y 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.hermite.hermfit
    numpy.polynomial.hermite_e.hermefit
    polyval : Evaluates a polynomial.
    polyvander : Vandermonde matrix for powers.
    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 polynomial `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) over-determined 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 (and `full` == ``False``), a `RankWarning` will be raised.
    This means that the coefficient values may be poorly determined.
    Fitting to a lower order polynomial will usually get rid of the warning
    (but may not be what you want, of course; if you have independent
    reason(s) for choosing the degree which isn't working, you may have to:
    a) reconsider those reasons, and/or b) reconsider the quality of your
    data).  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.

    Polynomial fits using double precision tend to "fail" at about
    (polynomial) degree 20. Fits using Chebyshev or Legendre series are
    generally better conditioned, but much can still depend on the
    distribution of the sample points and the smoothness of the data.  If
    the quality of the fit is inadequate, splines may be a good
    alternative.

    Examples
    --------
    >>> np.random.seed(123)
    >>> from numpy.polynomial import polynomial as P
    >>> x = np.linspace(-1,1,51) # x "data": [-1, -0.96, ..., 0.96, 1]
    >>> y = x**3 - x + np.random.randn(len(x))  # x^3 - x + Gaussian noise
    >>> c, stats = P.polyfit(x,y,3,full=True)
    >>> np.random.seed(123)
    >>> c # c[0], c[2] should be approx. 0, c[1] approx. -1, c[3] approx. 1
    array([ 0.01909725, -1.30598256, -0.00577963,  1.02644286]) # may vary
    >>> stats # note the large SSR, explaining the rather poor results
     [array([ 38.06116253]), 4, array([ 1.38446749,  1.32119158,  0.50443316, # may vary
              0.28853036]), 1.1324274851176597e-014]

    Same thing without the added noise

    >>> y = x**3 - x
    >>> c, stats = P.polyfit(x,y,3,full=True)
    >>> c # c[0], c[2] should be "very close to 0", c[1] ~= -1, c[3] ~= 1
    array([-6.36925336e-18, -1.00000000e+00, -4.08053781e-16,  1.00000000e+00])
    >>> stats # note the minuscule SSR
    [array([  7.46346754e-31]), 4, array([ 1.38446749,  1.32119158, # may vary
               0.50443316,  0.28853036]), 1.1324274851176597e-014]

    )