import numpy as np


class ProximalDecoder:
    """Class implementing the Proximal Decoding algorithm. See "Proximal Decoding for LDPC Codes"
    by Tadashi Wadayama, and Satoshi Takabe.
    """

    # TODO: Is 'R' actually called 'decoding matrix'?
    # TODO: How large should eta be?
    # TODO: How large should step_size be?
    def __init__(self, H: np.array, R: np.array, K: int = 100, step_size: float = 0.1,
                 gamma: float = 0.05, eta: float = 1.5):
        """Construct a new ProximalDecoder Object.

        :param H: Parity Check Matrix
        :param R: Decoding matrix
        :param K: Max number of iterations to perform when decoding
        :param step_size: Step size for the gradient descent process
        :param gamma: Positive constant. Arises in the approximation of the prior PDF
        :param eta: Positive constant slightly larger than one. See 3.2,  p. 3
        """
        self._H = H
        self._R = R
        self._K = K
        self._step_size = step_size
        self._gamma = gamma
        self._eta = eta

        self._A = []
        self._B = []

        for row in self._H:
            A_k = np.argwhere(row == 1)
            self._A.append(A_k[:, 0])

        for column in self._H.T:
            B_k = np.argwhere(column == 1)
            self._B.append(B_k[:, 0])

    @staticmethod
    def _L_awgn(s: np.array, y: np.array) -> np.array:
        """Variation of the negative log-likelihood for the special case of AWGN noise.
        See 4.1, p. 4.
        """
        return s - y

    # TODO: Is this correct?
    def _grad_h(self, x: np.array) -> np.array:
        """Gradient of the code-constraint polynomial. See 2.3, p. 2."""
        # Calculate first term

        result = 4 * (x**2 - 1) * x

        # Calculate second term

        for k, x_k in enumerate(x):
            sum_result = 0

            for i in self._B[k]:
                prod = np.prod(x[self._A[i]])
                sum_result += prod**2 - prod

            term_2 = 2 / x_k * sum_result

            result[k] += term_2

        return np.array(result)

    # TODO: Is the 'projection onto [-eta, eta]' actually just clipping?
    def _projection(self, x):
        """Project a vector onto [-eta, eta]^n in order to avoid numerical instability.
        Detailed in 3.2, p. 3 (Equation (15)).

        :param x:
        :return: x clipped to [-eta, eta]^n
        """
        return np.clip(x, -self._eta, self._eta)

    def _check_parity(self, y_hat: np.array) -> bool:
        """Perform a parity check for a given codeword.

        :param y_hat: codeword to be checked (element of [0, 1]^n)
        :return: True if the parity check passes, i.e. the codeword is valid. False otherwise
        """
        syndrome = np.dot(self._H, y_hat) % 2
        return not np.any(syndrome)

    def decode(self, y: np.array) -> np.array:
        """Decode a received signal. The algorithm is detailed in 3.2, p.3.

        This function assumes a BPSK-like modulated signal ([-1, 1]^n instead of [0, 1]^n)
        and an AWGN channel.

        :param y: Vector of received values. (y = x + w, where 'x' is element of [-1, 1]^n
            and 'w' is noise)
        :return: Most probably sent dataword (element of [0, 1]^k)
        """
        s = np.zeros(y.size)
        x_hat = np.zeros(y.size)
        for k in range(self._K):
            r = s - self._step_size * self._L_awgn(s, y)

            s = r - self._gamma * self._grad_h(r)
            s = self._projection(s)  # Equation (15)

            x_hat = np.sign(s)
            x_hat = (x_hat == 1) * 1  # Map the codeword from [-1, 1]^n to [0, 1]^n

            if self._check_parity(x_hat):
                break

        return np.dot(self._R, x_hat)