numpy.polynomial.chebyshev.chebmul(c1, c2) [source] Multiply one Chebyshev series by another. Returns the product of two Chebyshev series c1 * c2. The arguments are sequences of coefficients, from lowest order ?term? to highest, e.g., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2. Parameters: c1, c2 : array_like 1-D arrays of Chebyshev series coefficients ordered from low to high. Returns: out : ndarray Of Chebyshev series coefficients representing their product. See also cheba

numpy.polynomial.chebyshev.chebline(off, scl) [source] Chebyshev 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 Chebyshev series for off + scl*x. See also polyline Examples >>> import numpy.polynomial.chebyshev as C >>> C.chebline(3,2) array([3, 2]) >>> C.chebval(-3, C.chebline(3,2)) # should be -3 -3.0

numpy.polynomial.chebyshev.chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0) [source] Integrate a Chebyshev series. Returns the Chebyshev 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 in

numpy.polynomial.chebyshev.chebgrid3d(x, y, z, c) [source] Evaluate a 3-D Chebyshev 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.chebyshev.chebgrid2d(x, y, c) [source] Evaluate a 2-D Chebyshev 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.chebyshev.chebgauss(deg) [source] Gauss-Chebyshev quadrature. Computes the sample points and weights for Gauss-Chebyshev 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 New

numpy.polynomial.chebyshev.chebfromroots(roots) [source] Generate a Chebyshev series with given roots. The function returns the coefficients of the polynomial in Chebyshev 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.chebyshev.chebfit(x, y, deg, rcond=None, full=False, w=None) [source] Least squares fit of Chebyshev series to data. Return the coefficients of a Legendre 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) a

numpy.polynomial.chebyshev.chebdomain = array([-1, 1])

numpy.polynomial.chebyshev.chebdiv(c1, c2) [source] Divide one Chebyshev series by another. Returns the quotient-with-remainder of two Chebyshev series c1 / c2. The arguments are sequences of coefficients from lowest order ?term? to highest, e.g., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2. Parameters: c1, c2 : array_like 1-D arrays of Chebyshev series coefficients ordered from low to high. Returns: [quo, rem] : ndarrays Of Chebyshev series coefficients representing the quotien