#' Smriti Automated Longitudinal Imputation
#'
#' This function performs an automated routing and refinement for longitudinal
#' missing data. It establishes a target covariance manifold from observed data,
#' performs initial machine learning imputation, and then projects the result
#' back toward the structural manifold using a Lagrangian constraint.
#'
#' @param data A data frame containing missing values.
#' @param time_cols A character vector or numeric vector specifying the
#'   longitudinal columns.
#' @param lambda A numeric value specifying the penalty weight for the
#'   Lagrangian constraint.
#' @param robust A logical value. Setting it to TRUE sacrifices a marginal
#'   degree of asymptotic efficiency on perfect Gaussian data to secure
#'   structural integrity against heavy-tailed skew (the robustness-efficiency
#'   tradeoff).
#'
#' @return A data frame with imputed and structurally refined values.
#' @export
smriti_impute <- function(data, time_cols, lambda = 0.5, robust = TRUE) {
        # Generate a dense starting point via non-parametric imputation.
        # We utilize missForest to establish an initial point-cloud that is then
        # routed toward the target manifold; this intermediate step is required
        # because robust estimators like the Minimum Covariance Determinant (MCD)
        # cannot be directly computed on datasets with missing values.
        raw_imp_obj <- missForest::missForest(data)
        x_hallucinated <- as.matrix(raw_imp_obj$ximp[, time_cols])

        if (robust) {
                # Employ a robust estimator to protect the structural manifold against
                # distributional contamination. Using the MCD estimator ensures that
                # the target covariance is not biased by outliers or heavy-tailed skew,
                # which would otherwise distort the Lagrangian projection.
                sigma_target <- MASS::cov.rob(x_hallucinated, method = "mcd")$cov
        } else {
                # Establish the target manifold based on all available pairwise
                # information, prioritizing maximal use of observed data over
                # robustness to extreme deviations.
                sigma_target <- stats::cov(data[, time_cols], use = "pairwise.complete.obs")
        }

        x_refined <- constrain_covariance(
                X_imp = x_hallucinated,
                Sigma_target = sigma_target,
                lambda = lambda,
                lr = 1e-7,
                max_iter = 1000
        )

        final_data <- data
        final_data[, time_cols] <- x_refined
        return(final_data)
}
