code: def hermfit(x, y, deg, rcond=None, full=False, w=None):
      """
      Least squares fit of Hermite series to data.
  
      Return the coefficients of a Hermite series of degree `deg` that is the
      least squares fit to the data values `y` given at points `x`. If `y` is
      1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple
      fits are done, one for each column of `y`, and the resulting
      coefficients are stored in the corresponding columns of a 2-D return.
      The fitted polynomial(s) are in the form
  
      .. math::  p(x) = c_0 + c_1 * H_1(x) + ... + c_n * H_n(x),
  
      where `n` is `deg`.
  
      Parameters
      ----------
      x : array_like, shape (M,)
          x-coordinates 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.RankWarning)
  
      See Also
      --------
      numpy.polynomial.chebyshev.chebfit
      numpy.polynomial.legendre.legfit
      numpy.polynomial.laguerre.lagfit
      numpy.polynomial.polynomial.polyfit
      numpy.polynomial.hermite_e.hermefit
      hermval : Evaluates a Hermite series.
      hermvander : Vandermonde matrix of Hermite series.
      hermweight : Hermite 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 Hermite 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 weighted pseudo Vandermonde matrix of `x`, `c` are the
      coefficients to be solved for, `w` are the weights, `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 `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 Hermite series are probably most useful when the data can be
      approximated by ``sqrt(w(x)) * p(x)``, where `w(x)` is the Hermite
      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 `hermweight`.
  
      References
      ----------
      .. [1] Wikipedia, "Curve fitting",
             https://en.wikipedia.org/wiki/Curve_fitting
  
      Examples
      --------
      >>> from numpy.polynomial.hermite import hermfit, hermval
      >>> x = np.linspace(-10, 10)
      >>> err = np.random.randn(len(x))/10
      >>> y = hermval(x, [1, 2, 3]) + err
      >>> hermfit(x, y, 2)
      array([1.0218, 1.9986, 2.9999]) # may vary
  
      """
      return pu._fit(hermvander, x, y, deg, rcond, full, w)
  
imports: import numpy
  import numpy.linalg
  from numpy.core.multiarray import normalize_axis_index
  from .None import polyutils
  from ._polybase import ABCPolyBase
label_desc: Use image node_id 21 for calling a global function with example usage: hermfit(x, y, deg, rcond, full, w) and returns: pu