torchcurves.functional.legendre_curves

torchcurves.functional.legendre_curves(x, coefficients, checkpoint_segments=None)

Evaluate curves parametrized by Legendre polynomials.

Parameters:

• coefficients (Tensor) – A tensor of size \((N, C, D)\) of curve coefficients, of a set of \(C\) polynomial curves in \(\mathbb{R}^D\) of degree \(N-1\), represented in the Legendre basis.

• x (Tensor) – Batch of size \((B, C)\), where x[:, j] is the batch of inputs for the j-th curve in the batch.

• checkpoint_segments (Optional[int]) – Optional number of segments for gradient checkpointing. Larger values save memory but increase compute. Only used when gradients are enabled.

Return type:

Tensor

Returns:

Evaluated points on the curves, shape \((B, C, D)\).

Note

Uses the Clenshaw recursive algorithm, and thus requires \(O(N)\) time. Implementation is vectorized along the \(B\) and \(D\) dimensions, but the algorithm requires a loop over the polynomial degree.