fips.InverseProblem

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

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

Methods

from_file(path)	Load object from a pickle file.
get_block(component, block[, crossblock])	Get block from a component (Vector or Matrix).
solve(estimator, **kwargs)	Solve the inverse problem using the specified estimator.
to_file(path)	Save object to a pickle file.