(* Title: HOL/Matrix/cplex/CplexMatrixConverter.ML ID: $Id: CplexMatrixConverter.ML,v 1.5 2007/05/13 16:17:48 haftmann Exp $ Author: Steven Obua *) signature MATRIX_BUILDER = sig type vector type matrix val empty_vector : vector val empty_matrix : matrix exception Nat_expected of int val set_elem : vector -> int -> string -> vector val set_vector : matrix -> int -> vector -> matrix end; signature CPLEX_MATRIX_CONVERTER = sig structure cplex : CPLEX structure matrix_builder : MATRIX_BUILDER type vector = matrix_builder.vector type matrix = matrix_builder.matrix type naming = int * (int -> string) * (string -> int) exception Converter of string (* program must fulfill is_normed_cplexProg and must be an element of the image of elim_nonfree_bounds *) (* convert_prog maximize c A b naming *) val convert_prog : cplex.cplexProg -> bool * vector * matrix * vector * naming (* results must be optimal, converts_results returns the optimal value as string and the solution as vector *) (* convert_results results name2index *) val convert_results : cplex.cplexResult -> (string -> int) -> string * vector end; functor MAKE_CPLEX_MATRIX_CONVERTER (structure cplex: CPLEX and matrix_builder: MATRIX_BUILDER) : CPLEX_MATRIX_CONVERTER = struct structure cplex = cplex structure matrix_builder = matrix_builder type matrix = matrix_builder.matrix type vector = matrix_builder.vector type naming = int * (int -> string) * (string -> int) open matrix_builder open cplex exception Converter of string; fun neg_term (cplexNeg t) = t | neg_term (cplexSum ts) = cplexSum (map neg_term ts) | neg_term t = cplexNeg t fun convert_prog (cplexProg (s, goal, constrs, bounds)) = let fun build_naming index i2s s2i [] = (index, i2s, s2i) | build_naming index i2s s2i (cplexBounds (cplexNeg cplexInf, cplexLeq, cplexVar v, cplexLeq, cplexInf)::bounds) = build_naming (index+1) (Inttab.update (index, v) i2s) (Symtab.update_new (v, index) s2i) bounds | build_naming _ _ _ _ = raise (Converter "nonfree bound") val (varcount, i2s_tab, s2i_tab) = build_naming 0 Inttab.empty Symtab.empty bounds fun i2s i = case Inttab.lookup i2s_tab i of NONE => raise (Converter "index not found") | SOME n => n fun s2i s = case Symtab.lookup s2i_tab s of NONE => raise (Converter ("name not found: "^s)) | SOME i => i fun num2str positive (cplexNeg t) = num2str (not positive) t | num2str positive (cplexNum num) = if positive then num else "-"^num | num2str _ _ = raise (Converter "term is not a (possibly signed) number") fun setprod vec positive (cplexNeg t) = setprod vec (not positive) t | setprod vec positive (cplexVar v) = set_elem vec (s2i v) (if positive then "1" else "-1") | setprod vec positive (cplexProd (cplexNum num, cplexVar v)) = set_elem vec (s2i v) (if positive then num else "-"^num) | setprod _ _ _ = raise (Converter "term is not a normed product") fun sum2vec (cplexSum ts) = Library.foldl (fn (vec, t) => setprod vec true t) (empty_vector, ts) | sum2vec t = setprod empty_vector true t fun constrs2Ab j A b [] = (A, b) | constrs2Ab j A b ((_, cplexConstr (cplexLeq, (t1,t2)))::cs) = constrs2Ab (j+1) (set_vector A j (sum2vec t1)) (set_elem b j (num2str true t2)) cs | constrs2Ab j A b ((_, cplexConstr (cplexGeq, (t1,t2)))::cs) = constrs2Ab (j+1) (set_vector A j (sum2vec (neg_term t1))) (set_elem b j (num2str true (neg_term t2))) cs | constrs2Ab j A b ((_, cplexConstr (cplexEq, (t1,t2)))::cs) = constrs2Ab j A b ((NONE, cplexConstr (cplexLeq, (t1,t2))):: (NONE, cplexConstr (cplexGeq, (t1, t2)))::cs) | constrs2Ab _ _ _ _ = raise (Converter "no strict constraints allowed") val (A, b) = constrs2Ab 0 empty_matrix empty_vector constrs val (goal_maximize, goal_term) = case goal of (cplexMaximize t) => (true, t) | (cplexMinimize t) => (false, t) in (goal_maximize, sum2vec goal_term, A, b, (varcount, i2s, s2i)) end fun convert_results (cplex.Optimal (opt, entries)) name2index = let fun setv (v, (name, value)) = (matrix_builder.set_elem v (name2index name) value) in (opt, Library.foldl setv (matrix_builder.empty_vector, entries)) end | convert_results _ _ = raise (Converter "No optimal result") end; structure SimpleMatrixBuilder : MATRIX_BUILDER = struct type vector = (int * string) list type matrix = (int * vector) list val empty_matrix = [] val empty_vector = [] exception Nat_expected of int; fun set_elem v i s = v @ [(i, s)] fun set_vector m i v = m @ [(i, v)] end; structure SimpleCplexMatrixConverter = MAKE_CPLEX_MATRIX_CONVERTER(structure cplex = Cplex and matrix_builder = SimpleMatrixBuilder);