# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 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.

"""
Convert graph partitioning instances into Pauli list
Deal with Gset format. See https://web.stanford.edu/~yyye/yyye/Gset/
"""

import logging

import numpy as np

from qiskit.quantum_info import Pauli
from qiskit.aqua.operators import WeightedPauliOperator

logger = logging.getLogger(__name__)


def get_operator(weight_matrix):
    r"""Generate Hamiltonian for the graph partitioning

    Notes:
        Goals:
            1 separate the vertices into two set of the same size
            2 make sure the number of edges between the two set is minimized.
        Hamiltonian:
            H = H_A + H_B
            H_A = sum\_{(i,j)\in E}{(1-ZiZj)/2}
            H_B = (sum_{i}{Zi})^2 = sum_{i}{Zi^2}+sum_{i!=j}{ZiZj}
            H_A is for achieving goal 2 and H_B is for achieving goal 1.

    Args:
        weight_matrix (numpy.ndarray) : adjacency matrix.

    Returns:
        WeightedPauliOperator: operator for the Hamiltonian
        float: a constant shift for the obj function.
    """
    num_nodes = len(weight_matrix)
    pauli_list = []
    shift = 0

    for i in range(num_nodes):
        for j in range(i):
            if weight_matrix[i, j] != 0:
                x_p = np.zeros(num_nodes, dtype=bool)
                z_p = np.zeros(num_nodes, dtype=bool)
                z_p[i] = True
                z_p[j] = True
                pauli_list.append([-0.5, Pauli((z_p, x_p))])
                shift += 0.5

    for i in range(num_nodes):
        for j in range(num_nodes):
            if i != j:
                x_p = np.zeros(num_nodes, dtype=bool)
                z_p = np.zeros(num_nodes, dtype=bool)
                z_p[i] = True
                z_p[j] = True
                pauli_list.append([1, Pauli((z_p, x_p))])
            else:
                shift += 1
    return WeightedPauliOperator(paulis=pauli_list), shift


def objective_value(x, w):
    """Compute the value of a cut.

    Args:
        x (numpy.ndarray): binary string as numpy array.
        w (numpy.ndarray): adjacency matrix.

    Returns:
        float: value of the cut.
    """
    # pylint: disable=invalid-name
    X = np.outer(x, (1 - x))
    w_01 = np.where(w != 0, 1, 0)
    return np.sum(w_01 * X)


def get_graph_solution(x):
    """Get graph solution from binary string.

    Args:
        x (numpy.ndarray) : binary string as numpy array.

    Returns:
        numpy.ndarray: graph solution as binary numpy array.
    """
    return 1 - x
