numpy.polynomial.chebyshev.chebder()

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_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:

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 `sclm`. 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.

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.])

Links:

https://docs.scipy.org/doc/numpy-1.11.0/reference/generated/numpy.polynomial.chebyshev.chebder.html

doc_NumPy

2025-01-10 15:47:30

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