/
ak_linear_fit.py
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/
ak_linear_fit.py
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# BSD 3-Clause License; see https://github.com/scikit-hep/awkward/blob/main/LICENSE
from __future__ import annotations
import awkward as ak
from awkward._backends.numpy import NumpyBackend
from awkward._dispatch import high_level_function
from awkward._layout import HighLevelContext, ensure_same_backend
from awkward._nplikes import ufuncs
from awkward._nplikes.numpy_like import NumpyMetadata
from awkward._regularize import regularize_axis
__all__ = ("linear_fit",)
cpu = NumpyBackend.instance()
np = NumpyMetadata.instance()
@high_level_function()
def linear_fit(
x,
y,
weight=None,
axis=None,
*,
keepdims=False,
mask_identity=False,
highlevel=True,
behavior=None,
attrs=None,
):
"""
Args:
x: One coordinate to use in the linear fit (anything #ak.to_layout recognizes).
y: The other coordinate to use in the linear fit (anything #ak.to_layout recognizes).
weight: Data that can be broadcasted to `x` and `y` to give each point
a weight. Weighting points equally is the same as no weights;
weighting some points higher increases the significance of those
points. Weights can be zero or negative.
axis (None or int): If None, combine all values from the array into
a single scalar result; if an int, group by that axis: `0` is the
outermost, `1` is the first level of nested lists, etc., and
negative `axis` counts from the innermost: `-1` is the innermost,
`-2` is the next level up, etc.
keepdims (bool): If False, this function decreases the number of
dimensions by 1; if True, the output values are wrapped in a new
length-1 dimension so that the result of this operation may be
broadcasted with the original array.
mask_identity (bool): If True, the application of this function on
empty lists results in None (an option type); otherwise, the
calculation is followed through with the reducers' identities,
usually resulting in floating-point `nan`.
highlevel (bool): If True, return an #ak.Array; otherwise, return
a low-level #ak.contents.Content subclass.
behavior (None or dict): Custom #ak.behavior for the output array, if
high-level.
attrs (None or dict): Custom attributes for the output array, if
high-level.
Computes the linear fit of `y` with respect to `x` (many types supported,
including all Awkward Arrays and Records, must be broadcastable to each
other). The grouping is performed the same way as for reducers, though
this operation is not a reducer and has no identity.
This function has no NumPy equivalent.
Passing all arguments to the reducers, the linear fit is calculated as
sumw = ak.sum(weight)
sumwx = ak.sum(weight * x)
sumwy = ak.sum(weight * y)
sumwxx = ak.sum(weight * x**2)
sumwxy = ak.sum(weight * x * y)
delta = (sumw*sumwxx) - (sumwx*sumwx)
intercept = ((sumwxx*sumwy) - (sumwx*sumwxy)) / delta
slope = ((sumw*sumwxy) - (sumwx*sumwy)) / delta
intercept_error = np.sqrt(sumwxx / delta)
slope_error = np.sqrt(sumw / delta)
The results, `intercept`, `slope`, `intercept_error`, and `slope_error`,
are given as an #ak.Record with four fields. The values of these fields
might be arrays or even nested arrays; they match the structure of `x` and
`y`.
See #ak.sum for a complete description of handling nested lists and
missing values (None) in reducers, and #ak.mean for an example with another
non-reducer.
"""
# Dispatch
yield x, y, weight
# Implementation
return _impl(
x, y, weight, axis, keepdims, mask_identity, highlevel, behavior, attrs
)
def _impl(x, y, weight, axis, keepdims, mask_identity, highlevel, behavior, attrs):
axis = regularize_axis(axis)
with HighLevelContext(behavior=behavior, attrs=attrs) as ctx:
x_layout, y_layout, weight_layout = ensure_same_backend(
ctx.unwrap(x, allow_record=False, primitive_policy="error"),
ctx.unwrap(y, allow_record=False, primitive_policy="error"),
ctx.unwrap(
weight,
allow_record=False,
allow_unknown=False,
primitive_policy="error",
none_policy="pass-through",
),
)
x = ctx.wrap(x_layout)
y = ctx.wrap(y_layout)
weight = ctx.wrap(weight_layout, allow_other=True)
with np.errstate(invalid="ignore", divide="ignore"):
if weight is None:
sumw = ak.operations.ak_count._impl(
x,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwx = ak.operations.ak_sum._impl(
x,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwy = ak.operations.ak_sum._impl(
y,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwxx = ak.operations.ak_sum._impl(
x**2,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwxy = ak.operations.ak_sum._impl(
x * y,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
else:
sumw = ak.operations.ak_sum._impl(
x * 0 + weight,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwx = ak.operations.ak_sum._impl(
x * weight,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwy = ak.operations.ak_sum._impl(
y * weight,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwxx = ak.operations.ak_sum._impl(
(x**2) * weight,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
sumwxy = ak.operations.ak_sum._impl(
x * y * weight,
axis,
keepdims,
mask_identity,
highlevel=True,
behavior=ctx.behavior,
attrs=ctx.attrs,
)
delta = (sumw * sumwxx) - (sumwx * sumwx)
intercept = ((sumwxx * sumwy) - (sumwx * sumwxy)) / delta
slope = ((sumw * sumwxy) - (sumwx * sumwy)) / delta
intercept_error = ufuncs.sqrt(sumwxx / delta)
slope_error = ufuncs.sqrt(sumw / delta)
is_scalar = not isinstance(
ak.operations.to_layout(intercept, primitive_policy="pass-through"),
ak.contents.Content,
)
intercept = ak.operations.to_layout(intercept)
slope = ak.operations.to_layout(slope)
intercept_error = ak.operations.to_layout(intercept_error)
slope_error = ak.operations.to_layout(slope_error)
out = ak.contents.RecordArray(
[intercept, slope, intercept_error, slope_error],
["intercept", "slope", "intercept_error", "slope_error"],
parameters={"__record__": "LinearFit"},
)
if is_scalar:
out = out[0]
return ctx.wrap(out, highlevel=highlevel, allow_other=is_scalar)