#  Copyright (c) 2021 zfit

# TODO(Mayou36): update docs above

import functools
import inspect
import itertools
import warnings
from abc import abstractmethod
from collections import defaultdict
from contextlib import suppress
from typing import Callable, Iterable, Mapping, Optional, Tuple, Union

import numpy as np
import tensorflow as tf
from tensorflow.python.util.deprecation import deprecated

import zfit
import zfit.z.numpy as znp

from .. import z
from ..settings import ztypes
from ..util import ztyping
from ..util.container import convert_to_container
from ..util.exception import (AxesIncompatibleError, AxesNotSpecifiedError,
                              BreakingAPIChangeError,
                              CannotConvertToNumpyError,
                              CoordinatesIncompatibleError,
                              CoordinatesUnderdefinedError,
                              IllegalInGraphModeError, IntentionAmbiguousError,
                              InvalidLimitSubspaceError,
                              LimitsIncompatibleError, LimitsNotSpecifiedError,
                              LimitsUnderdefinedError,
                              MultipleLimitsNotImplemented,
                              NormRangeNotImplemented,
                              NumberOfEventsIncompatibleError,
                              ObsIncompatibleError, ObsNotSpecifiedError,
                              OverdefinedError, ShapeIncompatibleError,
                              SpaceIncompatibleError)
from .baseobject import BaseObject
from .coordinates import (Coordinates, _convert_obs_to_str, convert_to_axes,
                          convert_to_obs_str)
from .dimension import common_axes, common_obs, limits_overlap
from .interfaces import ZfitLimit, ZfitOrderableDimensional, ZfitSpace


class LimitRangeDefinition:
    pass


# Singleton
class Any(LimitRangeDefinition):
    _singleton_instance = None

    def __new__(cls, *args, **kwargs):
        instance = cls._singleton_instance
        if instance is None:
            instance = super().__new__(cls)
            cls._singleton_instance = instance

        return instance

    def __init_subclass__(cls, **kwargs):
        super().__init_subclass__(**kwargs)
        cls._singleton_instance = None  # each subclass is a singleton of "itself"

    def __repr__(self):
        return '<Any>'

    def __lt__(self, other):
        return True

    def __le__(self, other):
        return True

    # def __eq__(self, other):
    #     return True

    def __ge__(self, other):
        return True

    def __gt__(self, other):
        return True

    # def __hash__(self):
    #     return hash(id(self))


class AnyLower(Any):
    def __repr__(self):
        return '<Any Lower Limit>'

    # def __eq__(self, other):
    #     return False

    # def __ge__(self, other):
    #     return False
    #
    # def __gt__(self, other):
    #     return False


class AnyUpper(Any):
    def __repr__(self):
        return '<Any Upper Limit>'

    # def __eq__(self, other):
    #     return False

    # def __le__(self, other):
    #     return False
    #
    # def __lt__(self, other):
    #     return False


ANY = Any()
ANY_LOWER = AnyLower()
ANY_UPPER = AnyUpper()


# TODO(warning): set a changeable warning system in zfit
def warn_or_fail_not_rect(func):
    warned = False

    def wrapped_func(*args, **kwargs):
        self = args[0]
        if self.has_limits and not self.has_rect_limits:
            raise RuntimeError(f"Cannot call {func} as the space {self} has functional,"
                               f" not rectangular limits. Use `rect_*` functions to obtain the"
                               f" rectangular limits/area or `inside`/`filter` to test if values are"
                               f" inside of the space.")
        nonlocal warned
        if not warned:
            warnings.warn(f"The function {func} may does not return the actual area/limits"
                          f" but rather the rectangular limits. {self} can also have functional"
                          f" limits that are arbitrarily defined and lay inside the rect_limits."
                          f" To test if a value is inside, use `inside` or `filter`.",
                          stacklevel=2)
            warned = True
        return func(*args, **kwargs)

    return wrapped_func


@z.function(wraps='tensor', experimental_relax_shapes=True)
def calculate_rect_area(rect_limits):
    lower, upper = rect_limits
    diff = upper - lower
    area = z.unstable.reduce_prod(diff, axis=-1)
    return area


@z.function(wraps='tensor', experimental_relax_shapes=True)
def inside_rect_limits(x, rect_limits):
    if not x.shape.ndims > 1:
        raise ValueError("x has ndims <= 1, which is most probably not wanted. The default shape for array-like"
                         " structures is (nevents, n_obs).")
    lower, upper = z.unstack_x(rect_limits, axis=0)
    lower = z.convert_to_tensor(lower)
    upper = z.convert_to_tensor(upper)
    below_upper = znp.all(tf.less_equal(x, upper), axis=-1)  # if all obs inside
    above_lower = znp.all(tf.greater_equal(x, lower), axis=-1)
    inside = tf.logical_and(above_lower, below_upper)
    return inside


@z.function(wraps='tensor', experimental_relax_shapes=True)
def filter_rect_limits(x, rect_limits, axis=None):
    return tf.boolean_mask(tensor=x, mask=inside_rect_limits(x, rect_limits=rect_limits, axis=axis))


def convert_to_tensor_or_numpy(obj, dtype=ztypes.float):
    if contains_tensor(obj):
        return z.convert_to_tensor(obj, dtype=dtype)
    else:
        with suppress(AttributeError):
            dtype = dtype.as_numpy_dtype
        return np.array(obj, dtype=dtype)


def _sanitize_x_input(x, n_obs):
    x = z.convert_to_tensor(x)
    if not x.shape.ndims > 1 and n_obs > 1:
        raise ValueError("x has ndims <= 1, which is most probably not wanted. The default shape for array-like"
                         " structures is (nevents, n_obs).")
    elif x.shape.ndims <= 1 and n_obs == 1:
        if x.shape.ndims == 0:
            x = tf.broadcast_to(x, (1, 1))
        else:
            x = znp.expand_dims(x, axis=-1)
    if tf.get_static_value(x.shape[-1]) != n_obs:
        raise ShapeIncompatibleError("n_obs and the last dim of x do not agree. Assuming x has shape (..., n_obs)")
    return x


def is_range_definition(limit):
    if isinstance(limit, LimitRangeDefinition):
        return True
    elif (isinstance(limit, np.ndarray) and limit.dtype != object) or tf.is_tensor(limit):
        return False
    try:
        return any(is_range_definition(lim) for lim in limit)
    except TypeError:
        return False  # not iterable and was not a LimitRangeDefinition in the beginning


class Limit(ZfitLimit):
    _experimental_allow_vectors = False

    def __init__(self, limit_fn: ztyping.LimitsFuncTypeInput = None,
                 rect_limits: ztyping.LimitsTypeInput = None,
                 n_obs: int = None):
        """Specify a limit with rectangular limits (and possiblty an arbitrary function).

        Args:
            limit_fn: Function that works as `inside`: return true if a point is inside of the limits.
                The function should take one tensor-like argument with shape (..., n_obs) and should return
                a shape without the last dimension.
            rect_limits: Rectangular limits, a tuple of tensor-like objects with shape (typically) (1, n_obs) or similar
                such as only a tuple/list of values that will be interpreted as the last dimension. They should cover an
                area that includes `limit_fn` fully.
            n_obs: dimensionality of the Limits, the last dimension.
        """
        super().__init__()
        limit_fn, rect_limits, n_obs, is_rect, sublimits = self._check_convert_input_limits(limit_fn=limit_fn,
                                                                                            rect_limits=rect_limits,
                                                                                            n_obs=n_obs)
        self._limit_fn = limit_fn
        self._rect_limits = rect_limits
        self._n_obs = n_obs
        self._is_rect = is_rect
        self._sublimits = sublimits

    def _check_convert_input_limits(self, limit_fn, rect_limits, n_obs):
        if isinstance(limit_fn, ZfitLimit):
            if not isinstance(limit_fn, Limit):  # because of the limit_fn, that is private. Maybe use `inside` instead?
                raise TypeError(
                    "If limits_fn is an instance of ZfitLimit, it has to be an instance of Limit (currently)")
            if rect_limits is not None or n_obs != limit_fn.n_obs:
                raise OverdefinedError("limits_fn is a ZfitLimit. rect_limits and n_obs must not be specified"
                                       "(or n_obs coincide).")
            limit = limit_fn

            limit_fn = limit.limit_fn
            rect_limits = limit.rect_limits
            n_obs = limit.n_obs
            # return limit._limit_fn, limit.rect_limits, limit.n_obs, limit.has_rect_limits, (self,)
        limits_are_rect = True

        # if the limits are False or None, we can take a shortcut and don't need to do any preprocessing
        return_limits_short = False
        if limit_fn is False:
            if rect_limits in (False, None):
                limits_short = False
                return_limits_short = True
        elif limit_fn is None:
            if rect_limits is False:
                limits_short = False
                return_limits_short = True
            elif rect_limits is None:
                limits_short = None
                return_limits_short = True
            else:  # start from limits are anything, rect is None
                limit_fn = rect_limits
                rect_limits = None
        if return_limits_short:
            if n_obs > 1:
                sublimits = [type(self)(limit_fn=limits_short, n_obs=1) for _ in range(n_obs)]
            else:
                sublimits = (self,)
            return limits_short, limits_short, n_obs, limits_short, sublimits

        if not callable(limit_fn):  # limits_fn is actually rect_limits
            rect_limits = limit_fn
            limit_fn = None

        else:
            limits_are_rect = False
            if rect_limits in (None, False):
                raise ValueError("Limits given as a function need also rect_limits, cannot be None or False")
        try:
            lower, upper = rect_limits
        except TypeError as err:
            raise TypeError(
                "The outermost shape of `rect_limits` has to be 2 to represent (lower, upper).") from err

        lower = self._sanitize_rect_limit(lower)
        upper = self._sanitize_rect_limit(upper)

        # vectors means more than one n_events, in the first dim
        if not self._experimental_allow_vectors:
            lower_nevents = tf.get_static_value(lower.shape[0])
            upper_nevents = tf.get_static_value(upper.shape[0])
            if lower_nevents != 1 or upper_nevents != 1:
                raise LimitsIncompatibleError("Vectors (limits with n_events != 1) are not allowed. Experimental"
                                              " flag (_experimental_allow_vectors) can be switched on if desired."
                                              " This happened most likely due to the new Space limits layout:"
                                              " To create multiple limits, use the addition operator of simple spaces.")

        lower_nobs = tf.get_static_value(lower.shape[-1])
        upper_nobs = tf.get_static_value(upper.shape[-1])

        if not lower_nobs == upper_nobs:
            raise ShapeIncompatibleError(
                f"Last dimension of lower ({lower_nobs}) and upper ({upper_nobs}) have to coincide.")
        if n_obs is not None and not lower_nobs == n_obs:
            raise ShapeIncompatibleError(f"Inferred last dimension ({lower_nobs}) does not coincide with "
                                         f"given n_obs ({n_obs})")

        if not any(is_range_definition(limit) for limit in (lower, upper)):
            tf.assert_greater(upper, lower, message="All upper limits have to be larger than the lower limits and are"
                                                    " given as (lower, upper). Maybe (upper, lower) was entered?")

        n_obs = lower_nobs  # in case it was None
        rect_limits = (lower, upper)

        # It can be that there is a function that depends on multiple dimensions, e.g. if we have
        # a `limit_fn` and n_obs > 1. But if we have only rectangular limits, we can split them up
        # which allows later (the Space) to better combine and get subspaces

        # create sublimits to iterate if possible
        sublimits = []
        if limits_are_rect and n_obs > 1:
            for i in range(n_obs):
                low = z.unstable.gather(lower, (i,), axis=-1)
                up = z.unstable.gather(upper, (i,), axis=-1)
                sublimits.append(type(self)(rect_limits=(low, up), n_obs=1))
        else:
            sublimits.append(self)

        sublimits = tuple(sublimits)

        return limit_fn, rect_limits, n_obs, limits_are_rect, sublimits

    @staticmethod
    def _sanitize_rect_limit(limit) -> ztyping.RectLowerReturnType:
        """Sanitize the input limit and return if it is numerical or not.

        Args:
            limit:

        Returns:
        """
        if is_range_definition(limit):  # as the above ANY
            dtype = object
        else:
            dtype = ztypes.float
        limit = convert_to_tensor_or_numpy(limit, dtype=dtype)
        if len(limit.shape) == 0:
            limit = z.unstable.broadcast_to(limit, shape=(1, 1))
        if len(limit.shape) == 1:
            limit = z.unstable.expand_dims(limit, axis=0)
        return limit

    @property
    def has_rect_limits(self) -> bool:
        """If the limits are rectangular."""
        return self.has_limits and self._is_rect

    @property
    def rect_limits(self) -> ztyping.RectLimitsReturnType:
        """Return the rectangular limits as `np.ndarray``tf.Tensor` if they are set and not false.

            The rectangular limits can be used for sampling. They do not in general represent the limits
            of the object as a functional limit can be set and to check if something is inside the limits,
            the method :py:meth:`~Limit.inside` should be used.

            In order to test if the limits are False or None, it is recommended to use the appropriate methods
            `limits_are_false` and `limits_are_set`.

        Returns:
            The lower and upper limits.
        Raises:
            LimitsNotSpecifiedError: If there are not limits set or they are False.
        """
        if not self.has_limits:
            raise LimitsNotSpecifiedError(f"Limits are False or not set, cannot return the rectangular limits.")
        rect_limits = self._rect_limits
        return rect_limits

    @property
    def _rect_limits_tf(self) -> ztyping.RectLimitsTFReturnType:
        rect_limits = self._rect_limits
        if rect_limits in (None, False):
            return rect_limits
        lower = z.convert_to_tensor(rect_limits[0])
        upper = z.convert_to_tensor(rect_limits[1])
        return z.convert_to_tensor((lower, upper))

    @property
    def rect_limits_np(self) -> ztyping.RectLimitsNPReturnType:
        """Return the rectangular limits as `np.ndarray`. Raise error if not possible.

        Rectangular limits are returned as numpy arrays which can be useful when doing checks that do not
        need to be involved in the computation later on as they allow direct interaction with Python as
        compared to `tf.Tensor` inside a graph function.


        Returns:
            A tuple of two `np.ndarray` with shape (1, n_obs) typically. The last
                dimension is always `n_obs`, the first can be vectorized. This allows unstacking
                with `z.unstack_x()` as can be done with data.

        Raises:
            CannotConvertToNumpyError: In case the conversion fails.
        """
        lower, upper = self._rect_limits

        lower = z.unstable._try_convert_numpy(lower)
        upper = z.unstable._try_convert_numpy(upper)
        return lower, upper

    @property
    def rect_lower(self) -> ztyping.RectLowerReturnType:
        """The lower, rectangular limits, equivalent to `rect_limits[0] with shape (..., n_obs)`

        Returns:
            The lower, rectangular limits as `np.ndarray` or `tf.Tensor`
        """
        return self.rect_limits[0]

    @property
    def rect_upper(self) -> ztyping.RectUpperReturnType:
        """The upper, rectangular limits, equivalent to `rect_limits[1]` with shape (..., n_obs)

        Returns:
            The lower, rectangular limits as `np.ndarray` or `tf.Tensor`
        """
        return self.rect_limits[1]

    def rect_area(self) -> Union[float, np.ndarray, tf.Tensor]:
        """Calculate the total rectangular area of all the limits and axes.

        Useful, for example, for MC integration.
        """
        return calculate_rect_area(rect_limits=self._rect_limits_tf)

    def inside(self, x: ztyping.XTypeInput, guarantee_limits: bool = False) -> ztyping.XTypeReturnNoData:
        """Test if `x` is inside the limits.

        This function should be used to test if values are inside the limits. If the given x is already inside
        the rectangular limits, e.g. because it was sampled from within them

        Args:
            x: Values to be checked whether they are inside of the limits. The shape is expected to have the last
                dimension equal to n_obs.
            guarantee_limits: Guarantee that the values are already inside the rectangular limits.

        Returns:
            Return a boolean tensor-like object with the same shape as the input `x` except of the
                last dimension removed.
        """
        x = _sanitize_x_input(x, n_obs=self.n_obs)
        if not self.has_limits:
            raise LimitsNotSpecifiedError("Cannot call `inside` without limits defined.")
        if guarantee_limits and self.has_rect_limits:
            return tf.broadcast_to(True, x.shape)
        else:
            return self._inside(x, guarantee_limits)

    def _inside(self, x, guarantee_limits):
        del guarantee_limits
        if self.has_rect_limits:
            return inside_rect_limits(x, rect_limits=self._rect_limits_tf)
        else:
            return self._limit_fn(x)

    def filter(self, x: ztyping.XTypeInput,
               guarantee_limits: bool = False,
               axis: Optional[int] = None
               ) -> ztyping.XTypeReturnNoData:
        """Filter `x` by removing the elements along `axis` that are not inside the limits.

        This is similar to `tf.boolean_mask`.

        Args:
            x: Values to be checked whether they are inside of the limits. If not, the corresonding element (in the
                specified `axis`) is removed. The shape is expected to have the last dimension equal to n_obs.
            guarantee_limits: Guarantee that the values are already inside the rectangular limits.
            axis: The axis to remove the elements from. Defaults to 0.

        Returns:
            Return an object with the same shape as `x` except that along `axis` elements have been
                removed.
        """

        if not self.has_limits:
            raise LimitsNotSpecifiedError("Cannot call `filter` without limits defined.")
        x = _sanitize_x_input(x, n_obs=self.n_obs)

        # shortcut, everything already inside
        if guarantee_limits and self.has_rect_limits:
            return x

        return self._filter(x, guarantee_limits, axis=axis)

    def _filter(self, x, guarantee_limits, axis):
        return tf.boolean_mask(tensor=x, mask=self.inside(x, guarantee_limits=guarantee_limits), axis=axis)

    @property
    def limit_fn(self):
        return self._limit_fn

    @property
    def rect_limits_are_tensors(self) -> bool:
        """Return True if the rectangular limits are tensors.

        If a limit with tensors is evaluated inside a graph context, comparison operations will fail.

        Returns:
            If the rectangular limits are tensors.
        """
        try:
            _ = self.rect_limits_np
        except CannotConvertToNumpyError:
            return True
        else:
            return False

    @property
    def limits_are_set(self) -> bool:
        """If the limits have never explicitly been set to a limit or to False.

        Returns:
        """
        return self._rect_limits is not None

    @property
    def limits_are_false(self) -> bool:
        """If the limits have been set to False, so the object on purpose does not contain limits.

        Returns:
        """
        return self._rect_limits is False

    @property
    def has_limits(self) -> bool:
        """If there are limits set and they are not false.

        Returns:
        """
        return not (self.limits_are_false or (not self.limits_are_set))

    @property
    def n_obs(self) -> int:
        """Dimensionality, the number of observables, of the limits. Equals to the last axis in rectangular limits.

        Returns:
            Dimensionality of the limits.
        """
        return self._n_obs

    @property
    def n_events(self) -> Union[int, None]:
        """

        Returns:
            Return the number of events, the dimension of the first shape. If this is > 1 or None,
                it's vectorized.
        """
        if not self.has_limits:
            return 1
        return self.rect_lower.shape[0]

    def equal(self, other: object, allow_graph: bool = True) -> Union[bool, tf.Tensor]:
        """Compare the limits on equality. For ANY objects, this also returns true.

        If called inside a graph context *and* the limits are tensors, this will return a symbolic `tf.Tensor`.

        Args:
            other: Any other object to compare with
            allow_graph: If False and the function returns a symbolic tensor, raise IllegalInGraphModeError instead.

        Returns:
            Either a Python boolean or a `tf.Tensor`
         Raises:
             IllegalInGraphModeError: if `allow_graph`
        """
        if not isinstance(other, ZfitLimit):
            return False
        return equal_limits(self, other, allow_graph=allow_graph)

    def __eq__(self, other: object) -> bool:
        """Compares two Limits for equality without graph mode allowed.

        Returns:

        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, ZfitLimit):
            return NotImplemented
        return self.equal(other, allow_graph=False)

        # TODO: use below?
        # try:
        #     return self.equal(other, allow_graph=False)
        # except IllegalInGraphModeError:
        #     warnings.warn(f"Comparing instances ({self, other}) in graph mode (space/limit) contains Tensor. This returns"
        #                   " identity tests. To prevent this, use numpy objects, not tensors, for limits if not needed.")
        #     return self is other

    def less_equal(self,
                   other: object,
                   allow_graph: bool = True
                   ) -> Union[bool, tf.Tensor]:
        """Set-like comparison for compatibility. If an object is less_equal to another, the limits are combatible.

        This can be used to determine whether a fitting range specification can handle another limit.

        If called inside a graph context *and* the limits are tensors, this will return a symbolic `tf.Tensor`.


        Args:
            other: Any other object to compare with
            allow_graph: If False and the function returns a symbolic tensor, raise IllegalInGraphModeError instead.


        Returns:
            Result of the comparison
        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, ZfitLimit):
            return False
        return less_equal_limits(self, other, allow_graph=allow_graph)

    def __le__(self, other: object) -> bool:
        """Set-like comparison for compatibility. If an object is less_equal to another, the limits are combatible.

        This can be used to determine whether a fitting range specification can handle another limit.

        Returns:
            Result of the comparison
        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, ZfitLimit):
            return NotImplemented
        return self.less_equal(other, allow_graph=False)

    def get_sublimits(self) -> Iterable[ZfitLimit]:
        """Splits itself into multiple sublimits with smaller n_obs.

        If this is not possible, if the limits are not rectangular, just returns itself.

        Returns:
            The sublimits if it was able to split.
        """
        return self._sublimits

    def __hash__(self) -> int:
        objects = (self._limit_fn, self.n_obs)  # not rect limits, not hashable and unprecise
        return hash(tuple(objects))

    def __repr__(self) -> str:
        class_name = str(self.__class__).split('.')[-1].split('\'')[0]
        if not self.limits_are_set:
            limits = None
        elif self.limits_are_false:
            limits = False
        else:
            if self.n_obs < 5 and not self.n_events > 1:
                limits = self.rect_limits
            else:
                limits = 'rectangular'

        return f"<zfit {class_name} rect_limits={limits}, limit_fn={not self.has_rect_limits}>"


def rect_limits_are_any(limit: ZfitLimit) -> bool:
    """True if all limits in limit are ANY objects."""
    if limit.rect_limits_are_tensors:
        return False
    if all(isinstance(ele, Any) for lim in limit.rect_limits_np for ele in lim.flatten()):
        return True
    else:
        return False


def less_equal_limits(limit1: Limit, limit2: Limit, allow_graph=True) -> bool:
    if rect_limits_are_any(limit1) or rect_limits_are_any(limit2):
        return True

    try:
        lower1, upper1 = limit1.rect_limits_np
        lower2, upper2 = limit2.rect_limits_np
    except CannotConvertToNumpyError:
        if not allow_graph:
            raise IllegalInGraphModeError(
                "Cannot use equality in graph mode, e.g. inside a `tf.function` decorated "
                "function. To retrieve a symbolic Tensor, use `.equal(..., allow_graph=True)`")
        else:
            lower1, upper1 = limit1.rect_limits
            lower2, upper2 = limit2.rect_limits

    lower_le = z.unstable.reduce_all(z.unstable.less_equal(lower1, lower2), axis=-1)
    upper_le = z.unstable.reduce_all(z.unstable.less_equal(upper1, upper2), axis=-1)
    rect_limits_le = z.unstable.logical_and(lower_le, upper_le)
    # if both are functional, they have to coincide
    if not (limit1.has_rect_limits or limit2.has_rect_limits):
        funcs_equal = limit1.limit_fn == limit2.limit_fn

    # if one is functional, one is rect: the bigger one can be rect
    elif not limit1.has_rect_limits and limit2.has_rect_limits:
        funcs_equal = True
    else:
        funcs_equal = limit1.limit_fn == limit2.limit_fn
    return z.unstable.logical_and(rect_limits_le, funcs_equal)


def equal_limits(limit1: Limit, limit2: Limit, allow_graph=True) -> bool:
    # if both are functional, we just need to compare their functions; the rect limits are "irrelevant"
    if not (limit1.has_rect_limits or limit2.has_rect_limits):
        return limit1.limit_fn == limit2.limit_fn

    # if one is functional, one is rect: they are not the same
    elif limit1.has_rect_limits ^ limit2.has_rect_limits:
        return False

    try:
        lower, upper = limit1.rect_limits_np
        lower_other, upper_other = limit2.rect_limits_np
    except CannotConvertToNumpyError:
        if not allow_graph:
            raise IllegalInGraphModeError(
                "Cannot use equality in graph mode, e.g. inside a `tf.function` decorated "
                "function. To retrieve a symbolic Tensor, use `.equal(..., allow_graph=True)`")
        else:
            lower, upper = limit1.rect_limits
            lower_other, upper_other = limit2.rect_limits

    # TODO add tols
    lower_limits_equal = z.unstable.reduce_all(z.unstable.allclose_anyaware(lower, lower_other))
    upper_limits_equal = z.unstable.reduce_all(z.unstable.allclose_anyaware(upper, upper_other))
    rect_limits_equal = z.unstable.logical_and(lower_limits_equal, upper_limits_equal)
    funcs_equal = limit1.limit_fn == limit2.limit_fn
    return z.unstable.logical_and(rect_limits_equal, funcs_equal)


class BaseSpace(ZfitSpace, BaseObject):

    def __init__(self, obs, axes, name, **kwargs):
        super().__init__(name, **kwargs)
        coords = Coordinates(obs, axes)
        self.coords = coords

    def inside(self, x: ztyping.XTypeInput, guarantee_limits: bool = False) -> ztyping.XTypeReturn:
        """Test if `x` is inside the limits.

        This function should be used to test if values are inside the limits. If the given x is already inside
        the rectangular limits, e.g. because it was sampled from within them

        Args:
            x: Values to be checked whether they are inside of the limits. The shape is expected to have the last
                dimension equal to n_obs.
            guarantee_limits: Guarantee that the values are already inside the rectangular limits.

        Returns:
            Return a boolean tensor-like object with the same shape as the input `x` except of the
                last dimension removed.
        """
        x = _sanitize_x_input(x, n_obs=self.n_obs)
        if self.has_rect_limits and guarantee_limits:
            return tf.broadcast_to(True, x.shape)
        inside = self._inside(x, guarantee_limits)
        return inside

    @abstractmethod
    def _inside(self, x, guarantee_limits):
        raise NotImplementedError

    def filter(self, x: ztyping.XTypeInput,
               guarantee_limits: bool = False,
               axis: Optional[int] = None
               ) -> ztyping.XTypeReturnNoData:
        """Filter `x` by removing the elements along `axis` that are not inside the limits.

        This is similar to `tf.boolean_mask`.

        Args:
            x: Values to be checked whether they are inside of the limits. If not, the corresonding element (in the
                specified `axis`) is removed. The shape is expected to have the last dimension equal to n_obs.
            guarantee_limits: Guarantee that the values are already inside the rectangular limits.
            axis: The axis to remove the elements from. Defaults to 0.

        Returns:
            Return an object with the same shape as `x` except that along `axis` elements have been
                removed.
        """
        if self.has_rect_limits and guarantee_limits:
            return x
        filtered = self._filter(x, guarantee_limits)
        return filtered

    def _filter(self, x, guarantee_limits):
        filtered = tf.boolean_mask(tensor=x, mask=self.inside(x, guarantee_limits=guarantee_limits))
        return filtered

    @property
    def n_obs(self) -> int:
        """Return the number of observables/axes.

        Returns:
            int >= 1
        """
        return self.coords.n_obs

    @property
    def obs(self) -> ztyping.ObsTypeReturn:
        """The observables ("axes with str")the space is defined in.

        Returns:
        """
        return self.coords.obs

    @property
    def axes(self) -> ztyping.AxesTypeReturn:
        """The axes ("obs with int") the space is defined in.

        Returns:
        """
        return self.coords.axes

    @property
    def n_limits(self) -> int:
        return len(tuple(self))

    def __iter__(self) -> Iterable[ZfitSpace]:
        yield self

    def get_reorder_indices(self,
                            obs: ztyping.ObsTypeInput = None,
                            axes: ztyping.AxesTypeInput = None
                            ) -> Tuple[int]:
        """Indices that would order the instances obs as `obs` respectively the instances axes as `axes`.

        Args:
            obs: Observables that the instances obs should be ordered to. Does not reorder, but just
                return the indices that could be used to reorder.
            axes: Axes that the instances obs should be ordered to. Does not reorder, but just
                return the indices that could be used to reorder.

        Returns:
            New indices that would reorder the instances obs to be obs respectively axes.

        Raises:
            CoordinatesUnderdefinedError: If neither `obs` nor `axes` is given
        """
        return self.coords.get_reorder_indices(obs=obs, axes=axes)

    # TODO: remove, in coords
    def _check_convert_input_axes(self, axes: ztyping.AxesTypeInput,
                                  allow_none: bool = False) -> ztyping.AxesTypeReturn:
        if axes is None:
            if allow_none:
                return None
            else:
                raise AxesNotSpecifiedError("TODO: Cannot be None")
        if isinstance(axes, ZfitSpace):
            axes = axes.axes
        else:
            axes = convert_to_container(value=axes, container=tuple)  # TODO(Mayou36): extend like _check_obs?

        return axes

    # TODO: remove, in coords
    def _check_convert_input_obs(self, obs: ztyping.ObsTypeInput,
                                 allow_none: bool = False) -> ztyping.ObsTypeReturn:
        """Input check: Convert `NOT_SPECIFIED` to None or check if obs are all strings.

        Args:
            obs:

        Returns:
        """
        if obs is None:
            if allow_none:
                return None
            else:
                raise ObsNotSpecifiedError("TODO: Cannot be None")

        if isinstance(obs, ZfitSpace):
            obs = obs.obs
        else:
            obs = convert_to_container(obs, container=tuple)
            obs_not_str = tuple(o for o in obs if not isinstance(o, str))
            if obs_not_str:
                raise ValueError(f"The following observables are not strings: {obs_not_str}")
        return obs

    def _check_coords_allowed(self, obs: ztyping.ObsTypeInput = None, axes: ztyping.AxesTypeInput = None,
                              allow_superset: bool = True, allow_subset: bool = True):
        to_check = []
        if obs is not None and self.obs is not None:
            to_check.append(obs, self.obs)
        if axes is not None and self.axes is not None:
            to_check.append(axes, self.axes)

        for coord, self_coord in to_check:
            coord = frozenset(coord)
            self_coord = frozenset(self_coord)
            if coord != self_coord:

                if not allow_superset and coord.issuperset(self_coord):
                    raise CoordinatesIncompatibleError(f"Superset is not allowed, but {coord} is a superset"
                                                       f" of {self_coord}")

                if not allow_subset and coord.issubset(self_coord):
                    raise CoordinatesIncompatibleError(f"subset is not allowed, but {coord} is a subset"
                                                       f" of {self_coord}")

    def __repr__(self):
        class_name = str(self.__class__).split('.')[-1].split('\'')[0]
        if not self.limits_are_set:
            limits = None
        elif self.limits_are_false:
            limits = False
        elif self.has_rect_limits:
            if self.n_obs < 3 and not self.n_events > 1:
                limits = self.rect_limits
            else:
                limits = 'rectangular'
        else:
            limits = 'functional'
        return f"<zfit {class_name} obs={self.obs}, axes={self.axes}, limits={limits}>"

    def __add__(self, other):
        if not isinstance(other, ZfitSpace):
            raise TypeError(f"Cannot add a {type(self)} and a {type(other)}")
        return add_spaces(self, other)

    # TODO: implement properly, just sketch
    def get_sublimits(self):
        limits = self.extract_limits()
        return list(limits.values())

    def add(self, *other: ztyping.SpaceOrSpacesTypeInput):
        """Add the limits of the spaces. Only works for the same obs.

        In case the observables are different, the order of the first space is taken.

        Args:
            other:

        Returns:
            :py:class:`~zfit.Space`:
        """
        # other = convert_to_container(other, container=list)
        new_space = add_spaces(self, *other)
        return new_space

    def combine(self, *other: ztyping.SpaceOrSpacesTypeInput) -> ZfitSpace:
        """Combine spaces with different obs (but consistent limits).

        Args:
            other:

        Returns:
            :py:class:`~zfit.Space`:
        """
        # other = convert_to_container(other, container=list)
        new_space = combine_spaces(self, *other)
        return new_space

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

    def __ge__(self, other):
        return NotImplemented

    def __eq__(self, other):
        if not isinstance(other, ZfitSpace):
            return NotImplemented
        return equal_space(self, other)

    def equal(self, other: object, allow_graph: bool) -> Union[bool, tf.Tensor]:
        """Compare the limits on equality. For ANY objects, this also returns true.

        If called inside a graph context *and* the limits are tensors, this will return a symbolic `tf.Tensor`.

        Returns:
            Result of the comparison
        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, ZfitSpace):
            return False
        return equal_space(self, other, allow_graph=allow_graph)

    def __eq__(self, other: object) -> bool:
        """Compares two Limits for equality without graph mode allowed.

        Returns:

        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, ZfitSpace):
            return NotImplemented
        return self.equal(other=other, allow_graph=False)

    def less_equal(self, other, allow_graph):
        """Set-like comparison for compatibility. If an object is less_equal to another, the limits are combatible.

        This can be used to determine whether a fitting range specification can handle another limit.

        If called inside a graph context *and* the limits are tensors, this will return a symbolic `tf.Tensor`.


        Args:
            other: Any other object to compare with
            allow_graph: If False and the function returns a symbolic tensor, raise IllegalInGraphModeError instead.

        Returns:
            Result of the comparison
        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, ZfitSpace):
            return False
        return less_equal_space(self, other, allow_graph=allow_graph)

    def __le__(self, other: object) -> bool:
        """Set-like comparison for compatibility. If an object is less_equal to another, the limits are combatible.

        This can be used to determine whether a fitting range specification can handle another limit.

        Returns:
            Result of the comparison
        Raises:
             IllegalInGraphModeError: it the comparison happens with tensors in a graph context.
        """
        if not isinstance(other, type(self)):
            return NotImplemented
        return self.less_equal(other, allow_graph=False)

    def __hash__(self):
        limits_frozen = tuple(((key, tuple(ldict.items())) for key, ldict in self._limits_dict.items()))
        hash_val = hash(tuple((limits_frozen, hash(self.coords))))
        return hash_val

    def reorder_x(self, x, x_obs, x_axes, func_obs, func_axes):
        return self.coords.reorder_x(x, x_obs=x_obs, x_axes=x_axes,
                                     func_obs=func_obs, func_axes=func_axes)

    def __len__(self):
        if not self:
            return 0
        else:
            return sum(1 for _ in self)

    def __bool__(self):
        return self.has_limits


class Space(BaseSpace):
    AUTO_FILL = object()
    ANY = ANY
    ANY_LOWER = ANY_LOWER  # TODO: needed? or move everything inside?
    ANY_UPPER = ANY_UPPER

    def __init__(self, obs: Optional[ztyping.ObsTypeInput] = None,
                 limits: Optional[ztyping.LimitsTypeInput] = None,
                 axes=None, rect_limits=None,
                 name: Optional[str] = "Space"):
        """Define a space with the name (`obs`) of the axes (and it's number) and possibly it's limits.

        A space can be thought of as coordinates, possibly with the definition of a range (limits). For most use-cases,
        it is sufficient to specify a `Space` via observables; simple string identifiers. They can be multidimensional.

        Observables are like the columns of a spreadsheet/dataframe, and are therefore needed for any object that does
        numerical operations or holds data in order to match the right axes. On object creation, the observables are
        assigned using a `Space`. This is often used as the default space of an object and can be used as the
        default `norm_range`, sampling limits etc.

        Axes are the same concept as observables, but numbers, indexes, and are used *inside* an object. There,
        axes 0 corresponds to the 0th data column we get (which corresponds to a certain observable).

        Every space can have limits; they are either rectangular or an arbitrary function (together with rectangular
        limits). Spaces can be combined (multiplied) to create higher dimensional spaces.
        `Spaces` can be added, which combines them into one `Space` consisting of two disconnected limits.

        So integrating over the space consisting of the two added disconnected ranges,
        e.g. 0 to 1 and 2 to 3 will return the sum of the two separate integrals.

        .. code-block:: python

            lower_band = zfit.Space('obs1', (0, 1))
            upper_band = zfit.Space('obs1', (2, 3))
            combined_obs = lower_band + upper_band
            integral_comb = model.integrate(limits=combined_obs)
            # which is equivalent to the lower
            integral_sep = model.integrate(limits=lower_band) + model.integrate(limits=upper_band)
            assert integral_comb == integral_sep


        In principle, the same behavior could also be achieved by specifying an arbitrary function. Using the addition
        allows for certain optimizations inside.



        Args:
            obs:
            limits:
            name:
        """
        if name is None:
            name = "Space"
        super().__init__(obs=obs, axes=axes, name=name)
        limits_dict = self._check_convert_input_limits(limit=limits, rect_limits=rect_limits, obs=self.obs,
                                                       axes=self.axes, n_obs=self.n_obs)
        self._limits_dict = limits_dict

    @property
    def has_rect_limits(self) -> bool:
        """If there are limits and whether they are rectangular."""
        return all(limit.has_rect_limits for limit in list(self._limits_dict.values())[0].values())

    def _check_convert_input_limits(self, limit: Union[ztyping.LowerTypeInput, ztyping.UpperTypeInput],
                                    rect_limits, obs, axes, n_obs) -> Union[
        ztyping.LowerTypeReturn, ztyping.UpperTypeReturn]:
        """Check and sanitize the input limits as well as the rectangular limits.

        Args:
            limit:

        Returns:
            Limits dictionary containing the observables and/or the axes as a key matching
                `ZfitLimits` objects.
        """
        limits_dict = defaultdict(dict)
        input_limits = limit
        if isinstance(input_limits, Space):
            space = input_limits

            # get the subset of obs/axes, then drop the other coord if not given
            if obs and not axes:
                space = space.with_obs(obs, allow_subset=True, allow_superset=True)
                space = space.with_axes(None)
            elif not obs and axes:
                space = space.with_axes(axes, allow_subset=True, allow_superset=True)
                space = space.with_obs(None)
            elif obs and axes:
                coords = Coordinates(obs=obs, axes=axes)
                space = space.with_coords(coords, allow_superset=True, allow_subset=True)
            input_limits = space.get_limits()

            obs = space.obs
            axes = space.axes
        if not isinstance(input_limits, dict) and not isinstance(rect_limits, dict):
            # if not input_limits and rect_limits:
            #     input_limits = rect_limits
            limit = Limit(limit_fn=limit, rect_limits=rect_limits, n_obs=n_obs)
            i_old = 0
            for lim in limit.get_sublimits():  # split into smaller ones if possible
                i = i_old + lim.n_obs
                if obs is not None:
                    limits_dict['obs'][obs[i_old:i]] = lim
                if axes is not None:
                    limits_dict['axes'][axes[i_old:i]] = lim
                i_old = i
            input_limits = limits_dict

        if isinstance(input_limits, dict):
            input_limits = input_limits.copy()
        elif isinstance(rect_limits, dict):
            input_limits = rect_limits.copy()

        if not 'axes' in input_limits and not 'obs' in input_limits:
            raise ValueError("Probably internal error: wrong format of limits_dict")

        # check if obs is in the limits dict. If not, copy it from the axes
        if obs:
            if 'obs' in input_limits:
                obs_limit_dict = input_limits['obs']
            else:
                obs_limit_dict = {}
                for axes_lim, lim in input_limits['axes'].items():
                    obs_coords = tuple(obs[axes.index(ax)] for ax in axes_lim)
                    if isinstance(lim, ZfitOrderableDimensional):
                        lim = lim.with_coords(self.space)
                    obs_limit_dict[obs_coords] = lim
            limits_dict['obs'] = obs_limit_dict

        if axes:
            if 'axes' in input_limits:
                axes_limit_dict = input_limits['axes']
            else:
                axes_limit_dict = {}
                for obs_lim, lim in input_limits['obs'].items():
                    axes_coords = tuple(axes[obs.index(ob)] for ob in obs_lim)
                    if isinstance(lim, ZfitOrderableDimensional):
                        lim = lim.with_coords(self.space)
                    axes_limit_dict[axes_coords] = lim
            limits_dict['axes'] = axes_limit_dict

        if not axes and 'axes' in limits_dict:
            limits_dict.pop('axes')

        if not obs and 'obs' in limits_dict:
            limits_dict.pop('obs')

        # TODO: extend input processing?
        return limits_dict

    def get_limits(self,
                   obs: ztyping.ObsTypeInput = None,
                   axes: ztyping.AxesTypeInput = None
                   ) -> Union[ztyping.LimitsDictWithCoords, ztyping.LimitsDictNoCoords]:
        return_dict = {}
        both_none_or_true = obs is None and axes is None or obs is True and axes is True

        if obs is True and axes is None or both_none_or_true:
            if not self.obs:
                if obs is True:
                    raise ObsIncompatibleError("Obs are not defined for this instance, no limits set for obs.")
            else:
                return_dict['obs'] = self._limits_dict['obs'].copy()
        if axes is True and obs is None or both_none_or_true:
            if not self.axes:
                if axes is True:
                    raise AxesIncompatibleError("Axes are not defined for this instance, no limits set for axes.")
            else:
                return_dict['axes'] = self._limits_dict['axes'].copy()
        else:
            if obs:
                return_dict['obs'] = extract_limits_from_dict(self._limits_dict, obs=obs)
            if axes:
                return_dict['axes'] = extract_limits_from_dict(self._limits_dict, axes=axes)
        return return_dict

    @property
    # @deprecated(date=None, instructions="`limits` is depreceated (currently) due to the unambiguous nature of the word."
    #                                     " Use `inside` to check if an Tensor is inside the limits or"
    #                                     " `rect_limits` if you need to retreave the rectangular limits.")
    @warn_or_fail_not_rect
    def limits(self) -> ztyping.LimitsTypeReturn:
        """Return the limits.

        Returns:
        """
        return self.rect_limits

    @property
    def rect_limits(self) -> ztyping.RectLimitsReturnType:
        """Return the rectangular limits as `np.ndarray``tf.Tensor` if they are set and not false.

            The rectangular limits can be used for sampling. They do not in general represent the limits
            of the object as a functional limit can be set and to check if something is inside the limits,
            the method :py:meth:`~Limit.inside` should be used.

            In order to test if the limits are False or None, it is recommended to use the appropriate methods
            `limits_are_false` and `limits_are_set`.

        Returns:
            The lower and upper limits.
        Raises:
            LimitsNotSpecifiedError: If there are not limits set or they are False.
        """
        if not self.has_limits:
            raise LimitsNotSpecifiedError(f"Limits are False or not set, cannot return the rectangular limits.")
        lower_ordered, upper_ordered = self._rect_limits_z()
        rect_limits = lower_ordered, upper_ordered
        return rect_limits

    @property
    def _rect_limits_tf(self) -> ztyping.LimitsTypeReturn:
        """Return the limits as `tf.Tensor`.

        Returns:
        """
        if not self.has_limits:
            raise LimitsNotSpecifiedError(f"Limits are False or not set, cannot return the rectangular limits.")
        lower_ordered, upper_ordered = self._rect_limits_z()
        rect_limits = z.convert_to_tensor(lower_ordered), z.convert_to_tensor(upper_ordered)
        return rect_limits

    @property
    def rect_limits_np(self) -> ztyping.RectLimitsNPReturnType:
        """Return the rectangular limits as `np.ndarray`. Raise error if not possible.

        Rectangular limits are returned as numpy arrays which can be useful when doing checks that do not
        need to be involved in the computation later on as they allow direct interaction with Python as
        compared to `tf.Tensor` inside a graph function.

        In order to test if the limits are False or None, it is recommended to use the appropriate methods
        `limits_are_false` and `limits_are_set`.

        Returns:
            A tuple of two `np.ndarray` with shape (1, n_obs) typically. The last
                dimension is always `n_obs`, the first can be vectorized. This allows unstacking
                with `z.unstack_x()` as can be done with data.

        Raises:
            CannotConvertToNumpyError: In case the conversion fails.
            LimitsNotSpecifiedError: If the limits are not set
        """
        lower, upper = self._rect_limits_z()

        lower = z.unstable._try_convert_numpy(lower)
        upper = z.unstable._try_convert_numpy(upper)
        return lower, upper

    @property
    def rect_lower(self) -> ztyping.RectLowerReturnType:
        """The lower, rectangular limits, equivalent to `rect_limits[0]` with shape (..., n_obs)

        Returns:
            The lower, rectangular limits as `np.ndarray` or `tf.Tensor`
        Raises:
            LimitsNotSpecifiedError: If the limits are not set or are false
        """
        return self.rect_limits[0]

    @property
    def rect_upper(self) -> ztyping.UpperTypeReturn:
        """The upper, rectangular limits, equivalent to `rect_limits[1]` with shape (..., n_obs)

        Returns:
            The upper, rectangular limits as `np.ndarray` or `tf.Tensor`
        Raises:
            LimitsNotSpecifiedError: If the limits are not set or are false
        """
        return self.rect_limits[1]

    def _rect_limits_z(self):
        limits_coords = []
        rect_lower_unordered = []
        rect_upper_unordered = []
        obs_in_use = self.obs is not None
        limits_dict = self._limits_dict['obs' if obs_in_use else 'axes']

        for coord_limit, limit in limits_dict.items():  # TODO: maybe refactor with extract limits?
            limits_coords.extend(coord_limit)
            lower, upper = limit.rect_limits  # to get the numpy or tensor
            rect_lower_unordered.append(lower)
            rect_upper_unordered.append(upper)
        reorder_kwargs = {'x_obs' if obs_in_use else 'x_axes': limits_coords}

        # stack the limits and reorder them according to the own coords
        lower_stacked = z.unstable.concat(rect_lower_unordered,
                                          axis=-1)
        lower_ordered = self.reorder_x(lower_stacked, **reorder_kwargs)
        upper_stacked = z.unstable.concat(rect_upper_unordered,
                                          axis=-1)
        upper_ordered = self.reorder_x(upper_stacked, **reorder_kwargs)
        return lower_ordered, upper_ordered

    def rect_area(self) -> Union[float, np.ndarray, tf.Tensor]:
        """Calculate the total rectangular area of all the limits and axes.

        Useful, for example, for MC integration.
        """
        return calculate_rect_area(rect_limits=self._rect_limits_tf)

    @property
    def rect_limits_are_tensors(self) -> bool:
        """Return True if the rectangular limits are tensors.

        If a limit with tensors is evaluated inside a graph context, comparison operations will fail.

        Returns:
            If the rectangular limits are tensors.
        """
        try:
            _ = self.rect_limits_np
        except CannotConvertToNumpyError:
            return True
        else:
            return False

    @property
    def has_rect_limits(self) -> bool:
        """If there are limits and whether they are rectangular."""
        if self.obs is not None:
            limits_dict = self._limits_dict.get('obs')
        else:
            limits_dict = self._limits_dict.get('axes')
        if not limits_dict:
            return False
        rect_limits = [limit.has_rect_limits for limit in limits_dict.values()]
        all_rect_limits = all(rect_limits)
        return all_rect_limits and len(rect_limits) > 0

    @property
    def limits_are_false(self) -> bool:
        """If the limits have been set to False, so the object on purpose does not contain limits.

        Returns:
            True if limits is False
        """
        return all(limit.limits_are_false
                   for limit in self._limits_dict['obs' if self.obs else 'axes'].values())

    @property
    def has_limits(self) -> bool:
        """Whether there are limits set and they are not false.

        Returns:
        """
        return self.limits_are_set and not self.limits_are_false

    @property
    def limits_are_set(self):
        return all(limit.limits_are_set
                   for limit in self._limits_dict['obs' if self.obs else 'axes'].values())

    @property
    def n_events(self) -> Union[int, None]:
        """Return the number of events, the dimension of the first shape.

        Returns:
            Number of events, the dimension of the first shape. If this is > 1 or None,
                it's vectorized.
        """
        if not self.has_limits:
            return 1
        return self.rect_lower.shape[0]

    @property
    @deprecated(date=None, instructions="Depreceated, use .rect_limits or .inside to check if a value is inside or use"
                                        "rect_limits to receive the rectangular limits.")
    @warn_or_fail_not_rect
    def limit2d(self) -> Tuple[float, float, float, float]:
        """Simplified `limits` for exactly 2 obs, 1 limit: return the tuple(low_obs1, low_obs2, up_obs1, up_obs2).

        Returns:
            So `low_x, low_y, up_x, up_y = space.limit2d` for a single, 2 obs limit.
                low_x is the lower limit in x, up_x is the upper limit in x etc.

        Raises:
            RuntimeError: if the conditions (n_obs or n_limits) are not satisfied.
        """
        if not self.n_obs == 2:
            raise RuntimeError("Nobs is not two.")
        lower, upper = self.rect_limits
        return lower[:, 0], lower[:, 1], upper[:, 0], upper[:, 1]
        # raise BreakingAPIChangeError("This function is gone, use .rect_limits or .inside instead")

    @property
    def limits1d(self) -> Tuple[float]:
        """Simplified `.limits` for exactly 1 obs, n limits: return the tuple(low_1, ..., low_n, up_1, ..., up_n).

        Returns:
            So `low_1, low_2, up_1, up_2 = space.limits1d` for several, 1 obs limits.
                low_1 to up_1 is the first interval, low_2 to up_2 is the second interval etc.

        Raises:
            RuntimeError: if the conditions (n_obs or n_limits) are not satisfied.
        """
        raise BreakingAPIChangeError("This function is gone. Instead iterate through the space and get each limit out.")

    @property
    # @deprecated(date=None, instructions="Depreceated (currently) due to the unambiguous nature of the word."
    #                                     " Use `rect_lower` instead.")
    @warn_or_fail_not_rect
    def lower(self) -> ztyping.LowerTypeReturn:
        """Return the lower limits.

        Returns:
        """
        return self.rect_lower
        # raise BreakingAPIChangeError("Use rect_lower")

    @property
    # @deprecated(date=None, instructions="depreceated (currently) due to the unambiguous nature of the word."
    #                                     " Use `rect_upper` instead.")
    @warn_or_fail_not_rect
    def upper(self) -> ztyping.UpperTypeReturn:
        """Return the upper limits.

        Returns:
        """
        return self.rect_upper

    @property
    def n_limits(self) -> int:
        """The number of different limits.

        Returns:
            int >= 1
        """
        return len(tuple(self))

    @property
    @deprecated(date=None, instructions="Iterate over the space directly and"
                                        " use the limits from the spaces.")
    def iter_limits(self, as_tuple: bool = True) -> ztyping._IterLimitsTypeReturn:
        """REMOVED.Return the limits, either as :py:class:`~zfit.Space` objects or as pure limits-tuple.

        This makes iterating over limits easier: `for limit in space.iter_limits()`
        allows to, for example, pass `limit` to a function that can deal with simple limits
        only or if `as_tuple` is True the `limit` can be directly used to calculate something.

        Example:
            .. code:: python

                for lower, upper in space.iter_limits(as_tuple=True):
                    integrals = integrate(lower, upper)  # calculate integral
                integral = sum(integrals)


        Returns:
            List[:py:class:`~zfit.Space`] or List[limit,...]:
        """
        raise BreakingAPIChangeError

    def with_limits(self,
                    limits: ztyping.LimitsTypeInput = None,
                    rect_limits: Optional[ztyping.RectLimitsInputType] = None,
                    name: Optional[str] = None
                    ) -> ZfitSpace:
        """Return a copy of the space with the new `limits` (and the new `name`).

        Args:
            limits: Limits to use. Can be rectangular, a function (requires to also specify `rect_limits`
                or an instance of ZfitLimit.
            rect_limits: Rectangular limits that will be assigned with the instance
            name: Human readable name

        Returns:
            Copy of the current object with the new limits.
        """
        new_space = type(self)(obs=self.coords, limits=limits, rect_limits=rect_limits,
                               name=name)
        return new_space

    def reorder_x(self, x: Union[tf.Tensor, np.ndarray],
                  *,
                  x_obs: ztyping.ObsTypeInput = None,
                  x_axes: ztyping.AxesTypeInput = None,
                  func_obs: ztyping.ObsTypeInput = None,
                  func_axes: ztyping.AxesTypeInput = None
                  ) -> ztyping.XTypeReturnNoData:
        """Reorder x in the last dimension either according to its own obs or assuming a function ordered with func_obs.

        There are two obs or axes around: the one associated with this Coordinate object and the one associated with x.
        If x_obs or x_axes is given, then this is assumed to be the obs resp. the axes of x and x will be reordered
        according to `self.obs` resp. `self.axes`.

        If func_obs resp. func_axes is given, then x is assumed to have `self.obs` resp. `self.axes` and will be
        reordered to align with a function ordered with `func_obs` resp. `func_axes`.

        Switching `func_obs` for `x_obs` resp. `func_axes` for `x_axes` inverts the reordering of x.

        Args:
            x: Tensor to be reordered, last dimension should be n_obs resp. n_axes
            x_obs: Observables associated with x. If both, x_obs and x_axes are given, this has precedency over the
                latter.
            x_axes: Axes associated with x.
            func_obs: Observables associated with a function that x will be given to. Reorders x accordingly and assumes
                self.obs to be the obs of x. If both, `func_obs` and `func_axes` are given, this has precedency over the
                latter.
            func_axes: Axe associated with a function that x will be given to. Reorders x accordingly and assumes
                self.axes to be the axes of x.

        Returns:
            The reordered array-like object
        """
        return self.coords.reorder_x(x=x, x_obs=x_obs, x_axes=x_axes, func_obs=func_obs, func_axes=func_axes)

    def with_obs(self,
                 obs: Optional[ztyping.ObsTypeInput],
                 allow_superset: bool = True,
                 allow_subset: bool = True) -> ZfitSpace:
        """Create a new Space that has `obs`; sorted by or set or dropped.

        The behavior is as follows:

         * obs are already set:

           * input obs are None: the observables will be dropped. If no axes are set, an error
             will be raised, as no coordinates will be assigned to this instance anymore.
           * input obs are not None: the instance will be sorted by the incoming obs. If axes or other
             objects have an associated order (e.g. data, limits,...), they will be reordered as well.
             If a strict subset is given (and allow_subset is True), only a subset will be returned.
             This can be used to take a subspace of limits, data etc.
             If a strict superset is given (and allow_superset is True), the obs will be sorted accordingly as
             if the obs not contained in the instances obs were not in the input obs.
         * obs are not set:

           * if the input obs are None, the same object is returned.
           * if the input obs are not None, they will be set as-is and now correspond to the already
             existing axes in the object.

        Args:
            obs: Observables to sort/associate this instance with
            allow_superset: if False and a strict superset of the own observables is given, an error
            is raised.
            allow_subset:if False and a strict subset of the own observables is given, an error
            is raised.

        Returns:
            A copy of the object with the new ordering/observables

        Raises:
            CoordinatesUnderdefinedError: if obs is None and the instance does not have axes
            ObsIncompatibleError: if `obs` is a superset and allow_superset is False or a subset and
                allow_allow_subset is False
        """
        if obs is None:  # drop obs, check if there are axes
            if self.obs is None:
                return self
            if self.axes is None:
                raise AxesIncompatibleError("Cannot remove obs (using None) for a Space without axes")
            new_limits = self._limits_dict.copy()
            new_space = self.copy(obs=obs, limits=new_limits)
        else:
            obs = _convert_obs_to_str(obs)
            coords = self.coords.with_obs(obs, allow_superset=allow_superset, allow_subset=allow_subset)
            new_space = type(self)(coords, limits=self._limits_dict)
        return new_space

    def with_axes(self,
                  axes: Optional[ztyping.AxesTypeInput],
                  allow_superset: bool = True,
                  allow_subset: bool = True) -> ZfitSpace:
        """Create a new instance that has `axes`; sorted by or set or dropped.

        The behavior is as follows:

         * axes are already set:

           * input axes are None: the axes will be dropped. If no observables are set, an error
             will be raised, as no coordinates will be assigned to this instance anymore.
           * input axes are not None: the instance will be sorted by the incoming axes. If obs or other
             objects have an associated order (e.g. data, limits,...), they will be reordered as well.
             If a strict subset is given (and allow_subset is True), only a subset will be returned. This can
             be used to retrieve a subspace of limits, data etc.
             If a strict superset is given (and allow_superset is True), the axes will be sorted accordingly as
             if the axes not contained in the instances axes were not present in the input axes.
         * axes are not set:

           * if the input axes are None, the same object is returned.
           * if the input axes are not None, they will be set as-is and now correspond to the already
             existing obs in the object.

        Args:
            axes: Axes to sort/associate this instance with
            allow_superset: if False and a strict superset of the own axeservables is given, an error
            is raised.
            allow_subset:if False and a strict subset of the own axeservables is given, an error
            is raised.

        Returns:
            A copy of the object with the new ordering/axes
        Raises:
            CoordinatesUnderdefinedError: if obs is None and the instance does not have axes
            AxesIncompatibleError: if `axes` is a superset and allow_superset is False or a subset and
                allow_allow_subset is False
        """
        if axes is None:  # drop axes
            if self.axes is None:
                return self
            if self.obs is None:
                raise ObsIncompatibleError("Cannot remove axes (using None) for a Space without obs")
            new_limits = self._limits_dict.copy()
            new_space = self.copy(axes=axes, limits=new_limits)
        else:
            axes = convert_to_axes(axes)
            if self.axes is None:
                if not len(axes) == len(self.obs):
                    raise AxesIncompatibleError(f"Trying to set axes {axes} to object with obs {self.obs}")
                new_space = self.copy(axes=axes, limits=self._limits_dict)
            else:

                coords = self.coords.with_axes(axes=axes, allow_superset=allow_superset, allow_subset=allow_subset)
                new_space = type(self)(coords, limits=self._limits_dict)

        return new_space

    def with_coords(self,
                    coords: ZfitOrderableDimensional,
                    allow_superset: bool = True,
                    allow_subset: bool = True) -> "Space":
        """Create a new :py:class:`~zfit.Space` with reordered observables and/or axes.

        The behavior is that _at least one coordinate (obs or axes) has to be set in both instances
        (the space itself or in `coords`). If both match, observables is taken as the defining coordinate.
        The space is sorted according to the defining coordinate and the other coordinate is sorted as well.
        If either the space did not have the "weaker coordinate" (e.g. both have observables, but only coords
        has axes), then the resulting Space will have both.
        If both have both coordinates, obs and axes, and sorting for obs results in non-matchin axes results
        in axes being dropped.

        Args:
            coords: An instance of :py:class:`Coordinates`
            allow_superset: If `False` and a strict superset is given, an error is raised
            allow_subset: If `False` and a strict subset is given, an error is raised

        Returns:
            :py:class:`~zfit.Space`:
        Raises:
            CoordinatesUnderdefinedError: if neither both obs or axes are specified.
            CoordinatesIncompatibleError: if `coords` is a superset and allow_superset is False or a subset and
                allow_allow_subset is False
        """
        if self.obs is not None and coords.obs is not None:
            new_space_obs = self.with_obs(coords.obs, allow_superset=allow_superset, allow_subset=allow_subset)

            if coords.axes is not None:  # use this axes: first drop the other one
                if new_space_obs.axes is not None:
                    new_space_obs = new_space_obs.with_axes(None)
                # filter in case there are super/subsets
                coords_axes = coords.with_obs(new_space_obs.obs, allow_superset=allow_superset,
                                              allow_subset=allow_subset)
                new_space_obs = new_space_obs.with_axes(coords_axes.axes)  # are the same or self.axes is None
            new_space = new_space_obs


        elif self.axes is not None and coords.axes is not None:
            new_space_axes = self.with_axes(coords.axes, allow_superset=allow_superset, allow_subset=allow_subset)
            if coords.obs is not None:
                # filter in case there are super/subsets
                coords_obs = coords.with_axes(new_space_axes.axes, allow_superset=allow_superset,
                                              allow_subset=allow_subset)
                new_space_axes = new_space_axes.with_obs(coords_obs.obs)
            new_space = new_space_axes
        else:
            raise CoordinatesUnderdefinedError(f"Neither the axes nor the obs are specified in both objects"
                                               f" {self} and {coords}")

        return new_space

    def with_autofill_axes(self, overwrite: bool = False) -> "zfit.Space":
        """Overwrite the axes of the current object with axes corresponding to range(len(n_obs)).

        This effectively fills with (0, 1, 2,...) and can be used mostly when an object enters a PDF or
        similar. `overwrite` allows to remove the axis first in case there are already some set.

        .. code-block::

            object.obs -> ('x', 'z', 'y')
            object.axes -> None

            object.with_autofill_axes()

            object.obs -> ('x', 'z', 'y')
            object.axes -> (0, 1, 2)


        Args:
            overwrite: If axes are already set, replace the axes with the autofilled ones.
                If axes is already set and `overwrite` is False, raise an error.

        Returns:
            The object with the new axes

        Raises:
            AxesIncompatibleError: if the axes are already set and `overwrite` is False.
        """
        new_coords = self.coords.with_autofill_axes(overwrite=overwrite)
        # new_space = self.with_coords(new_coords)
        if self.axes is None or overwrite:
            new_space = self.copy(axes=new_coords.axes)
        else:
            new_space = self
        return new_space

    def get_subspace(self,
                     obs: ztyping.ObsTypeInput = None,
                     axes: ztyping.AxesTypeInput = None,
                     name: Optional[str] = None
                     ) -> "Space":
        """Create a :py:class:`~zfit.Space` consisting of only a subset of the `obs`/`axes` (only one allowed).

        Args:
            obs: Observables of the subspace to return.
            axes: Axes of the subspace to return.
            name: Human readable names

        Returns:
            A space containing only a subspace (and sublimits etc.)
        """
        if obs is not None and axes is not None:
            raise ValueError("Cannot specify `obs` *and* `axes` to get subspace.")
        if axes is None and obs is None:
            raise ValueError("Either `obs` or `axes` has to be specified and not None")

        # try to use observables to get index
        obs = self._check_convert_input_obs(obs=obs, allow_none=True)
        axes = self._check_convert_input_axes(axes=axes, allow_none=True)
        if obs is not None:
            limits_dict = self.get_limits(obs=obs)
            new_coords = self.coords.with_obs(obs, allow_subset=True, allow_superset=True)
        else:
            limits_dict = self.get_limits(axes=axes)
            new_coords = self.coords.with_axes(axes=axes, allow_subset=True, allow_superset=True)
        new_space = type(self)(obs=new_coords, limits=limits_dict)
        return new_space

    def with_obs_axes(self, **kwargs):
        raise BreakingAPIChangeError("What is this needed for?")

    def get_obs_axes(self, obs: ztyping.ObsTypeInput = None, axes: ztyping.AxesTypeInput = None):
        raise BreakingAPIChangeError("Simply get the coords if needed")

    # @deprecated(date=None, instructions="Use rect_area to obtain the rectangular area.")

    @property
    def obs_axes(self):
        raise BreakingAPIChangeError

    @warn_or_fail_not_rect
    def area(self) -> float:
        """Return the total area of all the limits and axes.

        Useful, for example, for MC integration.
        """
        return self.rect_area()

    def copy(self, **overwrite_kwargs) -> "zfit.Space":
        """Create a new :py:class:`~zfit.Space` using the current attributes and overwriting with
        `overwrite_overwrite_kwargs`.

        Args:
            name: The new name. If not given, the new instance will be named the same as the
                current one.
            **overwrite_kwargs:

        Returns:
            :py:class:`~zfit.Space`
        """
        kwargs = {'name': self.name,
                  'limits': self._limits_dict,
                  'axes': self.axes,
                  'obs': self.obs}
        kwargs.update(overwrite_kwargs)
        if set(overwrite_kwargs) - set(kwargs):
            raise KeyError(f"Not usable keys in `overwrite_kwargs`: {set(overwrite_kwargs) - set(kwargs)}")

        new_space = type(self)(**kwargs)
        return new_space

    # Operators

    def _inside(self, x, guarantee_limits):
        xs_inside = []
        obs_in_use = self.obs is not None
        limits_dict = self._limits_dict['obs' if obs_in_use else 'axes']
        for coords, limit in limits_dict.items():
            reorder_kwargs = {'func_obs' if obs_in_use else 'func_axes': coords}
            x_sub = self.reorder_x(x, **reorder_kwargs)
            x_inside = limit.inside(x_sub)
            xs_inside.append(x_inside)
        all_inside = znp.all(xs_inside, axis=0)
        return all_inside

    @property  # TODO(discussion): depreceate 1d limits? or keep?
    # @deprecated(date=None, instructions="depreceated, use `rect_limits` instead which has a similar functionality"
    #                                     " Use `inside` to check if an Tensor is inside the limits.")
    @warn_or_fail_not_rect
    def limit1d(self) -> Tuple[float, float]:
        """Simplified limits getter for 1 obs, 1 limit only: return the tuple(lower, upper).

        Returns:
            So :code:`lower, upper = space.limit1d` for a simple, 1 obs limit.

        Raises:
            RuntimeError: if the conditions (n_obs or n_limits) are not satisfied.
        """
        if self.n_obs > 1:
            raise RuntimeError(f"Cannot call `limit1d, as `Space` has more than one observables: {self.n_obs}")
        if self.n_limits > 1:
            raise RuntimeError(f"Cannot call `limit1d, as `Space` has several limits: {self.n_limits}")
        lower, upper = self.rect_limits
        return lower[0][0], upper[0][0]

    @classmethod
    @deprecated(date=None, instructions="Use directly the class to create a Space. E.g. zfit.Space(axes=(0, 1), ...)")
    def from_axes(cls, axes: ztyping.AxesTypeInput,
                  limits: Optional[ztyping.LimitsTypeInput] = None,
                  rect_limits=None,
                  name: str = None) -> "zfit.Space":
        """Create a space from `axes` instead of from `obs`.

        Args:
            rect_limits:
            axes:
            limits:
            name:

        Returns:
            :py:class:`~zfit.Space`
        """
        # TODO(v0.5):
        # raise BreakingAPIChangeError("from_axes is not needed anymore, create a Space directly.")
        axes = convert_to_container(value=axes, container=tuple)
        if axes is None:
            raise AxesNotSpecifiedError("Axes cannot be `None`")
        new_space = cls(axes=axes, limits=limits, rect_limits=rect_limits, name=name)
        return new_space


def extract_limits_from_dict(limits_dict, obs=None, axes=None):
    if (obs is None) and (axes is None):
        raise ValueError("Need to specify at least one, obs or axes.")
    elif (obs is not None) and (axes is not None):
        axes = None  # obs has precedency
    if obs is None:
        obs_in_use = False
        coords_to_extract = axes
    else:
        obs_in_use = True
        coords_to_extract = obs
    coords_to_extract = convert_to_container(coords_to_extract)
    coords_to_extract = set(coords_to_extract)

    limits_to_eval = {}
    limit_dict = limits_dict['obs' if obs_in_use else 'axes'].items()
    keys_sorted = sorted(limit_dict, key=lambda x: len(x[0]), reverse=True)
    for key_coords, limit in keys_sorted:
        coord_intersec = frozenset(key_coords).intersection(coords_to_extract)
        if not coord_intersec:  # this limit does not contain any requested obs
            continue
        if coord_intersec == frozenset(key_coords):
            if isinstance(limit, ZfitOrderableDimensional):  # drop coordinates if given
                if obs_in_use:
                    limit = limit.with_axes(None)
                else:
                    limit = limit.with_obs(None)
            limits_to_eval[key_coords] = limit
        else:
            coord_limit = [coord for coord in key_coords if coord in coord_intersec]
            kwargs = {'obs' if obs_in_use else 'axes': coord_limit}
            try:
                sublimit = limit.get_subspace(**kwargs)
            except InvalidLimitSubspaceError:
                raise InvalidLimitSubspaceError(f"Cannot extract {coord_intersec} from limit {limit}.")
            sublimit_coord = limit.obs if obs_in_use else limit.axes
            if isinstance(sublimit, ZfitOrderableDimensional):  # drop coordinates if given
                if obs_in_use:
                    sublimit = sublimit.with_axes(None)
                else:
                    sublimit = sublimit.with_obs(None)
            limits_to_eval[sublimit_coord] = sublimit
            coords_to_extract -= coord_intersec
    return limits_to_eval


def add_spaces(*spaces: Iterable["ZfitSpace"], name=None):
    """Add two spaces and merge their limits if possible or return False.

    Args:
        spaces:

    Returns:
        Union[None, :py:class:`~zfit.Space`, bool]:

    Raises:
        LimitsIncompatibleError: if limits of the `spaces` cannot be merged because they overlap
    """
    # spaces = convert_to_container(spaces)
    if not all(isinstance(space, ZfitSpace) for space in spaces):
        raise TypeError(f"Can only add type ZfitSpace, not {spaces}")
    return MultiSpace(spaces, name=name)


def get_coord(space, obs_in_use=True):
    if obs_in_use:
        return space.obs
    else:
        return space.axes


def combine_spaces(*spaces: Iterable[Space]):
    """Combine spaces with different `obs` and `limits` to one `space`.

    Checks if the limits in each obs coincide *exactly*. If this is not the case, the combination
    is not unambiguous and `False` is returned

    Args:
        spaces:

    Returns:
        Returns False if the limits don't coincide in one or more obs. Otherwise
            return the :py:class:`~zfit.Space` with all obs from `spaces` sorted by the order of `spaces` and with the
            combined limits.
    Raises:
        ValueError: if only one space is given
        LimitsIncompatibleError: If the limits of one or more spaces (or within a space) overlap
        LimitsNotSpecifiedError: If the limits for one or more obs but not all are None or False.
    """
    spaces = convert_to_container(spaces, container=tuple)
    # if len(spaces) <= 1:
    #     return spaces
    # raise ValueError("Need at least two spaces to test limit consistency.")  # TODO: allow? usecase?

    common_obs_ordered = common_obs(spaces=spaces)
    common_axes_ordered = common_axes(spaces=spaces)
    using_obs = bool(common_obs_ordered)
    common_coords_ordered = common_obs_ordered if using_obs else common_axes_ordered

    # sort the spaces
    if using_obs:
        spaces = tuple(space.with_obs(common_obs_ordered, allow_superset=True) for space in spaces)
        all_coords = [space.obs for space in spaces]
    elif common_axes_ordered:
        spaces = tuple(space.with_axes(common_axes_ordered, allow_superset=True) for space in spaces)
        all_coords = [space.axes for space in spaces]
    else:
        raise CoordinatesUnderdefinedError("Neither `obs` nor `axes` exist in all spaces.")

    all_limits_false = all([space.limits_are_false for space in spaces])
    all_limits_not_set = all([not space.limits_are_set for space in spaces])
    has_limits = [space.has_limits for space in spaces]
    if all_limits_false:
        limits = False
    elif all_limits_not_set:
        limits = None
    elif not all(has_limits):
        raise LimitsNotSpecifiedError("Limits either have to be set, not set, or False for all spaces to be combined.")
    else:
        space_combinations = tuple(itertools.product(*spaces))
        if len(space_combinations) > 1:  # there are MultiSpaces in there
            all_combinations = []
            for spa in space_combinations:
                with suppress(LimitsIncompatibleError):
                    all_combinations.append(combine_spaces(*spa))
                if not all_combinations:
                    raise LimitsIncompatibleError(f"The limits of {spaces} are all not compatible to be combined.")
            # filter, as can be False: non-overlapping limits e.g. if we have two MultiSpace
            filtered_combinations = [space for space in all_combinations if space is not False]

            return MultiSpace(spaces=all_combinations,
                              obs=common_obs_ordered if common_obs_ordered else None,
                              axes=common_axes_ordered if common_axes_ordered else None)
        # TODO: spaces that have multidim limits?
        limits_dict = {}

        non_unique_coords = set()
        unique_coords = set()
        for coord in common_coords_ordered:
            if sum(coord in coords for coords in all_coords) > 1:
                non_unique_coords.add(coord)
            else:
                unique_coords.add(coord)

        for coord in common_coords_ordered:
            if coord in unique_coords:
                space = [space for space in spaces if coord in get_coord(space, using_obs)][0]
                space = space.get_subspace(obs=unique_coords if using_obs else None,
                                           axes=None if using_obs else unique_coords)
                limits_dict.update(space.get_limits()['obs' if using_obs else 'axes'])
                for coord in get_coord(space, using_obs):
                    unique_coords.remove(coord)
            elif coord in non_unique_coords:
                non_unique_spaces = [space for space in spaces if coord in get_coord(space, using_obs)]
                common_coords_non_unique = list(set.intersection(*(set(get_coord(space, using_obs))
                                                                   for space in non_unique_spaces)))
                # do the below to check if we can take the subspace
                non_unique_subspaces = [space.get_subspace(obs=common_coords_non_unique if using_obs else None,
                                                           axes=None if using_obs else common_coords_non_unique)
                                        for space in non_unique_spaces]

                # TODO compare limits
                any_non_equal = any([non_unique_subspaces[0] != space for space in non_unique_subspaces[1:]])
                if any_non_equal:
                    raise LimitsIncompatibleError(f"Limits in coord {common_coords_non_unique} do not match for spaces"
                                                  f" {non_unique_subspaces}")

                non_unique_subspace = non_unique_subspaces[0]
                limits_dict.update(non_unique_subspace.get_limits()['obs' if using_obs else 'axes'])
                for coord in get_coord(non_unique_subspace, using_obs):
                    non_unique_coords.remove(coord)
            else:
                pass  # fine, since it is already satisfied by a space
        #
        # for coord in common_coords_ordered:
        #     space_with_coord = [space for space in spaces if coord in get_coord(space, using_obs)]
        #     assert not any(isinstance(space, MultiSpace) for space in space_with_coord), "bug, should be caught before."
        #     assert space_with_coord, "empty, cannot be. This is a bug."
        #     limits_coord = []
        #     for space in space_with_coord:
        #         if type(space) == Space:  # has to be the exact type, we use an implementation detail here
        #             limits_coord.append(space.get_limits(obs=coord if using_obs else None,
        #                                                  axes=coord if not using_obs else None))
        #         else:
        #             raise WorkInProgressError
        #             # limits_coord.append(space.with_obs(obs=coord) if using_obs else space.with_axes(axes=coord))
        #     any_non_equal = any([limits_coord[0][(coord,)] != limit[(coord,)] for limit in limits_coord[1:]])
        #     if any_non_equal:
        #         raise LimitsIncompatibleError(f"Limits in coord {coord} do not match for spaces {limits_coord}")
        #     limits_dict.update(limits_coord[0])

        limits = {'obs' if using_obs else 'axes': limits_dict}

    # all_lower = []
    # all_upper = []
    #
    # # create the lower and upper limits with all obs replacing missing dims with None
    # # With this, all limits have the same length
    # # TODO?
    # # if limits_overlap(spaces=spaces, allow_exact_match=True):
    # #     raise LimitsIncompatibleError("Limits overlap")
    #
    # for space in flatten_spaces(spaces):
    #     if space.limits is None:
    #         continue
    #     lowers, uppers = space.limits
    #     lower = [tuple(low[space.obs.index(ob)] for low in lowers) if ob in space.obs else None for ob in all_obs]
    #     upper = [tuple(up[space.obs.index(ob)] for up in uppers) if ob in space.obs else None for ob in all_obs]
    #     all_lower.append(lower)
    #     all_upper.append(upper)
    #
    # def check_extract_limits(limits_spaces):
    #     new_limits = []
    #
    #     if not limits_spaces:
    #         return None
    #     for index, obs in enumerate(all_obs):
    #         current_limit = None
    #         for limit in limits_spaces:
    #             lim = limit[index]
    #
    #             if lim is not None:
    #                 if current_limit is None:
    #                     current_limit = lim
    #                 elif not np.allclose(current_limit, lim):
    #                     return False
    #         else:
    #             if current_limit is None:
    #                 raise LimitsNotSpecifiedError("Limits in obs {} are not specified".format(obs))
    #             new_limits.append(current_limit)
    #
    #     n_limits = int(np.prod(tuple(len(lim) for lim in new_limits)))
    #     new_limits_comb = [[] for _ in range(n_limits)]
    #     for limit in new_limits:
    #         for lim in limit:
    #             for i in range(int(n_limits / len(limit))):
    #                 new_limits_comb[i].append(lim)
    #
    #     new_limits = tuple(tuple(limit) for limit in new_limits_comb)
    #     return new_limits

    # new_lower = check_extract_limits(all_lower)
    # new_upper = check_extract_limits(all_upper)
    # assert not (new_lower is None) ^ (new_upper is None), "Bug, please report issue. either both are defined or None."
    # if new_lower is None:
    #     limits = None
    # elif new_lower is False:
    #     return False
    # else:
    #     limits = (new_lower, new_upper)
    new_space = Space(obs=common_obs_ordered if using_obs else None, axes=None if using_obs else common_axes_ordered,
                      limits=limits)
    # if new_space.n_limits > 1:
    #     new_space = MultiSpace(Space, obs=all_obs)
    return new_space


def less_equal_space(space1, space2, allow_graph=True):
    return compare_multispace(space1=space1, space2=space2,
                              comparator=lambda limit1, limit2: limit1.less_equal(limit2, allow_graph=allow_graph))


def equal_space(space1, space2, allow_graph=True):
    return compare_multispace(space1=space1, space2=space2,
                              comparator=lambda limit1, limit2: limit1.equal(limit2, allow_graph=allow_graph))


def compare_multispace(space1: ZfitSpace, space2: ZfitSpace, comparator: Callable):
    """Compare multiple spaces if they have the same obs, axes, and, if a comparator is given, limits.

    It is automatically checked if the limits are set resp. are False

    Args:
        space1:
        space2:
        comparator:

    Returns:
    """
    axes_not_none = space1.axes is not None and space2.axes is not None
    obs_not_none = space1.obs is not None and space2.obs is not None
    if not (axes_not_none or obs_not_none):  # if both are None
        return False

    if obs_not_none:
        if set(space1.obs) != set(space2.obs):
            return False
    elif axes_not_none:  # axes only matter if there are no obs
        if set(space1.axes) != set(space2.axes):
            return False
    # check limits
    if not space1.limits_are_set:
        if not space2.limits_are_set:
            return True
        else:
            return False

    elif space1.limits_are_false:
        if space2.limits_are_false:
            return True
        else:
            return False

    return compare_limits_multispace(space1, space2, comparator=comparator)


def compare_limits_multispace(space1: ZfitSpace, space2: ZfitSpace, comparator: Callable) -> bool:
    if not len(space1) == len(space2):
        return False
    if not (space1.has_limits and space2.has_limits):
        return False
    space2_reordered = space2.with_coords(space1)

    comparison = []
    for space11 in space1:
        compare_spaces2 = []
        for space22 in space2_reordered:
            compare_spaces2.append(
                compare_limits_coords_dict(space11.get_limits(), space22.get_limits(), comparator=comparator))
        comparison.append(compare_spaces2)
    comparison = convert_to_tensor_or_numpy(comparison, dtype=tf.bool)
    space1_matches = z.unstable.reduce_any(comparison, axis=1)  # reduce over axis containing space2, has to match with
    # at least one space2.
    space2_matches = z.unstable.reduce_any(comparison, axis=0)
    all_space1_match = z.unstable.reduce_all(space1_matches, axis=0)
    all_space2_match = z.unstable.reduce_all(space2_matches, axis=0)

    return z.unstable.logical_and(all_space1_match, all_space2_match)


def compare_limits_coords_dict(limits1: Mapping[str, Mapping[Iterable, ZfitLimit]],
                               limits2: Mapping[str, Mapping[Iterable, ZfitLimit]],
                               comparator: Callable,
                               require_all_coord_types: bool = False) -> bool:
    if not limits1.keys() == limits2.keys() and require_all_coord_types:
        return False
    equal = []
    for coord_type, limit1_dict in limits1.items():
        limit2_dict = limits2.get(coord_type)
        if limit2_dict is None:
            continue
        equal.append(compare_limits_dict(limit1_dict, limit2_dict, comparator=comparator))
    return z.unstable.reduce_all(equal, axis=0)


def compare_limits_dict(dict1: Mapping, dict2: Mapping, comparator: Callable) -> bool:
    comparison = []
    limits2_to_check = dict2.copy()

    for coord, limit1 in dict1.items():
        for limit2cord, limit2 in limits2_to_check.items():
            if set(limit2cord) == set(coord):
                limit2 = limits2_to_check.pop(limit2cord)
                comparison.append(comparator(limit1, limit2))
                break

        else:  # no break, nothing matched
            return False
    return z.unstable.reduce_all(comparison, axis=0)


def flatten_spaces(spaces):
    return tuple(s for space in spaces for s in space)


class MultiSpace(BaseSpace):

    def __new__(cls,
                spaces: Iterable[ZfitSpace],
                obs: ztyping.ObsTypeInput = None,
                axes: ztyping.AxesTypeInput = None,
                name: str = None) -> Union[
        'Space', 'MultiSpace']:
        spaces, obs, axes = cls._check_convert_input_spaces_obs_axes(spaces, obs, axes)
        if len(spaces) == 1:
            return spaces[0]
        space = super().__new__(cls)

        # for the __init__ below, see there
        space._tmp_store_spaces_obs_axes = spaces, obs, axes

        return space

    def __init__(self, spaces: Iterable[ZfitSpace], obs=None, axes=None, name: str = None) -> None:
        # Since __new__ returns an instance of MultiSpace, __init__ is invoked. We don't want to reprocess
        # the input arguments here, so we store them above in the dummy attribute.
        del spaces, obs, axes  # not needed, we take the already preprocessed.
        spaces, obs, axes = self._tmp_store_spaces_obs_axes
        del self._tmp_store_spaces_obs_axes
        if name is None:
            name = "MultiSpace"
        super().__init__(obs, axes, name)
        self.spaces = spaces

    @staticmethod
    def _initialize_space(space, spaces, obs, axes):
        space._obs = obs
        space._axes = axes
        space.spaces = spaces
        return space

    @staticmethod
    def _check_convert_input_spaces_obs_axes(spaces, obs, axes):  # TODO: do something with axes
        spaces = flatten_spaces(spaces)
        all_have_obs = all(space.obs is not None for space in spaces)
        all_have_axes = all(space.axes is not None for space in spaces)
        n_events = [space.n_events in (spaces[0].n_events, None) for space in spaces]
        all_nevents_compatible = all(n_events)
        if not all_nevents_compatible:
            raise NumberOfEventsIncompatibleError("The number of events of the spaces do not coincide")
        if all_have_axes:
            axes = spaces[0].axes if axes is None else convert_to_axes(axes)

        if all_have_obs:
            obs = spaces[0].obs if obs is None else convert_to_obs_str(obs)
            spaces = [space.with_obs(obs, allow_subset=False, allow_superset=False) for space in spaces]
            if not (all_have_axes and all(space.axes == axes for space in spaces)):  # obs coincide, axes don't -> drop
                spaces = [space.with_axes(None) for space in spaces]
        elif all_have_axes:
            if all(space.obs is None for space in spaces):
                spaces = [space.with_axes(axes, allow_superset=False, allow_subset=False) for space in spaces]
            if not (all_have_obs and all(space.obs == obs for space in spaces)):  # axes coincide, obs don't -> drop
                spaces = [space.with_obs(None) for space in spaces]

        else:
            raise SpaceIncompatibleError("Spaces do not have consistent obs and/or axes.")

        if all(space.has_limits for space in spaces):
            # check overlap, reduce common limits
            pass
        elif not any(space.has_limits for space in spaces):
            spaces = [spaces[0]]  # if all are None, then nothing to add
        else:  # some have limits, some don't -> does not really make sense (or just drop the ones without limits?)
            raise LimitsIncompatibleError(
                "Some spaces have limits, other don't. This behavior may change in the future "
                "to allow spaces with None to be simply ignored.\n"
                "If you prefer this behavior, please open an issue on github.")

        spaces = tuple(spaces)

        return spaces, obs, axes

    # noinspection PyPropertyDefinition
    @property
    @warn_or_fail_not_rect
    def limits(self) -> None:
        self._raise_limits_not_implemented()

    # noinspection PyPropertyDefinition
    @property
    def rect_limits(self):
        self._raise_limits_not_implemented()

    # noinspection PyPropertyDefinition
    @property
    @warn_or_fail_not_rect
    def lower(self) -> None:
        self._raise_limits_not_implemented()

    # noinspection PyPropertyDefinition
    @property
    @warn_or_fail_not_rect
    def upper(self) -> None:
        self._raise_limits_not_implemented()

    # noinspection PyPropertyDefinition
    @property
    def rect_limits_np(self):
        self._raise_limits_not_implemented()

    # noinspection PyPropertyDefinition
    @property
    def rect_lower(self):
        self._raise_limits_not_implemented()

    # noinspection PyPropertyDefinition
    @property
    def rect_upper(self):
        self._raise_limits_not_implemented()

    def rect_area(self) -> Union[float, np.ndarray, tf.Tensor]:
        """Calculate the total rectangular area of all the limits and axes.

        Useful, for example, for MC integration.
        """
        return z.reduce_sum([space.rect_area() for space in self], axis=0)

    @property
    def rect_limits_are_tensors(self) -> bool:
        """Return True if the rectangular limits are tensors.

        If a limit with tensors is evaluated inside a graph context, comparison operations will fail.

        Returns:
            If the rectangular limits are tensors.
        """
        return all(space.limits_are_tensors for space in self)

    @property
    def has_rect_limits(self) -> bool:
        """If there are limits and whether they are rectangular."""
        return all(space.has_rect_limits for space in self.spaces)

    # noinspection PyPropertyDefinition

    @property
    def limits_are_false(self) -> bool:
        """If the limits have been set to False, so the object on purpose does not contain limits.

        Returns:
            True if limits is False
        """
        return all(space.limits_are_false for space in self.spaces)

    # noinspection PyPropertyDefinition

    @property
    def has_limits(self) -> bool:
        """Whether there are limits set and they are not false.

        Returns:
        """
        try:
            return self.limits_are_set and not self.limits_are_false
        except MultipleLimitsNotImplemented:
            return True

    @property
    def limits_are_set(self) -> bool:
        """If the limits have been set to a limit or are False.

        Returns:
            Whether the limits have been set or not.
        """
        return all(space.limits_are_set for space in self.spaces)

    @property
    def n_events(self) -> Union[int, None]:
        """Shape of the first dimension, usually reflects the number of events.

        Returns:
            Return the number of events, the dimension of the first shape. If this is > 1 or None,
                it's vectorized.
        """
        # get the first numeric n_events. Is None if a Tensor and not specified yet.
        n_events_first = [space.n_events for space in self if space.n_events is not None]
        n_events = None if not n_events_first else n_events_first[0]
        return n_events

    def with_limits(self,
                    limits: ztyping.LimitsTypeInput = None,
                    rect_limits: Optional[ztyping.RectLimitsInputType] = None,
                    name: Optional[str] = None
                    ) -> ZfitSpace:
        """Return a copy of the space with the new `limits` (and the new `name`).

        Args:
            limits: Limits to use. Can be rectangular, a function (requires to also specify `rect_limits`
                or an instance of ZfitLimit.
            rect_limits: Rectangular limits that will be assigned with the instance
            name: Human readable name

        Returns:
            Copy of the current object with the new limits.
        """
        new_space = self.copy(spaces=[space.with_limits(limits=limits, rect_limits=rect_limits)
                                      for space in self],
                              name=name)
        return new_space

    @warn_or_fail_not_rect
    def area(self) -> float:
        return self.rect_area()

    def with_obs(self,
                 obs: Optional[ztyping.ObsTypeInput],
                 allow_superset: bool = True,
                 allow_subset: bool = True) -> "MultiSpace":
        """Create a new Space that has `obs`; sorted by or set or dropped.

        The behavior is as follows:

         * obs are already set:
           * input obs are None: the observables will be dropped. If no axes are set, an error
             will be raised, as no coordinates will be assigned to this instance anymore.
           * input obs are not None: the instance will be sorted by the incoming obs. If axes or other
             objects have an associated order (e.g. data, limits,...), they will be reordered as well.
             If a strict subset is given (and allow_subset is True), only a subset will be returned.
             This can be used to take a subspace of limits, data etc.
             If a strict superset is given (and allow_superset is True), the obs will be sorted accordingly as
             if the obs not contained in the instances obs were not in the input obs.
         * obs are not set:
           * if the input obs are None, the same object is returned.
           * if the input obs are not None, they will be set as-is and now correspond to the already
             existing axes in the object.

        Args:
            obs: Observables to sort/associate this instance with
            allow_superset: if False and a strict superset of the own observables is given, an error
            is raised.
            allow_subset:if False and a strict subset of the own observables is given, an error
            is raised.

        Returns:
            A copy of the object with the new ordering/observables

        Raises:
            CoordinatesUnderdefinedError: if obs is None and the instance does not have axes
            ObsIncompatibleError: if `obs` is a superset and allow_superset is False or a subset and
                allow_allow_subset is False
        """
        spaces = [space.with_obs(obs, allow_superset=allow_superset, allow_subset=allow_subset)
                  for space in self.spaces]
        coords = self.coords.with_obs(obs, allow_subset=allow_subset, allow_superset=allow_superset)
        return self.copy(spaces=spaces, obs=coords.obs, axes=coords.axes)

    def with_axes(self,
                  axes: Optional[ztyping.AxesTypeInput],
                  allow_superset: bool = True,
                  allow_subset: bool = True) -> "MultiSpace":
        """Create a new instance that has `axes`; sorted by or set or dropped.

        The behavior is as follows:

         * axes are already set:
           * input axes are None: the axes will be dropped. If no observables are set, an error
             will be raised, as no coordinates will be assigned to this instance anymore.
           * input axes are not None: the instance will be sorted by the incoming axes. If obs or other
             objects have an associated order (e.g. data, limits,...), they will be reordered as well.
             If a strict subset is given (and allow_subset is True), only a subset will be returned. This can
             be used to retrieve a subspace of limits, data etc.
             If a strict superset is given (and allow_superset is True), the axes will be sorted accordingly as
             if the axes not contained in the instances axes were not present in the input axes.
         * axes are not set:
           * if the input axes are None, the same object is returned.
           * if the input axes are not None, they will be set as-is and now correspond to the already
             existing obs in the object.

        Args:
            axes: Axes to sort/associate this instance with
            allow_superset: if False and a strict superset of the own axeservables is given, an error
            is raised.
            allow_subset:if False and a strict subset of the own axeservables is given, an error
            is raised.

        Returns:
            A copy of the object with the new ordering/axes
        Raises:
            CoordinatesUnderdefinedError: if obs is None and the instance does not have axes
            AxesIncompatibleError: if `axes` is a superset and allow_superset is False or a subset and
                allow_allow_subset is False
        """
        spaces = [space.with_axes(axes, allow_superset=allow_superset, allow_subset=allow_subset)
                  for space in self.spaces]
        coords = self.coords.with_axes(axes, allow_subset=allow_subset, allow_superset=allow_superset)
        return self.copy(spaces=spaces, obs=coords.obs, axes=coords.axes)

    def with_coords(self,
                    coords: ZfitOrderableDimensional,
                    allow_superset: bool = True,
                    allow_subset: bool = True) -> "MultiSpace":
        """Create a new :py:class:`~zfit.Space` with reordered observables and/or axes.

        The behavior is that _at least one coordinate (obs or axes) has to be set in both instances
        (the space itself or in `coords`). If both match, observables is taken as the defining coordinate.
        The space is sorted according to the defining coordinate and the other coordinate is sorted as well.
        If either the space did not have the "weaker coordinate" (e.g. both have observables, but only coords
        has axes), then the resulting Space will have both.
        If both have both coordinates, obs and axes, and sorting for obs results in non-matchin axes results
        in axes being dropped.

        Args:
            coords: An instance of :py:class:`Coordinates`
            allow_superset: If false and a strict superset is given, an error is raised
            allow_subset: If false and a strict subset is given, an error is raised

        Returns:
            :py:class:`~zfit.Space`:
        Raises:
            CoordinatesUnderdefinedError: if neither both obs or axes are specified.
            CoordinatesIncompatibleError: if `coords` is a superset and allow_superset is False or a subset and
                allow_allow_subset is False
        """
        new_spaces = [space.with_coords(coords, allow_superset=allow_superset, allow_subset=allow_subset)
                      for space in self]
        return type(self)(spaces=new_spaces)

    def with_autofill_axes(self, overwrite: bool = False) -> "MultiSpace":
        """Overwrite the axes of the current object with axes corresponding to range(len(n_obs)).

        This effectively fills with (0, 1, 2,...) and can be used mostly when an object enters a PDF or
        similar. `overwrite` allows to remove the axis first in case there are already some set.

        .. code-block::

            object.obs -> ('x', 'z', 'y')
            object.axes -> None

            object.with_autofill_axes()

            object.obs -> ('x', 'z', 'y')
            object.axes -> (0, 1, 2)


        Args:
            overwrite: If axes are already set, replace the axes with the autofilled ones.
                If axes is already set and `overwrite` is False, raise an error.

        Returns:
            The object with the new axes

        Raises:
            AxesIncompatibleError: if the axes are already set and `overwrite` is False.
        """
        spaces = [space.with_autofill_axes(overwrite=overwrite) for space in self]
        return self.copy(spaces=spaces)

    def iter_limits(self, as_tuple=True):
        raise BreakingAPIChangeError("This should not be used anymore")

    def iter_areas(self, rel: bool = False) -> Tuple[float, ...]:
        raise BreakingAPIChangeError("This should not be used anymore")

    def get_subspace(self,
                     obs: ztyping.ObsTypeInput = None,
                     axes: ztyping.AxesTypeInput = None,
                     name: Optional[str] = None
                     ) -> "MultiSpace":
        """Create a :py:class:`~zfit.Space` consisting of only a subset of the `obs`/`axes` (only one allowed).

        Args:
            obs: Observables of the subspace to return.
            axes: Axes of the subspace to return.
            name: Human readable names

        Returns:
            A space containing only a subspace (and sublimits etc.)
        """
        spaces = [space.get_subspace(obs=obs, axes=axes) for space in self.spaces]
        return self.copy(spaces=spaces)

    def copy(self, *, deep: bool = False, name: Optional[str] = None, **overwrite_params) -> "MultiSpace":
        assert not deep, "deep not explicitly implemented, should not be needed for immutable objects"
        kwargs = dict(
            spaces=tuple(self),
            obs=self.obs,
            axes=self.axes,
        )
        kwargs.update(overwrite_params)
        kwargs['name'] = self.name if name is None else name
        new_space = type(self)(**kwargs)
        return new_space

    def _raise_limits_not_implemented(self):
        raise MultipleLimitsNotImplemented(
            "Limits/lower/upper not implemented for MultiSpace. This error is either caught"
            " automatically as part of the codes logic or the MultiLimit case should"
            " be considered. To do that, simply iterate through the MultiSpace, which returns"
            " a simple space. Iterating through a Spaces also works"
            "for simple spaces.")

    def _inside(self, x, guarantee_limits):
        inside_limits = [space.inside(x, guarantee_limits=guarantee_limits) for space in self]
        inside = znp.any(inside_limits, axis=0)  # has to be inside one limit
        return inside

    def __iter__(self) -> ZfitSpace:
        yield from self.spaces

    def __repr__(self):
        class_name = str(self.__class__).split('.')[-1].split('\'')[0]
        if not self.limits_are_set:
            limits = None
        elif self.limits_are_false:
            limits = False
        elif self.has_rect_limits:
            if self.n_obs < 3 and not self.n_events > 1 and self.n_limits <= 3:

                limits = [lim.rect_limits for lim in self]
            else:
                limits = 'rectangular'
        else:
            limits = 'functional'
        return f"<zfit {class_name} obs={self.obs}, axes={self.axes}, limits={limits}>"

    def __eq__(self, other):
        # in principle, two disjoint regions could have coinciding lower and upper limits equaling to an actually larger
        # space. However, we ignore this case and say that l1 to u1 and l2 to u2 is never the same as l1 to u2,
        # even if u1 == l2 (and they mathematically coincide).
        if not isinstance(other, MultiSpace):
            warnings.warn("Multispace limits compare never equal to Space.", stacklevel=2)
        all_equal = equal_space(self, other, allow_graph=False)
        return all_equal

    def __le__(self, other):
        # in principle, two disjoint regions could have coinciding lower and upper limits equaling to an actually larger
        # space. However, we ignore this case and say that l1 to u1 and l2 to u2 is never the same as l1 to u2,
        # even if u1 == l2 (and they mathematically coincide).
        if not isinstance(other, MultiSpace):
            warnings.warn("Multispace limits compare never equal to Space.", stacklevel=2)
        all_less_equal = less_equal_space(self, other, allow_graph=False)
        return all_less_equal

    def __hash__(self):
        return hash(self.spaces)


def convert_to_space(obs: Optional[ztyping.ObsTypeInput] = None, axes: Optional[ztyping.AxesTypeInput] = None,
                     limits: Optional[ztyping.LimitsTypeInput] = None,
                     *, overwrite_limits: bool = False, one_dim_limits_only: bool = True,
                     simple_limits_only: bool = True) -> Union[None, ZfitSpace, bool]:
    """Convert *limits* to a :py:class:`~zfit.Space` object if not already None or False.

    Args:
        obs:
        limits:
        axes:
        overwrite_limits: If `obs` or `axes` is a :py:class:`~zfit.Space` _and_ `limits` are given, return an instance
            of :py:class:`~zfit.Space` with the new limits. If the flag is `False`, the `limits` argument will be
            ignored if
        one_dim_limits_only:
        simple_limits_only:

    Returns:
        Union[:py:class:`~zfit.Space`, False, None]:

    Raises:
        OverdefinedError: if `obs` or `axes` is a :py:class:`~zfit.Space` and `axes` respectively `obs` is not `None`.
    """
    space = None

    # Test if already `Space` and handle
    if isinstance(obs, ZfitSpace):
        if axes is not None:
            raise OverdefinedError("if `obs` is a `Space`, `axes` cannot be defined.")
        space = obs
    elif isinstance(axes, ZfitSpace):
        if obs is not None:
            raise OverdefinedError("if `axes` is a `Space`, `obs` cannot be defined.")
        space = axes
    elif isinstance(limits, ZfitSpace):
        return limits
    if space is not None:
        # set the limits if given
        if limits is not None and (overwrite_limits or not space.limits_are_set):
            if isinstance(limits, ZfitSpace):  # figure out if compatible if limits is `Space`
                if not (limits.obs == space.obs or
                        (limits.axes == space.axes and limits.obs is None and space.obs is None)):
                    raise IntentionAmbiguousError(
                        "`obs`/`axes` is a `Space` as well as the `limits`, but the "
                        "obs/axes of them do not match")
                elif limits.limits_are_false:
                    limits = False
                else:
                    limits = limits.limits

            space = space.with_limits(limits=limits)
        return space

    # space is None again
    if not (obs is None and axes is None):
        # check if limits are allowed
        space = Space(obs=obs, axes=axes, limits=limits)  # create and test if valid
        if one_dim_limits_only and space.n_obs > 1 and space.has_limits:
            raise LimitsUnderdefinedError(
                "Limits more sophisticated than 1-dim cannot be auto-created from tuples. Use `Space` instead.")
        if simple_limits_only and space.has_limits and space.n_limits > 1:
            raise LimitsUnderdefinedError("Limits with multiple limits cannot be auto-created"
                                          " from tuples. Use `Space` instead.")
    return space


def no_norm_range(func):
    """Decorator: Catch the 'norm_range' kwargs. If not None, raise NormRangeNotImplementedError."""
    parameters = inspect.signature(func).parameters
    keys = list(parameters.keys())
    if 'norm_range' in keys:
        norm_range_index = keys.index('norm_range')
    else:
        norm_range_index = None

    @functools.wraps(func)
    def new_func(*args, **kwargs):
        norm_range = kwargs.get('norm_range')
        if isinstance(norm_range, ZfitSpace):
            norm_range_not_false = not norm_range.limits_are_false
        else:
            norm_range_not_false = not (norm_range is None or norm_range is False)
        if norm_range_index is not None:
            norm_range_is_arg = len(args) > norm_range_index
        else:
            norm_range_is_arg = False
            kwargs.pop('norm_range', None)  # remove if in signature (= norm_range_index not None)
        if norm_range_not_false or norm_range_is_arg:
            raise NormRangeNotImplemented()
        else:
            return func(*args, **kwargs)

    return new_func


def no_multiple_limits(func):
    """Decorator: Catch the 'limits' kwargs. If it contains multiple limits, raise MultipleLimitsNotImplementedError."""
    parameters = inspect.signature(func).parameters
    keys = list(parameters.keys())
    if 'limits' in keys:
        limits_index = keys.index('limits')
    else:
        return func  # no limits as parameters -> no problem

    @functools.wraps(func)
    def new_func(*args, **kwargs):
        limits_is_arg = len(args) > limits_index
        if limits_is_arg:
            limits = args[limits_index]
        else:
            limits = kwargs['limits']

        if limits.n_limits > 1:
            raise MultipleLimitsNotImplemented
        else:
            return func(*args, **kwargs)

    return new_func


def supports(*, norm_range: bool = False, multiple_limits: bool = False) -> Callable:
    """Decorator: Add (mandatory for some methods) on a method to control what it can handle.

    If any of the flags is set to False, it will check the arguments and, in case they match a flag
    (say if a *norm_range* is passed while the *norm_range* flag is set to `False`), it will
    raise a corresponding exception (in this example a `NormRangeNotImplementedError`) that will
    be catched by an earlier function that knows how to handle things.

    Args:
        norm_range: If False, no norm_range argument will be passed through resp. will be `None`
        multiple_limits: If False, only simple limits are to be expected and no iteration is
            therefore required.
    """
    decorator_stack = []
    if not multiple_limits:
        decorator_stack.append(no_multiple_limits)
    if not norm_range:
        decorator_stack.append(no_norm_range)

    def create_deco_stack(func):
        for decorator in reversed(decorator_stack):
            func = decorator(func)
        func.__wrapped__ = supports
        return func

    return create_deco_stack


def contains_tensor(objects):
    tensor_found = tf.is_tensor(objects)
    with suppress(TypeError):

        for obj in objects:
            if tensor_found:
                break
            tensor_found += contains_tensor(obj)
    return tensor_found


def shape_np_tf(objects):
    if contains_tensor(objects):
        shape = tuple(tf.convert_to_tensor(objects).shape.as_list())
    else:
        shape = np.shape(objects)
    return shape


def limits_consistent(spaces: Iterable["zfit.Space"]):
    """Check if space limits are the *exact* same in each obs they are defined and therefore are compatible.

    In this case, if a space has several limits, e.g. from -1 to 1 and from 2 to 3 (all in the same observable),
    to be consistent with this limits, other limits have to have (in this obs) also the limits
    from -1 to 1 and from 2 to 3. Only having the limit -1 to 1 _or_ 2 to 3 is considered _not_ consistent.

    This function is useful to check if several spaces with *different* observables can be _combined_.

    Args:
        spaces:

    Returns:
    """
    try:
        new_space = combine_spaces(*spaces)
    except LimitsIncompatibleError:
        return False
    else:
        return True


def add_spaces_old(spaces: Iterable["zfit.Space"]):
    """Add two spaces and merge their limits if possible or return False.

    Args:
        spaces:

    Returns:
        Union[None, :py:class:`~zfit.Space`, bool]:

    Raises:
        LimitsIncompatibleError: if limits of the `spaces` cannot be merged because they overlap
    """
    spaces = convert_to_container(spaces)
    if not all(isinstance(space, ZfitSpace) for space in spaces):
        raise TypeError("Cannot only add type ZfitSpace")
    if len(spaces) <= 1:
        raise ValueError("Need at least two spaces to be added.")  # TODO: allow? usecase?
    obs = frozenset(frozenset(space.obs) for space in spaces)

    if len(obs) != 1:
        return False

    obs1 = spaces[0].obs
    spaces = [space.with_obs(obs=obs1) if not space.obs == obs1 else space for space in spaces]

    if limits_overlap(spaces=spaces, allow_exact_match=True):
        raise LimitsIncompatibleError("Limits of spaces overlap, cannot merge spaces.")

    lowers = []
    uppers = []
    for space in spaces:
        if not space.limits_are_set:
            continue
        for lower, upper in space:
            for other_lower, other_upper in zip(lowers, uppers):
                lower_same = np.allclose(lower, other_lower)
                upper_same = np.allclose(upper, other_upper)
                assert not lower_same ^ upper_same, "Bug, please report as issue. limits_overlap did not catch right."
                if lower_same and upper_same:
                    break
            else:
                lowers.append(lower)
                uppers.append(upper)
    lowers = tuple(lowers)
    uppers = tuple(uppers)
    if len(lowers) == 0:
        limits = None
    else:
        limits = lowers, uppers
    new_space = zfit.Space(obs=spaces[0].obs, limits=limits)
    return new_space
