numpy.polynomial.hermite_e.hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0) [source] Integrate a Hermite_e series. Returns the Hermite_e 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 i

numpy.polynomial.hermite_e.hermegrid3d(x, y, z, c) [source] Evaluate a 3-D HermiteE 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 scala

numpy.polynomial.hermite_e.hermegrid2d(x, y, c) [source] Evaluate a 2-D HermiteE 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

numpy.polynomial.hermite_e.hermegauss(deg) [source] Gauss-HermiteE quadrature. Computes the sample points and weights for Gauss-HermiteE 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 re

numpy.polynomial.hermite_e.hermefromroots(roots) [source] Generate a HermiteE series with given roots. The function returns the coefficients of the polynomial in HermiteE 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

numpy.polynomial.hermite_e.hermefit(x, y, deg, rcond=None, full=False, w=None) [source] 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) ar

numpy.polynomial.hermite_e.hermedomain = array([-1, 1])

numpy.polynomial.hermite_e.hermediv(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 r

numpy.polynomial.hermite_e.hermeder(c, m=1, scl=1, axis=0) [source] Differentiate a Hermite_e series. Returns the 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*He_0 + 2*He_1 + 3*He_2 while [[1,2],[1,2]] represents 1*He_0(x)*He_0(y) + 1*He_1(x)*He_0

numpy.polynomial.hermite_e.hermecompanion(c) [source] Return the scaled companion matrix of c. The basis polynomials are scaled so that the companion matrix is symmetric when c is an HermiteE basis polynomial. This provides better eigenvalue estimates than the unscaled case and for basis polynomials the eigenvalues are guaranteed to be real if numpy.linalg.eigvalsh is used to obtain them. Parameters: c : array_like 1-D array of HermiteE series coefficients ordered from low to high degree.