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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 inroots
. If a zero has multiplicity n, then it must appear inroots
n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, thenroots
looks something like [2, 2, 2, 3, 3]. The roots can appear in any order.If the returned coefficients are
c
, thenThe 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, thenout
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])
numpy.polynomial.legendre.legfromroots()
2017-01-10 18:17:30
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