TensorSpline#

Bases: object

A class to handle a tensor spline for multi-dimensional interpolation and approximation.

This class allows you to store N-dimensional data and perform interpolation using a variety of spline bases and extension modes. It is flexible and can handle different extension modes and spline bases.

Parameters:

data (array_like) – The input N-dimensional array to be interpolated.
coordinates (array_like) – The coordinates corresponding to the input data.
bases (str or sequence of str) –
The spline bases used for interpolation. It can be a single basis applied across all axes or a sequence of bases for each axis.

The following spline bases are available:
- ”bspline0”, “bspline0-sym”: Zero-degree or piecewise constant B-splines and symmetric zero-degree or piecewise constant B-splines.
- ”bspline1” to “bspline9”: First to ninth-degree B-splines.
- ”omoms0”, “omoms0-sym”: Zero-degree O-MOMS splines and symmetric zero-degree O-MOMS splines.
- ”omoms1” to “omoms5”: First to fifth-degree O-MOMS splines.
- ”omoms2-sym”, “omoms4-sym”: Symmetric second and fourth-degree O-MOMS splines.
- ”nearest”, “nearest-sym”: Nearest neighbor interpolation.
- ”linear”: Linear interpolation.
- ”keys”: Keys spline interpolation.
modes (str or sequence of str) –
Signal extension modes used to handle boundaries. It can be a single mode applied across all axes or a sequence of modes for each axis.

The following extension modes are available for handling boundaries:
- ”zero” (0 0 0 0 | a b c d | 0 0 0 0) The input is extended by filling all values beyond the boundary with zeroes.
- ”mirror” (d c b | a b c d | c b a) The input is extended by reflecting around the center of the data points adjacent to the border.

Example

1D Interpolation:

Here’s an example to illustrate 1-dimensional interpolation using the TensorSpline class.

>>> import numpy as np
>>> from splineops.interpolate.tensorspline import TensorSpline
>>> data = np.array([1.0, 2.0, 3.0, 4.0])
>>> coordinates = np.linspace(0, data.size - 1, data.size)
>>> bases = "linear"  # Linear interpolation
>>> modes = "mirror"  # Mirror extension mode
>>> tensor_spline = TensorSpline(data=data, coordinates=coordinates, bases=bases, modes=modes)

To interpolate the data at a new point:

>>> eval_coords = np.array([1.5])
>>> data_eval = tensor_spline(coordinates=eval_coords, grid=False)
>>> print(data_eval)
[2.5]

In this example, the interpolated value at x = 1.5 is 2.5, which is the midpoint between data[1] (2.0) and data[2] (3.0).

2D Interpolation:

Here’s a simple example to illustrate 2-dimensional interpolation using the TensorSpline class.

>>> a = np.arange(12.).reshape((4, 3))
>>> a
array([[ 0.,  1.,  2.],
       [ 3.,  4.,  5.],
       [ 6.,  7.,  8.],
       [ 9., 10., 11.]])
>>> xx = np.linspace(0, a.shape[0] - 1, a.shape[0])
>>> yy = np.linspace(0, a.shape[1] - 1, a.shape[1])
>>> coordinates = xx, yy
>>> bases = ["bspline1", "bspline1"]  # Linear interpolation along both axes
>>> modes = ["mirror", "mirror"]      # Mirror extension mode handling along both axes
>>> tensor_spline = TensorSpline(data=a, coordinates=coordinates, bases=bases, modes=modes)

To interpolate the array a at coordinates (0.5, 0.5) and (2, 1):

>>> eval_coords = np.array([[0.5, 2], [0.5, 1]])
>>> data_eval_pts = tensor_spline(coordinates=eval_coords, grid=False)
>>> print(data_eval_pts)
[2. 7.]

In this example, the interpolated value at (0.5, 0.5) is 2.0, and the value at (2, 1) is 7.0.

Initialize the TensorSpline object with the given data, coordinates, bases, and modes.

Parameters:

data (array_like) – The input N-dimensional array to be interpolated.
coordinates (array_like) – The coordinates corresponding to the input data.
bases (str or sequence of str) – The spline bases used for interpolation. It can be a single basis applied across all axes or a sequence of bases for each axis.
modes (str or sequence of str) – Signal extension modes used to handle boundaries. It can be a single mode applied across all axes or a sequence of modes for each axis.

Example

>>> a = np.arange(12.).reshape((4, 3))
>>> xx = np.linspace(0, a.shape[0] - 1, a.shape[0])
>>> yy = np.linspace(0, a.shape[1] - 1, a.shape[1])
>>> coordinates = xx, yy
>>> tensor_spline = TensorSpline(data=a, coordinates=coordinates, bases="bspline1", modes="mirror")

eval(coordinates: ndarray[Any, dtype[_ScalarType_co]] | Sequence[ndarray[Any, dtype[_ScalarType_co]]], grid: bool = True) → ndarray[Any, dtype[_ScalarType_co]]#

Evaluate the tensor spline at the given coordinates.

Parameters:

coordinates (array_like) – The coordinates at which to evaluate the tensor spline. If grid is True, must be a sequence of 1-D arrays representing the grid points along each axis. If grid is False, must be a sequence of N-D arrays of the same shape.
grid (bool, optional) – If True (default), assumes the input coordinates define a grid and evaluates the tensor spline over this grid. If False, treats the input coordinates as a list of points at which to evaluate the tensor spline.

Returns:

data – The interpolated values at the specified coordinates.

Return type:

ndarray

Example

>>> a = np.arange(12.).reshape((4, 3))
>>> xx = np.linspace(0, a.shape[0] - 1, a.shape[0])
>>> yy = np.linspace(0, a.shape[1] - 1, a.shape[1])
>>> coordinates = xx, yy
>>> tensor_spline = TensorSpline(data=a, coordinates=coordinates, bases="bspline1", modes="mirror")
>>> eval_coords = np.array([[0.5, 2], [0.5, 1]])
>>> data_eval_pts = tensor_spline.eval(coordinates=eval_coords, grid=False)
>>> print(data_eval_pts)
[2. 7.]