numpy.polynomial.legendre.legfromroots — NumPy v1.13 Manual (original) (raw)
numpy.polynomial.legendre. legfromroots(roots)[source]¶
Generate a Legendre series with given roots.
The function returns the coefficients of the polynomial
in Legendre 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
The coefficient of the last term is not generally 1 for monic polynomials in Legendre 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, chebfromroots, lagfromroots, hermfromroots, hermefromroots.
Examples
import numpy.polynomial.legendre as L L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis array([ 0. , -0.4, 0. , 0.4]) j = complex(0,1) L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis array([ 1.33333333+0.j, 0.00000000+0.j, 0.66666667+0.j])