e3j.core.Monomial

class e3j.core.Monomial(exp: Array, coords: Array | str | None = None)

Batched monomials w.r.t. an optional coordinate basis.

Given an array m = m[:n,:d] of exponents, M = Monomial(m) will efficiently evaluate n monomials on a d-dimensional point cloud x:

M(x)[:, i] = x[:, 0] ** m[i,0] * ... * x[:, d-1] ** m[i, d-1]

Optionally, a (possibly complex) coordinate matrix can be used in place of the canonical degree-1 generators.

Note

The Monomial class is intended to store the collection of monomials that need to be evaluated by downstream Polynomial instances, i.e. before aggregation with a coefficient matrix.

Keeping these classes distinct (although monomials are one-term polynomials) is useful for having distinct product/power implementations.

Methods

C()
__call__(x)	Evaluate monomials on a point cloud.
__init__(exp[, coords])	Create monomials from exponents array and optional coordinate matrix.
concat(ms)
eval_coords(r)
exponentiate_and_multiply(x)

Attributes

__call__(x: Array) → Array

Evaluate monomials on a point cloud.

Parameters:

(jax.Array) (x) – a point cloud of shape [b, d]

Returns:

evaluated monomials of shape [b, n]

Return type:

mx (jax.Array)

__init__(exp: Array, coords: Array | str | None = None)

Create monomials from exponents array and optional coordinate matrix.

Parameters:

• (jax.Array) (exp) – exponents array of shape [n, d]

• None) (coords (jax.Array |) – an optional [d, d] matrix of coordinate functions.