from __future__ import annotations

from typing import Union

import numpy as np
from numbers import Complex

from load_test import sizeof_fmt

ListOrNdarray = Union[list, np.ndarray]


class Matrix(object):
    """Represents a quantum state as a vector in Hilbert space"""

    def __init__(self, m: ListOrNdarray = None, *args, **kwargs):
        """
        Can be initialized with a matrix, e.g. for |0> this is [[0],[1]]
        :param m: a matrix representing the quantum state
        :param name: the name of the state (optional)
        """
        if m is None:
            self.m = np.array([])
        elif type(m) is list:
            self.m = np.array(m)
        elif type(m) is np.ndarray:
            self.m = m
        else:
            raise TypeError("m needs to be a list or ndarray type")

    def __add__(self, other):
        return other.__class__(self.m + other.m)

    def __eq__(self, other):
        if isinstance(other, Complex):
            return bool(np.allclose(self.m, other))
        return np.allclose(self.m, other.m)

    def __mul_or_kron__(self, other):
        """
        Multiplication with a number is Linear op;
        with another state is a composition via the Kronecker/Tensor product
        """
        if isinstance(other, Complex):
            return self.__class__(self.m * other)
        elif isinstance(other, Matrix):
            return other.__class__(np.kron(self.m, other.m))
        raise NotImplementedError

    def __rmul__(self, other):
        return self.__mul_or_kron__(other)

    def __mul__(self, other):
        return self.__mul_or_kron__(other)

    def __or__(self, other):
        """Define inner product: <self|other>
        """
        return other.__class__(np.dot(self._conjugate_transpose(), other.m))

    def __len__(self):
        return len(self.m)

    def _conjugate_transpose(self):
        return self.m.transpose().conjugate()

    def _complex_conjugate(self):
        return self.m.conjugate()

    def conjugate_transpose(self):
        return State(self._conjugate_transpose())

    def complex_conjugate(self):
        return State(self._complex_conjugate())


class State(Matrix):
    def __init__(self, m: ListOrNdarray = None, name: str = '', *args, **kwargs):
        """An Operator turns one function into another"""
        super().__init__(m)
        self.name = name

    def __repr__(self):
        if self.name:
            return '|{}>'.format(self.name)
        return str(self.m)

    def norm(self):
        """Norm/Length of the vector = sqrt(<self|self>)"""
        return self.length()

    def length(self):
        """Norm/Length of the vector = sqrt(<self|self>)"""
        return np.sqrt((self | self).m).item(0)

    def is_orthogonal(self, other):
        """If the inner (dot) product is zero, this vector is orthogonal to other"""
        return self | other == 0

    def measure(self, j):
        """pr(j) = |<e_j|self>|^2"""
        # j_th basis vector
        e_j = State([[1] if i == int(j) else [0] for i in range(len(self.m))])
        return np.absolute((e_j | self).m.item(0)) ** 2


class Operator(object):
    def __init__(self, func=None, *args, **kwargs):
        """An Operator turns one function into another"""
        self.func = func

    def on(self, *args, **kwargs):
        return self(*args, **kwargs)

    def __call__(self, *args, **kwargs):
        return self.func(*args, **kwargs)


class UnitaryMatrix(Matrix):
    def __init__(self, m: ListOrNdarray, *args, **kwargs):
        """Represents a Unitary matrix that satisfies UU+ = I"""
        super().__init__(m, *args, **kwargs)
        if not self._is_unitary():
            raise TypeError("Not a Unitary matrix")

    def _is_unitary(self):
        """Checks if the matrix is
          1. square and
          2. the product of itself with conjugate transpose is Identity UU+ = I"""
        is_square = self.m.shape[0] == self.m.shape[1]
        UU_ = np.dot(self._conjugate_transpose(), self.m)
        I = np.eye(self.m.shape[0])
        return is_square and np.isclose(UU_, I).all()


class UnitaryOperator(Operator, UnitaryMatrix):
    def __init__(self, m: ListOrNdarray, name: str = '', *args, **kwargs):
        """UnitaryOperator inherits from both Operator and a Unitary matrix
        It is used to act on a State vector by defining the operator to be the dot product"""
        UnitaryMatrix.__init__(self, m=m, name=name, *args, **kwargs)
        Operator.__init__(self, func=lambda other: State(np.dot(self.m, other.m)), *args, **kwargs)


def test():
    _0 = State([[1], [0]], name='0')
    _1 = State([[0], [1]], name='1')
    _p = State([[1 / np.sqrt(2)], [1 / np.sqrt(2)]], name='+')
    m = State([[1 / np.sqrt(2)], [-1 / np.sqrt(2)]], name='-')

    # Test properties of Hilbert vector space
    # The four postulates of Quantum Mechanics
    # I: States | Associated to any physical system is a complex vector space
    #             known as the state space of the system. If the system is closed
    #             then the system is described completely by its state vector
    #             which is a unit vector in the space.
    # Mathematically, this vector space is also a function space
    assert _0 + _1 == _1 + _0  # commutativity of vector addition
    assert _0 + (_1 + _p) == (_0 + _1) + _p  # associativity of vector addition
    assert 8 * (_0 + _1) == 8 * _0 + 8 * _1  # Linear when multiplying by constants
    assert _0 | _0 == 1  # parallel have 1 product
    assert _0 | _1 == 0  # orthogonal have 0 product
    assert _0.is_orthogonal(_1)
    assert _1 | (8 * _0) == 8 * (_1 | _0)  # Inner product is linear multiplied by constants
    assert _p | (_1 + _0) == (_p | _1) + (_p | _0)  # Inner product is linear in superpos of vectors

    assert np.isclose(_1.length(), 1.0)  # all of the vector lengths are normalized
    assert np.isclose(_0.length(), 1.0)
    assert np.isclose(_p.length(), 1.0)

    assert _0 | _1 == (_1 | _0).complex_conjugate()  # non-commutative inner product

    # II: Dynamics | The evolution of a closed system is described by a unitary transformation
    #
    # Operators turn one vector into another
    # Pauli X gate flips the |0> to |1> and the |1> to |0>

    # the times 2 operator should return the times two multiplication
    _times_2 = Operator(lambda x: 2 * x)
    assert _times_2.on(5) == 10
    assert _times_2(5) == 10

    X = UnitaryOperator([[0, 1],
                         [1, 0]])
    assert X | _1 == _0
    assert X | _0 == _1

    # Test the Y Pauli operator with complex number literal notation
    Y = UnitaryOperator([[0, -1j],
                         [1j, 0], ])

    assert Y | _0 == State([[0],
                            [1j]])
    assert Y | _1 == State([[-1j],
                            [0]])

    # III: Measurement | A quantum measurement is described by an orthonormal basis |e_j>
    #                    for state space. If the initial state of the system is |psi>
    #                    then we get outcome j with probability pr(j) = |<e_j|psi>|^2

    assert _0.measure(0) == 1  # Probability for |0> in 0 is 1
    assert _0.measure(1) == 0  # Probability for |0> in 1 is 0

    assert _1.measure(0) == 0  # Probability for |1> in 0 is 0
    assert _1.measure(1) == 1  # Probability for |1> in 1 is 1

    assert np.isclose(_p.measure(0), 0.5)  # Probability for |+> in 0 is 0.5
    assert np.isclose(_p.measure(1), 0.5)  # Probability for |+> in 1 is 0.5

    # IV: Compositing | tensor/kronecker product when composing
    assert _0 * _0 == State([[1], [0], [0], [0]])
    assert _0 * _1 == State([[0], [1], [0], [0]])
    assert _1 * _0 == State([[0], [0], [1], [0]])
    assert _1 * _1 == State([[0], [0], [0], [1]])

    # CNOT applies a control qubit on a target.
    # If the control is a |0>, target remains unchanged.
    # If the control is a |1>, target is flipped.
    CNOT = UnitaryOperator([[1, 0, 0, 0],
                            [0, 1, 0, 0],
                            [0, 0, 0, 1],
                            [0, 0, 1, 0], ])
    assert CNOT.on(_0 * _0) == _0 * _0
    assert CNOT.on(_0 * _1) == _0 * _1
    assert CNOT.on(_1 * _0) == _1 * _1
    assert CNOT.on(_1 * _1) == _1 * _0

    # ALL FOUR NOW - Create a Bell state (I) that has H|0> (II), measures (III) and composition in CNOT (IV)
    # Bell state
    # First - create a superposition
    H = UnitaryOperator([[1 / np.sqrt(2), 1 / np.sqrt(2)],
                         [1 / np.sqrt(2), -1 / np.sqrt(2)], ])
    superpos = H | _0
    assert superpos == _p

    # Then CNOT the superposition with a |0> qubit
    bell = CNOT | (superpos * _0)
    assert bell == State([[1 / np.sqrt(2)],
                          [0.],
                          [0.],
                          [1 / np.sqrt(2)], ])

    assert np.isclose(bell.measure(0b00), 0.5)  # Probability for bell in 00 is 0.5
    assert np.isclose(bell.measure(0b01), 0)  # Probability for bell in 01 is 0.
    assert np.isclose(bell.measure(0b10), 0)  # Probability for bell in 10 is 0.
    assert np.isclose(bell.measure(0b11), 0.5)  # Probability for bell in 11 is 0.5


def naive_load_test(N):
    import os
    import psutil
    import gc
    from time import time
    from sys import getsizeof

    print("{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
        "qbits",
        "kron_len",
        "mem_used",
        "mem_per_q",
        "getsizeof",
        "getsiz/len",
        "nbytes",
        "nbytes/len",
        "time"))

    _0 = State([[1], [0]], name='0')

    process = psutil.Process(os.getpid())
    mem_init = process.memory_info().rss
    for i in range(2, N + 1):
        start = time()
        m = _0
        for _ in range(i):
            m = m * _0
        len_m = len(m)
        elapsed = time() - start
        mem_b = process.memory_info().rss - mem_init
        print("{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
            i,
            len(m),
            sizeof_fmt(mem_b),
            sizeof_fmt(mem_b / len_m),
            sizeof_fmt(getsizeof(m)),
            sizeof_fmt(getsizeof(m) / len_m),
            sizeof_fmt(m.m.nbytes),
            sizeof_fmt(m.m.nbytes / len_m),
            np.round(elapsed, 2)))

        gc.collect()


if __name__ == "__main__":
    naive_load_test(23)