# Space¶

class zfit.dimension.Space(obs=None, limits=None, axes=None, rect_limits=None, name='Space')[source]

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.

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.

Parameters
property rect_limits

Return the rectangular limits as np.ndarraytf.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 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.

Return type

Tuple[Union[ndarray, Tensor, float], Union[ndarray, Tensor, float]]

Returns

The lower and upper limits.

Raises

LimitsNotSpecifiedError – If there are not limits set or they are False.

property rect_limits_np

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.

Return type

Tuple[ndarray, ndarray]

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
property rect_lower

The lower, rectangular limits, equivalent to rect_limits[0] with shape (…, n_obs)

Return type

Union[ndarray, Tensor, float]

Returns

The lower, rectangular limits as np.ndarray or tf.Tensor

Raises

LimitsNotSpecifiedError – If the limits are not set or are false

property rect_upper

The upper, rectangular limits, equivalent to rect_limits[1] with shape (…, n_obs)

Return type

Union[ndarray, Tensor, None, bool]

Returns

The upper, rectangular limits as np.ndarray or tf.Tensor

Raises

LimitsNotSpecifiedError – If the limits are not set or are false

rect_area()[source]

Calculate the total rectangular area of all the limits and axes. Useful, for example, for MC integration.

Return type

Union[float, ndarray, Tensor]

property rect_limits_are_tensors

Return True if the rectangular limits are tensors.

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

Return type

bool

Returns

If the rectangular limits are tensors.

property has_rect_limits

If there are limits and whether they are rectangular.

Return type

bool

property limits_are_false

If the limits have been set to False, so the object on purpose does not contain limits.

Return type

bool

Returns

True if limits is False

property has_limits

Whether there are limits set and they are not false.

Returns:

Return type

bool

property n_events

Return the number of events, the dimension of the first shape.

Return type
Returns

Number of events, the dimension of the first shape. If this is > 1 or None,

it’s vectorized.

property limit2d

DEPRECATED FUNCTION

Warning: THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: Depreceated, use .rect_limits or .inside to check if a value is inside or userect_limits to receive the rectangular limits.

property limits1d

return the tuple(low_1, …, low_n, up_1, …, up_n).

Return type
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.

Type

Simplified .limits for exactly 1 obs, n limits

property n_limits

The number of different limits.

Return type

int

Returns

int >= 1

property iter_limits

REMOVED.Return the limits, either as Space objects or as pure limits-tuple. (deprecated)

Warning: THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: Iterate over the space directly and use the limits from the spaces.

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

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

Returns

Return type

List[Space] or List[limit,…]

with_limits(limits=None, rect_limits=None, name=None)[source]

Return a copy of the space with the new limits (and the new name).

Parameters
Return type

ZfitSpace

Returns

Copy of the current object with the new limits.

reorder_x(x, *, x_obs=None, x_axes=None, func_obs=None, func_axes=None)[source]

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.

Parameters
Return type

Union[ndarray, Tensor]

Returns

The reordered array-like object

with_obs(obs, allow_superset=True, allow_subset=True)[source]

Create a new Space that has obs; sorted by or set or dropped.

The behavior is as follows:

• 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.

Parameters
Return type

ZfitSpace

Returns

A copy of the object with the new ordering/observables

Raises
with_axes(axes, allow_superset=True, allow_subset=True)[source]

Create a new instance that has axes; sorted by or set or dropped.

The behavior is as follows:

• 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.

Parameters
Return type

ZfitSpace

Returns

A copy of the object with the new ordering/axes

Raises
with_coords(coords, allow_superset=True, allow_subset=True)[source]

Create a new 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.

Parameters
Returns

Return type

Space

Raises
with_autofill_axes(overwrite=False)[source]

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.

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

object.with_autofill_axes()

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

Parameters

overwrite (bool) – If axes are already set, replace the axes with the autofilled ones. If axes is already set and overwrite is False, raise an error.

Return type

Space

Returns

The object with the new axes

Raises

AxesIncompatibleError – if the axes are already set and overwrite is False.

get_subspace(obs=None, axes=None, name=None)[source]

Create a Space consisting of only a subset of the obs/axes (only one allowed).

Parameters
Return type

Space

Returns

A space containing only a subspace (and sublimits etc.)

copy(**overwrite_kwargs)[source]

Create a new Space using the current attributes and overwriting with overwrite_overwrite_kwargs.

Parameters
• name – The new name. If not given, the new instance will be named the same as the current one.

• **overwrite_kwargs

Return type

Space

Returns

Space

classmethod from_axes(cls, axes, limits=None, rect_limits=None, name=None)[source]

Create a space from axes instead of from obs. (deprecated)

Warning: THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: Use directly the class to create a Space. E.g. zfit.Space(axes=(0, 1), …)

Parameters
Return type

Space

Returns

Space

__eq__(other)

Compares two Limits for equality without graph mode allowed.

Returns:

Raises

IllegalInGraphModeError – it the comparison happens with tensors in a graph context.

Return type

bool

__le__(other)

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.

Return type

bool

Returns

Result of the comparison

Raises

IllegalInGraphModeError – it the comparison happens with tensors in a graph context.

add(*other)

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.

Parameters
Returns

Return type

Space

property axes

The axes (“obs with int”) the space is defined in.

Returns:

Return type
combine(*other)

Combine spaces with different obs (but consistent limits).

Parameters
Returns

Return type

Space

equal(other, allow_graph)

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.

Return type

Union[bool, Tensor]

Returns

Result of the comparison

Raises

IllegalInGraphModeError – it the comparison happens with tensors in a graph context.

filter(x, guarantee_limits=False, axis=None)

Filter x by removing the elements along axis that are not inside the limits.

Parameters
• x (Union[ndarray, Tensor, Data]) – 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 (bool) – Guarantee that the values are already inside the rectangular limits.

• axis (Optional[int]) – The axis to remove the elements from. Defaults to 0.

Return type

Union[ndarray, Tensor]

Returns

Return an object with the same shape as x except that along axis elements have been

removed.

get_reorder_indices(obs=None, axes=None)

Indices that would order the instances obs as obs respectively the instances axes as axes.

Parameters
Return type
Returns

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

Raises

CoordinatesUnderdefinedError – If neither obs nor axes is given

inside(x, guarantee_limits=False)

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

Parameters
• x (Union[ndarray, Tensor, Data]) – 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 (bool) – Guarantee that the values are already inside the rectangular limits.

Return type

Union[ndarray, Tensor, Data]

Returns

Return a boolean tensor-like object with the same shape as the input x except of the

last dimension removed.

less_equal(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.

Parameters
• 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.

property n_obs

Return the number of observables/axes.

Return type

int

Returns

int >= 1

property name

The name of the object.

Return type

str

property obs

The observables (“axes with str”)the space is defined in.

Returns:

Return type