(* Title: HOL/Matrix/cplex/fspmlp.ML ID: $Id: fspmlp.ML,v 1.3 2005/09/15 15:16:57 wenzelm Exp $ Author: Steven Obua *) signature FSPMLP = sig type linprog val y : linprog -> cterm val A : linprog -> cterm * cterm val b : linprog -> cterm val c : linprog -> cterm * cterm val r : linprog -> cterm val r12 : linprog -> cterm * cterm exception Load of string val load : string -> int -> bool -> linprog end structure fspmlp : FSPMLP = struct type linprog = cterm * (cterm * cterm) * cterm * (cterm * cterm) * cterm * (cterm * cterm) fun y (c1, c2, c3, c4, c5, _) = c1 fun A (c1, c2, c3, c4, c5, _) = c2 fun b (c1, c2, c3, c4, c5, _) = c3 fun c (c1, c2, c3, c4, c5, _) = c4 fun r (c1, c2, c3, c4, c5, _) = c5 fun r12 (c1, c2, c3, c4, c5, c6) = c6 structure CplexFloatSparseMatrixConverter = MAKE_CPLEX_MATRIX_CONVERTER(structure cplex = Cplex and matrix_builder = FloatSparseMatrixBuilder); datatype bound_type = LOWER | UPPER fun intbound_ord ((i1, b1),(i2,b2)) = if i1 < i2 then LESS else if i1 = i2 then (if b1 = b2 then EQUAL else if b1=LOWER then LESS else GREATER) else GREATER structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord)); structure VarGraph = TableFun(type key = int*bound_type val ord = intbound_ord); (* key -> (float option) * (int -> (float * (((float * float) * key) list)))) *) (* dest_key -> (sure_bound * (row_index -> (row_bound * (((coeff_lower * coeff_upper) * src_key) list)))) *) exception Internal of string; fun add_row_bound g dest_key row_index row_bound = let val x = case VarGraph.lookup g dest_key of NONE => (NONE, Inttab.update (row_index, (row_bound, [])) Inttab.empty) | SOME (sure_bound, f) => (sure_bound, case Inttab.lookup f row_index of NONE => Inttab.update (row_index, (row_bound, [])) f | SOME _ => raise (Internal "add_row_bound")) in VarGraph.update (dest_key, x) g end fun update_sure_bound g (key as (_, btype)) bound = let val x = case VarGraph.lookup g key of NONE => (SOME bound, Inttab.empty) | SOME (NONE, f) => (SOME bound, f) | SOME (SOME old_bound, f) => (SOME ((case btype of UPPER => FloatArith.min | LOWER => FloatArith.max) old_bound bound), f) in VarGraph.update (key, x) g end fun get_sure_bound g key = case VarGraph.lookup g key of NONE => NONE | SOME (sure_bound, _) => sure_bound (*fun get_row_bound g key row_index = case VarGraph.lookup g key of NONE => NONE | SOME (sure_bound, f) => (case Inttab.lookup f row_index of NONE => NONE | SOME (row_bound, _) => (sure_bound, row_bound))*) fun add_edge g src_key dest_key row_index coeff = case VarGraph.lookup g dest_key of NONE => raise (Internal "add_edge: dest_key not found") | SOME (sure_bound, f) => (case Inttab.lookup f row_index of NONE => raise (Internal "add_edge: row_index not found") | SOME (row_bound, sources) => VarGraph.update (dest_key, (sure_bound, Inttab.update (row_index, (row_bound, (coeff, src_key) :: sources)) f)) g) fun split_graph g = let fun split ((r1, r2), (key, (sure_bound, _))) = case sure_bound of NONE => (r1, r2) | SOME bound => (case key of (u, UPPER) => (r1, Inttab.update (u, bound) r2) | (u, LOWER) => (Inttab.update (u, bound) r1, r2)) in VarGraph.foldl split ((Inttab.empty, Inttab.empty), g) end fun it2list t = let fun tolist (l, a) = a::l in Inttab.foldl tolist ([], t) end (* If safe is true, termination is guaranteed, but the sure bounds may be not optimal (relative to the algorithm). If safe is false, termination is not guaranteed, but on termination the sure bounds are optimal (relative to the algorithm) *) fun propagate_sure_bounds safe names g = let (* returns NONE if no new sure bound could be calculated, otherwise the new sure bound is returned *) fun calc_sure_bound_from_sources g (key as (_, btype)) = let fun mult_upper x (lower, upper) = if FloatArith.is_negative x then FloatArith.mul x lower else FloatArith.mul x upper fun mult_lower x (lower, upper) = if FloatArith.is_negative x then FloatArith.mul x upper else FloatArith.mul x lower val mult_btype = case btype of UPPER => mult_upper | LOWER => mult_lower fun calc_sure_bound (sure_bound, (row_index, (row_bound, sources))) = let fun add_src_bound (sum, (coeff, src_key)) = case sum of NONE => NONE | SOME x => (case get_sure_bound g src_key of NONE => NONE | SOME src_sure_bound => SOME (FloatArith.add x (mult_btype src_sure_bound coeff))) in case Library.foldl add_src_bound (SOME row_bound, sources) of NONE => sure_bound | new_sure_bound as (SOME new_bound) => (case sure_bound of NONE => new_sure_bound | SOME old_bound => SOME (case btype of UPPER => FloatArith.min old_bound new_bound | LOWER => FloatArith.max old_bound new_bound)) end in case VarGraph.lookup g key of NONE => NONE | SOME (sure_bound, f) => let val x = Inttab.foldl calc_sure_bound (sure_bound, f) in if x = sure_bound then NONE else x end end fun propagate ((g, b), (key, _)) = case calc_sure_bound_from_sources g key of NONE => (g,b) | SOME bound => (update_sure_bound g key bound, if safe then case get_sure_bound g key of NONE => true | _ => b else true) val (g, b) = VarGraph.foldl propagate ((g, false), g) in if b then propagate_sure_bounds safe names g else g end exception Load of string; fun calcr safe_propagation xlen names prec A b = let val empty = Inttab.empty fun instab t i x = Inttab.update (i, x) t fun isnegstr x = String.isPrefix "-" x fun negstr x = if isnegstr x then String.extract (x, 1, NONE) else "-"^x fun test_1 (lower, upper) = if lower = upper then (if FloatArith.is_equal lower (IntInf.fromInt ~1, FloatArith.izero) then ~1 else if FloatArith.is_equal lower (IntInf.fromInt 1, FloatArith.izero) then 1 else 0) else 0 fun calcr (g, (row_index, a)) = let val b = FloatSparseMatrixBuilder.v_elem_at b row_index val (_, b2) = ExactFloatingPoint.approx_decstr_by_bin prec (case b of NONE => "0" | SOME b => b) val approx_a = FloatSparseMatrixBuilder.v_fold (fn (l, (i,s)) => (i, ExactFloatingPoint.approx_decstr_by_bin prec s)::l) [] a fun fold_dest_nodes (g, (dest_index, dest_value)) = let val dest_test = test_1 dest_value in if dest_test = 0 then g else let val (dest_key as (_, dest_btype), row_bound) = if dest_test = ~1 then ((dest_index, LOWER), FloatArith.neg b2) else ((dest_index, UPPER), b2) fun fold_src_nodes (g, (src_index, src_value as (src_lower, src_upper))) = if src_index = dest_index then g else let val coeff = case dest_btype of UPPER => (FloatArith.neg src_upper, FloatArith.neg src_lower) | LOWER => src_value in if FloatArith.is_negative src_lower then add_edge g (src_index, UPPER) dest_key row_index coeff else add_edge g (src_index, LOWER) dest_key row_index coeff end in Library.foldl fold_src_nodes ((add_row_bound g dest_key row_index row_bound), approx_a) end end in case approx_a of [] => g | [(u, a)] => let val atest = test_1 a in if atest = ~1 then update_sure_bound g (u, LOWER) (FloatArith.neg b2) else if atest = 1 then update_sure_bound g (u, UPPER) b2 else g end | _ => Library.foldl fold_dest_nodes (g, approx_a) end val g = FloatSparseMatrixBuilder.m_fold calcr VarGraph.empty A val g = propagate_sure_bounds safe_propagation names g val (r1, r2) = split_graph g fun add_row_entry m index value = let val vec = FloatSparseMatrixBuilder.cons_spvec (FloatSparseMatrixBuilder.mk_spvec_entry 0 value) FloatSparseMatrixBuilder.empty_spvec in FloatSparseMatrixBuilder.cons_spmat (FloatSparseMatrixBuilder.mk_spmat_entry index vec) m end fun abs_estimate i r1 r2 = if i = 0 then let val e = FloatSparseMatrixBuilder.empty_spmat in (e, (e, e)) end else let val index = xlen-i val (r, (r12_1, r12_2)) = abs_estimate (i-1) r1 r2 val b1 = case Inttab.lookup r1 index of NONE => raise (Load ("x-value not bounded from below: "^(names index))) | SOME x => x val b2 = case Inttab.lookup r2 index of NONE => raise (Load ("x-value not bounded from above: "^(names index))) | SOME x => x val abs_max = FloatArith.max (FloatArith.neg (FloatArith.negative_part b1)) (FloatArith.positive_part b2) in (add_row_entry r index abs_max, (add_row_entry r12_1 index b1, add_row_entry r12_2 index b2)) end val sign = FloatSparseMatrixBuilder.sign_term val (r, (r1, r2)) = abs_estimate xlen r1 r2 in (sign r, (sign r1, sign r2)) end fun load filename prec safe_propagation = let val prog = Cplex.load_cplexFile filename val prog = Cplex.elim_nonfree_bounds prog val prog = Cplex.relax_strict_ineqs prog val (maximize, c, A, b, (xlen, names, _)) = CplexFloatSparseMatrixConverter.convert_prog prog val (r, (r1, r2)) = calcr safe_propagation xlen names prec A b val _ = if maximize then () else raise Load "sorry, cannot handle minimization problems" val (dualprog, indexof) = FloatSparseMatrixBuilder.dual_cplexProg c A b val results = Cplex.solve dualprog val (optimal,v) = CplexFloatSparseMatrixConverter.convert_results results indexof val A = FloatSparseMatrixBuilder.cut_matrix v NONE A fun id x = x val v = FloatSparseMatrixBuilder.set_vector FloatSparseMatrixBuilder.empty_matrix 0 v val b = FloatSparseMatrixBuilder.transpose_matrix (FloatSparseMatrixBuilder.set_vector FloatSparseMatrixBuilder.empty_matrix 0 b) val c = FloatSparseMatrixBuilder.set_vector FloatSparseMatrixBuilder.empty_matrix 0 c val (y1, _) = FloatSparseMatrixBuilder.approx_matrix prec FloatArith.positive_part v val A = FloatSparseMatrixBuilder.approx_matrix prec id A val (_,b2) = FloatSparseMatrixBuilder.approx_matrix prec id b val c = FloatSparseMatrixBuilder.approx_matrix prec id c in (y1, A, b2, c, r, (r1, r2)) end handle CplexFloatSparseMatrixConverter.Converter s => (raise (Load ("Converter: "^s))) end