rnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- numpy.polynomial.polynomial.polyfit numpy.polynomial.legendre.legfit numpy.polynomial.chebyshev.chebfit numpy.polynomial.hermite.hermfit numpy.polynomial.hermite_e.hermefit lagval : Evaluates a Laguerre series. lagvander : pseudo Vandermonde matrix of Laguerre series. lagweight : Laguerre 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 Laguerre 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 as 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, 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, 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 Laguerre series are probably most useful when the data can be approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the Laguerre 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 `lagweight`. References ---------- .. [1] Wikipedia, "Curve fitting", https://en.wikipedia.org/wiki/Curve_fitting Examples -------- >>> from numpy.polynomial.laguerre import lagfit, lagval >>> x = np.linspace(0, 10) >>> err = np.random.randn(len(x))/10 >>> y = lagval(x, [1, 2, 3]) + err >>> lagfit(x, y, 2) array([ 0.96971004, 2.00193749, 3.00288744]) # may vary )