trigpolyroot: compute roots of a trigonometric polynomial

In polarzonoid: Compute Maps and Properties of Polar Zonoids

compute roots of a trigonometric polynomial

Description

Given a trigonometric polynomial of degree n, defined on the real interval [0,2\pi]. The function transforms it to a polynomial of degree 2n in the standard way, and then solves that polynomial. Only the real roots of the original trigonometric polynomial are returned.

Usage

trigpolyroot( ablist, tol=.Machine$double.eps^0.5 )

Arguments

ablist	a list with 3 items a0 the constant term of the trigonometric polynomial a real coefficients of cos(jt), ~ j = 1..n b real coefficients of sin(jt), ~ j = 1..n
tol	tolerance for the imaginary part; if the absolute value of the imaginary part of the root is less than or equal to tol, then the root is considered to be real, and is returned

Details

The given trigonometric polynomial is converted, using a change of variable and Euler's formula, to a standard polynomial of degree 2n, see Wikipedia. This polynomial is solved using base::polyroot(). After the inverse change of variable, the imaginary roots are removed using tol.

Value

trigpolyroot() returns the real roots in the interval [0,2\pi) and in increasing order (as a numeric vector). There may be duplicates, which correspond to multiple roots. It is up to the user to handle multiple roots.

The number of roots returned is always even, and in the set \{ 0,2,4,..,2n \}.

If n is 0, or all the coefficients are 0, it is an error. In case of error, the function returns NULL.

Source

Wikipedia. Trigonometric polynomial. https://en.wikipedia.org/wiki/Trigonometric_polynomial

See Also

polyroot()

polarzonoid documentation built on June 13, 2025, 9:08 a.m.