chebder(c, m=1, scl=1, axis=0)¶
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
xand axis=1 is
- 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).
- der : ndarray
Chebyshev series of the derivative.
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.
>>> 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.])