# Copyright (c) 2020 Horizon Robotics and ALF Contributors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import copy
import numpy as np
import torch
from typing import Callable

import alf
from alf.utils import common
from alf.utils import tensor_utils
from . import adam_tf, adamw


def _rbf_func(x):
    r"""
    Compute the rbf kernel and its gradient w.r.t. first entry
    :math:`K(x, x), \nabla_x K(x, x)`, for computing ``svgd``_grad.

    Args:
        x (Tensor): set of N particles, shape (N x D), where D is the
            dimenseion of each particle

    Returns:
        :math:`K(x, x)` (Tensor): the RBF kernel of shape (N x N)
        :math:`\nabla_x K(x, x)` (Tensor): the derivative of RBF kernel of shape (N x N x D)

    """
    N, D = x.shape
    diff = x.unsqueeze(1) - x.unsqueeze(0)  # [N, N, D]
    dist_sq = torch.sum(diff**2, -1)  # [N, N]
    h, _ = torch.median(dist_sq.view(-1), dim=0)
    if h == 0.:
        h = torch.ones_like(h)
    else:
        h = h / max(np.log(N), 1.)

    kappa = torch.exp(-dist_sq / h)  # [N, N]
    kappa_grad = -2 * kappa.unsqueeze(-1) * diff / h  # [N, N, D]
    return kappa, kappa_grad


def _score_func(x, alpha=1e-5):
    r"""
    Compute the stein estimator of the score function
    :math:`\nabla\log q = -(K + \alpha I)^{-1}\nabla K`,
    for computing ``gfsf``_grad.

    Args:
        x (Tensor): set of N particles, shape (N x D), where D is the
            dimenseion of each particle
        alpha (float): weight of regularization for inverse kernel
            this parameter turns out to be crucial for convergence.

    Returns:
        :math:`\nabla\log q` (Tensor): the score function of shape (N x D)

    """
    N, D = x.shape
    diff = x.unsqueeze(1) - x.unsqueeze(0)  # [N, N, D]
    dist_sq = torch.sum(diff**2, -1)  # [N, N]
    h, _ = torch.median(dist_sq.view(-1), dim=0)
    if h == 0.:
        h = torch.ones_like(h)
    else:
        h = h / max(np.log(N), 1.)

    kappa = torch.exp(-dist_sq / h)  # [N, N]
    kappa_inv = torch.inverse(kappa + alpha * torch.eye(N))  # [N, N]
    kappa_grad = -2 * kappa.unsqueeze(-1) * diff / h  # [N, N, D]
    kappa_grad = kappa_grad.sum(0)  # [N, D]

    return -kappa_inv @ kappa_grad


def wrap_optimizer(cls):
    """A helper function to construct torch optimizers with
    params as [{'params': []}]. After construction, new parameter
    groups can be added by using the add_param_group() method.

    This wrapper also clips gradients first before calling ``step()``.
    """
    NewClsName = cls.__name__ + "_"
    NewCls = type(NewClsName, (cls, ), {})
    NewCls.counter = 0

    @common.add_method(NewCls)
    def __init__(self,
                 *,
                 gradient_clipping=None,
                 clip_by_global_norm=False,
                 parvi=None,
                 repulsive_weight=1.,
                 name=None,
                 **kwargs):
        """
        Args:
            gradient_clipping (float): If not None, serve as a positive threshold
            clip_by_global_norm (bool): If True, use `tensor_utils.clip_by_global_norm`
                to clip gradient. If False, use `tensor_utils.clip_by_norms` for
                each grad.
            parvi (string): if not ``None``, paramters with attribute
                ``ensemble_group`` will be updated by particle-based vi algorithm
                specified by ``parvi``, options are [``svgd``, ``gfsf``],

                * Stein Variational Gradient Descent (SVGD)

                  Liu, Qiang, and Dilin Wang. "Stein Variational Gradient Descent:
                  A General Purpose Bayesian Inference Algorithm." NIPS. 2016.

                * Wasserstein Gradient Flow with Smoothed Functions (GFSF)

                  Liu, Chang, et al. "Understanding and accelerating particle-based
                  variational inference." ICML. 2019.

                To work with the ``parvi`` option, the parameters added to the
                optimizer (by ``add_param_group``) should have an (int) attribute
                ``ensemble_group``. See ``FCBatchEnsemble`` as an example.

            repulsive_weight (float): the weight of the repulsive gradient term
                for parameters with attribute ``ensemble_group``.
            name (str): the name displayed when summarizing the gradient norm. If
                None, then a global name in the format of "class_name_i" will be
                created, where "i" is the global optimizer id.
            kwargs: arguments passed to the constructor of the underline torch
                optimizer. If ``lr`` is given and it is a ``Callable``, it is
                treated as a learning rate scheduler and will be called everytime
                when ``step()`` is called to get the latest learning rate.
                Available schedulers are in ``alf.utils.schedulers``.
        """
        self._lr_scheduler = None
        if "lr" in kwargs:
            lr = kwargs["lr"]
            if isinstance(lr, Callable):
                self._lr_scheduler = lr
                kwargs["lr"] = float(lr())

        super(NewCls, self).__init__([{'params': []}], **kwargs)
        self._gradient_clipping = gradient_clipping
        self._clip_by_global_norm = clip_by_global_norm
        self._parvi = parvi
        if parvi is not None:
            assert parvi in ['svgd', 'gfsf'
                             ], ("parvi method %s is not supported." % (parvi))
            self._repulsive_weight = repulsive_weight
        self.name = name
        if name is None:
            self.name = NewClsName + str(NewCls.counter)
            NewCls.counter += 1

    @common.add_method(NewCls)
    def step(self, closure=None):
        """This function first clips the gradients if needed, then call the
        parent's ``step()`` function.
        """
        if self._lr_scheduler is not None:
            lr = float(self._lr_scheduler())
            for param_group in self.param_groups:
                param_group['lr'] = lr
        if self._gradient_clipping is not None:
            params = []
            for param_group in self.param_groups:
                params.extend(param_group["params"])
            grads = alf.nest.map_structure(lambda p: p.grad, params)
            if self._clip_by_global_norm:
                _, global_norm = tensor_utils.clip_by_global_norm(
                    grads, self._gradient_clipping, in_place=True)
                if alf.summary.should_record_summaries():
                    alf.summary.scalar("global_grad_norm/%s" % self.name,
                                       global_norm)
            else:
                tensor_utils.clip_by_norms(
                    grads, self._gradient_clipping, in_place=True)

        if self._parvi is not None:
            self._parvi_step()

        super(NewCls, self).step(closure=closure)

    @common.add_method(NewCls)
    def _parvi_step(self):
        for param_group in self.param_groups:
            if "parvi_grad" in param_group:
                params = param_group['params']
                batch_size = params[0].shape[0]
                params_tensor = torch.cat(
                    [p.view(batch_size, -1) for p in params],
                    dim=-1)  # [N, D], D=dim(params)
                if self._parvi == 'svgd':
                    # [N, N], [N, N, D]
                    kappa, kappa_grad = _rbf_func(params_tensor)
                    grads_tensor = torch.cat(
                        [p.grad.view(batch_size, -1) for p in params],
                        dim=-1).detach()  # [N, D]
                    kernel_logp = torch.matmul(kappa,
                                               grads_tensor) / batch_size
                    svgd_grad = torch.split(
                        kernel_logp -
                        self._repulsive_weight * kappa_grad.mean(0),
                        [p.nelement() // batch_size for p in params],
                        dim=-1)
                    for i in range(len(params)):
                        grad = params[i].grad.view(batch_size, -1)
                        grad.copy_(svgd_grad[i])
                else:
                    logq_grad = _score_func(params_tensor)  # [N, D]
                    gfsf_grad = torch.split(
                        logq_grad,
                        [p.nelement() // batch_size for p in params],
                        dim=-1)
                    for i in range(len(params)):
                        grad = params[i].grad.view(batch_size, -1)
                        grad.add_(self._repulsive_weight * gfsf_grad[i])

    @common.add_method(NewCls)
    def add_param_group(self, param_group):
        """This function first splits the input param_group into multiple
        param_groups according to their ``ensemble_group`` attributes, then
        calls the parent's ``add_param_group()`` function to add each of
        them to the optimizer.
        """
        assert isinstance(param_group, dict), "param_group must be a dict"

        params = param_group["params"]
        if isinstance(params, torch.Tensor):
            param_group['params'] = [params]
        elif isinstance(params, set):
            raise TypeError('Please use a list instead.')
        else:
            param_group['params'] = list(params)

        len_params = len(param_group['params'])
        std_param_group = []
        ensemble_param_groups = [[] for i in range(len_params)]
        group_batch_sizes = [0] * len_params
        for param in param_group['params']:
            if not isinstance(param, torch.Tensor):
                raise TypeError("optimizer can only optimize Tensors, "
                                "but one of the params is " +
                                torch.typename(param))
            if hasattr(param, 'ensemble_group'):
                assert isinstance(
                    param.ensemble_group,
                    int), ("ensemble_group attribute mis-specified.")
                ensemble_group_id = param.ensemble_group
                if group_batch_sizes[ensemble_group_id] == 0:
                    group_batch_sizes[ensemble_group_id] = param.shape[0]
                else:
                    assert param.shape[0] == group_batch_sizes[
                        ensemble_group_id], (
                            "batch_size of params does not match that of the "
                            "ensemble param_group %d." % (ensemble_group_id))
                ensemble_param_groups[ensemble_group_id].append(param)
            else:
                std_param_group.append(param)

        if len(alf.nest.flatten(ensemble_param_groups)) > 0:
            if len(std_param_group) > 0:
                super(NewCls, self).add_param_group({
                    'params': std_param_group
                })
            for ensemble_param_group in ensemble_param_groups:
                if len(ensemble_param_group) > 0:
                    super(NewCls, self).add_param_group({
                        'params': ensemble_param_group,
                        'parvi_grad': True
                    })
        else:
            super(NewCls, self).add_param_group(param_group)

    return NewCls


Adam = alf.configurable('Adam')(wrap_optimizer(torch.optim.Adam))

# TODO: uncomment this after removing `adamw.py`
#AdamW = alf.configurable('AdamW')(wrap_optimizer(torch.optim.AdamW))
AdamW = alf.configurable('AdamW')(wrap_optimizer(adamw.AdamW))

SGD = alf.configurable('SGD')(wrap_optimizer(torch.optim.SGD))

AdamTF = alf.configurable('AdamTF')(wrap_optimizer(adam_tf.AdamTF))

torch.typename torch.matmul torch.eye torch.ones_like torch.exp torch.sum