numpy.polynomial.chebyshev.chebder#

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_2 while [[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 is y.

Parameters:

carray_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.
mint, optional: Number of derivatives taken, must be non-negative. (Default: 1)
sclscalar, 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)
axisint, optional: Axis over which the derivative is taken. (Default: 0).

Returns:

derndarray: Chebyshev series of the derivative.

See also

chebint

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.])