class numpy.polynomial.laguerre.Laguerre(coef, domain=None, window=None) [source] A Laguerre series class. The Laguerre 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 Laguerre coefficients in order of increasing degree, i.e, (1, 2, 3) gives 1*L_0(x) + 2*L_1(X) + 3*L_2(x). domain : (2,) array_like, optional Domain to use. Th

numpy.polynomial.laguerre.lagroots(c) [source] Compute the roots of a Laguerre series. Return the roots (a.k.a. ?zeros?) of the polynomial Parameters: c : 1-D array_like 1-D array of coefficients. Returns: out : ndarray Array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. See also polyroots, legroots, chebroots, hermroots, hermeroots Notes The root estimates are obtained as the eigenvalues of the companion matrix, Roots fa

numpy.polynomial.laguerre.lagtrim(c, tol=0) [source] Remove ?small? ?trailing? coefficients from a polynomial. ?Small? means ?small in absolute value? and is controlled by the parameter tol; ?trailing? means highest order coefficient(s), e.g., in [0, 1, 1, 0, 0] (which represents 0 + x + x**2 + 0*x**3 + 0*x**4) both the 3-rd and 4-th order coefficients would be ?trimmed.? Parameters: c : array_like 1-d array of coefficients, ordered from lowest order to highest. tol : number, optional T

numpy.polynomial.laguerre.lagsub(c1, c2) [source] Subtract one Laguerre series from another. Returns the difference of two Laguerre series c1 - c2. The sequences of coefficients are 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 Of Laguerre series coefficients representing their difference. See also lagadd, lagmul,

numpy.polynomial.laguerre.lagpow(c, pow, maxpower=16) [source] Raise a Laguerre series to a power. Returns the Laguerre series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series P_0 + 2*P_1 + 3*P_2. Parameters: c : array_like 1-D array of Laguerre series coefficients ordered from low to high. pow : integer Power to which the series will be raised maxpower : integer, optional Maximum power allowed. This is mainl

numpy.polynomial.laguerre.lagone = array([1])

numpy.polynomial.laguerre.lagmul(c1, c2) [source] Multiply one Laguerre series by another. Returns the product 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: out : ndarray Of Laguerre series coefficients representing their product. See also lagadd, lag

numpy.polynomial.laguerre.lagmulx(c) [source] Multiply a Laguerre series by x. Multiply the Laguerre series c by x, where x is the independent variable. Parameters: c : array_like 1-D array of Laguerre series coefficients ordered from low to high. Returns: out : ndarray Array representing the result of the multiplication. Notes The multiplication uses the recursion relationship for Laguerre polynomials in the form xP_i(x) = (-(i + 1)*P_{i + 1}(x) + (2i + 1)P_{i}(x) - iP_{i - 1}(x

numpy.polynomial.laguerre.lagline(off, scl) [source] Laguerre series whose graph is a straight line. Parameters: off, scl : scalars The specified line is given by off + scl*x. Returns: y : ndarray This module?s representation of the Laguerre series for off + scl*x. See also polyline, chebline Examples >>> from numpy.polynomial.laguerre import lagline, lagval >>> lagval(0,lagline(3, 2)) 3.0 >>> lagval(1,lagline(3, 2)) 5.0

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.