Numeric

General numerical programming utilities.

It can be imported as:

from covvfit import numeric

or

import covvfit

covvfit.numeric.some_function()

Optimization

covvfit.numeric.OptimizeMultiResult dataclass

Multi-start optimization result.

Parameters:

Name	Type	Description	Default
x	ndarray	array of shape (dim,) representing minimum found	required
fun	float	value of the optimized function at x	required
best	OptimizeResult	optimization result (for the best start, yielding x)	required
runs	list	all the optimization results (for all starts)	required

covvfit.numeric.jax_multistart_minimize(loss_fn, theta0, n_starts=10, random_seed=42, maxiter=10000)

Multi-start gradient-based minimization.

Parameters:

Name	Type	Description	Default
loss_fn		loss function to be optimized	required
theta0	ndarray	vector of shape (dim,) providing an example starting point	required
n_starts	int	number of different starts	10
random_seed	int	seed used to perturb theta0	42
maxiter	int	maximum number of iterations per run	10000

Returns:

Type	Description
result	OptimizeMultiResult with the optimization information

Matrix operations

covvfit.numeric.log_matrix(a, threshold=1e-07)

Takes the logarithm of the entries, in a numerically stable manner. I.e., replaces values smaller than threshold with minimum value for the provided data type.

Parameters:

Name	Type	Description	Default
a	Float[Array, '*shape']	matrix which entries should be logarithmied	required
threshold	float	threshold used when to not calculate the logarithm	1e-07

Returns:

Type	Description
log_a	matrix with logarithmied entries

covvfit.numeric.log1mexp(x)

Computes log(1 - exp(x)) in a numerically stable way.

Parameters:

Name	Type	Description	Default
x	Float[Array, '*shape']	array	required

Returns:

Type	Description
log1mexp(x)	array of the same shape as x

covvfit.numeric.logsumexp_excluding_column(y, axis=-1)

Compute logsumexp across the given axis for each element, excluding the 'current' element at that axis index.

Parameters:

Name	Type	Description	Default
y	Float[Array, '*batch variants']	An array of shape [..., variants, ...].	required
axis	int	The axis along which we exclude each index before computing logsumexp.	-1

Returns:

Type	Description
Float[Array, '*batch variants']	An array of the same shape as y, whose element at index i along axis is the log-sum-exp of all other entries (j != i).