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 )