from __future__ import annotations

import math
import numpy as np

from typing import Any
from typing import cast
from typing import Optional


_EPS = 1e-8
_MEAN_MAX = 1e32
_SIGMA_MAX = 1e32


class SepCMA:
    """Separable CMA-ES stochastic optimizer class with ask-and-tell interface.

    Example:

        .. code::

           import numpy as np
           from cmaes import SepCMA

           def quadratic(x1, x2):
               return (x1 - 3) ** 2 + (10 * (x2 + 2)) ** 2

           optimizer = SepCMA(mean=np.zeros(2), sigma=1.3)

           for generation in range(50):
               solutions = []
               for _ in range(optimizer.population_size):
                   # Ask a parameter
                   x = optimizer.ask()
                   value = quadratic(x[0], x[1])
                   solutions.append((x, value))
                   print(f"#{generation} {value} (x1={x[0]}, x2 = {x[1]})")

               # Tell evaluation values.
               optimizer.tell(solutions)

    Args:

        mean:
            Initial mean vector of multi-variate gaussian distributions.

        sigma:
            Initial standard deviation of covariance matrix.

        bounds:
            Lower and upper domain boundaries for each parameter (optional).

        n_max_resampling:
            A maximum number of resampling parameters (default: 100).
            If all sampled parameters are infeasible, the last sampled one
            will be clipped with lower and upper bounds.

        seed:
            A seed number (optional).

        population_size:
            A population size (optional).
    """

    def __init__(
        self,
        mean: np.ndarray,
        sigma: float,
        bounds: Optional[np.ndarray] = None,
        n_max_resampling: int = 100,
        seed: Optional[int] = None,
        population_size: Optional[int] = None,
    ):
        assert sigma > 0, "sigma must be non-zero positive value"

        assert np.all(
            np.abs(mean) < _MEAN_MAX
        ), f"Abs of all elements of mean vector must be less than {_MEAN_MAX}"

        n_dim = len(mean)
        assert n_dim > 1, "The dimension of mean must be larger than 1"

        if population_size is None:
            population_size = 4 + math.floor(3 * math.log(n_dim))  # (eq. 48)
        assert population_size > 0, "popsize must be non-zero positive value."

        mu = population_size // 2

        # (eq.49)
        weights_prime = np.array(
            [math.log(mu + 1) - math.log(i + 1) for i in range(mu)]
        )
        weights = weights_prime / sum(weights_prime)
        mu_eff = 1 / sum(weights**2)

        # learning rate for the rank-one update
        alpha_cov = 2
        c1 = alpha_cov / ((n_dim + 1.3) ** 2 + mu_eff)
        # learning rate for the rank-μ update
        cmu_full = 2 / mu_eff / ((n_dim + np.sqrt(2)) ** 2) + (1 - 1 / mu_eff) * min(
            1, (2 * mu_eff - 1) / ((n_dim + 2) ** 2 + mu_eff)
        )
        cmu = (n_dim + 2) / 3 * cmu_full

        cm = 1  # (eq. 54)

        # learning rate for the cumulation for the step-size control
        c_sigma = (mu_eff + 2) / (n_dim + mu_eff + 3)
        d_sigma = 1 + 2 * max(0, math.sqrt((mu_eff - 1) / (n_dim + 1)) - 1) + c_sigma
        assert (
            c_sigma < 1
        ), "invalid learning rate for cumulation for the step-size control"

        # learning rate for cumulation for the rank-one update
        cc = 4 / (n_dim + 4)
        assert cc <= 1, "invalid learning rate for cumulation for the rank-one update"

        self._n_dim = n_dim
        self._popsize = population_size
        self._mu = mu
        self._mu_eff = mu_eff

        self._cc = cc
        self._c1 = c1
        self._cmu = cmu
        self._c_sigma = c_sigma
        self._d_sigma = d_sigma
        self._cm = cm

        # E||N(0, I)|| (p.28)
        self._chi_n = math.sqrt(self._n_dim) * (
            1.0 - (1.0 / (4.0 * self._n_dim)) + 1.0 / (21.0 * (self._n_dim**2))
        )

        self._weights = weights

        # evolution path
        self._p_sigma = np.zeros(n_dim)
        self._pc = np.zeros(n_dim)

        self._mean = mean
        self._sigma = sigma
        self._D: Optional[np.ndarray] = None
        self._C: np.ndarray = np.ones(n_dim)

        # bounds contains low and high of each parameter.
        assert bounds is None or _is_valid_bounds(bounds, mean), "invalid bounds"
        self._bounds = bounds
        self._n_max_resampling = n_max_resampling

        self._g = 0
        self._rng = np.random.RandomState(seed)

        # Termination criteria
        self._tolx = 1e-12 * sigma
        self._tolxup = 1e4
        self._tolfun = 1e-12
        self._tolconditioncov = 1e14

        self._funhist_term = 10 + math.ceil(30 * n_dim / population_size)
        self._funhist_values = np.empty(self._funhist_term * 2)

    @property
    def dim(self) -> int:
        """A number of dimensions"""
        return self._n_dim

    @property
    def population_size(self) -> int:
        """A population size"""
        return self._popsize

    @property
    def generation(self) -> int:
        """Generation number which is monotonically incremented
        when multi-variate gaussian distribution is updated."""
        return self._g

    @property
    def mean(self) -> np.ndarray:
        """Mean Vector"""
        return self._mean

    def reseed_rng(self, seed: int) -> None:
        self._rng.seed(seed)

    def __getstate__(self) -> dict[str, Any]:
        attrs = {}
        for name in self.__dict__:
            # Remove _rng in pickle serialized object.
            if name == "_rng":
                continue
            attrs[name] = getattr(self, name)
        return attrs

    def __setstate__(self, state: dict[str, Any]) -> None:
        self.__dict__.update(state)
        # Set _rng for unpickled object.
        setattr(self, "_rng", np.random.RandomState())

    def set_bounds(self, bounds: Optional[np.ndarray]) -> None:
        """Update boundary constraints"""
        assert bounds is None or _is_valid_bounds(bounds, self._mean), "invalid bounds"
        self._bounds = bounds

    def ask(self) -> np.ndarray:
        """Sample a parameter"""
        for i in range(self._n_max_resampling):
            x = self._sample_solution()
            if self._is_feasible(x):
                return x
        x = self._sample_solution()
        x = self._repair_infeasible_params(x)
        return x

    def _eigen_decomposition(self) -> np.ndarray:
        if self._D is not None:
            return self._D
        self._D = np.sqrt(np.where(self._C < 0, _EPS, self._C))
        return self._D

    def _sample_solution(self) -> np.ndarray:
        D = self._eigen_decomposition()
        z = self._rng.randn(self._n_dim)  # ~ N(0, I)
        y = D * z  # ~ N(0, C)
        x = self._mean + self._sigma * y  # ~ N(m, σ^2 C)
        return x

    def _is_feasible(self, param: np.ndarray) -> bool:
        if self._bounds is None:
            return True
        return cast(
            bool,
            np.all(param >= self._bounds[:, 0]) and np.all(param <= self._bounds[:, 1]),
        )  # Cast bool_ to bool

    def _repair_infeasible_params(self, param: np.ndarray) -> np.ndarray:
        if self._bounds is None:
            return param

        # clip with lower and upper bound.
        param = np.where(param < self._bounds[:, 0], self._bounds[:, 0], param)
        param = np.where(param > self._bounds[:, 1], self._bounds[:, 1], param)
        return param

    def tell(self, solutions: list[tuple[np.ndarray, float]]) -> None:
        """Tell evaluation values"""

        assert len(solutions) == self._popsize, "Must tell popsize-length solutions."
        for s in solutions:
            assert np.all(
                np.abs(s[0]) < _MEAN_MAX
            ), f"Abs of all param values must be less than {_MEAN_MAX} to avoid overflow errors"

        self._g += 1
        solutions.sort(key=lambda s: s[1])

        # Stores 'best' and 'worst' values of the
        # last 'self._funhist_term' generations.
        funhist_idx = 2 * (self.generation % self._funhist_term)
        self._funhist_values[funhist_idx] = solutions[0][1]
        self._funhist_values[funhist_idx + 1] = solutions[-1][1]

        # Sample new population of search_points, for k=1, ..., popsize
        D = self._eigen_decomposition()
        self._D = None

        x_k = np.array([s[0] for s in solutions])  # ~ N(m, σ^2 C)
        y_k = (x_k - self._mean) / self._sigma  # ~ N(0, C)

        # Selection and recombination
        y_w = np.sum(y_k[: self._mu].T * self._weights[: self._mu], axis=1)
        self._mean += self._cm * self._sigma * y_w

        # Step-size control
        self._p_sigma = (1 - self._c_sigma) * self._p_sigma + math.sqrt(
            self._c_sigma * (2 - self._c_sigma) * self._mu_eff
        ) * (y_w / D)

        norm_p_sigma = np.linalg.norm(self._p_sigma)
        self._sigma *= np.exp(
            (self._c_sigma / self._d_sigma) * (norm_p_sigma / self._chi_n - 1)
        )
        self._sigma = min(self._sigma, _SIGMA_MAX)

        # Covariance matrix adaption
        h_sigma_cond_left = norm_p_sigma / math.sqrt(
            1 - (1 - self._c_sigma) ** (2 * (self._g + 1))
        )
        h_sigma_cond_right = (1.4 + 2 / (self._n_dim + 1)) * self._chi_n
        h_sigma = 1.0 if h_sigma_cond_left < h_sigma_cond_right else 0.0  # (p.28)

        # (eq.45)
        self._pc = (1 - self._cc) * self._pc + h_sigma * math.sqrt(
            self._cc * (2 - self._cc) * self._mu_eff
        ) * y_w

        delta_h_sigma = (1 - h_sigma) * self._cc * (2 - self._cc)  # (p.28)
        assert delta_h_sigma <= 1

        # (eq.47)
        rank_one = self._pc**2
        rank_mu = np.sum(
            np.array([w * (y**2) for w, y in zip(self._weights, y_k)]), axis=0
        )
        self._C = (
            (
                1
                + self._c1 * delta_h_sigma
                - self._c1
                - self._cmu * np.sum(self._weights)
            )
            * self._C
            + self._c1 * rank_one
            + self._cmu * rank_mu
        )

    def should_stop(self) -> bool:
        D = self._eigen_decomposition()

        # Stop if the range of function values of the recent generation is below tolfun.
        if (
            self.generation > self._funhist_term
            and np.max(self._funhist_values) - np.min(self._funhist_values)
            < self._tolfun
        ):
            return True

        # Stop if the std of the normal distribution is smaller than tolx
        # in all coordinates and pc is smaller than tolx in all components.
        if np.all(self._sigma * self._C < self._tolx) and np.all(
            self._sigma * self._pc < self._tolx
        ):
            return True

        # Stop if detecting divergent behavior.
        if self._sigma * np.max(D) > self._tolxup:
            return True

        # No effect coordinates: stop if adding 0.2-standard deviations
        # in any single coordinate does not change m.
        if np.any(self._mean == self._mean + (0.2 * self._sigma * np.sqrt(self._C))):
            return True

        # No effect axis: stop if adding 0.1-standard deviation vector in
        # any principal axis direction of C does not change m. "pycma" check
        # axis one by one at each generation.
        i = self.generation % self.dim
        if np.all(
            self._mean == self._mean + (0.1 * self._sigma * D[i] * np.ones(self._n_dim))
        ):
            return True

        # Stop if the condition number of the covariance matrix exceeds 1e14.
        condition_cov = np.max(D) / np.min(D)
        if condition_cov > self._tolconditioncov:
            return True

        return False


def _is_valid_bounds(bounds: Optional[np.ndarray], mean: np.ndarray) -> bool:
    if bounds is None:
        return True
    if (mean.size, 2) != bounds.shape:
        return False
    if not np.all(bounds[:, 0] <= mean):
        return False
    if not np.all(mean <= bounds[:, 1]):
        return False
    return True