Custom Extensions

Custom functions (extensions) are easy to implement in tensortrax. Beside the function expression, three additional (dual) variation expressions have to be defined.

import numpy as np

from tensortrax import Tensor, Δ, Δδ, f, δ


def sin(A):
    return Tensor(
        x=np.sin(f(A)),
        δx=np.cos(f(A)) * δ(A),
        Δx=np.cos(f(A)) * Δ(A),
        Δδx=-np.sin(f(A)) * δ(A) * Δ(A) + np.cos(f(A)) * Δδ(A),
        ntrax=A.ntrax,
    )


x = np.eye(3)
y = sin(Tensor(x))

Note

Contrary to NumPy’s w, v = np.linalg.eigh(C), which returns eigenvalues and -vectors, the differentiable w, M = tm.linalg.eigh(C) function returns eigenvalues and eigenbases of symmetric real-valued tensors.

Tip

Feel free to contribute missing math-functions to src/tensortrax/math/_math_tensor.py 📃 ✏️.