rrors

.. math:: E = \sum_j w_j^2 * |y_j - p(x_j)|^2,

where the :math:`w_j` are the weights. This problem is solved by
setting up as the (typically) overdetermined matrix equation

.. math:: V(x) * c = w * y,

where ``V`` is the weighted pseudo Vandermonde matrix of `x`, ``c`` are the
coefficients to be solved for, `w` are the weights, and `y` are the
observed values.  This equation is then solved using the singular value
decomposition of ``V``.

If some of the singular values of `V` are so small that they are
neglected, then a `~exceptions.RankWarning` will be issued. This means that
the coefficient values may be poorly determined. Using a lower order fit
will usually get rid of the warning.  The `rcond` parameter can also be
set to a value smaller than its default, but the resulting fit may be
spurious and have large contributions from roundoff error.

Fits using Laguerre series are probably most useful when the data can
be approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the Laguerre
weight. In that case the weight ``sqrt(w(x[i]))`` should be used
together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is
available as `lagweight`.

References
----------
.. [1] Wikipedia, "Curve fitting",
       https://en.wikipedia.org/wiki/Curve_fitting

Examples
--------
>>> import numpy as np
>>> from numpy.polynomial.laguerre import lagfit, lagval
>>> x = np.linspace(0, 10)
>>> rng = np.random.default_rng()
>>> err = rng.normal(scale=1./10, size=len(x))
>>> y = lagval(x, [1, 2, 3]) + err
>>> lagfit(x, y, 2)
array([1.00578369, 1.99417356, 2.99827656]) # may vary

)