Document

legfromroots(roots)

The function returns the coefficients of the polynomial

p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),

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

p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x)

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).

Generate a Legendre series with given roots.

Examples

import numpy.polynomial.legendre as L
L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis

j = complex(0,1)
L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.polynomial.hermite_e:hermefromroots numpy.polynomial.polynomial:polyfromroots numpy.polynomial.laguerre:lagfromroots numpy.polynomial.chebyshev:chebfromroots numpy.polynomial.hermite:hermfromroots

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

GitHub : /numpy/polynomial/legendre.py#267
type: <class 'function'>
Commit:

Parameters

Returns

See Also

Examples

Back References

Local connectivity graph