R/158_reductions_dcp2cone_canonicalizers_log_det_canon.R

In CVXR: Disciplined Convex Optimization

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## DO NOT EDIT THIS FILE!! EDIT THE SOURCE INSTEAD: rsrc_tree/reductions/dcp2cone/canonicalizers/log_det_canon.R
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## CVXPY SOURCE: reductions/dcp2cone/canonicalizers/log_det_canon.py
## log_det(A) -> sum(log(d)) subject to PSD([[D, Z], [Z^T, A]]),
##   where Z = vec_to_upper_tri(z, strict=FALSE), d = diag_mat(Z), D = diag_vec(d)
## Then log(d) is further canonicalized via log_canon -> ExpCone constraints


log_det_canon <- function(expr, args, solver_context = NULL) {
  A <- args[[1L]]
  n <- A@shape[1L]

  ## z: vector for the upper triangle (including diagonal)
  z_len <- (n * (n + 1L)) %/% 2L
  z <- Variable(c(z_len, 1L))
  Z <- vec_to_upper_tri(z, strict = FALSE)
  d <- DiagMat(Z)  ## extract diagonal as a vector (n,1)
  D <- DiagVec(d)  ## create diagonal matrix from vector (n,n)

  ## Block matrix constraint
  X <- bmat(list(list(D, Z), list(t(Z), A)))
  constraints <- list(PSD(X))

  ## Recursive canonicalization of log(d) -> ExpCone
  log_expr <- Log(d)
  log_result <- log_canon(log_expr, log_expr@args)
  log_obj <- log_result[[1L]]
  log_constr <- log_result[[2L]]
  constraints <- c(constraints, log_constr)

  list(sum_entries(log_obj), constraints)
}

method(dcp_canonicalize, LogDet) <- log_det_canon
method(has_dcp_canon, LogDet) <- function(expr) TRUE