Package 'rlppinv'

Solve a linear program via Convex Least Squares Programming (CLSP).

Description

Solve a linear program via Convex Least Squares Programming (CLSP).

Usage

lppinv(
  c = NULL,
  A_ub = NULL,
  b_ub = NULL,
  A_eq = NULL,
  b_eq = NULL,
  non_negative = TRUE,
  bounds = NULL,
  replace_value = NA_real_,
  tolerance = sqrt(.Machine$double.eps),
  final = TRUE,
  alpha = NULL,
  cond_tolerance = NULL,
  ...
)

Arguments

c	numeric vector of length $p$, optional. Objective-function coefficients. Included for API parity with Python's pylppinv; not used by CLSP.
A_ub	numeric matrix of size $i \times p$, optional. Matrix of inequality constraints $\mathbf{A}_{ub} \mathbf{x} \le \mathbf{b}_{ub}$.
b_ub	numeric vector of length $i$, optional. Right-hand side for the inequality constraints.
A_eq	numeric matrix of size $j \times p$, optional. Matrix of equality constraints $\mathbf{A}_{eq} \mathbf{x} = \mathbf{b}_{eq}$.
b_eq	numeric vector of length $j$, optional. Right-hand side for the equality constraints.
non_negative	logical scalar, default = TRUE. If FALSE, no default nonnegativity bound is applied.
bounds	NULL, numeric(2), or list of numeric(2). Bounds on variables. If a single pair c(low, high) is given, it is applied to all variables. If NULL, defaults to c(0, NA) for each variable (non-negativity).
replace_value	numeric scalar or NA, default = NA. Final replacement value for any variable that violates the bounds by more than the given tolerance.
tolerance	numeric scalar, default = sqrt(.Machine$double.eps). Convergence tolerance for bounds.
final	logical scalar, default = TRUE If FALSE, only the first step of the CLSP estimator is performed.
alpha	numeric scalar, numeric vector, or NULL, Regularization parameter for the second step of the CLSP estimator.
cond_tolerance	numeric scalar or NULL, default = NULL Singular-value cutoff for the custom condition number function. If NULL, the implementation uses an internal relative cutoff of 1e-14.
...	Additional arguments passed to the rclsp solver.

Value

An object of class "clsp" containing the fitted CLSP model.

See Also

clsp

CVXR-package

Examples

## Linear Programming via Regularized Least Squares (LPPinv)
  ## Underdetermined and potentially infeasible LP system

  RNGkind("L'Ecuyer-CMRG")
  set.seed(123456789)

  # sample (dataset)
  A_ub <- matrix(rnorm(50 * 500), nrow = 50L, ncol = 500L)
  A_eq <- matrix(rnorm(25 * 500), nrow = 25L, ncol = 500L)
  b_ub <- matrix(rnorm(50),       ncol = 1L)
  b_eq <- matrix(rnorm(25),       ncol = 1L)

  # model (no default non-negativity, unique MNBLUE solution)
  model <- lppinv(
      A_ub = A_ub,
      A_eq = A_eq,
      b_ub = b_ub,
      b_eq = b_eq,
      non_negative = FALSE,
      final = TRUE,
      alpha = 1.0                                   # unique MNBLUE estimator
  )

  # coefficients
  print("x hat (x_M hat):")
  print(round(model$x, 4))

  # numerical stability (if available)
  if (!is.null(model$kappaC)) {
      cat("\nNumerical stability:\n")
      cat("  kappaC :", round(model$kappaC, 4), "\n")
  }
  if (!is.null(model$kappaB)) {
      cat("  kappaB :", round(model$kappaB, 4), "\n")
  }
  if (!is.null(model$kappaA)) {
      cat("  kappaA :", round(model$kappaA, 4), "\n")
  }

  # goodness-of-fit diagnostics (if available)
  if (!is.null(model$nrmse)) {
      cat("\nGoodness-of-fit:\n")
      cat("  NRMSE :", round(model$nrmse, 6), "\n")
  }
  if (!is.null(model$x_lower)) {
      cat("  Diagnostic band (min):", round(min(model$x_lower), 4), "\n")
  }
  if (!is.null(model$x_upper)) {
      cat("  Diagnostic band (max):", round(max(model$x_upper), 4), "\n")
  }

  # bootstrap NRMSE t-test (if supported by rclsp)
  if ("ttest" %in% names(model)) {
      cat("\nBootstrap t-test:\n")
      tt <- model$ttest(sample_size = 30L,
                        seed = 123456789,
                        distribution = "normal")
      for (nm in names(tt)) {
          cat("   ", nm, ": ", round(tt[[nm]], 6), "\n", sep = "")
      }
  }

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