R/088_atoms_norm1.R

In CVXR: Disciplined Convex Optimization

#####
## DO NOT EDIT THIS FILE!! EDIT THE SOURCE INSTEAD: rsrc_tree/atoms/norm1.R
#####

## CVXPY SOURCE: atoms/norm1.py
## Norm1 -- L1 norm (sum of absolute values), axis-aware


Norm1 <- new_class("Norm1", parent = AxisAtom, package = "CVXR",
  constructor = function(x, axis = NULL, keepdims = FALSE, id = NULL) {
    if (is.null(id)) id <- next_expr_id()
    x <- as_expr(x)
    if (!is.null(axis)) .validate_axis(axis, length(x@shape))
    shape <- .axis_shape(x@shape, axis, keepdims)

    obj <- new_object(S7_object(),
      id       = as.integer(id),
      .cache   = new.env(parent = emptyenv()),
      args     = list(x),
      shape    = shape,
      axis     = axis,
      keepdims = keepdims
    )
    obj
  }
)

# -- sign: always nonneg ------------------------------------------
method(sign_from_args, Norm1) <- function(x) {
  list(is_nonneg = TRUE, is_nonpos = FALSE)
}

# -- curvature: convex --------------------------------------------
method(is_atom_convex, Norm1) <- function(x) TRUE
method(is_atom_concave, Norm1) <- function(x) FALSE

# -- monotonicity -------------------------------------------------
method(is_incr, Norm1) <- function(x, idx, ...) is_nonneg(x@args[[1L]])
method(is_decr, Norm1) <- function(x, idx, ...) is_nonpos(x@args[[1L]])

# -- PWL ----------------------------------------------------------
method(is_pwl, Norm1) <- function(x) {
  is_pwl(x@args[[1L]]) && is_real(x@args[[1L]])
}

# -- numeric ------------------------------------------------------
method(numeric_value, Norm1) <- function(x, values, ...) {
  v <- values[[1L]]
  if (is.null(x@axis)) {
    matrix(sum(abs(v)), 1L, 1L)
  } else if (x@axis == 2L) {
    res <- colSums(abs(v))
    if (x@keepdims) matrix(res, nrow = 1L) else matrix(res, nrow = 1L)
  } else {
    res <- rowSums(abs(v))
    if (x@keepdims) matrix(res, ncol = 1L) else matrix(res, ncol = 1L)
  }
}

# -- graph_implementation: stub -----------------------------------
method(graph_implementation, Norm1) <- function(x, arg_objs, shape, data = NULL, ...) {
  cli_abort("graph_implementation for {.cls Norm1} not yet implemented.")
}

#' L1 norm of an expression
#'
#' @param x An Expression
#' @param axis NULL (all), 1 (row-wise), or 2 (column-wise)
#' @param keepdims Logical: keep reduced dimensions?
#' @returns A Norm1 atom
#' @export
norm1 <- function(x, axis = NULL, keepdims = FALSE) {
  Norm1(x, axis, keepdims)
}