t_is_not_zero.squeeze()

        else:

            # Compute noise values for t = 0.

            t_zeros = torch.zeros_like(s)

            gamma_0 = self.inflate_batch_array(self.gamma(t_zeros), ligand['x'])

            # Sample z_0 given x, h for timestep t, from q(z_t | x, h)

            z_0_lig, xh_pocket, eps_0_lig = \

                self.noised_representation(xh0_lig, xh0_pocket, ligand['mask'],

                                           pocket['mask'], gamma_0)

            net_out_0_lig, _ = self.dynamics(

                z_0_lig, xh_pocket, t_zeros, ligand['mask'], pocket['mask'])

            log_p_x_given_z0_without_constants_ligand, log_ph_given_z0 = \

                self.log_pxh_given_z0_without_constants(

                    ligand, z_0_lig, eps_0_lig, net_out_0_lig, gamma_0)

            loss_0_x_ligand = -log_p_x_given_z0_without_constants_ligand

            loss_0_h = -log_ph_given_z0

        # sample size prior

        log_pN = self.log_pN(ligand['size'], pocket['size'])

        info = {

            'eps_hat_lig_x': scatter_mean(

                net_out_lig[:, :self.n_dims].abs().mean(1), ligand['mask'],

                dim=0).mean(),

            'eps_hat_lig_h': scatter_mean(

                net_out_lig[:, self.n_dims:].abs().mean(1), ligand['mask'],

                dim=0).mean(),

        }

        loss_terms = (delta_log_px, error_t_lig, torch.tensor(0.0), SNR_weight,

                      loss_0_x_ligand, torch.tensor(0.0), loss_0_h,

                      neg_log_constants, kl_prior, log_pN,

                      t_int.squeeze(), xh_lig_hat)

        return (*loss_terms, info) if return_info else loss_terms

    def partially_noised_ligand(self, ligand, pocket, noising_steps):

        """

        Partially noises a ligand to be later denoised.

        """

        # Inflate timestep into an array

        t_int = torch.ones(size=(ligand['size'].size(0), 1),

            device=ligand['x'].device).float() * noising_steps

        # Normalize t to [0, 1].

        t = t_int / self.T

        # Compute gamma_s and gamma_t via the network.

        gamma_t = self.inflate_batch_array(self.gamma(t), ligand['x'])

        # Concatenate x, and h[categorical].

        xh0_lig = torch.cat([ligand['x'], ligand['one_hot']], dim=1)

        xh0_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)

        # Center the input nodes

        xh0_lig[:, :self.n_dims], xh0_pocket[:, :self.n_dims] = \

            self.remove_mean_batch(xh0_lig[:, :self.n_dims],

                                   xh0_pocket[:, :self.n_dims],

                                   ligand['mask'], pocket['mask'])

        # Find noised representation

        z_t_lig, xh_pocket, eps_t_lig = \

            self.noised_representation(xh0_lig, xh0_pocket, ligand['mask'],

                                       pocket['mask'], gamma_t)

        return z_t_lig, xh_pocket, eps_t_lig

    def diversify(self, ligand, pocket, noising_steps):

        """

        Diversifies a set of ligands via noise-denoising

        """

        # Normalize data, take into account volume change in x.

        ligand, pocket = self.normalize(ligand, pocket)

        z_lig, xh_pocket, _ = self.partially_noised_ligand(ligand, pocket, noising_steps)

        timesteps = self.T

        n_samples = len(pocket['size'])

        device = pocket['x'].device

        # xh0_pocket is the original pocket while xh_pocket might be a

        # translated version of it

        xh0_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)

        lig_mask = ligand['mask']

        self.assert_mean_zero_with_mask(z_lig[:, :self.n_dims], lig_mask)

        # Iteratively sample p(z_s | z_t) for t = 1, ..., T, with s = t - 1.

        for s in reversed(range(0, noising_steps)):

            s_array = torch.full((n_samples, 1), fill_value=s,

                                 device=z_lig.device)

            t_array = s_array + 1

            s_array = s_array / timesteps

            t_array = t_array / timesteps

            z_lig, xh_pocket = self.sample_p_zs_given_zt(

                s_array, t_array, z_lig.detach(), xh_pocket.detach(), lig_mask, pocket['mask'])

        # Finally sample p(x, h | z_0).

        x_lig, h_lig, x_pocket, h_pocket = self.sample_p_xh_given_z0(

            z_lig, xh_pocket, lig_mask, pocket['mask'], n_samples)

        self.assert_mean_zero_with_mask(x_lig, lig_mask)

        # Overwrite last frame with the resulting x and h.

        out_lig = torch.cat([x_lig, h_lig], dim=1)

        out_pocket = torch.cat([x_pocket, h_pocket], dim=1)

        # remove frame dimension if only the final molecule is returned

        return out_lig, out_pocket, lig_mask, pocket['mask']

    def xh_given_zt_and_epsilon(self, z_t, epsilon, gamma_t, batch_mask):

        """ Equation (7) in the EDM paper """

        alpha_t = self.alpha(gamma_t, z_t)

        sigma_t = self.sigma(gamma_t, z_t)

        xh = z_t / alpha_t[batch_mask] - epsilon * sigma_t[batch_mask] / \

             alpha_t[batch_mask]

        return xh

    def sample_p_zt_given_zs(self, zs_lig, xh0_pocket, ligand_mask, pocket_mask,

                             gamma_t, gamma_s, fix_noise=False):

        sigma2_t_given_s, sigma_t_given_s, alpha_t_given_s = \

            self.sigma_and_alpha_t_given_s(gamma_t, gamma_s, zs_lig)

        mu_lig = alpha_t_given_s[ligand_mask] * zs_lig

        zt_lig, xh0_pocket = self.sample_normal_zero_com(

            mu_lig, xh0_pocket, sigma_t_given_s, ligand_mask, pocket_mask,

            fix_noise)

        return zt_lig, xh0_pocket

    def sample_p_zs_given_zt(self, s, t, zt_lig, xh0_pocket, ligand_mask,

                             pocket_mask, fix_noise=False):

        """Samples from zs ~ p(zs | zt). Only used during sampling."""

        gamma_s = self.gamma(s)

        gamma_t = self.gamma(t)

        sigma2_t_given_s, sigma_t_given_s, alpha_t_given_s = \

            self.sigma_and_alpha_t_given_s(gamma_t, gamma_s, zt_lig)

        sigma_s = self.sigma(gamma_s, target_tensor=zt_lig)

        sigma_t = self.sigma(gamma_t, target_tensor=zt_lig)

        # Neural net prediction.

        eps_t_lig, _ = self.dynamics(

            zt_lig, xh0_pocket, t, ligand_mask, pocket_mask)

        # Compute mu for p(zs | zt).

        # Note: mu_{t->s} = 1 / alpha_{t|s} z_t - sigma_{t|s}^2 / sigma_t / alpha_{t|s} epsilon

        # follows from the definition of mu_{t->s} and Equ. (7) in the EDM paper

        mu_lig = zt_lig / alpha_t_given_s[ligand_mask] - \

                 (sigma2_t_given_s / alpha_t_given_s / sigma_t)[ligand_mask] * \

                 eps_t_lig

        # Compute sigma for p(zs | zt).

        sigma = sigma_t_given_s * sigma_s / sigma_t

        # Sample zs given the parameters derived from zt.

        zs_lig, xh0_pocket = self.sample_normal_zero_com(

            mu_lig, xh0_pocket, sigma, ligand_mask, pocket_mask, fix_noise)

        self.assert_mean_zero_with_mask(zt_lig[:, :self.n_dims], ligand_mask)

        return zs_lig, xh0_pocket

    def sample_combined_position_feature_noise(self, lig_indices, xh0_pocket,

                                               pocket_indices):

        """

        Samples mean-centered normal noise for z_x, and standard normal noise

        for z_h.

        """

        raise NotImplementedError("Use sample_normal_zero_com() instead.")

    def sample(self, *args):

        raise NotImplementedError("Conditional model does not support sampling "

                                  "without given pocket.")

    @torch.no_grad()

    def sample_given_pocket(self, pocket, num_nodes_lig, return_frames=1,

                            timesteps=None):

        """

        Draw samples from the generative model. Optionally, return intermediate

        states for visualization purposes.

        """

        timesteps = self.T if timesteps is None else timesteps

        assert 0 < return_frames <= timesteps

        assert timesteps % return_frames == 0

        n_samples = len(pocket['size'])

        device = pocket['x'].device

        _, pocket = self.normalize(pocket=pocket)

        # xh0_pocket is the original pocket while xh_pocket might be a

        # translated version of it

        xh0_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)

        lig_mask = utils.num_nodes_to_batch_mask(

            n_samples, num_nodes_lig, device)

        # Sample from Normal distribution in the pocket center

        mu_lig_x = scatter_mean(pocket['x'], pocket['mask'], dim=0)

        mu_lig_h = torch.zeros((n_samples, self.atom_nf), device=device)

        mu_lig = torch.cat((mu_lig_x, mu_lig_h), dim=1)[lig_mask]

        sigma = torch.ones_like(pocket['size']).unsqueeze(1)

        z_lig, xh_pocket = self.sample_normal_zero_com(

            mu_lig, xh0_pocket, sigma, lig_mask, pocket['mask'])

        self.assert_mean_zero_with_mask(z_lig[:, :self.n_dims], lig_mask)

        out_lig = torch.zeros((return_frames,) + z_lig.size(),

                              device=z_lig.device)

        out_pocket = torch.zeros((return_frames,) + xh_pocket.size(),

                                 device=device)

        # Iteratively sample p(z_s | z_t) for t = 1, ..., T, with s = t - 1.

        for s in reversed(range(0, timesteps)):

            s_array = torch.full((n_samples, 1), fill_value=s,

                                 device=z_lig.device)

            t_array = s_array + 1

            s_array = s_array / timesteps

            t_array = t_array / timesteps

            z_lig, xh_pocket = self.sample_p_zs_given_zt(

                s_array, t_array, z_lig, xh_pocket, lig_mask, pocket['mask'])

            # save frame

            if (s * return_frames) % timesteps == 0:

                idx = (s * return_frames) // timesteps

                out_lig[idx], out_pocket[idx] = \

                    self.unnormalize_z(z_lig, xh_pocket)

        # Finally sample p(x, h | z_0).

        x_lig, h_lig, x_pocket, h_pocket = self.sample_p_xh_given_z0(

            z_lig, xh_pocket, lig_mask, pocket['mask'], n_samples)

        self.assert_mean_zero_with_mask(x_lig, lig_mask)

        # Correct CoM drift for examples without intermediate states

        if return_frames == 1:

            max_cog = scatter_add(x_lig, lig_mask, dim=0).abs().max().item()

            if max_cog > 5e-2:

                print(f'Warning CoG drift with error {max_cog:.3f}. Projecting '

                      f'the positions down.')

                x_lig, x_pocket = self.remove_mean_batch(

                    x_lig, x_pocket, lig_mask, pocket['mask'])

        # Overwrite last frame with the resulting x and h.

        out_lig[0] = torch.cat([x_lig, h_lig], dim=1)

        out_pocket[0] = torch.cat([x_pocket, h_pocket], dim=1)

        # remove frame dimension if only the final molecule is returned

        return out_lig.squeeze(0), out_pocket.squeeze(0), lig_mask, \

               pocket['mask']

    @torch.no_grad()

    def inpaint(self, ligand, pocket, lig_fixed, resamplings=1, return_frames=1,

                timesteps=None, center='ligand'):

        """

        Draw samples from the generative model while fixing parts of the input.

        Optionally, return intermediate states for visualization purposes.

        Inspired by Algorithm 1 in:

        Lugmayr, Andreas, et al.

        "Repaint: Inpainting using denoising diffusion probabilistic models."

        Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern

        Recognition. 2022.

        """

        timesteps = self.T if timesteps is None else timesteps

        assert 0 < return_frames <= timesteps

        assert timesteps % return_frames == 0

        if len(lig_fixed.size()) == 1:

            lig_fixed = lig_fixed.unsqueeze(1)

        n_samples = len(ligand['size'])

        device = pocket['x'].device

        # Normalize

        ligand, pocket = self.normalize(ligand, pocket)

        # xh0_pocket is the original pocket while xh_pocket might be a

        # translated version of it

        xh0_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)

        com_pocket_0 = scatter_mean(pocket['x'], pocket['mask'], dim=0)

        xh0_ligand = torch.cat([ligand['x'], ligand['one_hot']], dim=1)

        xh_ligand = xh0_ligand.clone()

        # Center initial system, subtract COM of known parts

        if center == 'ligand':

            mean_known = scatter_mean(ligand['x'][lig_fixed.bool().view(-1)],

                                      ligand['mask'][lig_fixed.bool().view(-1)],

                                      dim=0)

        elif center == 'pocket':

            mean_known = scatter_mean(pocket['x'], pocket['mask'], dim=0)

        else:

            raise NotImplementedError(

                f"Centering option {center} not implemented")

        # Sample from Normal distribution in the ligand center

        mu_lig_x = mean_known

        mu_lig_h = torch.zeros((n_samples, self.atom_nf), device=device)

        mu_lig = torch.cat((mu_lig_x, mu_lig_h), dim=1)[ligand['mask']]

        sigma = torch.ones_like(pocket['size']).unsqueeze(1)

        z_lig, xh_pocket = self.sample_normal_zero_com(

            mu_lig, xh0_pocket, sigma, ligand['mask'], pocket['mask'])

        # Output tensors

        out_lig = torch.zeros((return_frames,) + z_lig.size(),

                              device=z_lig.device)

        out_pocket = torch.zeros((return_frames,) + xh_pocket.size(),

                                 device=device)

        # Iteratively sample with resampling iterations

        for s in reversed(range(0, timesteps)):

            # resampling iterations

            for u in range(resamplings):

                # Denoise one time step: t -> s

                s_array = torch.full((n_samples, 1), fill_value=s,

                                     device=device)

                t_array = s_array + 1

                s_array = s_array / timesteps

                t_array = t_array / timesteps

                gamma_t = self.gamma(t_array)

                gamma_s = self.gamma(s_array)

                # sample inpainted part

                z_lig_unknown, xh_pocket = self.sample_p_zs_given_zt(

                    s_array, t_array, z_lig, xh_pocket, ligand['mask'],

                    pocket['mask'])

                # sample known nodes from the input

                com_pocket = scatter_mean(xh_pocket[:, :self.n_dims],

                                          pocket['mask'], dim=0)

                xh_ligand[:, :self.n_dims] = \

                    ligand['x'] + (com_pocket - com_pocket_0)[ligand['mask']]

                z_lig_known, xh_pocket, _ = self.noised_representation(

                    xh_ligand, xh_pocket, ligand['mask'], pocket['mask'],

                    gamma_s)

                # move center of mass of the noised part to the center of mass

                # of the corresponding denoised part before combining them

                # -> the resulting system should be COM-free

                com_noised = scatter_mean(

                    z_lig_known[lig_fixed.bool().view(-1)][:, :self.n_dims],

                    ligand['mask'][lig_fixed.bool().view(-1)], dim=0)

                com_denoised = scatter_mean(

                    z_lig_unknown[lig_fixed.bool().view(-1)][:, :self.n_dims],

                    ligand['mask'][lig_fixed.bool().view(-1)], dim=0)

                dx = com_denoised - com_noised

                z_lig_known[:, :self.n_dims] = z_lig_known[:, :self.n_dims] + dx[ligand['mask']]

                xh_pocket[:, :self.n_dims] = xh_pocket[:, :self.n_dims] + dx[pocket['mask']]

                # combine

                z_lig = z_lig_known * lig_fixed + z_lig_unknown * (

                            1 - lig_fixed)

                if u < resamplings - 1:

                    # Noise the sample

                    z_lig, xh_pocket = self.sample_p_zt_given_zs(

                        z_lig, xh_pocket, ligand['mask'], pocket['mask'],

                        gamma_t, gamma_s)

                # save frame at the end of a resampling cycle

                if u == resamplings - 1:

                    if (s * return_frames) % timesteps == 0:

                        idx = (s * return_frames) // timesteps

                        out_lig[idx], out_pocket[idx] = \

                            self.unnormalize_z(z_lig, xh_pocket)

        # Finally sample p(x, h | z_0).

        x_lig, h_lig, x_pocket, h_pocket = self.sample_p_xh_given_z0(

            z_lig, xh_pocket, ligand['mask'], pocket['mask'], n_samples)

        # Overwrite last frame with the resulting x and h.

        out_lig[0] = torch.cat([x_lig, h_lig], dim=1)

        out_pocket[0] = torch.cat([x_pocket, h_pocket], dim=1)

        # remove frame dimension if only the final molecule is returned

        return out_lig.squeeze(0), out_pocket.squeeze(0), ligand['mask'], \

               pocket['mask']

    @classmethod

    def remove_mean_batch(cls, x_lig, x_pocket, lig_indices, pocket_indices):

        # Just subtract the center of mass of the sampled part

        mean = scatter_mean(x_lig, lig_indices, dim=0)

        x_lig = x_lig - mean[lig_indices]

        x_pocket = x_pocket - mean[pocket_indices]

        return x_lig, x_pocket

# ------------------------------------------------------------------------------

# The same model without subspace-trick

# ------------------------------------------------------------------------------

class SimpleConditionalDDPM(ConditionalDDPM):

    """

    Simpler conditional diffusion module without subspace-trick.

    - rotational equivariance is guaranteed by construction

    - translationally equivariant likelihood is achieved by first mapping

      samples to a space where the context is COM-free and evaluating the

      likelihood there

    - molecule generation is equivariant because we can first sample in the

      space where the context is COM-free and translate the whole system back to

      the original position of the context later

    """

    def subspace_dimensionality(self, input_size):

        """ Override because we don't use the linear subspace anymore. """

        return input_size * self.n_dims

    @classmethod

    def remove_mean_batch(cls, x_lig, x_pocket, lig_indices, pocket_indices):

        """ Hacky way of removing the centering steps without changing too much

        code. """

        return x_lig, x_pocket

    @staticmethod

    def assert_mean_zero_with_mask(x, node_mask, eps=1e-10):

        return

    def forward(self, ligand, pocket, return_info=False):

        # Subtract pocket center of mass

        pocket_com = scatter_mean(pocket['x'], pocket['mask'], dim=0)

        ligand['x'] = ligand['x'] - pocket_com[ligand['mask']]

        pocket['x'] = pocket['x'] - pocket_com[pocket['mask']]

        return super(SimpleConditionalDDPM, self).forward(

            ligand, pocket, return_info)

    @torch.no_grad()

    def sample_given_pocket(self, pocket, num_nodes_lig, return_frames=1,

                            timesteps=None):

        # Subtract pocket center of mass

        pocket_com = scatter_mean(pocket['x'], pocket['mask'], dim=0)

        pocket['x'] = pocket['x'] - pocket_com[pocket['mask']]

        return super(SimpleConditionalDDPM, self).sample_given_pocket(

            pocket, num_nodes_lig, return_frames, timesteps)