`numpy.polynomial.chebyshev:chebfromroots`

source: /numpy/polynomial/chebyshev.py :512

Signature

def chebfromroots ( roots )

Summary

Generate a Chebyshev series with given roots.

Extended Summary

The function returns the coefficients of the polynomial

p (x) = (x - r_{0}) * (x - r_{1}) * ... * (x - r_{n}),

in Chebyshev form, where the $r_{n}$ are the roots specified in roots. If a zero has multiplicity n, then it must appear in roots n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then roots looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.

If the returned coefficients are c, then

p (x) = c_{0} + c_{1} * T_{1} (x) + ... + c_{n} * T_{n} (x)

The coefficient of the last term is not generally 1 for monic polynomials in Chebyshev form.

Parameters

roots : array_like: Sequence containing the roots.

Returns

out : ndarray: 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real (see Examples below).

Examples

import numpy.polynomial.chebyshev as C
C.chebfromroots((-1,0,1)) # x^3 - x relative to the standard basis
j = complex(0,1)
C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis

✓

Aliases

numpy.polynomial.Chebyshev._fromroots
numpy.polynomial.chebyshev.chebfromroots