numpy.polynomial.chebyshev.chebdiv¶
- 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 quotient and remainder.
Notes
In general, the (polynomial) division of one C-series by another results in quotient and remainder terms that are not in the Chebyshev polynomial basis set. Thus, to express these results as C-series, it is typically necessary to “reproject” the results onto said basis set, which typically produces “unintuitive” (but correct) results; see Examples section below.
Examples
>>> from numpy.polynomial import chebyshev as C >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> C.chebdiv(c1,c2) # quotient "intuitive," remainder not (array([ 3.]), array([-8., -4.])) >>> c2 = (0,1,2,3) >>> C.chebdiv(c2,c1) # neither "intuitive" (array([ 0., 2.]), array([-2., -4.]))