fips.InverseProblem

class fips.InverseProblem(obs, prior, forward_operator, modeldata_mismatch, prior_error, constant=None, round_index=6)

Bases: Pickleable

Inverse problem combining observations, priors, and forward model.

Organizes state vectors, observations, forward operators, and error covariances into a unified framework for solving inverse problems via different estimators.

Parameters:

• obs (VectorLike) – Observation vector.

• prior (VectorLike) – Prior state vector.

• forward_operator (MatrixLike) – Forward operator mapping state space to observation space.

• modeldata_mismatch (MatrixLike) – Covariance matrix representing model-data mismatch (observation error).

• prior_error (MatrixLike) – Covariance matrix representing prior error.

• constant (VectorLike or float, optional) – Optional constant term added to the forward model (e.g., background or bias).

• round_index (int, optional) – Number of decimal places to round to. If None, no rounding is performed.

Attributes

averaging_kernel	Averaging kernel matrix (A).
constant	Optional constant term added to the forward model (e.g., background or bias).
desroziers	Desroziers et al. (2005) diagnosed observation error covariance.
estimator	Return the fitted estimator (raises if not solved).
forward_operator	Forward operator mapping state space to observation space.
kalman_gain	Kalman gain matrix (K).
modeldata_mismatch	Covariance matrix representing model-data mismatch (observation error).
n_obs	Return number of observations.
n_state	Return number of state variables.
obs	Observation vector.
obs_index	Return the observation space index.
posterior	Posterior state estimate.
posterior_error	Posterior error covariance.
posterior_obs	Modeled observations (H @ posterior).
prior	Prior state vector.
prior_error	Covariance matrix representing prior error.
prior_obs	Modeled observations using the prior (H @ prior).
prior_obs_error	Prior error covariance in observation space (H @ S_0 @ H.T).
state_index	Return the state space index.

Methods

get_block(component, block[, crossblock])	Get block from a component (Vector or Matrix).
solve(estimator, **kwargs)	Solve the inverse problem using the specified estimator.

Inherited

From Pickleable: from_file, to_file