numpy.polynomial.hermite.hermcompanion(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 Hermite 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 Hermite series coefficients ordered from low to high degree. Re

numpy.polynomial.hermite.hermadd(c1, c2) [source] Add one Hermite series to another. Returns the sum of two Hermite series c1 + c2. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [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: out : ndarray Array representing the Hermite series of their sum. See also hermsub, hermmul, hermdiv,

numpy.polynomial.hermite.herm2poly(c) [source] Convert a Hermite series to a polynomial. Convert an array representing the coefficients of a Hermite series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the ?standard? basis) ordered from lowest to highest degree. Parameters: c : array_like 1-D array containing the Hermite series coefficients, ordered from lowest order term to highest. Returns: pol : ndarray 1-D array c

numpy.polynomial.chebyshev.poly2cheb(pol) [source] Convert a polynomial to a Chebyshev series. Convert an array representing the coefficients of a polynomial (relative to the ?standard? basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Chebyshev series, ordered from lowest to highest degree. Parameters: pol : array_like 1-D array containing the polynomial coefficients Returns: c : ndarray 1-D array containing the coefficients of the equiva

numpy.polynomial.chebyshev.chebzero = array([0])

class numpy.polynomial.chebyshev.Chebyshev(coef, domain=None, window=None) [source] A Chebyshev series class. The Chebyshev class provides the standard Python numerical methods ?+?, ?-?, ?*?, ?//?, ?%?, ?divmod?, ?**?, and ?()? as well as the methods listed below. Parameters: coef : array_like Chebyshev coefficients in order of increasing degree, i.e., (1, 2, 3) gives 1*T_0(x) + 2*T_1(x) + 3*T_2(x). domain : (2,) array_like, optional Domain to use. The interval [domain[0], domain[1]] is

numpy.polynomial.chebyshev.chebx = array([0, 1])

numpy.polynomial.chebyshev.chebweight(x) [source] The weight function of the Chebyshev polynomials. The weight function is and the interval of integration is . The Chebyshev polynomials are orthogonal, but not normalized, with respect to this weight function. Parameters: x : array_like Values at which the weight function will be computed. Returns: w : ndarray The weight function at x. Notes New in version 1.7.0.

numpy.polynomial.chebyshev.chebvander3d(x, y, z, deg) [source] Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y, z). If l, m, n are the given degrees in x, y, z, then The pseudo-Vandermonde matrix is defined by where 0 <= i <= l, 0 <= j <= m, and 0 <= j <= n. The leading indices of V index the points (x, y, z) and the last index encodes the degrees of the Chebyshev polynomials. If V = chebvander3d(x

numpy.polynomial.chebyshev.chebvander2d(x, y, deg) [source] Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees deg and sample points (x, y). The pseudo-Vandermonde matrix is defined by where 0 <= i <= deg[0] and 0 <= j <= deg[1]. The leading indices of V index the points (x, y) and the last index encodes the degrees of the Chebyshev polynomials. If V = chebvander2d(x, y, [xdeg, ydeg]), then the columns of V correspond to the elements