fips.Estimator

class fips.Estimator(z, x_0, H, S_0, S_z, c=None)

Bases: ABC

Base inversion estimator class.

Parameters:

• z (np.ndarray) – Observed data.

• x_0 (np.ndarray) – Prior model state estimate.

• H (np.ndarray) – Forward operator.

• S_0 (np.ndarray) – Prior error covariance.

• S_z (np.ndarray) – Model-data mismatch covariance.

• c (np.ndarray or float, optional) – Constant data, defaults to 0.0.

Attributes

A	Averaging kernel matrix.
c	Constant data, which can be a scalar or an array matching the shape of z.
desroziers	Desroziers et al. (2005) diagnosed observation error covariance.
DOFS	Degrees Of Freedom for Signal (DOFS).
H	Forward operator.
K	Kalman gain matrix.
n_x	Number of state variables (length of x_0).
n_z	Number of observations (length of z).
R2	Coefficient of determination (R-squared).
reduced_chi2	Reduced Chi-squared statistic.
RMSE	Root mean square error (RMSE).
S_0	Prior error covariance.
S_hat	Posterior error covariance matrix.
S_y0	Prior error covariance in observation space.
S_z	Model-data mismatch covariance.
U_red	Uncertainty reduction vector.
uncertainty_reduction	Uncertainty reduction metric.
x_0	Prior model state estimate.
x_hat	Posterior mean model state estimate (solution).
y_0	Prior mean data estimate.
y_hat	Posterior mean observation estimate.
z	Observed data.

Methods

cost(x)	Cost/loss/misfit function.
forward(x)	Forward model calculation.
leverage(x)	Calculate the leverage matrix.
residual(x)	Forward model residual.