code: def hermefit(x, y, deg, rcond=None, full=False, w=None):
      """
      Least squares fit of Hermite series to data.
  
      Return the coefficients of a HermiteE 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 * He_1(x) + ... + c_n * He_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 contribution of each point
          ``(x[i],y[i])`` to the fit is weighted by `w[i]`. Ideally the
          weights are chosen so that the errors of the products ``w[i]*y[i]``
          all have the same variance.  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
  
          resid -- sum of squared residuals of the least squares fit
          rank -- the numerical rank of the scaled Vandermonde matrix
          sv -- singular values of the scaled Vandermonde matrix
          rcond -- value of `rcond`.
  
          For more details, see `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', RankWarning)
  
      See Also
      --------
      chebfit, legfit, polyfit, hermfit, polyfit
      hermeval : Evaluates a Hermite series.
      hermevander : pseudo Vandermonde matrix of Hermite series.
      hermeweight : HermiteE weight function.
      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 `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
      --------
      >>> from numpy.polynomial.hermite_e import hermefit, hermeval
      >>> x = np.linspace(-10, 10)
      >>> err = np.random.randn(len(x))/10
      >>> y = hermeval(x, [1, 2, 3]) + err
      >>> hermefit(x, y, 2)
      array([ 1.01690445,  1.99951418,  2.99948696])
  
      """
      x = np.asarray(x) + 0.0
      y = np.asarray(y) + 0.0
      deg = np.asarray(deg)
  
      # check arguments.
      if deg.ndim > 1 or deg.dtype.kind not in "iu" or deg.size == 0:
          raise TypeError(
              "deg must be an int or non-empty 1-D array of int"
          )
      if deg.min() < 0:
          raise ValueError("expected deg >= 0")
      if x.ndim != 1:
          raise TypeError("expected 1D vector for x")
      if x.size == 0:
          raise TypeError("expected non-empty vector for x")
      if y.ndim < 1 or y.ndim > 2:
          raise TypeError("expected 1D or 2D array for y")
      if len(x) != len(y):
          raise TypeError("expected x and y to have same length")
  
      if deg.ndim == 0:
          lmax = deg
          order = lmax + 1
          van = hermevander(x, lmax)
      else:
          deg = np.sort(deg)
          lmax = deg[-1]
          order = len(deg)
          van = hermevander(x, lmax)[:, deg]
  
      # set up the least squares matrices in transposed form
      lhs = van.T
      rhs = y.T
      if w is not None:
          w = np.asarray(w) + 0.0
          if w.ndim != 1:
              raise TypeError("expected 1D vector for w")
          if len(x) != len(w):
              raise TypeError("expected x and w to have same length")
          # apply weights. Don't use inplace operations as they
          # can cause problems with NA.
          lhs = lhs * w
          rhs = rhs * w
  
      # set rcond
      if rcond is None:
          rcond = len(x) * np.finfo(x.dtype).eps
  
      # Determine the norms of the design matrix columns.
      if issubclass(lhs.dtype.type, np.complexfloating):
          scl = np.sqrt(
              (np.square(lhs.real) + np.square(lhs.imag)).sum(1)
          )
      else:
          scl = np.sqrt(np.square(lhs).sum(1))
      scl[scl == 0] = 1
  
      # Solve the least squares problem.
      c, resids, rank, s = la.lstsq(lhs.T / scl, rhs.T, rcond)
      c = (c.T / scl).T
  
      # Expand c to include non-fitted coefficients which are set to zero
      if deg.ndim > 0:
          if c.ndim == 2:
              cc = np.zeros((lmax + 1, c.shape[1]), dtype=c.dtype)
          else:
              cc = np.zeros(lmax + 1, dtype=c.dtype)
          cc[deg] = c
          c = cc
  
      # warn on rank reduction
      if rank != order and not full:
          msg = "The fit may be poorly conditioned"
          warnings.warn(msg, pu.RankWarning, stacklevel=2)
  
      if full:
          return c, [resids, rank, s, rcond]
      else:
          return c
  
imports: from __future__ import division, absolute_import, print_function
  import warnings
  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: hermefit(x, y, deg, rcond, full, w) and returns: c,  list, c