Boltz.Basis API Reference

Warning

The function calls for these basis functions should be considered experimental and are subject to change without deprecation. However, the functions themselves are stable and can be freely used in combination with the other Layers and Models.

Boltz.Basis.Chebyshev Method

Chebyshev(n; dim::Int=1)

Constructs a Chebyshev basis of the form $[T_0(x),T_1(x),\dots ,T_{n-1}(x)]$ where $T_j(.)$ is the $j^{th}$ Chebyshev polynomial of the first kind.

Arguments

• n: number of terms in the polynomial expansion.

Keyword Arguments

• dim::Int=1: The dimension along which the basis functions are applied.

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Boltz.Basis.Cos Method

Cos(n; dim::Int=1)

Constructs a cosine basis of the form $[\cos (x),\cos (2x),\dots ,\cos (nx)]$.

Arguments

• n: number of terms in the cosine expansion.

Keyword Arguments

• dim::Int=1: The dimension along which the basis functions are applied.

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Boltz.Basis.Fourier Method

Fourier(n; dim=1)

Constructs a Fourier basis of the form

$$F_j(x)=\{\begin{array}{ll}cos\left(\frac{j}{2}x\right)& \text{if }j\text{ is even}\\ sin\left(\frac{j}{2}x\right)& \text{if }j\text{ is odd}\end{array}$$

Arguments

• n: number of terms in the Fourier expansion.

Keyword Arguments

• dim::Int=1: The dimension along which the basis functions are applied.

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Boltz.Basis.Legendre Method

Legendre(n; dim::Int=1)

Constructs a Legendre basis of the form $[P_0(x),P_1(x),\dots ,P_{n-1}(x)]$ where $P_j(.)$ is the $j^{th}$ Legendre polynomial.

Arguments

• n: number of terms in the polynomial expansion.

Keyword Arguments

• dim::Int=1: The dimension along which the basis functions are applied.

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Boltz.Basis.Polynomial Method

Polynomial(n; dim::Int=1)

Constructs a Polynomial basis of the form $[1,x,\dots ,x^{(n-1)}]$.

Arguments

• n: number of terms in the polynomial expansion.

Keyword Arguments

• dim::Int=1: The dimension along which the basis functions are applied.

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Boltz.Basis.Sin Method

Sin(n; dim::Int=1)

Constructs a sine basis of the form $[\sin (x),\sin (2x),\dots ,\sin (nx)]$.

Arguments

• n: number of terms in the sine expansion.

Keyword Arguments

• dim::Int=1: The dimension along which the basis functions are applied.

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