class numpy.polynomial.hermite.Hermite(coef, domain=None, window=None) [source] An Hermite series class. The Hermite class provides the standard Python numerical methods ?+?, ?-?, ?*?, ?//?, ?%?, ?divmod?, ?**?, and ?()? as well as the attributes and methods listed in the ABCPolyBase documentation. Parameters: coef : array_like Hermite coefficients in order of increasing degree, i.e, (1, 2, 3) gives 1*H_0(x) + 2*H_1(X) + 3*H_2(x). domain : (2,) array_like, optional Domain to use. The in

numpy.polynomial.hermite.hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0) [source] Integrate a Hermite series. Returns the Hermite series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable. (?Buyer beware?: note that, depending on what one is doing, one may want scl to be the reciprocal of what one might expect; for more informat

numpy.polynomial.hermite.hermgrid3d(x, y, z, c) [source] Evaluate a 3-D Hermite series on the Cartesian product of x, y, and z. This function returns the values: where the points (a, b, c) consist of all triples formed by taking a from x, b from y, and c from z. The resulting points form a grid with x in the first dimension, y in the second, and z in the third. The parameters x, y, and z are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars.

numpy.polynomial.hermite.hermgrid2d(x, y, c) [source] Evaluate a 2-D Hermite series on the Cartesian product of x and y. This function returns the values: where the points (a, b) consist of all pairs formed by taking a from x and b from y. The resulting points form a grid with x in the first dimension and y in the second. The parameters x and y are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either x and y or their elem

numpy.polynomial.hermite.hermgauss(deg) [source] Gauss-Hermite quadrature. Computes the sample points and weights for Gauss-Hermite quadrature. These sample points and weights will correctly integrate polynomials of degree or less over the interval with the weight function . Parameters: deg : int Number of sample points and weights. It must be >= 1. Returns: x : ndarray 1-D ndarray containing the sample points. y : ndarray 1-D ndarray containing the weights. Notes The results

numpy.polynomial.hermite.hermfromroots(roots) [source] Generate a Hermite series with given roots. The function returns the coefficients of the polynomial in Hermite form, where the r_n are the roots specified in roots. If a zero has multiplicity n, then it must appear in roots n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then roots looks something like [2, 2, 2, 3, 3]. The roots can appear in any order. If the returned coefficients are c

numpy.polynomial.hermite.hermfit(x, y, deg, rcond=None, full=False, w=None) [source] 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

numpy.polynomial.hermite.hermdomain = array([-1, 1])

numpy.polynomial.hermite.hermdiv(c1, c2) [source] Divide one Hermite series by another. Returns the quotient-with-remainder of two Hermite series c1 / c2. The arguments are sequences of coefficients from lowest order ?term? to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2. Parameters: c1, c2 : array_like 1-D arrays of Hermite series coefficients ordered from low to high. Returns: [quo, rem] : ndarrays Of Hermite series coefficients representing the quotient and rema

numpy.polynomial.hermite.hermder(c, m=1, scl=1, axis=0) [source] Differentiate a Hermite series. Returns the Hermite series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument c is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series 1*H_0 + 2*H_1 + 3*H_2 while [[1,2],[1,2]] represents 1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y)