class Update:
    """
    Sparse object that holds an update of parameters.
    """

    def __init__(self, positions=None, values=None):
        """
        positions: array of int
        values: array of float
        """
        if positions is None and values is None:
            self._positions = list([])
            self._values = list([])
        else:
            self._positions = list(positions)
            self._values = list(values)

    def assign_mul(self, coeff):
        """
        self = self * coeff
        coeff: float
        """
        self._values = [item * coeff for item in self._values]

    def assign_madd(self, update, coeff):
        """
        self = self + update * coeff
        coeff: float
        """
        for position, v in zip(update._positions, update._values):
            if position in self._positions:
                v_index = self._positions.index(position)
                self._values[v_index] += self._values[v_index] * coeff
            else:
                self._positions.append(position)
                self._values.append(v)