# File CplexMatrixConverter.ML

    (*  Title:      HOL/Matrix/cplex/CplexMatrixConverter.ML
        ID:         $Id: CplexMatrixConverter.ML,v 1.4 2005/09/15 15:16:57 wenzelm 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);