# This code is part of Qiskit.
#
# (C) Copyright IBM 2021
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""
Readout mitigator class based on the A-matrix inversion method
"""

from typing import Optional, List, Tuple, Iterable, Callable, Union, Dict
import numpy as np

from qiskit.exceptions import QiskitError
from ..distributions.quasi import QuasiDistribution
from ..counts import Counts
from .base_readout_mitigator import BaseReadoutMitigator
from .utils import counts_probability_vector, z_diagonal, str2diag


class CorrelatedReadoutMitigator(BaseReadoutMitigator):
    """N-qubit readout error mitigator.

    Mitigates :meth:`expectation_value` and :meth:`quasi_probabilities`.
    The mitigation_matrix should be calibrated using qiskit experiments.
    This mitigation method should be used in case the readout errors of the qubits
    are assumed to be correlated. The mitigation_matrix of *N* qubits is of size
    :math:`2^N x 2^N` so the mitigation complexity is :math:`O(4^N)`.
    """

    def __init__(self, assignment_matrix: np.ndarray, qubits: Optional[Iterable[int]] = None):
        """Initialize a CorrelatedReadoutMitigator

        Args:
            assignment_matrix: readout error assignment matrix.
            qubits: Optional, the measured physical qubits for mitigation.

        Raises:
            QiskitError: matrix size does not agree with number of qubits
        """
        if np.any(assignment_matrix < 0) or not np.allclose(np.sum(assignment_matrix, axis=0), 1):
            raise QiskitError("Assignment matrix columns must be valid probability distributions")
        assignment_matrix = np.asarray(assignment_matrix, dtype=float)
        matrix_qubits_num = int(np.log2(assignment_matrix.shape[0]))
        if qubits is None:
            self._num_qubits = matrix_qubits_num
            self._qubits = range(self._num_qubits)
        else:
            if len(qubits) != matrix_qubits_num:
                raise QiskitError(
                    "The number of given qubits ({}) is different than the number of "
                    "qubits inferred from the matrices ({})".format(len(qubits), matrix_qubits_num)
                )
            self._qubits = qubits
            self._num_qubits = len(self._qubits)
        self._qubit_index = dict(zip(self._qubits, range(self._num_qubits)))
        self._assignment_mat = assignment_matrix
        self._mitigation_mats = {}

    @property
    def settings(self) -> Dict:
        """Return settings."""
        return {"assignment_matrix": self._assignment_mat, "qubits": self._qubits}

    def expectation_value(
        self,
        data: Counts,
        diagonal: Union[Callable, dict, str, np.ndarray] = None,
        qubits: Iterable[int] = None,
        clbits: Optional[List[int]] = None,
        shots: Optional[int] = None,
    ) -> Tuple[float, float]:
        r"""Compute the mitigated expectation value of a diagonal observable.

        This computes the mitigated estimator of
        :math:`\langle O \rangle = \mbox{Tr}[\rho. O]` of a diagonal observable
        :math:`O = \sum_{x\in\{0, 1\}^n} O(x)|x\rangle\!\langle x|`.

        Args:
            data: Counts object
            diagonal: Optional, the vector of diagonal values for summing the
                      expectation value. If ``None`` the default value is
                      :math:`[1, -1]^\otimes n`.
            qubits: Optional, the measured physical qubits the count
                    bitstrings correspond to. If None qubits are assumed to be
                    :math:`[0, ..., n-1]`.
            clbits: Optional, if not None marginalize counts to the specified bits.
            shots: the number of shots.

        Returns:
            (float, float): the expectation value and an upper bound of the standard deviation.

        Additional Information:
            The diagonal observable :math:`O` is input using the ``diagonal`` kwarg as
            a list or Numpy array :math:`[O(0), ..., O(2^n -1)]`. If no diagonal is specified
            the diagonal of the Pauli operator
            :math`O = \mbox{diag}(Z^{\otimes n}) = [1, -1]^{\otimes n}` is used.
            The ``clbits`` kwarg is used to marginalize the input counts dictionary
            over the specified bit-values, and the ``qubits`` kwarg is used to specify
            which physical qubits these bit-values correspond to as
            ``circuit.measure(qubits, clbits)``.
        """

        if qubits is None:
            qubits = self._qubits
        probs_vec, shots = counts_probability_vector(
            data, qubit_index=self._qubit_index, clbits=clbits, qubits=qubits
        )

        # Get qubit mitigation matrix and mitigate probs
        mit_mat = self.mitigation_matrix(qubits)

        # Get operator coeffs
        if diagonal is None:
            diagonal = z_diagonal(2**self._num_qubits)
        elif isinstance(diagonal, str):
            diagonal = str2diag(diagonal)

        # Apply transpose of mitigation matrix
        coeffs = mit_mat.T.dot(diagonal)
        expval = coeffs.dot(probs_vec)
        stddev_upper_bound = self.stddev_upper_bound(shots)

        return (expval, stddev_upper_bound)

    def quasi_probabilities(
        self,
        data: Counts,
        qubits: Optional[List[int]] = None,
        clbits: Optional[List[int]] = None,
        shots: Optional[int] = None,
    ) -> QuasiDistribution:
        """Compute mitigated quasi probabilities value.

        Args:
            data: counts object
            qubits: qubits the count bitstrings correspond to.
            clbits: Optional, marginalize counts to just these bits.
            shots: Optional, the total number of shots, if None shots will
                be calculated as the sum of all counts.

        Returns:
            QuasiDistibution: A dictionary containing pairs of [output, mean] where "output"
                is the key in the dictionaries,
                which is the length-N bitstring of a measured standard basis state,
                and "mean" is the mean of non-zero quasi-probability estimates.
        """
        if qubits is None:
            qubits = self._qubits
        probs_vec, calculated_shots = counts_probability_vector(
            data, qubit_index=self._qubit_index, clbits=clbits, qubits=qubits
        )
        if shots is None:
            shots = calculated_shots

        # Get qubit mitigation matrix and mitigate probs
        mit_mat = self.mitigation_matrix(qubits)

        # Apply transpose of mitigation matrix
        probs_vec = mit_mat.dot(probs_vec)
        probs_dict = {}
        for index, _ in enumerate(probs_vec):
            probs_dict[index] = probs_vec[index]

        quasi_dist = QuasiDistribution(
            probs_dict, stddev_upper_bound=self.stddev_upper_bound(shots)
        )

        return quasi_dist

    def mitigation_matrix(self, qubits: List[int] = None) -> np.ndarray:
        r"""Return the readout mitigation matrix for the specified qubits.

        The mitigation matrix :math:`A^{-1}` is defined as the inverse of the
        :meth:`assignment_matrix` :math:`A`.

        Args:
            qubits: Optional, qubits being measured.

        Returns:
            np.ndarray: the measurement error mitigation matrix :math:`A^{-1}`.
        """
        if qubits is None:
            qubits = self._qubits
        qubits = tuple(sorted(qubits))

        # Check for cached mitigation matrix
        # if not present compute
        if qubits not in self._mitigation_mats:
            marginal_matrix = self.assignment_matrix(qubits)
            try:
                mit_mat = np.linalg.inv(marginal_matrix)
            except np.linalg.LinAlgError:
                # Use pseudo-inverse if matrix is singular
                mit_mat = np.linalg.pinv(marginal_matrix)
            self._mitigation_mats[qubits] = mit_mat

        return self._mitigation_mats[qubits]

    def assignment_matrix(self, qubits: List[int] = None) -> np.ndarray:
        r"""Return the readout assignment matrix for specified qubits.

        The assignment matrix is the stochastic matrix :math:`A` which assigns
        a noisy readout probability distribution to an ideal input
        readout distribution: :math:`P(i|j) = \langle i | A | j \rangle`.

        Args:
            qubits: Optional, qubits being measured.

        Returns:
            np.ndarray: the assignment matrix A.
        """
        if qubits is None:
            qubits = self._qubits
        if qubits == self._num_qubits:
            return self._assignment_mat

        if isinstance(qubits, int):
            qubits = [qubits]

        qubit_indices = [self._qubit_index[qubit] for qubit in qubits]
        # Compute marginal matrix
        axis = tuple(
            self._num_qubits - 1 - i for i in set(range(self._num_qubits)).difference(qubit_indices)
        )
        num_qubits = len(qubits)

        new_amat = np.zeros(2 * [2**num_qubits], dtype=float)
        for i, col in enumerate(self._assignment_mat.T[self._keep_indexes(qubit_indices)]):
            new_amat[i] = (
                np.reshape(col, self._num_qubits * [2]).sum(axis=axis).reshape([2**num_qubits])
            )
        new_amat = new_amat.T
        return new_amat

    @staticmethod
    def _keep_indexes(qubits):
        indexes = [0]
        for i in sorted(qubits):
            indexes += [idx + (1 << i) for idx in indexes]
        return indexes

    def _compute_gamma(self):
        """Compute gamma for N-qubit mitigation"""
        mitmat = self.mitigation_matrix(qubits=self._qubits)
        return np.max(np.sum(np.abs(mitmat), axis=0))

    def stddev_upper_bound(self, shots: int):
        """Return an upper bound on standard deviation of expval estimator.

        Args:
            shots: Number of shots used for expectation value measurement.

        Returns:
            float: the standard deviation upper bound.
        """
        gamma = self._compute_gamma()
        return gamma / np.sqrt(shots)

    @property
    def qubits(self) -> Tuple[int]:
        """The device qubits for this mitigator"""
        return self._qubits
