rlppinv (version 0.2.0)

lppinv: 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,
  ...
)

Value

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

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.

...

Additional arguments passed to the rclsp solver.

See Also

clsp

CVXR-package

Examples

# \donttest{
  ## 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 = "")
      }
  }
# }