e3x.nn.functions.bernstein.basic_bernstein

e3x.nn.functions.bernstein.basic_bernstein(x, num, limit=1.0)

Basic Bernstein polynomial basis functions.

\[\begin{split}\mathrm{bernstein}_k(x) = \begin{cases} 0 & x < 0\\ \binom{K-1}{k} \left(\frac{x}{l}\right)^{k} \left(1-\frac{x}{l}\right)^{K-1-k}, & 0 \le x \le l \\ 0 & x > l \,, \end{cases}\end{split}\]

where \(k=0 \dots K-1\) with \(K\) = num and \(l\) = limit.

Plot for \(K = 5\) and \(l = 1\):

Parameters:

• x (<class 'Float[Array, '...']'>) – Input array.

• num (int) – Number of basis functions \(K\).

• limit (Union[Float[Array, ''], float], default: 1.0) – Basis functions are distributed between 0 and limit.

Return type:

<class 'Float[Array, '... num']'>

Returns:

Value of all basis functions for all values in x. The output shape follows the input, with an additional dimension of size num appended.