File FloatSparseMatrixBuilder.ML (Isabelle2005: October 2005)

# File FloatSparseMatrixBuilder.ML

    (*  Title:      HOL/Matrix/cplex/FloatSparseMatrixBuilder.ML
        ID:         $Id: FloatSparseMatrixBuilder.ML,v 1.4 2005/09/15 15:16:57 wenzelm Exp $
        Author:     Steven Obua
    *)

    structure FloatSparseMatrixBuilder :
    sig
        include MATRIX_BUILDER

        structure cplex : CPLEX

        type float = IntInf.int*IntInf.int
        type floatfunc = float -> float

        val float2cterm : IntInf.int * IntInf.int -> cterm

        val approx_value : int -> floatfunc -> string -> cterm * cterm
        val approx_vector : int -> floatfunc -> vector -> cterm * cterm
        val approx_matrix : int -> floatfunc -> matrix -> cterm * cterm

        val mk_spvec_entry : int -> float -> term
        val empty_spvec : term
        val cons_spvec : term -> term -> term
        val empty_spmat : term
        val mk_spmat_entry : int -> term -> term
        val cons_spmat : term -> term -> term
        val sign_term : term -> cterm

        val v_elem_at : vector -> int -> string option
        val m_elem_at : matrix -> int -> vector option
        val v_only_elem : vector -> int option
        val v_fold : ('a * (int * string) -> 'a) -> 'a -> vector -> 'a
        val m_fold : ('a * (int * vector) -> 'a) -> 'a -> matrix -> 'a

        val transpose_matrix : matrix -> matrix

        val cut_vector : int -> vector -> vector
        val cut_matrix : vector -> (int option) -> matrix -> matrix

        (* cplexProg c A b *)
        val cplexProg : vector -> matrix -> vector -> (cplex.cplexProg * (string -> int))
        (* dual_cplexProg c A b *)
        val dual_cplexProg : vector -> matrix -> vector -> (cplex.cplexProg * (string -> int))

        val real_spmatT : typ
        val real_spvecT : typ
    end
    =
    struct

    structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));

    type vector = string Inttab.table
    type matrix = vector Inttab.table
    type float = IntInf.int*IntInf.int
    type floatfunc = float -> float

    val th = theory "FloatSparseMatrix"
    val sg = sign_of th

    fun readtype s = Sign.intern_type sg s
    fun readterm s = Sign.intern_const sg s

    val ty_list = readtype "list"
    val term_Nil = readterm "Nil"
    val term_Cons = readterm "Cons"

    val spvec_elemT = HOLogic.mk_prodT (HOLogic.natT, HOLogic.realT)
    val spvecT = Type (ty_list, [spvec_elemT])
    val spmat_elemT = HOLogic.mk_prodT (HOLogic.natT, spvecT)
    val spmatT = Type (ty_list, [spmat_elemT])

    val real_spmatT = spmatT
    val real_spvecT = spvecT

    val empty_matrix_const = Const (term_Nil, spmatT)
    val empty_vector_const = Const (term_Nil, spvecT)

    val Cons_spvec_const = Const (term_Cons, spvec_elemT --> spvecT --> spvecT)
    val Cons_spmat_const = Const (term_Cons, spmat_elemT --> spmatT --> spmatT)

    val float_const = Float.float_const

    (*val float_const = Const (readterm "float", HOLogic.mk_prodT (HOLogic.intT, HOLogic.intT) --> HOLogic.realT)*)

    val zero = IntInf.fromInt 0
    val minus_one = IntInf.fromInt ~1
    val two = IntInf.fromInt 2

    val mk_intinf = Float.mk_intinf
    (*    let
    	fun mk_bit n = if n = zero then HOLogic.false_const else HOLogic.true_const

    	fun bin_of n =
    	    if n = zero then HOLogic.pls_const
    	    else if n = minus_one then HOLogic.min_const
    	    else
    		let
    		    (*val (q,r) = IntInf.divMod (n, two): doesn't work in SML 10.0.7, but in newer versions!!!*)
    	            val q = IntInf.div (n, two)
    		    val r = IntInf.mod (n, two)
    		in
    		    HOLogic.bit_const $ bin_of q $ mk_bit r
    		end
        in
    	HOLogic.number_of_const ty $ (bin_of n)
        end*)

    val mk_float  = Float.mk_float
    (*    float_const $ (HOLogic.mk_prod ((mk_intinf HOLogic.intT a), (mk_intinf HOLogic.intT b)))*)

    fun float2cterm (a,b) = cterm_of sg (mk_float (a,b))

    fun approx_value_term prec f = Float.approx_float prec (fn (x, y) => (f x, f y))
    (*    let
    	val (flower, fupper) = ExactFloatingPoint.approx_decstr_by_bin prec value
    	val (flower, fupper) = (f flower, f fupper)
        in
    	(mk_float flower, mk_float fupper)
        end*)

    fun approx_value prec pprt value =
        let
    	val (flower, fupper) = approx_value_term prec pprt value
        in
    	(cterm_of sg flower, cterm_of sg fupper)
        end

    fun sign_term t = cterm_of sg t

    val empty_spvec = empty_vector_const

    val empty_spmat = empty_matrix_const

    fun mk_spvec_entry i f =
        let
    	val term_i = mk_intinf HOLogic.natT (IntInf.fromInt i)
    	val term_f = mk_float f
        in
    	HOLogic.mk_prod (term_i, term_f)
        end

    fun mk_spmat_entry i e =
        let
    	val term_i = mk_intinf HOLogic.natT (IntInf.fromInt i)
        in
    	HOLogic.mk_prod (term_i, e)
        end

    fun cons_spvec h t = Cons_spvec_const $ h $ t

    fun cons_spmat h t = Cons_spmat_const $ h $ t

    fun approx_vector_term prec pprt vector =
        let
    	fun app ((vlower, vupper), (index, s)) =
    	    let
    		val (flower, fupper) = approx_value_term prec pprt s
    		val index = mk_intinf HOLogic.natT (IntInf.fromInt index)
    		val elower = HOLogic.mk_prod (index, flower)
    		val eupper = HOLogic.mk_prod (index, fupper)
    	    in
    		(Cons_spvec_const $ elower $ vlower,
    		 Cons_spvec_const $ eupper $ vupper)
    	    end
        in
    	Inttab.foldl app ((empty_vector_const, empty_vector_const), vector)
        end

    fun approx_matrix_term prec pprt matrix =
        let
    	fun app ((mlower, mupper), (index, vector)) =
    	    let
    		val (vlower, vupper) = approx_vector_term prec pprt vector
    		val index = mk_intinf HOLogic.natT (IntInf.fromInt index)
    		val elower = HOLogic.mk_prod (index, vlower)
    		val eupper = HOLogic.mk_prod (index, vupper)
    	    in
    		(Cons_spmat_const $ elower $ mlower,
    		 Cons_spmat_const $ eupper $ mupper)
    	    end

    	val (mlower, mupper) = Inttab.foldl app ((empty_matrix_const, empty_matrix_const), matrix)
        in
    	Inttab.foldl app ((empty_matrix_const, empty_matrix_const), matrix)
        end

    fun approx_vector prec pprt vector =
        let
    	val (l, u) = approx_vector_term prec pprt vector
        in
    	(cterm_of sg l, cterm_of sg u)
        end

    fun approx_matrix prec pprt matrix =
        let
    	val (l, u) = approx_matrix_term prec pprt matrix
        in
    	(cterm_of sg l, cterm_of sg u)
        end

    exception Nat_expected of int;

    val zero_interval = approx_value_term 1 I "0"

    fun set_elem vector index str =
        if index < 0 then
    	raise (Nat_expected index)
        else if (approx_value_term 1 I str) = zero_interval then
    	vector
        else
    	Inttab.update (index, str) vector

    fun set_vector matrix index vector =
        if index < 0 then
    	raise (Nat_expected index)
        else if Inttab.is_empty vector then
    	matrix
        else
    	Inttab.update (index, vector) matrix

    val empty_matrix = Inttab.empty
    val empty_vector = Inttab.empty

    (* dual stuff *)

    structure cplex = Cplex

    fun transpose_matrix matrix =
        let
    	fun upd m j i x =
    	    case Inttab.lookup m j of
    		SOME v => Inttab.update (j, Inttab.update (i, x) v) m
    	      | NONE => Inttab.update (j, Inttab.update (i, x) Inttab.empty) m

    	fun updv j (m, (i, s)) = upd m i j s

    	fun updm (m, (j, v)) = Inttab.foldl (updv j) (m, v)
        in
    	Inttab.foldl updm (empty_matrix, matrix)
        end

    exception No_name of string;

    exception Superfluous_constr_right_hand_sides

    fun cplexProg c A b =
        let
    	val ytable = ref Inttab.empty
    	fun indexof s =
    	    if String.size s = 0 then raise (No_name s)
    	    else case Int.fromString (String.extract(s, 1, NONE)) of
    		     SOME i => i | NONE => raise (No_name s)

    	fun nameof i =
    	    let
    		val s = "x"^(Int.toString i)
    		val _ = change ytable (Inttab.update (i, s))
    	    in
    		s
    	    end

    	fun split_numstr s =
    	    if String.isPrefix "-" s then (false,String.extract(s, 1, NONE))
    	    else if String.isPrefix "+" s then (true, String.extract(s, 1, NONE))
    	    else (true, s)

    	fun mk_term index s =
    	    let
    		val (p, s) = split_numstr s
    		val prod = cplex.cplexProd (cplex.cplexNum s, cplex.cplexVar (nameof index))
    	    in
    		if p then prod else cplex.cplexNeg prod
    	    end

    	fun vec2sum vector =
    	    cplex.cplexSum (Inttab.foldl (fn (list, (index, s)) => (mk_term index s)::list) ([], vector))

    	fun mk_constr index vector c =
    	    let
    		val s = case Inttab.lookup c index of SOME s => s | NONE => "0"
    		val (p, s) = split_numstr s
    		val num = if p then cplex.cplexNum s else cplex.cplexNeg (cplex.cplexNum s)
    	    in
    		(NONE, cplex.cplexConstr (cplex.cplexLeq, (vec2sum vector, num)))
    	    end

    	fun delete index c = Inttab.delete index c handle Inttab.UNDEF _ => c

    	val (list, b) = Inttab.foldl
    			    (fn ((list, c), (index, v)) => ((mk_constr index v c)::list, delete index c))
    			    (([], b), A)
    	val _ = if Inttab.is_empty b then () else raise Superfluous_constr_right_hand_sides

    	fun mk_free y = cplex.cplexBounds (cplex.cplexNeg cplex.cplexInf, cplex.cplexLeq,
    					   cplex.cplexVar y, cplex.cplexLeq,
    					   cplex.cplexInf)

    	val yvars = Inttab.foldl (fn (l, (i, y)) => (mk_free y)::l) ([], !ytable)

    	val prog = cplex.cplexProg ("original", cplex.cplexMaximize (vec2sum c), list, yvars)
        in
    	(prog, indexof)
        end

    fun dual_cplexProg c A b =
        let
    	fun indexof s =
    	    if String.size s = 0 then raise (No_name s)
    	    else case Int.fromString (String.extract(s, 1, NONE)) of
    		     SOME i => i | NONE => raise (No_name s)

    	fun nameof i = "y"^(Int.toString i)

    	fun split_numstr s =
    	    if String.isPrefix "-" s then (false,String.extract(s, 1, NONE))
    	    else if String.isPrefix "+" s then (true, String.extract(s, 1, NONE))
    	    else (true, s)

    	fun mk_term index s =
    	    let
    		val (p, s) = split_numstr s
    		val prod = cplex.cplexProd (cplex.cplexNum s, cplex.cplexVar (nameof index))
    	    in
    		if p then prod else cplex.cplexNeg prod
    	    end

    	fun vec2sum vector =
    	    cplex.cplexSum (Inttab.foldl (fn (list, (index, s)) => (mk_term index s)::list) ([], vector))

    	fun mk_constr index vector c =
    	    let
    		val s = case Inttab.lookup c index of SOME s => s | NONE => "0"
    		val (p, s) = split_numstr s
    		val num = if p then cplex.cplexNum s else cplex.cplexNeg (cplex.cplexNum s)
    	    in
    		(NONE, cplex.cplexConstr (cplex.cplexEq, (vec2sum vector, num)))
    	    end

    	fun delete index c = Inttab.delete index c handle Inttab.UNDEF _ => c

    	val (list, c) = Inttab.foldl
    			    (fn ((list, c), (index, v)) => ((mk_constr index v c)::list, delete index c))
    			    (([], c), transpose_matrix A)
    	val _ = if Inttab.is_empty c then () else raise Superfluous_constr_right_hand_sides

    	val prog = cplex.cplexProg ("dual", cplex.cplexMinimize (vec2sum b), list, [])
        in
    	(prog, indexof)
        end

    fun cut_vector size v =
        let
    	val count = ref 0
    	fun app (v, (i, s)) =
    	    if (!count < size) then
    		(count := !count +1 ; Inttab.update (i,s) v)
    	    else
    		v
        in
    	Inttab.foldl app (empty_vector, v)
        end

    fun cut_matrix vfilter vsize m =
        let
    	fun app (m, (i, v)) =
    	    if Inttab.lookup vfilter i = NONE then
    		m
    	    else
    		case vsize of
    		    NONE => Inttab.update (i,v) m
    		  | SOME s => Inttab.update (i, cut_vector s v) m
        in
    	Inttab.foldl app (empty_matrix, m)
        end

    fun v_elem_at v i = Inttab.lookup v i
    fun m_elem_at m i = Inttab.lookup m i

    fun v_only_elem v =
        case Inttab.min_key v of
    	NONE => NONE
          | SOME vmin => (case Inttab.max_key v of
    			  NONE => SOME vmin
    			| SOME vmax => if vmin = vmax then SOME vmin else NONE)

    fun v_fold f a v = Inttab.foldl f (a,v)

    fun m_fold f a m = Inttab.foldl f (a,m)

    end;