interpolation1d.py
705bf01b59aemaster

interpolation1d.py
View Options

			import torch

			# Function `_Hermite_spline` and `_Interpolate` are borrowed from @chausies and @Julius's answers
			# to the question "How to do cubic spline interpolation and integration in Pytorch" on stackoverflow.com,
			# with some modifications. -- Daichao Chen, 2021.3.14
			# (see https://stackoverflow.com/questions/61616810/how-to-do-cubic-spline-interpolation-and-integration-in-pytorch)

			A = torch.tensor([[1, 0, -3, 2],
			[0, 1, -2, 1],
			[0, 0, 3, -2],
			[0, 0, -1, 1]] )

			def _Hermite_spline(t):
			'''
			Helper function for cubic Hermite spline interpolation.
			'''
			global A
			A = torch.as_tensor(A, dtype = t.dtype, device=t.device)
			return A @ (t.view(1, -1) ** torch.arange(4, device=t.device).view(-1, 1) )

			def _Interpolate(x, y, xs, zero_grad_pos = None):
			'''
			Cubic Hermite spline interpolation for finding upper and lower envolopes
			during the sifting process.
			'''
			m = (y[1:] - y[:-1]) / (x[1:] - x[:-1])
			m = torch.cat( ( m[0].unsqueeze(0),
			(m[1:] + m[:-1]) / 2,
			m[-1].unsqueeze(0) )
			)
			if (zero_grad_pos is not None):
			m[zero_grad_pos] = 0

			idxs = torch.searchsorted(x, xs) - 1

			dx = x[idxs + 1] - x[idxs]

			h = _Hermite_spline((xs - x[idxs]) / dx)
			return h[0] * y[idxs] \
			+ h[1] * m[idxs] * dx \
			+ h[2] * y[idxs + 1] \
			+ h[3] * m[idxs + 1] * dx