Space, Observable and Range#
Space defines the domain of objects by specifying the observables/axes and maybe also
the limits. Any model and data needs to be specified in a certain domain, which is usually done using the
obs argument. It is crucial that the axis used by the observable of the data and the model match, and this matching is
handle by the
import zfit from zfit import z import numpy as np
obs = zfit.Space("x") model = zfit.pdf.Gauss(obs=obs, ...) data = zfit.Data.from_numpy(obs=obs, ...)
Space: an n-dimensional definition of a domain (either by using one or more observables or axes), with or without limits.
Difference to RooFit
compared to ``RooFit``, a space is **not* the equivalent of an observable but rather corresponds
to an object combining a set of observables (which of course can be of size 1). Furthermore,
there is a strong distinction in zfit between a
Space (or observables)
Parameter, both conceptually and in terms of implementation and usage.*
Observable: a string defining the axes; a named axes.
(for advanced usage only, can be skipped on first read) Axis: integer defining the axes internally of a model. There is always a mapping of observables <-> axes once inside a model.
- Limit The range on a certain axis. Typically defines an interval. In fact, there are two times of limits:
rectangular: This type is the usual limit as e.g.
(-2, 5)for a simple, 1 dimensional interval. It is rectangular. This can either be given as
functional: In order to define arbitrary limits, a function can be used that receives a tensor-like object
Trueon every position that is inside the limits,
Falsefor every value outside. When a functional limit is given, rectangular limits that contain the functional limit as a subset must be defined as well.
Since every object has a well defined domain, it is possible to combine them in an unambiguous way.
While not enforced, a space should usually be created with limits that define the default space of an object.
This correspond for example to the default normalization range
norm_range or sampling range.
lower1, upper1 = [0, 1], [2, 3] lower2, upper2 = [-4, 1], [10, 3] obs1 = zfit.Space(['x', 'y'], limits=(lower1, upper2)) obs2 = zfit.Space(['z', 'y'], limits=(lower2, upper2)) model1 = zfit.pdf.Gauss(obs=obs1, ...) model2 = zfit.pdf.Gauss(obs=obs2, ...) # creating a composite pdf product = model1 * model2 # OR, equivalently product = zfit.pdf.ProductPDF([model1, model2]) assert obs1 * obs2 == product.space
product is now defined in the space with observables
['x', 'y', 'z']. Any
to be combined with
product has to be specified in the same space.
# create the space combined_obs = obs1 * obs2 data = zfit.Data.from_numpy(obs=combined_obs, ...)
Now we have a
Data object that is defined in the same domain as
and can be used to build a loss function.
In many places, just defining the observables is not enough and an interval, specified by its limits, is required. Examples are a normalization range, the limits of an integration or sampling in a certain region.
Simple, 1-dimensional limits can be specified as follows. Operations like addition (creating a space with two intervals) or combination (increase the dimensionality) are also possible.
simple_limit1 = zfit.Space(obs='obs1', limits=(-5, 1)) simple_limit2 = zfit.Space(obs='obs1', limits=(3, 7.5)) added_limits = simple_limit1 + simple_limit2
In this case,
added_limits is now a
zfit.Space with observable
obs1' defined in the intervals
(-5, 1) and (3, 7.5). This can be useful, e.g., when fitting in two regions.
An example of the product of different
zfit.Space instances has been shown before as
Limits can be defined by a function that returns whether a value is inside the boundaries or not and rectangular
limits (note that specifying
rect_limit does not enforce them, the function itself has to take care of that).
This example specifies the bounds between (-4, 0.5) with the
limit_fn (which, in this simple case, could be better
achieved by directly specifying them as rectangular limits).
def limit_fn(x): x = z.unstack_x(x) inside_lower = tf.greater_equal(x, -4) inside_upper = tf.less_equal(x, 0.5) inside = tf.logical_and(inside_lower, inside_upper) return inside space = zfit.Space(obs='obs1', limits=limit_fn, rect_limits=(-5, 1))
To define simple, 1-dimensional limits, a tuple with two numbers or a functional
limit in 1 dimension is enough. For anything more complicated,
the operators product
* or addition
+ respectively their functional API
zfit.dimension.add_spaces() can be used.
A working code example of
Space handling is provided in spaces.py.
Using the limits#
To use the limits of any object, the methods
(to test if values are inside or outside of the boundaries)
filter() can be used.
The rectangular limits can also direclty be accessed by
The returned shape is of
(n_events, n_obs), for the lower respectively upper limit (
rect_limits is a tuple of
This should be used with caution and only if the rectangular limits are desired.