Generate a Chebyshev series with given roots.
The function returns the coefficients of the polynomial
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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
System Message: WARNING/2 (p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x)
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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).
|
See also
polyfromroots, legfromroots, lagfromroots, hermfromroots, hermefromroots.
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])