numpy.polynomial.chebyshev.chebder — NumPy v1.13 Manual (original) (raw)
numpy.polynomial.chebyshev. chebder(c, m=1, scl=1, axis=0)[source]¶
Differentiate a Chebyshev series.
Returns the Chebyshev 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*T_0 + 2*T_1 + 3*T_2while [[1,2],[1,2]] represents 1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) + 2*T_1(x)*T_1(y) if axis=0 is x and axis=1 isy.
| Parameters: | c : array_like Array of Chebyshev series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. m : int, optional Number of derivatives taken, must be non-negative. (Default: 1) scl : scalar, optional Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1) axis : int, optional Axis over which the derivative is taken. (Default: 0). New in version 1.7.0. |
|---|---|
| Returns: | der : ndarray Chebyshev series of the derivative. |
Notes
In general, the result of differentiating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.
Examples
from numpy.polynomial import chebyshev as C c = (1,2,3,4) C.chebder(c) array([ 14., 12., 24.]) C.chebder(c,3) array([ 96.]) C.chebder(c,scl=-1) array([-14., -12., -24.]) C.chebder(c,2,-1) array([ 12., 96.])