construct_ki_and_variances

romanisim.ramp.construct_ki_and_variances(atcinva, atcinv, covars)

Construct the \(k_i\) weights and variances for ramp fitting.

Following Casertano (2022), the ramp fit resultants are k.dot(differences), where \(k=(A^T C^{-1} A)^{-1} A^T C^{-1}\), and differences is the result of resultants_to_differences(resultants). Meanwhile the variances are \(k C k^T\). This function computes these k and variances.

Parameters:

atcinvanp.ndarray[2, 2] (float)

\(A^T C^{-1} A\) from construct_ramp_fitting_matrices

atcinvnp.ndarray[2, n_resultant] (float)

\(A^T C^{-1}\) from construct_ramp_fitting_matrices

covarslist[np.ndarray[n_resultant, n_resultant]]

covariance matrices to contract against \(k\) to compute variances

Returns:

knp.ndarray[2, n_resultant]

\(k = (A^T C^{-1} A)^-1 A^T C^{-1}\) from Casertano (2022)

varianceslist[np.ndarray[2, 2]] (float)

\(k C_i k^T\) for different covariance matrices C_i supplied in covars