R/162_reductions_dcp2cone_canonicalizers_matrix_frac_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/matrix_frac_canon.R
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## CVXPY SOURCE: reductions/dcp2cone/canonicalizers/matrix_frac_canon.py
## matrix_frac(X, P) -> trace(T) subject to PSD([[P, X], [X^T, T]]), symmetry check


matrix_frac_canon <- function(expr, args, solver_context = NULL) {
  X <- args[[1L]]
  P <- args[[2L]]

  ## CVXPY: handle 1D X by reshaping to column vector
  ## In R X is always 2D, but may be (n,1) naturally -- no special handling needed
  n <- X@shape[1L]
  m <- X@shape[2L]

  T_var <- Variable(c(m, m), symmetric = TRUE)
  ## Schur complement: [[P, X], [X^T, T]] >> 0
  ## ensures T - X^T P^{-1} X >> 0
  M <- bmat(list(list(P, X), list(t(X), T_var)))
  constraints <- list(PSD(M))

  ## Enforce symmetry on P if not already known symmetric
  if (!is_symmetric(P)) {
    ut <- upper_tri(P)
    lt <- upper_tri(t(P))
    constraints <- c(constraints, list(ut == lt))
  }

  list(matrix_trace(T_var), constraints)
}

method(dcp_canonicalize, MatrixFrac) <- matrix_frac_canon
method(has_dcp_canon, MatrixFrac) <- function(expr) TRUE