corr: Compute the structural correlogram of the CLSP constraint system.

Description

This method performs a row-deletion sensitivity analysis on the canonical constraint matrix \([C | S]\), denoted as \(C_{\text{canon}}\), and evaluates the marginal effect of each constraint row on numerical stability, angular alignment, and estimator sensitivity.

Usage

corr(object, reset = FALSE, threshold = 0)

Value

A named list containing per-row diagnostic values:

constraint: Vector of constraint indices (1-based).
rmsa_i: List of \(\mathrm{RMSA}_i\) values.
rmsa_dkappaC: List of \(\Delta\kappa(C)\) after deleting row i.
rmsa_dkappaB: List of \(\Delta\kappa(B)\) after deleting row i.
rmsa_dkappaA: List of \(\Delta\kappa(A)\) after deleting row i.
rmsa_dnrmse: List of \(\Delta\mathrm{NRMSE}\) after deleting row i.
rmsa_dzhat: List of \(\Delta\hat{z}\) after deleting row i.
rmsa_dz: List of \(\Delta z\) after deleting row i.
rmsa_dx: List of \(\Delta x\) after deleting row i.

Arguments

object: An object of class "clsp".
reset: Logical, default = FALSE. If TRUE, forces recomputation of all diagnostic values.
threshold: Numeric, default = 0. If positive, limits the output to constraints with \(\mathrm{RMSA}_i \ge \text{threshold}\).

Details

For each row \(i\) in \(C_{\text{canon}}\), it computes:

The Root Mean Square Alignment (\(\mathrm{RMSA}_i\)) with all other rows \(j \ne i\).
The change in condition numbers \(\kappa(C)\), \(\kappa(B)\), and \(\kappa(A)\) when row \(i\) is deleted.
The effect on estimation quality: changes in NRMSE, \(\hat{z}\), \(z\), and \(x\).

Additionally, it computes the total RMSA statistic across all rows, summarizing the overall angular alignment of the constraint block.