R/128_atoms_sign.R

In CVXR: Disciplined Convex Optimization

#####
## DO NOT EDIT THIS FILE!! EDIT THE SOURCE INSTEAD: rsrc_tree/atoms/sign.R
#####

## CVXPY SOURCE: atoms/sign.py
## Sign -- sign of a scalar variable: -1 if x <= 0, +1 if x > 0.
## A DQCP atom (both quasiconvex AND quasiconcave) on scalar input;
## not DQCP on vector input.  Numerically a step function with zero
## subgradient on each plateau; CVXPY returns _grad = [None] and we
## mirror via .grad returning list(NULL).
##
## User-facing dispatch: base R's `sign()` on a CVXR Expression is
## routed through the Math group handler in
## rsrc_tree/zzz_R_specific/operators.R, which delegates here.
## `expr_sign(x)` is the unrelated *curvature-query* generic and is
## not changed by this atom (see CLAUDE.md note about the rename).

# ===================================================================
# Sign -- DQCP atom (scalar): step function sign of an Expression
# ===================================================================

Sign <- new_class("Sign", parent = Atom, package = "CVXR",
  constructor = function(x) {
    if (FALSE) new_object(S7_object())  ## S7 static-check guard
    x <- as_expr(x)
    id <- next_expr_id()
    obj <- .fast_new(Sign, S7_object(),
      id    = as.integer(id),
      .cache = new.env(parent = emptyenv()),
      args  = list(x),
      shape = .shape(x)       ## mirrors CVXPY shape_from_args: same as arg
    )
    validate_arguments(obj)
    obj
  }
)

## shape_from_args mirrors CVXPY:36-38: returns the argument's shape.
method(shape_from_args, Sign) <- function(x) .arg_shape(x)

## sign_from_args mirrors CVXPY:41-44: the atom's own sign is the
## argument's sign (nonneg if arg is nonneg; nonpos if arg is nonpos).
method(sign_from_args, Sign) <- function(x) {
  list(is_nonneg = is_nonneg(.args(x)[[1L]]),
       is_nonpos = is_nonpos(.args(x)[[1L]]))
}

## Sign is neither convex nor concave (CVXPY:46-54).
method(is_atom_convex, Sign)  <- function(x) FALSE
method(is_atom_concave, Sign) <- function(x) FALSE

## Sign is not log-log either.
method(is_atom_log_log_convex, Sign)  <- function(x) FALSE
method(is_atom_log_log_concave, Sign) <- function(x) FALSE

## DQCP only when the argument is scalar (CVXPY:56-63).
## For vector input, is_dqcp() on the containing Problem will
## correctly return FALSE because both flags are FALSE here.
method(is_atom_quasiconvex, Sign)  <- function(x) is_scalar(.args(x)[[1L]])
method(is_atom_quasiconcave, Sign) <- function(x) is_scalar(.args(x)[[1L]])

## Step function: neither monotone increasing nor decreasing globally
## (CVXPY:65-73).
method(is_incr, Sign) <- function(x, idx, ...) FALSE
method(is_decr, Sign) <- function(x, idx, ...) FALSE

## CVXPY:31-35 numeric: +1 where val > 0, -1 elsewhere (including 0).
method(numeric_value, Sign) <- function(x, values, ...) {
  val <- values[[1L]]
  out <- val
  out[val  > 0] <-  1.0
  out[val <= 0] <- -1.0
  out
}

## Subgradient: undefined.  Mirrors CVXPY:75-76 (_grad returns [None]).
## Returning list(NULL) propagates NULL up the chain rule for every
## variable that flows through Sign.
method(.grad, Sign) <- function(x, values, ...) {
  list(NULL)
}

method(get_data, Sign) <- function(x) NULL