dense

This module uses tinygp to construct dense representations of kernels for testing/benchmarking performance and accuracy.

Danger

They are not meant for use on large datasets!

Kernels defined here:

• SHOKernel: A stochastic harmonic oscillator (SHO) kernel

• IntegratedSHOKernel: A tinygp/JAX implementation of the integrated SHO kernel from Luhn et al. 2026.

Classes

SHOKernel	The base class for all kernel implementations
IntegratedSHOKernel	The base class for all kernel implementations

Functions

extract_leaf_kernels(kernel[, all])	Recursively extract all tinygp leaf kernels from a sum or product of tinygp kernels
unpack_coordinates(X1, X2)	Unpack the input coordinates X1 and X2 into time, instrument ID, and exposure time.

Module Contents

smolgp.kernels.dense.extract_leaf_kernels(kernel, all=False)

Recursively extract all tinygp leaf kernels from a sum or product of tinygp kernels

smolgp.kernels.dense.unpack_coordinates(X1, X2)

Unpack the input coordinates X1 and X2 into time, instrument ID, and exposure time.

X1 and X2 can either be

t1 and t2 for single instrument, no exposure times

or

(t1, instid1) and (t2, instid2) for multiple instruments, no exposure times

or

(t1, instid1, delta1) and (t2, instid2, delta2) for exposure times, also requires instrument IDs

Returns

(t1, instid1, delta1), (t2, instid2, delta2) where instid and delta are arrays of zeros if not provided

class smolgp.kernels.dense.SHOKernel(S=None, w=None, Q=None, rho=None, tau=None, sig=None)

Bases: tinygp.kernels.Kernel

The base class for all kernel implementations

This subclass provides default implementations to add and multiply kernels. Subclasses should accept parameters in their __init__ and then override Kernel.evaluate() with custom behavior.

S: jax.Array | float

w: jax.Array | float

Q: jax.Array | float

rho: jax.Array | float

tau: jax.Array | float

sig: jax.Array | float

evaluate(X1, X2)

Calculate the kernel for given pair of times X1 and X2.

X1 and X2 can either be

t1 and t2 for single instrument, no exposure times

or

(t1, instid1) and (t2, instid2) for multiple instruments, no exposure times

or

(t1, delta1, instid1) and (t2, delta2, instid2) for exposure times,

also requires instrument IDs even if a single instrument

__repr__()

class smolgp.kernels.dense.IntegratedSHOKernel(S=None, w=None, Q=None, rho=None, tau=None, sig=None)

Bases: tinygp.kernels.Kernel

The base class for all kernel implementations

This subclass provides default implementations to add and multiply kernels. Subclasses should accept parameters in their __init__ and then override Kernel.evaluate() with custom behavior.

S: jax.Array | float

w: jax.Array | float

Q: jax.Array | float

rho: jax.Array | float

tau: jax.Array | float

sig: jax.Array | float

eta: jax.Array | float

a: jax.Array | float

__repr__()

Delta(X1, X2)

Time difference (absolute value) between pairs of observations X1, X2.

Delta = | t1 - t2 |

latent_process(Delta)

Latent kernel for given time difference Delta

I0(y)

Helper function for single integral (Eq. 11 in L26)

I1(lower, upper)

Helper function for double integrals (Eq. 14 in L26)

I2(lower, upper)

Helper function for double integrals (Eq. 15 in L26)

integrated_separate(Delta, delta1, delta2)

The double integral for two non-overlapping observations. Depends on the time-lag (Delta) and the two exposure times (delta1, delta2)

Eq. 17 in L26

integrated_overlap(delta)

The double integral for two perfectly overlapping observations (i.e. zero time-lag). As such, this only depends on the exposure time (delta)

Eq. 13 in L26

integrated_single(Delta, delta)

The single integral for when one observation has zero exposure time (e.g. latent curve)

Eq. 10 in L26

full_single_integral(Delta, delta)

This helper function handles the logic for the single integral case.

For pairs of observation coordinates separated by Delta, such that one is the 0-exposure test point (i.e., the latent curve) and the other has exposure time delta, this function handles the logic to break up the integral and call self.integrated_single() for the sub-exposures where appropriate

evaluate(X1, X2)

Compute the integrated SHO kernel for a pair of observations X1 and X2.

X1 and X2 can either be

(t1, texp1) and (t2, texp2) for single instrument

or

(t1, texp1, instid1) and (t2, texp2, instid2) for multiple instruments