numpy.polynomial.chebyshev.chebfromroots()

numpy.polynomial.chebyshev.chebfromroots(roots) [source]

Generate a Chebyshev series with given roots.

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:

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).

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
array([ 0.  , -0.25,  0.  ,  0.25])
>>> j = complex(0,1)
>>> C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis
array([ 1.5+0.j,  0.0+0.j,  0.5+0.j])

Links:

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

doc_NumPy

2017-01-10 18:16:36

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