oordinates of the M sample points ``(x[i], y[i])``.
y : array_like, shape (M,) or (M, K)
    y-coordinates of the sample points. Several data sets of sample
    points sharing the same x-coordinates can be fitted at once by
    passing in a 2D-array that contains one dataset per column.
deg : int or 1-D array_like
    Degree(s) of the fitting polynomials. If `deg` is a single integer
    all terms up to and including the `deg`'th term are included in the
    fit. For NumPy versions >= 1.11.0 a list of integers specifying the
    degrees of the terms to include may be used instead.
rcond : float, optional
    Relative condition number of the fit. Singular values smaller than
    this relative to the largest singular value will be ignored. The
    default value is len(x)*eps, where eps is the relative precision of
    the float type, about 2e-16 in most cases.
full : bool, optional
    Switch determining nature of return value. When it is False (the
    default) just the coefficients are returned, when True diagnostic
    information from the singular value decomposition is also returned.
w : array_like, shape (`M`,), optional
    Weights. If not None, the weight ``w[i]`` applies to the unsquared
    residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
    chosen so that the errors of the products ``w[i]*y[i]`` all have the
    same variance.  When using inverse-variance weighting, use
    ``w[i] = 1/sigma(y[i])``.  The default value is None.

Returns
-------
coef : ndarray, shape (M,) or (M, K)
    Hermite coefficients ordered from low to high. If `y` was 2-D,
    the coefficients for the data in column k  of `y` are in column
    `k`.

[residuals, rank, singular_values, rcond] : list
    These values are only returned if ``full == True``

    - residuals -- sum of squared residuals of the least squares fit
    - rank -- the numerical rank of the scaled Vandermonde matrix
    - singular_values -- singular values of the scaled Vandermonde matrix
    - rcond -- value of `rcond`.

    For more details, see `numpy.linalg.lstsq`.

Warns
-----
RankWarning
    The rank of the coefficient matrix in the least-squares fit is
    deficient. The warning is only raised if ``full = False``.  The
    warnings can be turned off by

    >>> import warnings
    >>> warnings.simplefilter('ignore', np.exceptions.RankWarning)

See Also
--------
numpy.polynomial.chebyshev.chebfit
numpy.polynomial.legendre.legfit
numpy.polynomial.polynomial.polyfit
numpy.polynomial.hermite.hermfit
numpy.polynomial.laguerre.lagfit
hermeval : Evaluates a Hermite series.
hermevander : pseudo Vandermonde matrix of Hermite series.
hermeweight : HermiteE weight function.
numpy.linalg.lstsq : Computes a least-squares fit from the matrix.
scipy.interpolate.UnivariateSpline : Computes spline fits.

Notes
-----
The solution is the coefficients of the HermiteE series `p` that
minimizes the sum of the weighted squared errors

.. 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 the (typically) overdetermined matrix equation

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

where `V` is the pseudo Vandermonde matrix of `x`, the elements of `c`
are the coefficients to be solved for, and the elements of `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 HermiteE series are probably most useful when the data can
be approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the HermiteE
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 `hermeweight`.

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

Examples
--------
>>> import numpy as np
>>> from numpy.polynomial.hermite_e import hermefit, hermeval
>>> x = np.linspace(-10, 10)
>>> rng = np.random.default_rng()
>>> err = rng.normal(scale=1./10, size=len(x))
>>> y = hermeval(x, [1, 2, 3]) + err
>>> hermefit(x, y, 2)
array([1.02284196, 2.00032805, 2.99978457]) # may vary

)