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# Source code for astropy.units.quantity

    # -*- coding: utf-8 -*-
    # Licensed under a 3-clause BSD style license - see LICENSE.rst
    """
    This module defines the `Quantity` object, which represents a number with some
    associated units. `Quantity` objects support operations like ordinary numbers,
    but will deal with unit conversions internally.
    """

    from __future__ import (absolute_import, unicode_literals, division,
                            print_function)

    # Standard library
    import numbers

    import numpy as np

    # AstroPy
    from ..extern import six
    from .core import (Unit, dimensionless_unscaled, UnitBase, UnitsError,
                       get_current_unit_registry)
    from .format.latex import Latex
    from ..utils.compat import NUMPY_LT_1_7, NUMPY_LT_1_8, NUMPY_LT_1_9
    from ..utils.compat.fractions import Fraction
    from ..utils.compat.misc import override__dir__
    from ..utils.misc import isiterable, InheritDocstrings
    from ..utils.data_info import ParentDtypeInfo
    from .utils import validate_power
    from .. import config as _config

    __all__ = ["Quantity"]

    # We don't want to run doctests in the docstrings we inherit from Numpy
    __doctest_skip__ = ['Quantity.*']

    _UNIT_NOT_INITIALISED = "(Unit not initialised)"

    class Conf(_config.ConfigNamespace):
        """
        Configuration parameters for Quantity
        """
        latex_array_threshold = _config.ConfigItem(100,
            'The maximum size an array Quantity can be before its LaTeX '
            'representation for IPython gets "summarized" (meaning only the first '
            'and last few elements are shown with "..." between). Setting this to a '
            'negative number means that the value will instead be whatever numpy '
            'gets from get_printoptions.')
    conf = Conf()

    def _can_have_arbitrary_unit(value):
        """Test whether the items in value can have arbitrary units

        Numbers whose value does not change upon a unit change, i.e.,
        zero, infinity, or not-a-number

        Parameters
        ----------
        value : number or array

        Returns
        -------
        `True` if each member is either zero or not finite, `False` otherwise
        """
        return np.all(np.logical_or(np.equal(value, 0.), ~np.isfinite(value)))

    class QuantityIterator(object):
        """
        Flat iterator object to iterate over Quantities

        A `QuantityIterator` iterator is returned by ``q.flat`` for any Quantity
        ``q``.  It allows iterating over the array as if it were a 1-D array,
        either in a for-loop or by calling its `next` method.

        Iteration is done in C-contiguous style, with the last index varying the
        fastest. The iterator can also be indexed using basic slicing or
        advanced indexing.

        See Also
        --------
        Quantity.flatten : Returns a flattened copy of an array.

        Notes
        -----
        `QuantityIterator` is inspired by `~numpy.ma.core.MaskedIterator`.  It
        is not exported by the `~astropy.units` module.  Instead of
        instantiating a `QuantityIterator` directly, use `Quantity.flat`.
        """
        def __init__(self, q):
            self._quantity = q
            self._dataiter = q.view(np.ndarray).flat

        def __iter__(self):
            return self

        def __getitem__(self, indx):
            out = self._dataiter.__getitem__(indx)
            # For single elements, ndarray.flat.__getitem__ returns scalars; these
            # need a new view as a Quantity.
            if isinstance(out, type(self._quantity)):
                return out
            else:
                return self._quantity._new_view(out)

        def __setitem__(self, index, value):
            self._dataiter[index] = self._quantity._to_own_unit(value)

        def __next__(self):
            """
            Return the next value, or raise StopIteration.
            """
            out = next(self._dataiter)
            # ndarray.flat._dataiter returns scalars, so need a view as a Quantity.
            return self._quantity._new_view(out)

        next = __next__

    class QuantityInfo(ParentDtypeInfo):
        """
        Container for meta information like name, description, format.  This is
        required when the object is used as a mixin column within a table, but can
        be used as a general way to store meta information.
        """
        attrs_from_parent = set(['dtype', 'unit'])  # dtype and unit taken from parent
        _supports_indexing = True

        @staticmethod
        def default_format(val):
            return '{0.value:}'.format(val)

    @six.add_metaclass(InheritDocstrings)
    class Quantity(np.ndarray):
        """ A `~astropy.units.Quantity` represents a number with some associated unit.

        Parameters
        ----------
        value : number, `~numpy.ndarray`, `Quantity` object, or sequence of `Quantity` objects.
            The numerical value of this quantity in the units given by unit.  If a
            `Quantity` or sequence of them (or any other valid object with a
            ``unit`` attribute), creates a new `Quantity` object, converting to
            `unit` units as needed.

        unit : `~astropy.units.UnitBase` instance, str
            An object that represents the unit associated with the input value.
            Must be an `~astropy.units.UnitBase` object or a string parseable by
            the :mod:`~astropy.units` package.

        dtype : ~numpy.dtype, optional
            The dtype of the resulting Numpy array or scalar that will
            hold the value.  If not provided, it is determined from the input,
            except that any input that cannot represent float (integer and bool)
            is converted to float.

        copy : bool, optional
            If `True` (default), then the value is copied.  Otherwise, a copy will
            only be made if ``__array__`` returns a copy, if value is a nested
            sequence, or if a copy is needed to satisfy an explicitly given
            ``dtype``.  (The `False` option is intended mostly for internal use,
            to speed up initialization where a copy is known to have been made.
            Use with care.)

        order : {'C', 'F', 'A'}, optional
            Specify the order of the array.  As in `~numpy.array`.  This parameter
            is ignored if the input is a `Quantity` and ``copy=False``.

        subok : bool, optional
            If `False` (default), the returned array will be forced to be a
            `Quantity`.  Otherwise, `Quantity` subclasses will be passed through.

        ndmin : int, optional
            Specifies the minimum number of dimensions that the resulting array
            should have.  Ones will be pre-pended to the shape as needed to meet
            this requirement.  This parameter is ignored if the input is a
            `Quantity` and ``copy=False``.

        Raises
        ------
        TypeError
            If the value provided is not a Python numeric type.
        TypeError
            If the unit provided is not either a :class:`~astropy.units.Unit`
            object or a parseable string unit.
        """
        # Need to set a class-level default for _equivalencies, or
        # Constants can not initialize properly
        _equivalencies = []

        __array_priority__ = 10000

        def __new__(cls, value, unit=None, dtype=None, copy=True, order=None,
                    subok=False, ndmin=0):

            if unit is not None:
                # convert unit first, to avoid multiple string->unit conversions
                unit = Unit(unit)

            # optimize speed for Quantity with no dtype given, copy=False
            if isinstance(value, Quantity):
                if unit is not None and unit is not value.unit:
                    value = value.to(unit)
                    # the above already makes a copy (with float dtype)
                    copy = False

                if type(value) is not cls and not (subok and
                                                   isinstance(value, cls)):
                    value = value.view(cls)

                if dtype is None:
                    if not copy:
                        return value

                    if not np.can_cast(np.float32, value.dtype):
                        dtype = np.float

                return np.array(value, dtype=dtype, copy=copy, order=order,
                                subok=True, ndmin=ndmin)

            # Maybe list/tuple of Quantity? short-circuit array for speed
            if (not isinstance(value, np.ndarray) and isiterable(value) and
                all(isinstance(v, Quantity) for v in value)):
                # Convert all quantities to the same unit.
                if unit is None:
                    unit = value[0].unit
                value = [q.to(unit).value for q in value]
                value_unit = unit  # signal below that conversion has been done
                copy = False  # copy already made

            else:
                # If the value has a `unit` attribute and if not None
                # (for Columns with uninitialized unit), treat it like a quantity.
                value_unit = getattr(value, 'unit', None)
                if value_unit is None:
                    # Default to dimensionless for no (initialized) unit attribute.
                    if unit is None:
                        unit = dimensionless_unscaled
                    value_unit = unit  # signal below that no conversion is needed
                else:
                    try:
                        value_unit = Unit(value_unit)
                    except Exception as exc:
                        raise TypeError("The unit attribute {0} of the input could "
                                        "not be parsed as an astropy Unit, raising "
                                        "the following exception:\n{1}"
                                        .format(repr(value.unit), exc))

                    if unit is None:
                        unit = value_unit
                    elif unit is not value_unit:
                        copy = False  # copy will be made in conversion at end

            value = np.array(value, dtype=dtype, copy=copy, order=order,
                             subok=False, ndmin=ndmin)

            # check that array contains numbers or long int objects
            if (value.dtype.kind in 'OSU' and
                not (value.dtype.kind == 'O' and
                     isinstance(value.item(() if value.ndim == 0 else 0),
                                numbers.Number))):
                raise TypeError("The value must be a valid Python or "
                                "Numpy numeric type.")

            # by default, cast any integer, boolean, etc., to float
            if dtype is None and (not np.can_cast(np.float32, value.dtype)
                                  or value.dtype.kind == 'O'):
                value = value.astype(np.float)

            value = value.view(cls)
            value._unit = value_unit
            if unit is value_unit:
                return value
            else:
                # here we had non-Quantity input that had a "unit" attribute
                # with a unit different from the desired one.  So, convert.
                return value.to(unit)

        def __array_finalize__(self, obj):
            self._unit = getattr(obj, '_unit', None)

            # Copy info if the original had `info` defined.  Because of the way the
            # DataInfo works, `'info' in obj.__dict__` is False until the
            # `info` attribute is accessed or set.  Note that `obj` can be an
            # ndarray which doesn't have a `__dict__`.
            if 'info' in getattr(obj, '__dict__', ()):
                self.info = obj.info

        def __array_prepare__(self, obj, context=None):
            # This method gets called by Numpy whenever a ufunc is called on the
            # array. The object passed in ``obj`` is an empty version of the
            # output array which we can e.g. change to an array sub-class, add
            # attributes to, etc. After this is called, then the ufunc is called
            # and the values in this empty array are set.

            # If no context is set, just return the input
            if context is None:
                return obj

            # Find out which ufunc is being used
            function = context[0]

            from .quantity_helper import UNSUPPORTED_UFUNCS, UFUNC_HELPERS

            # Check whether we even support this ufunc
            if function in UNSUPPORTED_UFUNCS:
                raise TypeError("Cannot use function '{0}' with quantities"
                                .format(function.__name__))

            # Now find out what arguments were passed to the ufunc, usually, this
            # will include at least the present object, and another, which could
            # be a Quantity, or a Numpy array, etc. when using two-argument ufuncs.
            args = context[1][:function.nin]
            units = [getattr(arg, 'unit', None) for arg in args]

            # If the ufunc is supported, then we call a helper function (defined
            # in quantity_helper.py) which returns the scale by which the inputs
            # should be multiplied before being passed to the ufunc, as well as
            # the unit the output from the ufunc will have.
            if function in UFUNC_HELPERS:
                converters, result_unit = UFUNC_HELPERS[function](function, *units)
            else:
                raise TypeError("Unknown ufunc {0}.  Please raise issue on "
                                "https://github.com/astropy/astropy"
                                .format(function.__name__))

            if any(converter is False for converter in converters):
                # for two-argument ufuncs with a quantity and a non-quantity,
                # the quantity normally needs to be dimensionless, *except*
                # if the non-quantity can have arbitrary unit, i.e., when it
                # is all zero, infinity or NaN.  In that case, the non-quantity
                # can just have the unit of the quantity
                # (this allows, e.g., `q > 0.` independent of unit)
                maybe_arbitrary_arg = args[converters.index(False)]
                try:
                    if _can_have_arbitrary_unit(maybe_arbitrary_arg):
                        converters = [None, None]
                    else:
                        raise UnitsError("Can only apply '{0}' function to "
                                         "dimensionless quantities when other "
                                         "argument is not a quantity (unless the "
                                         "latter is all zero/infinity/nan)"
                                         .format(function.__name__))
                except TypeError:
                    # _can_have_arbitrary_unit failed: arg could not be compared
                    # with zero or checked to be finite.  Then, ufunc will fail too.
                    raise TypeError("Unsupported operand type(s) for ufunc {0}: "
                                    "'{1}' and '{2}'"
                                    .format(function.__name__,
                                            args[0].__class__.__name__,
                                            args[1].__class__.__name__))

            # In the case of np.power, the unit itself needs to be modified by an
            # amount that depends on one of the input values, so we need to treat
            # this as a special case.
            # TODO: find a better way to deal with this case
            if function is np.power and result_unit is not dimensionless_unscaled:

                if units[1] is None:
                    p = args[1]
                else:
                    p = args[1].to(dimensionless_unscaled).value

                result_unit = result_unit ** validate_power(p)

            # We now prepare the output object

            if self is obj:

                # this happens if the output object is self, which happens
                # for in-place operations such as q1 += q2

                # In some cases, the result of a ufunc should be a plain Numpy
                # array, which we can't do if we are doing an in-place operation.
                if result_unit is None:
                    raise TypeError("Cannot store non-quantity output from {0} "
                                    "function in {1} instance"
                                    .format(function.__name__, type(self)))

                if self.__quantity_subclass__(result_unit)[0] is not type(self):
                    raise TypeError(
                        "Cannot store output with unit '{0}' from {1} function "
                        "in {2} instance.  Use {3} instance instead."
                        .format(result_unit, function.__name__, type(self),
                                self.__quantity_subclass__(result_unit)[0]))

                # If the Quantity has an integer dtype, in-place operations are
                # dangerous because in some cases the quantity will be e.g.
                # decomposed, which involves being scaled by a float, but since
                # the array is an integer the output then gets converted to an int
                # and truncated.
                result_dtype = np.result_type(*((args + (float,))
                                                if any(converters) else args))
                if not np.can_cast(result_dtype, obj.dtype, casting='same_kind'):
                    raise TypeError("Arguments cannot be cast safely to inplace "
                                    "output with dtype={0}".format(self.dtype))

                result = self  # no view needed since we return the object itself

                # in principle, if self is also an argument, it could be rescaled
                # here, since it won't be needed anymore.  But maybe not change
                # inputs before the calculation even if they will get destroyed

            else:  # normal case: set up output as a Quantity

                result = self._new_view(obj, result_unit)

            # We now need to treat the case where the inputs have to be scaled -
            # the issue is that we can't actually scale the inputs since that
            # would be changing the objects passed to the ufunc, which would not
            # be expected by the user.
            if any(converters):

                # If self is both output and input (which happens for in-place
                # operations), input will get overwritten with junk. To avoid
                # that, hide it in a new object
                if self is obj and any(self is arg for arg in args):
                    # but with two outputs it would become unhidden too soon
                    # [ie., np.modf(q1, q1, other)].  Bail.
                    if context[2] < function.nout - 1:
                        raise TypeError("Cannot apply multi-output {0} function "
                                        "to quantities with in-place replacement "
                                        "of an input by any but the last output."
                                        .format(function.__name__))

                    # If self is already contiguous, we don't need to do
                    # an additional copy back into the original array, so
                    # we store it in `result._result`.  Otherwise, we
                    # store it in `result._contiguous`.  `__array_wrap__`
                    # knows how to handle putting either form back into
                    # the original array.
                    if self.flags['C_CONTIGUOUS']:
                        result = self.copy()
                        result._result = self
                    else:
                        result._contiguous = self.copy()

                # ensure we remember the scales we need
                result._converters = converters

            # unit output will get (setting _unit could prematurely change input
            # if obj is self, which happens for in-place operations; see above)
            result._result_unit = result_unit
            return result

        def __array_wrap__(self, obj, context=None):
            if context is None:
                # Methods like .squeeze() created a new `ndarray` and then call
                # __array_wrap__ to turn the array into self's subclass.
                return self._new_view(obj)

            else:
                # with context defined, we are continuing after a ufunc evaluation.
                if hasattr(obj, '_result_unit'):
                    result_unit = obj._result_unit
                    del obj._result_unit
                else:
                    result_unit = None

                # We now need to re-calculate quantities for which the input
                # needed to be scaled.
                if hasattr(obj, '_converters'):

                    converters = obj._converters
                    del obj._converters

                    # For in-place operations, input will get overwritten with
                    # junk. To avoid that, we hid it in a new object in
                    # __array_prepare__ and retrieve it here.
                    if hasattr(obj, '_result'):
                        obj = obj._result
                    elif hasattr(obj, '_contiguous'):
                        obj[()] = obj._contiguous
                        del obj._contiguous

                    # take array view to which output can be written without
                    # getting back here
                    obj_array = obj.view(np.ndarray)

                    # Find out which ufunc was called and with which inputs
                    function = context[0]
                    args = context[1][:function.nin]

                    # Set the inputs, rescaling as necessary
                    inputs = []
                    for arg, converter in zip(args, converters):
                        if converter:
                            inputs.append(converter(arg.value))
                        else:  # with no conversion, input can be non-Quantity.
                            inputs.append(getattr(arg, 'value', arg))

                    # For output arrays that require scaling, we can reuse the
                    # output array to perform the scaling in place, as long as the
                    # array is not integral. Here, we set the obj_array to `None`
                    # when it can not be used to store the scaled result.
                    if not (result_unit is None or
                            np.can_cast(np.result_type(*inputs), obj_array.dtype)):
                        obj_array = None

                    # Re-compute the output using the ufunc
                    if function.nin == 1:
                        if function.nout == 1:
                            out = function(inputs[0], obj_array)
                        else:  # 2-output function (np.modf, np.frexp); 1 input
                            if context[2] == 0:
                                out, _ = function(inputs[0], obj_array, None)
                            else:
                                _, out = function(inputs[0], None, obj_array)
                    else:
                        out = function(inputs[0], inputs[1], obj_array)

                    if obj_array is None:
                        obj = self._new_view(out, result_unit)

                if result_unit is None:  # return a plain array
                    obj = obj.view(np.ndarray)
                else:
                    obj._unit = result_unit

            return obj

        def __deepcopy__(self, memo):
            # If we don't define this, ``copy.deepcopy(quantity)`` will
            # return a bare Numpy array.
            return self.copy()

        def __quantity_subclass__(self, unit):
            """
            Overridden by subclasses to change what kind of view is
            created based on the output unit of an operation.

            Parameters
            ----------
            unit : UnitBase
                The unit for which the appropriate class should be returned

            Returns
            -------
            tuple :
                - `Quantity` subclass
                - bool: True is subclasses of the given class are ok
            """
            return Quantity, True

        def _new_view(self, obj, unit=None):
            """
            Create a Quantity view of obj, and set the unit

            By default, return a view of ``obj`` of the same class as ``self``
            and with the unit passed on, or that of ``self``.  Subclasses can
            override the type of class used with ``__quantity_subclass__``, and
            can ensure other properties of ``self`` are copied using
            `__array_finalize__`.

            Parameters
            ----------
            obj : ndarray or scalar
                The array to create a view of.  If obj is a numpy or python scalar,
                it will be converted to an array scalar.

            unit : `UnitBase`, or anything convertible to a :class:`~astropy.units.Unit`, or `None`
                The unit of the resulting object.  It is used to select a
                subclass, and explicitly assigned to the view if not `None`.
                If `None` (default), the unit is set by `__array_finalize__`
                to self._unit.

            Returns
            -------
            view : Quantity subclass
            """
            # python and numpy scalars cannot be viewed as arrays and thus not as
            # Quantity either; turn them into zero-dimensional arrays
            # (These are turned back into scalar in `.value`)
            if not isinstance(obj, np.ndarray):
                obj = np.array(obj)

            if unit is None:
                subclass = self.__class__
            else:
                unit = Unit(unit)
                subclass, subok = self.__quantity_subclass__(unit)
                if subok:
                    subclass = self.__class__

            view = obj.view(subclass)
            view.__array_finalize__(self)
            if unit is not None:
                view._unit = unit
            return view

        def __reduce__(self):
            # patch to pickle Quantity objects (ndarray subclasses), see
            # http://www.mail-archive.com/numpy-discussion@scipy.org/msg02446.html

            object_state = list(super(Quantity, self).__reduce__())
            object_state[2] = (object_state[2], self.__dict__)
            return tuple(object_state)

        def __setstate__(self, state):
            # patch to unpickle Quantity objects (ndarray subclasses), see
            # http://www.mail-archive.com/numpy-discussion@scipy.org/msg02446.html

            nd_state, own_state = state
            super(Quantity, self).__setstate__(nd_state)
            self.__dict__.update(own_state)

        def to(self, unit, equivalencies=[]):
            """
            Returns a new `~astropy.units.Quantity` object with the specified
            units.

            Parameters
            ----------
            unit : `~astropy.units.UnitBase` instance, str
                An object that represents the unit to convert to. Must be
                an `~astropy.units.UnitBase` object or a string parseable
                by the `~astropy.units` package.

            equivalencies : list of equivalence pairs, optional
                A list of equivalence pairs to try if the units are not
                directly convertible.  See :ref:`unit_equivalencies`.
                If not provided or ``[]``, class default equivalencies will be used
                (none for `~astropy.units.Quantity`, but may be set for subclasses)
                If `None`, no equivalencies will be applied at all, not even any
                set globally or within a context.
            """
            if equivalencies == []:
                equivalencies = self._equivalencies
            unit = Unit(unit)
            new_val = self.unit.to(unit, self.view(np.ndarray),
                                   equivalencies=equivalencies)
            return self._new_view(new_val, unit)

        info = QuantityInfo()

        @property
        def value(self):
            """ The numerical value of this quantity. """
            value = self.view(np.ndarray)
            if self.shape:
                return value
            else:
                return value.item()

        @property
        def unit(self):
            """
            A `~astropy.units.UnitBase` object representing the unit of this
            quantity.
            """

            return self._unit

        # this ensures that if we do a view, __repr__ and __str__ do not balk
        _unit = None

        @property
        def equivalencies(self):
            """
            A list of equivalencies that will be applied by default during
            unit conversions.
            """

            return self._equivalencies

        @property
        def si(self):
            """
            Returns a copy of the current `Quantity` instance with SI units. The
            value of the resulting object will be scaled.
            """
            si_unit = self.unit.si
            return self._new_view(self.value * si_unit.scale,
                                  si_unit / si_unit.scale)

        @property
        def cgs(self):
            """
            Returns a copy of the current `Quantity` instance with CGS units. The
            value of the resulting object will be scaled.
            """
            cgs_unit = self.unit.cgs
            return self._new_view(self.value * cgs_unit.scale,
                                  cgs_unit / cgs_unit.scale)

        @property
        def isscalar(self):
            """
            True if the `value` of this quantity is a scalar, or False if it
            is an array-like object.

            .. note::
                This is subtly different from `numpy.isscalar` in that
                `numpy.isscalar` returns False for a zero-dimensional array
                (e.g. ``np.array(1)``), while this is True for quantities,
                since quantities cannot represent true numpy scalars.
            """
            return not self.shape

        # This flag controls whether convenience conversion members, such
        # as `q.m` equivalent to `q.to(u.m).value` are available.  This is
        # not turned on on Quantity itself, but is on some subclasses of
        # Quantity, such as `astropy.coordinates.Angle`.
        _include_easy_conversion_members = False

        @override__dir__
        def __dir__(self):
            """
            Quantities are able to directly convert to other units that
            have the same physical type.  This function is implemented in
            order to make autocompletion still work correctly in IPython.
            """
            if not self._include_easy_conversion_members:
                return []
            extra_members = set()
            equivalencies = Unit._normalize_equivalencies(self.equivalencies)
            for equivalent in self.unit._get_units_with_same_physical_type(
                    equivalencies):
                extra_members.update(equivalent.names)
            return extra_members

        def __getattr__(self, attr):
            """
            Quantities are able to directly convert to other units that
            have the same physical type.
            """
            if not self._include_easy_conversion_members:
                raise AttributeError(
                    "'{0}' object has no '{1}' member".format(
                        self.__class__.__name__,
                        attr))

            def get_virtual_unit_attribute():
                registry = get_current_unit_registry().registry
                to_unit = registry.get(attr, None)
                if to_unit is None:
                    return None

                try:
                    return self.unit.to(
                        to_unit, self.value, equivalencies=self.equivalencies)
                except UnitsError:
                    return None

            value = get_virtual_unit_attribute()

            if value is None:
                raise AttributeError(
                    "{0} instance has no attribute '{1}'".format(
                        self.__class__.__name__, attr))
            else:
                return value

        if not NUMPY_LT_1_9:
            # Equality (return False if units do not match) needs to be handled
            # explicitly for numpy >=1.9, since it no longer traps errors.
            def __eq__(self, other):
                try:
                    try:
                        return super(Quantity, self).__eq__(other)
                    except DeprecationWarning:
                        # We treat the DeprecationWarning separately, since it may
                        # mask another Exception.  But we do not want to just use
                        # np.equal, since super's __eq__ treats recarrays correctly.
                        return np.equal(self, other)
                except UnitsError:
                    return False
                except TypeError:
                    return NotImplemented

            def __ne__(self, other):
                try:
                    try:
                        return super(Quantity, self).__ne__(other)
                    except DeprecationWarning:
                        return np.not_equal(self, other)
                except UnitsError:
                    return True
                except TypeError:
                    return NotImplemented

        # Arithmetic operations
        def __mul__(self, other):
            """ Multiplication between `Quantity` objects and other objects."""

            if isinstance(other, (UnitBase, six.string_types)):
                try:
                    return self._new_view(self.copy(), other * self.unit)
                except UnitsError:  # let other try to deal with it
                    return NotImplemented

            return super(Quantity, self).__mul__(other)

        def __imul__(self, other):
            """In-place multiplication between `Quantity` objects and others."""

            if isinstance(other, (UnitBase, six.string_types)):
                self._unit = other * self.unit
                return self

            return super(Quantity, self).__imul__(other)

        def __rmul__(self, other):
            """ Right Multiplication between `Quantity` objects and other
            objects.
            """

            return self.__mul__(other)

        def __truediv__(self, other):
            """ Division between `Quantity` objects and other objects."""

            if isinstance(other, (UnitBase, six.string_types)):
                try:
                    return self._new_view(self.copy(), self.unit / other)
                except UnitsError:  # let other try to deal with it
                    return NotImplemented

            return super(Quantity, self).__truediv__(other)

        def __itruediv__(self, other):
            """Inplace division between `Quantity` objects and other objects."""

            if isinstance(other, (UnitBase, six.string_types)):
                self._unit = self.unit / other
                return self

            return super(Quantity, self).__itruediv__(other)

        def __rtruediv__(self, other):
            """ Right Division between `Quantity` objects and other objects."""

            if isinstance(other, (UnitBase, six.string_types)):
                return self._new_view(1. / self.value, other / self.unit)

            return super(Quantity, self).__rtruediv__(other)

        def __div__(self, other):
            """ Division between `Quantity` objects. """
            return self.__truediv__(other)

        def __idiv__(self, other):
            """ Division between `Quantity` objects. """
            return self.__itruediv__(other)

        def __rdiv__(self, other):
            """ Division between `Quantity` objects. """
            return self.__rtruediv__(other)

        def __divmod__(self, other):
            other_value = self._to_own_unit(other)
            result_tuple = divmod(self.value, other_value)

            return (self._new_view(result_tuple[0], dimensionless_unscaled),
                    self._new_view(result_tuple[1]))

        def __pow__(self, other):
            if isinstance(other, Fraction):
                # Avoid getting object arrays by raising the value to a Fraction.
                return self._new_view(self.value ** float(other),
                                      self.unit ** other)

            return super(Quantity, self).__pow__(other)

        def __pos__(self):
            """
            Plus the quantity. This is implemented in case users use +q where q is
            a quantity.  (Required for scalar case.)
            """
            return self.copy()

        # other overrides of special functions
        def __hash__(self):
            return hash(self.value) ^ hash(self.unit)

        def __iter__(self):
            if self.isscalar:
                raise TypeError(
                    "'{cls}' object with a scalar value is not iterable"
                    .format(cls=self.__class__.__name__))

            # Otherwise return a generator
            def quantity_iter():
                for val in self.value:
                    yield self._new_view(val)

            return quantity_iter()

        def __getitem__(self, key):
            try:
                out = super(Quantity, self).__getitem__(key)
            except IndexError:
                # We want zero-dimensional Quantity objects to behave like scalars,
                # so they should raise a TypeError rather than an IndexError.
                if self.isscalar:
                    raise TypeError(
                        "'{cls}' object with a scalar value does not support "
                        "indexing".format(cls=self.__class__.__name__))
                else:
                    raise
            # For single elements, ndarray.__getitem__ returns scalars; these
            # need a new view as a Quantity.
            if type(out) is not type(self):
                out = self._new_view(out)
            return out

        def __setitem__(self, i, value):
            # update indices
            if not self.isscalar:
                self.info.adjust_indices(i, value, len(self))
            self.view(np.ndarray).__setitem__(i, self._to_own_unit(value))

        def __setslice__(self, i, j, value):
            # update indices
            if not self.isscalar:
                self.info.adjust_indices(slice(i, j), value, len(self))
            self.view(np.ndarray).__setslice__(i, j, self._to_own_unit(value))

        # __contains__ is OK

        def __nonzero__(self):
            """Quantities should always be treated as non-False; there is too much
            potential for ambiguity otherwise.
            """
            return True
        if six.PY3:
            __bool__ = __nonzero__

        def __len__(self):
            if self.isscalar:
                raise TypeError("'{cls}' object with a scalar value has no "
                                "len()".format(cls=self.__class__.__name__))
            else:
                return len(self.value)

        # Numerical types
        def __float__(self):
            try:
                return float(self.to(dimensionless_unscaled).value)
            except (UnitsError, TypeError):
                raise TypeError('Only dimensionless scalar quantities can be '
                                'converted to Python scalars')

        def __int__(self):
            try:
                return int(self.to(dimensionless_unscaled).value)
            except (UnitsError, TypeError):
                raise TypeError('Only dimensionless scalar quantities can be '
                                'converted to Python scalars')

        def __index__(self):
            # for indices, we do not want to mess around with scaling at all,
            # so unlike for float, int, we insist here on unscaled dimensionless
            try:
                assert self.unit.is_unity()
                return self.value.__index__()
            except:
                raise TypeError('Only integer dimensionless scalar quantities '
                                'can be converted to a Python index')

        if six.PY2:
            def __long__(self):
                try:
                    return long(self.to(dimensionless_unscaled).value)
                except (UnitsError, TypeError):
                    raise TypeError('Only dimensionless scalar quantities can be '
                                    'converted to Python scalars')

        @property
        def _unitstr(self):
            if self.unit is None:
                unitstr = _UNIT_NOT_INITIALISED
            else:
                unitstr = str(self.unit)

            if unitstr:
                unitstr = ' ' + unitstr

            return unitstr

        # Display
        # TODO: we may want to add a hook for dimensionless quantities?
        def __str__(self):
            return '{0}{1:s}'.format(self.value, self._unitstr)

        def __repr__(self):
            prefixstr = '<' + self.__class__.__name__ + ' '
            arrstr = np.array2string(self.view(np.ndarray), separator=',',
                                     prefix=prefixstr)
            return '{0}{1}{2:s}>'.format(prefixstr, arrstr, self._unitstr)

        def _repr_latex_(self):
            """
            Generate a latex representation of the quantity and its unit.

            The behavior of this function can be altered via the
            `numpy.set_printoptions` function and its various keywords.  The
            exception to this is the ``threshold`` keyword, which is controlled via
            the ``[units.quantity]`` configuration item ``latex_array_threshold``.
            This is treated separately because the numpy default of 1000 is too big
            for most browsers to handle.

            Returns
            -------
            lstr
                A LaTeX string with the contents of this Quantity
            """
            if NUMPY_LT_1_7:
                if self.isscalar:
                    latex_value = Latex.format_exponential_notation(self.value)
                else:
                    raise NotImplementedError('Cannot represent Quantity arrays '
                                              'in LaTex format for numpy < v1.7.')
            else:
                # need to do try/finally because "threshold" cannot be overridden
                # with array2string
                pops = np.get_printoptions()
                try:
                    formatter = {'all' : Latex.format_exponential_notation,
                                 'str_kind': lambda x: x}
                    if conf.latex_array_threshold > -1:
                        np.set_printoptions(threshold=conf.latex_array_threshold,
                                            formatter=formatter)

                    # the view is needed for the scalar case - value might be float
                    latex_value = np.array2string(self.view(np.ndarray),
                                                  style=Latex.format_exponential_notation,
                                                  max_line_width=np.inf,
                                                  separator=',~')
                    latex_value = latex_value.replace('...', r'\dots')
                finally:
                    np.set_printoptions(**pops)

            # Format unit
            # [1:-1] strips the '$' on either side needed for math mode
            latex_unit = (self.unit._repr_latex_()[1:-1]  # note this is unicode
                          if self.unit is not None
                          else _UNIT_NOT_INITIALISED)

            return '${0} \; {1}$'.format(latex_value, latex_unit)

        def __format__(self, format_spec):
            """
            Format quantities using the new-style python formatting codes
            as specifiers for the number.

            If the format specifier correctly applies itself to the value,
            then it is used to format only the value. If it cannot be
            applied to the value, then it is applied to the whole string.

            """
            try:
                value = format(self.value, format_spec)
                full_format_spec = "s"
            except ValueError:
                value = self.value
                full_format_spec = format_spec

            return format("{0}{1:s}".format(value, self._unitstr),
                          full_format_spec)

        def decompose(self, bases=[]):
            """
            Generates a new `Quantity` with the units
            decomposed. Decomposed units have only irreducible units in
            them (see `astropy.units.UnitBase.decompose`).

            Parameters
            ----------
            bases : sequence of UnitBase, optional
                The bases to decompose into.  When not provided,
                decomposes down to any irreducible units.  When provided,
                the decomposed result will only contain the given units.
                This will raises a `~astropy.units.UnitsError` if it's not possible
                to do so.

            Returns
            -------
            newq : `~astropy.units.Quantity`
                A new object equal to this quantity with units decomposed.
            """
            return self._decompose(False, bases=bases)

        def _decompose(self, allowscaledunits=False, bases=[]):
            """
            Generates a new `Quantity` with the units decomposed. Decomposed
            units have only irreducible units in them (see
            `astropy.units.UnitBase.decompose`).

            Parameters
            ----------
            allowscaledunits : bool
                If True, the resulting `Quantity` may have a scale factor
                associated with it.  If False, any scaling in the unit will
                be subsumed into the value of the resulting `Quantity`

            bases : sequence of UnitBase, optional
                The bases to decompose into.  When not provided,
                decomposes down to any irreducible units.  When provided,
                the decomposed result will only contain the given units.
                This will raises a `~astropy.units.UnitsError` if it's not possible
                to do so.

            Returns
            -------
            newq : `~astropy.units.Quantity`
                A new object equal to this quantity with units decomposed.

            """

            new_unit = self.unit.decompose(bases=bases)

            # Be careful here because self.value usually is a view of self;
            # be sure that the original value is not being modified.
            if not allowscaledunits and hasattr(new_unit, 'scale'):
                new_value = self.value * new_unit.scale
                new_unit = new_unit / new_unit.scale
                return self._new_view(new_value, new_unit)
            else:
                return self._new_view(self.copy(), new_unit)

        # These functions need to be overridden to take into account the units
        # Array conversion
        # http://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html#array-conversion

        def item(self, *args):
            return self._new_view(super(Quantity, self).item(*args))

        def tolist(self):
            raise NotImplementedError("cannot make a list of Quantities.  Get "
                                      "list of values with q.value.list()")

        def _to_own_unit(self, value, check_precision=True):
            try:
                # for speed, "unit.to(...)" instead of "value.to(self.unit).value
                _value = value.unit.to(self.unit, value.value)
            except AttributeError:
                try:
                    _value = dimensionless_unscaled.to(self.unit, value)
                except UnitsError as exc:
                    if _can_have_arbitrary_unit(value):
                        _value = value
                    else:
                        raise exc

            if check_precision:
                value_dtype = getattr(value, 'dtype', None)
                if self.dtype != value_dtype:
                    self_dtype_array = np.array(_value, self.dtype)
                    value_dtype_array = np.array(_value, dtype=value_dtype,
                                                 copy=False)
                    if not np.all(np.logical_or(self_dtype_array ==
                                                value_dtype_array,
                                                np.isnan(value_dtype_array))):
                        raise TypeError("cannot convert value type to array type "
                                        "without precision loss")
            return _value

        def itemset(self, *args):
            if len(args) == 0:
                raise ValueError("itemset must have at least one argument")

            self.view(np.ndarray).itemset(*(args[:-1] +
                                            (self._to_own_unit(args[-1]),)))

        def tostring(self, order='C'):
            raise NotImplementedError("cannot write Quantities to string.  Write "
                                      "array with q.value.tostring(...).")

        def tofile(self, fid, sep="", format="%s"):
            raise NotImplementedError("cannot write Quantities to file.  Write "
                                      "array with q.value.tofile(...)")

        def dump(self, file):
            raise NotImplementedError("cannot dump Quantities to file.  Write "
                                      "array with q.value.dump()")

        def dumps(self):
            raise NotImplementedError("cannot dump Quantities to string.  Write "
                                      "array with q.value.dumps()")

        # astype, byteswap, copy, view, getfield, setflags OK as is

        def fill(self, value):
            self.view(np.ndarray).fill(self._to_own_unit(value))

        # Shape manipulation: resize cannot be done (does not own data), but
        # shape, transpose, swapaxes, flatten, ravel, squeeze all OK.  Only
        # the flat iterator needs to be overwritten, otherwise single items are
        # returned as numbers.
        @property
        def flat(self):
            """A 1-D iterator over the Quantity array.

            This returns a ``QuantityIterator`` instance, which behaves the same
            as the `~numpy.flatiter` instance returned by `~numpy.ndarray.flat`,
            and is similar to, but not a subclass of, Python's built-in iterator
            object.
            """
            return QuantityIterator(self)

        @flat.setter
        def flat(self, value):
            y = self.ravel()
            y[:] = value

        # Item selection and manipulation
        # take, repeat, sort, compress, diagonal OK
        def put(self, indices, values, mode='raise'):
            self.view(np.ndarray).put(indices, self._to_own_unit(values), mode)

        def choose(self, choices, out=None, mode='raise'):
            raise NotImplementedError("cannot choose based on quantity.  Choose "
                                      "using array with q.value.choose(...)")

        # ensure we do not return indices as quantities
        def argsort(self, axis=-1, kind='quicksort', order=None):
            return self.view(np.ndarray).argsort(axis=axis, kind=kind, order=order)

        def searchsorted(self, v, *args, **kwargs):
            return np.searchsorted(np.array(self),
                                   self._to_own_unit(v, check_precision=False),
                                   *args, **kwargs)  # avoid numpy 1.6 problem

        def argmax(self, axis=None, out=None):
            return self.view(np.ndarray).argmax(axis, out=out)

        def argmin(self, axis=None, out=None):
            return self.view(np.ndarray).argmin(axis, out=out)

        # Calculation -- override ndarray methods to take into account units.
        # We use the corresponding numpy functions to evaluate the results, since
        # the methods do not always allow calling with keyword arguments.
        # For instance, np.array([0.,2.]).clip(a_min=0., a_max=1.) gives
        # TypeError: 'a_max' is an invalid keyword argument for this function
        def _wrap_function(self, function, *args, **kwargs):
            """Wrap a numpy function, returning a Quantity with the proper unit

            Parameters
            ----------
            function : callable
                numpy function to wrap
            args : positional arguments
                any positional arguments to the function.
            kwargs : keyword arguments
                Keyword arguments to the function.

            If present, the following arguments are treated specially:

            unit : `~astropy.units.Unit` or `None`
                unit of the output result.  If not given or `None` (default),
                the unit of `self`.
            out : `~astropy.units.Quantity`
                A Quantity instance in which to store the output.

            Notes
            -----
            Output should always be assigned via a keyword argument.

            Returns
            -------
            out : `~astropy.units.Quantity`
                Result of the function call, with the unit set properly.
            """

            unit = kwargs.pop('unit', None)
            out = kwargs.get('out', None)
            if out is not None:
                if unit is None:
                    unit = self.unit

                if (isinstance(out, Quantity) and
                    out.__quantity_subclass__(unit)[0] is type(out)):
                    # Set out to ndarray view to prevent calling __array_prepare__.
                    kwargs['out'] = out.view(np.ndarray)

                else:
                    ok_class =  (out.__quantity_subclass__(out, unit)[0]
                                 if isinstance(out, Quantity) else Quantity)
                    raise TypeError("out cannot be assigned to a {0} instance; "
                                    "use a {1} instance instead.".format(
                                        out.__class__, ok_class))

            value = function(self.view(np.ndarray), *args, **kwargs)
            if out is None:
                return self._new_view(value, unit)
            else:
                out._unit = unit
                return out

        def clip(self, a_min, a_max, out=None):
            return self._wrap_function(np.clip, self._to_own_unit(a_min),
                                       self._to_own_unit(a_max), out=out)

        def trace(self, offset=0, axis1=0, axis2=1, dtype=None, out=None):
            return self._wrap_function(np.trace, offset, axis1, axis2, dtype,
                                       out=out)

        def var(self, axis=None, dtype=None, out=None, ddof=0):
            return self._wrap_function(np.var, axis, dtype,
                                       out=out, ddof=ddof, unit=self.unit**2)

        def std(self, axis=None, dtype=None, out=None, ddof=0):
            return self._wrap_function(np.std, axis, dtype, out=out, ddof=ddof)

        def mean(self, axis=None, dtype=None, out=None):
            return self._wrap_function(np.mean, axis, dtype, out=out)

        def ptp(self, axis=None, out=None):
            return self._wrap_function(np.ptp, axis, out=out)

        def round(self, decimals=0, out=None):
            return self._wrap_function(np.round, decimals, out=out)

        if NUMPY_LT_1_7:
            # 'keepdims' was not yet available.
            def max(self, axis=None, out=None):
                return self._wrap_function(np.max, axis, out=out)

            def min(self, axis=None, out=None):
                return self._wrap_function(np.min, axis, out=out)

            def sum(self, axis=None, dtype=None, out=None):
                return self._wrap_function(np.sum, axis, dtype, out=out)

            def prod(self, axis=None, dtype=None, out=None):
                if not self.unit.is_unity():
                    raise ValueError("cannot use prod on scaled or "
                                     "non-dimensionless Quantity arrays")
                return self._wrap_function(np.prod, axis, dtype, out=out)

            # 'out' was not yet available.
            def dot(self, b):
                result_unit = self.unit * getattr(b, 'unit', dimensionless_unscaled)
                return self._wrap_function(np.dot, b, unit=result_unit)

        else:
            def max(self, axis=None, out=None, keepdims=False):
                return self._wrap_function(np.max, axis, out=out, keepdims=keepdims)

            def min(self, axis=None, out=None, keepdims=False):
                return self._wrap_function(np.min, axis, out=out, keepdims=keepdims)

            def sum(self, axis=None, dtype=None, out=None, keepdims=False):
                return self._wrap_function(np.sum, axis, dtype, out=out,
                                           keepdims=keepdims)

            def prod(self, axis=None, dtype=None, out=None, keepdims=False):
                if not self.unit.is_unity():
                    raise ValueError("cannot use prod on scaled or "
                                     "non-dimensionless Quantity arrays")
                return self._wrap_function(np.prod, axis, dtype, out=out,
                                           keepdims=keepdims)

            def dot(self, b, out=None):
                result_unit = self.unit * getattr(b, 'unit', dimensionless_unscaled)
                return self._wrap_function(np.dot, b, out=out, unit=result_unit)

        def cumsum(self, axis=None, dtype=None, out=None):
            return self._wrap_function(np.cumsum, axis, dtype, out=out)

        def cumprod(self, axis=None, dtype=None, out=None):
            if not self.unit.is_unity():
                raise ValueError("cannot use cumprod on scaled or "
                                 "non-dimensionless Quantity arrays")
            return self._wrap_function(np.cumprod, axis, dtype, out=out)

        # Calculation: override methods that do not make sense.

        def all(self, axis=None, out=None):
            raise NotImplementedError("cannot evaluate truth value of quantities. "
                                      "Evaluate array with q.value.all(...)")

        def any(self, axis=None, out=None):
            raise NotImplementedError("cannot evaluate truth value of quantities. "
                                      "Evaluate array with q.value.any(...)")

        # Calculation --numpy functions that can be overridden with methods

        def diff(self, n=1, axis=-1):
            return self._wrap_function(np.diff, n, axis)

        def ediff1d(self, to_end=None, to_begin=None):
            return self._wrap_function(np.ediff1d, to_end, to_begin)

        if NUMPY_LT_1_8:
            def nansum(self, axis=None):
                return self._wrap_function(np.nansum, axis)
        else:
            def nansum(self, axis=None, out=None, keepdims=False):
                return self._wrap_function(np.nansum, axis,
                                           out=out, keepdims=keepdims)

        def insert(self, obj, values, axis=None):
            """
            Insert values along the given axis before the given indices and return
            a new `~astropy.units.Quantity` object.

            This is a thin wrapper around the `numpy.insert` function.

            Parameters
            ----------
            obj : int, slice or sequence of ints
                Object that defines the index or indices before which ``values`` is
                inserted.
            values : array-like
                Values to insert.  If the type of ``values`` is different
                from that of quantity, ``values`` is converted to the matching type.
                ``values`` should be shaped so that it can be broadcast appropriately
                The unit of ``values`` must be consistent with this quantity.
            axis : int, optional
                Axis along which to insert ``values``.  If ``axis`` is None then
                the quantity array is flattened before insertion.

            Returns
            -------
            out : `~astropy.units.Quantity`
                A copy of quantity with ``values`` inserted.  Note that the
                insertion does not occur in-place: a new quantity array is returned.

            Examples
            --------
            >>> import astropy.units as u
            >>> q = [1, 2] * u.m
            >>> q.insert(0, 50 * u.cm)
            <Quantity [ 0.5,  1.,  2.] m>

            >>> q = [[1, 2], [3, 4]] * u.m
            >>> q.insert(1, [10, 20] * u.m, axis=0)
            <Quantity [[  1.,  2.],
                       [ 10., 20.],
                       [  3.,  4.]] m>

            >>> q.insert(1, 10 * u.m, axis=1)
            <Quantity [[  1., 10.,  2.],
                       [  3., 10.,  4.]] m>

            """
            out_array = np.insert(self.value, obj, self._to_own_unit(values), axis)
            return self._new_view(out_array)