--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Matrix_LP/fspmlp.ML Sat Mar 17 12:52:40 2012 +0100
@@ -0,0 +1,313 @@
+(* Title: HOL/Matrix/fspmlp.ML
+ Author: Steven Obua
+*)
+
+signature FSPMLP =
+sig
+ type linprog
+ type vector = FloatSparseMatrixBuilder.vector
+ type matrix = FloatSparseMatrixBuilder.matrix
+
+ val y : linprog -> term
+ val A : linprog -> term * term
+ val b : linprog -> term
+ val c : linprog -> term * term
+ val r12 : linprog -> term * term
+
+ exception Load of string
+
+ val load : string -> int -> bool -> linprog
+end
+
+structure Fspmlp : FSPMLP =
+struct
+
+type vector = FloatSparseMatrixBuilder.vector
+type matrix = FloatSparseMatrixBuilder.matrix
+
+type linprog = term * (term * term) * term * (term * term) * (term * term)
+
+fun y (c1, _, _, _, _) = c1
+fun A (_, c2, _, _, _) = c2
+fun b (_, _, c3, _, _) = c3
+fun c (_, _, _, c4, _) = c4
+fun r12 (_, _, _, _, c6) = c6
+
+structure CplexFloatSparseMatrixConverter =
+MAKE_CPLEX_MATRIX_CONVERTER(structure cplex = Cplex and matrix_builder = FloatSparseMatrixBuilder);
+
+datatype bound_type = LOWER | UPPER
+
+fun intbound_ord ((i1: int, 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 = Table(type key = int val ord = (rev_order o int_ord));
+
+structure VarGraph = Table(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 => Float.min
+ | LOWER => Float.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 (key, (sure_bound, _)) (r1, r2) = 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.fold split g (Inttab.empty, Inttab.empty) 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 Float.sign x = LESS then
+ Float.mult x lower
+ else
+ Float.mult x upper
+
+ fun mult_lower x (lower, upper) =
+ if Float.sign x = LESS then
+ Float.mult x upper
+ else
+ Float.mult x lower
+
+ val mult_btype = case btype of UPPER => mult_upper | LOWER => mult_lower
+
+ fun calc_sure_bound (_, (row_bound, sources)) sure_bound =
+ let
+ fun add_src_bound (coeff, src_key) sum =
+ case sum of
+ NONE => NONE
+ | SOME x =>
+ (case get_sure_bound g src_key of
+ NONE => NONE
+ | SOME src_sure_bound => SOME (Float.add x (mult_btype src_sure_bound coeff)))
+ in
+ case fold add_src_bound sources (SOME row_bound) 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 => Float.min old_bound new_bound
+ | LOWER => Float.max old_bound new_bound))
+ end
+ in
+ case VarGraph.lookup g key of
+ NONE => NONE
+ | SOME (sure_bound, f) =>
+ let
+ val x = Inttab.fold calc_sure_bound f sure_bound
+ in
+ if x = sure_bound then NONE else x
+ end
+ end
+
+ fun propagate (key, _) (g, b) =
+ 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.fold propagate g (g, false)
+ in
+ if b then propagate_sure_bounds safe names g else g
+ end
+
+exception Load of string;
+
+val empty_spvec = @{term "Nil :: real spvec"};
+fun cons_spvec x xs = @{term "Cons :: nat * real => real spvec => real spvec"} $ x $ xs;
+val empty_spmat = @{term "Nil :: real spmat"};
+fun cons_spmat x xs = @{term "Cons :: nat * real spvec => real spmat => real spmat"} $ x $ xs;
+
+fun calcr safe_propagation xlen names prec A b =
+ let
+ fun test_1 (lower, upper) =
+ if lower = upper then
+ (if Float.eq (lower, (~1, 0)) then ~1
+ else if Float.eq (lower, (1, 0)) then 1
+ else 0)
+ else 0
+
+ fun calcr (row_index, a) g =
+ let
+ val b = FloatSparseMatrixBuilder.v_elem_at b row_index
+ val (_, b2) = FloatArith.approx_decstr_by_bin prec (case b of NONE => "0" | SOME b => b)
+ val approx_a = FloatSparseMatrixBuilder.v_fold (fn (i, s) => fn l =>
+ (i, FloatArith.approx_decstr_by_bin prec s)::l) a []
+
+ fun fold_dest_nodes (dest_index, dest_value) g =
+ 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), Float.neg b2)
+ else
+ ((dest_index, UPPER), b2)
+
+ fun fold_src_nodes (src_index, src_value as (src_lower, src_upper)) g =
+ if src_index = dest_index then g
+ else
+ let
+ val coeff = case dest_btype of
+ UPPER => (Float.neg src_upper, Float.neg src_lower)
+ | LOWER => src_value
+ in
+ if Float.sign src_lower = LESS 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
+ fold fold_src_nodes approx_a (add_row_bound g dest_key row_index row_bound)
+ 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) (Float.neg b2)
+ else if atest = 1 then
+ update_sure_bound g (u, UPPER) b2
+ else
+ g
+ end
+ | _ => fold fold_dest_nodes approx_a g
+ end
+
+ val g = FloatSparseMatrixBuilder.m_fold calcr A VarGraph.empty
+
+ val g = propagate_sure_bounds safe_propagation names g
+
+ val (r1, r2) = split_graph g
+
+ fun add_row_entry m index f vname value =
+ let
+ val v = (case value of
+ SOME value => FloatSparseMatrixBuilder.mk_spvec_entry 0 value
+ | NONE => FloatSparseMatrixBuilder.mk_spvec_entry' 0 (f $ (Var ((vname,0), HOLogic.realT))))
+ val vec = cons_spvec v empty_spvec
+ in
+ cons_spmat (FloatSparseMatrixBuilder.mk_spmat_entry index vec) m
+ end
+
+ fun abs_estimate i r1 r2 =
+ if i = 0 then
+ let val e = empty_spmat in (e, e) end
+ else
+ let
+ val index = xlen-i
+ val (r12_1, r12_2) = abs_estimate (i-1) r1 r2
+ val b1 = Inttab.lookup r1 index
+ val b2 = Inttab.lookup r2 index
+ in
+ (add_row_entry r12_1 index @{term "lbound :: real => real"} ((names index)^"l") b1,
+ add_row_entry r12_2 index @{term "ubound :: real => real"} ((names index)^"u") b2)
+ end
+
+ val (r1, r2) = abs_estimate xlen r1 r2
+
+ in
+ (r1, 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 (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 (_, 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 Float.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, (r1, r2))
+ end handle CplexFloatSparseMatrixConverter.Converter s => (raise (Load ("Converter: "^s)))
+
+end