numpy.polynomial.laguerre.laggrid3d(x, y, z, c) [source] Evaluate a 3-D Laguerre 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.laguerre.laggrid2d(x, y, c) [source] Evaluate a 2-D Laguerre 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 ele

numpy.polynomial.laguerre.laggauss(deg) [source] Gauss-Laguerre quadrature. Computes the sample points and weights for Gauss-Laguerre 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 resul

numpy.polynomial.laguerre.lagfromroots(roots) [source] Generate a Laguerre series with given roots. The function returns the coefficients of the polynomial in Laguerre 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

numpy.polynomial.laguerre.lagfit(x, y, deg, rcond=None, full=False, w=None) [source] Least squares fit of Laguerre series to data. Return the coefficients of a Laguerre 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

numpy.polynomial.laguerre.lagdomain = array([0, 1])

numpy.polynomial.laguerre.lagdiv(c1, c2) [source] Divide one Laguerre series by another. Returns the quotient-with-remainder of two Laguerre 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 Laguerre series coefficients ordered from low to high. Returns: [quo, rem] : ndarrays Of Laguerre series coefficients representing the quotient and

numpy.polynomial.laguerre.lagder(c, m=1, scl=1, axis=0) [source] Differentiate a Laguerre series. Returns the Laguerre 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*L_0 + 2*L_1 + 3*L_2 while [[1,2],[1,2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y

numpy.polynomial.laguerre.lagcompanion(c) [source] Return the companion matrix of c. The usual companion matrix of the Laguerre polynomials is already symmetric when c is a basis Laguerre polynomial, so no scaling is applied. Parameters: c : array_like 1-D array of Laguerre series coefficients ordered from low to high degree. Returns: mat : ndarray Companion matrix of dimensions (deg, deg). Notes

numpy.polynomial.laguerre.lagadd(c1, c2) [source] Add one Laguerre series to another. Returns the sum of two Laguerre 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 Laguerre series coefficients ordered from low to high. Returns: out : ndarray Array representing the Laguerre series of their sum. See also lagsub, lagmul, lagdiv