tidy3d.plugins.autograd.primitives.interpolate_spline

class interpolate_spline

Bases:

Differentiable spline interpolation of a given order with optional endpoint derivatives.

Parameters:

• x_points (np.ndarray) – X coordinates of the data points (must be strictly monotonic)

• y_points (np.ndarray) – Y coordinates of the data points

• num_points (int) – Number of points in the output interpolation

• order (int) – Order of the spline (1=linear, 2=quadratic, 3=cubic)

• endpoint_derivatives (tuple[float, float] = (None, None)) –

  Derivatives at the endpoints (left, right) Note: For order=1 (linear), all endpoint derivatives are ignored.

  For order=2 (quadratic), only the left endpoint derivative is used. For order=3 (cubic), both endpoint derivatives are used if provided.

Returns:

Tuple of (x_interpolated, y_interpolated) values

Return type:

tuple[np.ndarray, np.ndarray]

Examples

>>> import numpy as np
>>> x = np.array([0, 1, 2])
>>> y = np.array([0, 1, 0])
>>> # Linear interpolation
>>> x_interp, y_interp = interpolate_spline(x, y, num_points=5, order=1)
>>> print(y_interp)
[0.   0.5  1.   0.5  0. ]

>>> # Quadratic interpolation with left endpoint derivative
>>> x_interp, y_interp = interpolate_spline(x, y, num_points=5, endpoint_derivatives=(0, None), order=2)
>>> print(np.round(y_interp, 3))
[0.    0.25  1.    1.25   0.  ]

>>> # Cubic interpolation with both endpoint derivatives
>>> x_interp, y_interp = interpolate_spline(x, y, num_points=5, endpoint_derivatives=(0, 0), order=3)
>>> print(np.round(y_interp, 3))
[0.    0.5  1.    0.5  0.  ]

Inherited Common Usage