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Evaluates a polynomial on the Tchebytchev polynomial basis.
If \((a_i)_{0\le i\le n-1}\) denotes the coefficients of the polynomial, the Tchebeval scheme evaluates the polynom \(\sum_0^{n-1} a_i T_{i}(x)\), where \(T_{i}\) is the \(i^{th}\) Tchebytchev polynomial of the first kind.
Defined in header
[a,b]
.Parameters
x
: real floating argument.a
, b
: real floating arguments. If present, they are the bounds of the interval for which the Tchebytchev polynomial must be evaluated ( -1 and 1 by default). A change of variable \( x -> \frac{2x-a-b}{b-a}\) is internally performed.cs
: values expansion pack associated to the coefficients \((a_i)_{0\le i \lt n}\).r
: range containing The polynomial coefficients.Return value
the value of the polynom at x
is returned.
Notes If the coefficients are simd values of cardinal N, this means you simultaneously compute the values of N polynomials.