ak.linear_fit
-------------
.. py:module: ak.linear_fit
Defined in `awkward.operations.ak_linear_fit `__ on `line 18 `__.
.. py:function:: ak.linear_fit(x, y, weight=None, axis=None, *, keepdims=False, mask_identity=False)
:param x: One coordinate to use in the linear fit (anything :py:obj:`ak.to_layout` recognizes).
:param y: The other coordinate to use in the linear fit (anything :py:obj:`ak.to_layout` recognizes).
:param 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.
:param axis: 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.
:type axis: None or int
:param keepdims: 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.
:type keepdims: bool
:param mask_identity: 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``.
:type mask_identity: bool
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
.. code-block:: python
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 :py:obj:`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 :py:obj:`ak.sum` for a complete description of handling nested lists and
missing values (None) in reducers, and :py:obj:`ak.mean` for an example with another
non-reducer.