nifty8.re.structured_kernel_interpolation module

class HarmonicSKI(grid_shape: Tuple[int], grid_bounds: Tuple[Tuple[float, float]], sampling_points: Array | ndarray, harmonic_kernel: Callable | None = None, padding: float = 0.5, subslice=None, jitter: bool | float | None = True)

Bases: object

__call__(x, harmonic_kernel=None) → Array | ndarray

Applies the Covariance matrix.

__init__(grid_shape: Tuple[int], grid_bounds: Tuple[Tuple[float, float]], sampling_points: Array | ndarray, harmonic_kernel: Callable | None = None, padding: float = 0.5, subslice=None, jitter: bool | float | None = True)

Instantiate a KISS-GP model of the covariance using a harmonic representation of the kernel.

Parameters:

• grid_shape – Number of pixels along each axes of the inducing points within grid_bounds.

• grid_bounds – Tuple of boundaries of length of the number of dimensions. The boundaries should denote the leftmost and rightmost edge of the modeling space.

• sampling_points – Locations of the modeled points within the grid.

• harmonic_kernel – Harmonically transformed kernel.

• padding – Padding factor which to apply along each axis.

• subslice – Slice of the inducing points which to use to model sampling_points. By default, the subslice is determined by the padding.

• jitter – Strength of the diagonal jitter which to add to the covariance.

amplitude(harmonic_kernel=None)

correlated_field(x, harmonic_kernel=None) → Array | ndarray

evaluate(harmonic_kernel=None)

Instantiate the full covariance matrix.

evaluate_(kernel) → Array | ndarray

property harmonic_kernel: Callable

Yields the harmonic kernel specified during initialization or throw a TypeError.

harmonic_transform(x) → Array | ndarray

power(harmonic_kernel=None) → Array | ndarray

sandwich(x, harmonic_kernel=None) → Array | ndarray

class ToeplitzSKI(grid_shape: Tuple[int], grid_bounds: Tuple[Tuple[float, float]], sampling_points: Array | ndarray, kernel: Callable | None = None, jitter: bool | float | None = True)

Bases: object

__call__(x, kernel=None) → Array | ndarray

Applies the Covariance matrix.

__init__(grid_shape: Tuple[int], grid_bounds: Tuple[Tuple[float, float]], sampling_points: Array | ndarray, kernel: Callable | None = None, jitter: bool | float | None = True)

Instantiate a KISS-GP model of the covariance using a Toeplitz matrix representation of the kernel.

Parameters:

• grid_shape – Number of pixels along each axes of the inducing points within grid_bounds.

• grid_bounds – Tuple of boundaries of length of the number of dimensions. The boundaries should denote the leftmost and rightmost edge of the modeling space.

• sampling_points – Locations of the modeled points within the grid.

• kernel – Position space kernel.

• jitter – Strength of the diagonal jitter which to add to the covariance.

evaluate(kernel=None)

Instantiate the full covariance matrix.

evaluate_(kernel=None) → Array | ndarray

property kernel: Callable

Yields the harmonic kernel specified during initialization or throw a TypeError.

interp_mat(grid_shape, grid_bounds, sampling_points, *, distances=None)

matmul_toeplitz(c, x)

Efficiently compute the product of an implicit Toeplitz matrix with a vector.

Parameters:

• c (ndarray) – One-dimensional column of the Toeplitz matrix. It is assumed that the row r is given by r = conjugate(c).

• x ((M,) or (M, K) ndarray) – Vector or matrix which to multiply from the right to the Toeplitz matrix.

Returns:

Toeplitz @ x – Result of the matrix multiplication.

Return type:

(M,) or (M, K) ndarray