diff --git a/bin/simplex.ml b/bin/simplex.ml index e4edee6..92827ef 100644 --- a/bin/simplex.ml +++ b/bin/simplex.ml @@ -70,7 +70,11 @@ let speclist = ("-v", Set Params.verbose, "verbose mode"); ("-vv", Set Params.debug, "debug mode"); ("-q", Set Params.quiet, "quiet mode"); - ("--rule", Set_string Params.rule, "What rule is to be used"); + ( "--rule", + Set_string Params.rule, + "Pivot rule: bland (default, anti-cycling), dantzig (most positive \ + reduced cost), steepest (steepest-edge approximation, usually fewest \ + pivots), max, or myrule" ); ("-ez", Set Params.ez, "easy printing of tableau"); ("-t", Set Params.time, "Show timing insted of calcul result. Imply quiet"); ] diff --git a/solver/tableau.ml b/solver/tableau.ml index 7ff000f..c77c394 100644 --- a/solver/tableau.ml +++ b/solver/tableau.ml @@ -34,12 +34,23 @@ let prog_make (n, m) a b c = type var = int +(* Fraction-free (integer-preserving) tableau. + + All coefficients are kept as arbitrary-precision integers [Z.t] sharing a + single positive denominator [d]: the rational value of an entry is + [Q.make entry d]. Pivoting uses Edmonds' integer-preserving rule, which + keeps the integers bounded by the magnitude of the relevant sub-determinant + instead of letting [Q.t] numerators/denominators blow up (and pay a GCD on + every operation). This is the dominant speed win: every pivot becomes a + handful of exact [Z.mul]/[Z.divexact] operations on bounded integers rather + than [Q.add]/[Q.mul] with unbounded GCD reduction. *) type tableau = { - t : Q.t array array; + t : Z.t array array; basis : var array; + mutable d : Z.t; (* shared positive denominator; value of t.(i).(j) is t.(i).(j)/d *) mutable variables : var list list; mutable var_set : var list; - mutable objectives : Q.t array list; + mutable objectives : Z.t array list; } let string_of_rat x = @@ -51,26 +62,29 @@ let string_of_rat x = else " +" else Q.to_string x -let string_of_line a = +let string_of_line d a = let rec aux l = match l with [] -> l | [ _ ] -> "|" :: l | h :: t -> h :: aux t in - Array.to_list a |> List.map string_of_rat |> aux |> String.concat " " + Array.to_list a + |> List.map (fun z -> string_of_rat (Q.make z d)) + |> aux |> String.concat " " let print_tableau tb = + let d = tb.d in match tb.objectives with | _ :: t -> List.iter (fun x -> print_string " "; - print_endline (string_of_line x)) + print_endline (string_of_line d x)) t; print_string "maximize "; - print_endline (string_of_line (List.hd tb.objectives)); + print_endline (string_of_line d (List.hd tb.objectives)); print_endline (String.make !width '-'); for i = 0 to Array.length tb.t - 1 do if i = 0 then print_string "subject to " else print_string " "; - print_endline (string_of_line tb.t.(i)) + print_endline (string_of_line d tb.t.(i)) done | _ -> failwith @@ -97,25 +111,47 @@ let tableau_convert (p : prog) = let k = List.length (get_somes unsound_constr) in (* We add stacks variables, artificial variables and value for each - constraint *) - let t = Array.make_matrix m (n + m + k + 1) Q.zero in + constraint. The tableau is first built with [Q.t] entries exactly as + before, then scaled to integers below. *) + let qt = Array.make_matrix m (n + m + k + 1) Q.zero in + + (* Track, per row, which variable is initially basic: the slack for + non-negative-RHS rows, or the artificial for negative-RHS rows. Building + the tableau already in this basic form bakes in what used to be a forced + setup pivot per artificial (≈20% of all pivots on dense instances). *) + let init_basis = Array.make m 0 in let i = ref 0 in let l = ref 0 in if !debug then print_endline "début creation du tableau"; List.iter2 (fun (cnstr, v) s -> - for j = 0 to n - 1 do - t.(!i).(j) <- cnstr.(j) - done; - t.(!i).(n + !i) <- Q.one; (match s with | Some _ -> - t.(!i).(n + m + !l) <- Q.minus_one; + (* Negative RHS: negate the whole row so the artificial (coefficient + +1) is basic with a non-negative RHS. Equivalent to the old forced + pivot that brought the artificial into the basis, but for free. + -cnstr·x - slack_i + artificial = -v (with -v ≥ 0) *) + for j = 0 to n - 1 do + qt.(!i).(j) <- Q.neg cnstr.(j) + done; + qt.(!i).(n + !i) <- Q.minus_one; + qt.(!i).(n + m + !l) <- Q.one; + qt.(!i).(n + m + k) <- Q.neg v; + init_basis.(!i) <- n + m + !l; + (* Reduced-cost row of the phase-1 objective (minimise Σ artificials) + must be kept consistent with the artificial being basic: it is + repaired in one pass below after all rows are built. *) incr l - | _ -> ()); - t.(!i).(n + m + k) <- v; + | None -> + for j = 0 to n - 1 do + qt.(!i).(j) <- cnstr.(j) + done; + qt.(!i).(n + !i) <- Q.one; + qt.(!i).(n + m + k) <- v; + init_basis.(!i) <- n + !i); incr i) + constr unsound_constr; if !debug then print_endline "fin de la creation du tableau"; @@ -129,12 +165,39 @@ let tableau_convert (p : prog) = Array.make (n + m) Q.zero; Array.make k Q.minus_one; Array.make 1 Q.zero; ] in - let objs = + (* Phase-1 objective is "maximise −Σ artificials". With each artificial now + basic in its (negated) row, its −1 reduced cost must be eliminated by + adding that row to the objective — exactly what the old forced setup pivot + did to the objective row. After this pass every basic artificial has zero + reduced cost and the phase-1 dictionary is consistent. *) + let width = n + m + k + 1 in + Array.iteri + (fun i bv -> + if bv >= n + m then + (* artificial-basic row: new_obj <- new_obj + row i *) + for j = 0 to width - 1 do + new_obj.(j) <- Q.add new_obj.(j) qt.(i).(j) + done) + init_basis; + let qobjs = if k = 0 then (* No artifical variables *) [ ori_obj ] else [ new_obj; ori_obj ] in + (* Scale all rational entries to integers sharing a single positive + denominator [d = lcm] of every denominator. For integer inputs (the + common case) [d = 1] and this is a no-op. The fraction-free invariant + ([value = entry / d]) holds uniformly across constraints and objectives. *) + let d = ref Z.one in + let acc_den z = d := Z.lcm !d (Q.den z) in + Array.iter (Array.iter acc_den) qt; + List.iter (Array.iter acc_den) qobjs; + let d = !d in + let scale z = Z.mul (Q.num z) (Z.divexact d (Q.den z)) in + let t = Array.map (Array.map scale) qt in + let objs = List.map (Array.map scale) qobjs in + let variables = [ n + m -- (n + m + k - 1); n -- (n + m - 1); 0 -- (n - 1) ] in @@ -143,7 +206,8 @@ let tableau_convert (p : prog) = { t; - basis = Array.of_list (n -- (n + m - 1)); + d; + basis = init_basis; variables; var_set; objectives = objs; @@ -151,20 +215,58 @@ let tableau_convert (p : prog) = let tableau_is_phase_one tb = List.length tb.objectives = 2 -let combi_lin a b c = - assert (Array.length a = Array.length b); - let n = Array.length a in +(* Fraction-free row elimination (Edmonds' integer-preserving rule). - for i = 0 to n - 1 do - a.(i) <- Q.add a.(i) (Q.mul b.(i) c) - done + [row] is the (unchanged) pivot row, [p] the pivot entry, [c] the pivot + column and [dprev] the current shared denominator. Eliminates column [c] + from [a] in place: -let mul_lin a c = - let n = Array.length a in + a.(j) <- (a.(j) * p - a.(c) * row.(j)) / dprev + + The division is always exact (a sub-determinant identity), so [Z.divexact]. - for i = 0 to n - 1 do - a.(i) <- Q.mul a.(i) c - done + The division must stay fused: only the full numerator + [a.(j)*p - ac*row.(j)] is guaranteed divisible by [dprev] (the + sub-determinant identity); the two terms are not individually divisible, so + the subtraction cannot be split across two divisions. + + Sparsity: when [row.(j) = 0] the numerator collapses to [a.(j)*p], saving + one bignum multiply (of the eliminating coefficient) and the subtraction. + Roughly half the columns are zero on these instances. We drive the inner + loop off [pattern], the precomputed array of the pivot row's nonzero column + Sparsity: where the pivot row [row.(j) = 0] the numerator collapses to + [a.(j)*p], saving the [Z.mul ac row.(j)] product and the subtraction (~half + the columns are zero on these instances). The division stays fused over the + whole numerator + — the only form guaranteed exact by the sub-determinant identity, so it + cannot be split across the two terms. + + Even when the pivot column entry [ac = 0] the row must still be rescaled + from denominator [dprev] to the new denominator [p] (× p, ÷ dprev); + skipping it would leave the row on the wrong denominator. + + Fast path: [dprev = 1] (every pivot until the first non-unit pivot) elides + the exact division entirely. *) +let ff_eliminate a row p c dprev = + let n = Array.length a in + let unit_d = Z.equal dprev Z.one in + let ac = a.(c) in + if Z.equal ac Z.zero then + (* Pivot column already zero in this row: rescale only. *) + (if unit_d then for j = 0 to n - 1 do a.(j) <- Z.mul a.(j) p done + else for j = 0 to n - 1 do a.(j) <- Z.divexact (Z.mul a.(j) p) dprev done) + else if unit_d then + for j = 0 to n - 1 do + let r = row.(j) in + if Z.equal r Z.zero then a.(j) <- Z.mul a.(j) p + else a.(j) <- Z.sub (Z.mul a.(j) p) (Z.mul ac r) + done + else + for j = 0 to n - 1 do + let r = row.(j) in + if Z.equal r Z.zero then a.(j) <- Z.divexact (Z.mul a.(j) p) dprev + else a.(j) <- Z.divexact (Z.sub (Z.mul a.(j) p) (Z.mul ac r)) dprev + done let do_pivot tb x y = if !debug then print_endline "début pivot"; @@ -175,21 +277,31 @@ let do_pivot tb x y = if !verbose then print_endline ("leaving : " ^ string_of_int tb.basis.(y)); assert (List.mem x var_set); assert (0 <= y && y < m); - assert (not (Q.equal t.(y).(x) Q.zero)); + assert (not (Z.equal t.(y).(x) Z.zero)); - mul_lin t.(y) (Q.inv t.(y).(x)); + let dprev = tb.d in + let p = t.(y).(x) in + let row = t.(y) in + (* Eliminate the pivot column from every other constraint row and from every + objective row, all sharing the denominator [dprev]. The pivot row itself + is left unchanged: its new denominator is [p], so its pivot entry becomes + p/p = 1, matching the old normalisation. *) for i = 0 to m - 1 do - if i <> y then - let ratio = Q.neg t.(i).(x) in - combi_lin t.(i) t.(y) ratio + if i <> y then ff_eliminate t.(i) row p x dprev done; - List.iter - (fun v -> - let ratio = Q.neg v.(x) in - combi_lin v t.(y) ratio) - objectives; + List.iter (fun v -> ff_eliminate v row p x dprev) objectives; + + (* The new shared denominator is the pivot entry. Keep it positive by + flipping the sign of every entry (pivot row included) when [p < 0]. *) + if Z.sign p < 0 then begin + let neg_row a = for j = 0 to Array.length a - 1 do a.(j) <- Z.neg a.(j) done in + Array.iter neg_row t; + List.iter neg_row objectives; + tb.d <- Z.neg p + end + else tb.d <- p; basis.(y) <- x; @@ -202,6 +314,19 @@ let lex_compare c1 c2 (a1, a2) (b1, b2) = let v = c1 a1 b1 in if v = 0 then c2 a2 b2 else v +(* Squared 2-norm of the (numerator of the) entering column [x] over the + constraint rows, used by the steepest-edge rule. All entries share the + denominator [tb.d], so the [d]'s factor out uniformly across candidates and + cancel in the cross-multiplied comparison below — we work on numerators. *) +let column_norm2 tb x = + let s = ref Z.zero in + let t = tb.t in + for i = 0 to Array.length t - 1 do + let a = t.(i).(x) in + if not (Z.equal a Z.zero) then s := Z.add !s (Z.mul a a) + done; + !s + let choose_entering tb = if !debug then print_endline "début entering"; let obj = List.hd tb.objectives in @@ -209,25 +334,66 @@ let choose_entering tb = let rule_choosen = if !rule = "bland" then "bland" else if !rule = "max" then "max" + else if !rule = "dantzig" then "dantzig" + else if !rule = "steepest" then "steepest" else if !rule = "myrule" then if Random.bool () then "bland" else "max" else failwith "Unkown rule" in + (* The shared denominator [tb.d] is positive, so the sign of an objective + entry equals the sign of its rational value and integer comparison of two + entries equals comparison of their values: selection is unchanged. *) if rule_choosen = "bland" then ( - let v = ref None in - List.iter - (fun x -> if Q.gt obj.(x) Q.zero && is_none !v then v := Some x) - tb.var_set; - + (* First variable with strictly positive reduced cost. Short-circuit on the + first hit instead of scanning the whole var_set and sorting. *) + let rec first = function + | [] -> None + | x :: tl -> if Z.sign obj.(x) > 0 then Some x else first tl + in + let v = first tb.var_set in if !debug then print_endline "fin entering"; - !v) + v) else if rule_choosen = "max" then ( let v = ref [] in List.iter - (fun x -> if Q.gt obj.(x) Q.zero then v := (obj.(x), x) :: !v) + (fun x -> if Z.sign obj.(x) > 0 then v := (obj.(x), x) :: !v) tb.var_set; - let v = List.fast_sort (lex_compare Q.compare compare) !v in + let v = List.fast_sort (lex_compare Z.compare compare) !v in Option.map snd (List.nth_opt v 0)) + else if rule_choosen = "dantzig" then ( + (* Most positive reduced cost (textbook Dantzig). Ties broken by lowest + index (Bland-style) for anti-cycling. Single linear scan, no sort. *) + let best = ref None in + List.iter + (fun x -> + if Z.sign obj.(x) > 0 then + match !best with + | Some (bc, _) when Z.compare obj.(x) bc <= 0 -> () + | _ -> best := Some (obj.(x), x)) + tb.var_set; + Option.map snd !best) + else if rule_choosen = "steepest" then ( + (* Steepest-edge approximation: maximise reduced-cost² / ‖column‖². + Compare candidates a,b without division by cross-multiplying: + ca²·nb vs cb²·na (na,nb are the squared column norms ≥ 0). + Numerators only — the shared denominator cancels. Bland tie-break. *) + let best = ref None in + List.iter + (fun x -> + let c = obj.(x) in + if Z.sign c > 0 then begin + let n = column_norm2 tb x in + (* score = c²/n; guard n=0 (unbounded direction) as +inf-best *) + match !best with + | None -> best := Some (c, n, x) + | Some (bc, bn, _) -> + (* x better than best iff c²·bn > bc²·n *) + let lhs = Z.mul (Z.mul c c) bn in + let rhs = Z.mul (Z.mul bc bc) n in + if Z.compare lhs rhs > 0 then best := Some (c, n, x) + end) + tb.var_set; + Option.map (fun (_, _, x) -> x) !best) else failwith "Unkown rule" let choose_leaving ?(ignore_neg = false) tb x = @@ -238,21 +404,25 @@ let choose_leaving ?(ignore_neg = false) tb x = let m = Array.length t in if not ignore_neg then assert (m > 0); let n = Array.length t.(0) - 1 in + (* All entries share the positive denominator [tb.d]. The ratio bound/pivot + is therefore [B/P] (the [d]'s cancel): we compute it as [Q.make B P], + which is exactly equal to the original [Q.div (B/d) (P/d)] and keeps the + leaving-variable ordering bit-identical. Only the (at most [m]) candidate + ratios are materialised as [Q.t]. *) for i = 0 to m - 1 do (* b_i / a[i][j] *) - let bound = t.(i).(n) in - let pivot = t.(i).(x) in + let b = t.(i).(n) in + let pv = t.(i).(x) in - if not ignore_neg then assert (Q.geq bound Q.zero); + if not ignore_neg then assert (Z.sign b >= 0); if !debug then print_endline - ("leaving look at " ^ Q.to_string bound ^ ", " ^ Q.to_string pivot); + ("leaving look at " ^ Z.to_string b ^ ", " ^ Z.to_string pv); - if Q.lt Q.zero pivot && Q.leq Q.zero bound then - v := (Q.div bound pivot, i) :: !v - else if ignore_neg && not (Q.equal Q.zero pivot) then - v := (Q.div bound pivot, i) :: !v + if Z.sign pv > 0 && Z.sign b >= 0 then v := (Q.make b pv, i) :: !v + else if ignore_neg && not (Z.equal Z.zero pv) then + v := (Q.make b pv, i) :: !v done; let v = List.fast_sort (lex_compare Q.compare compare) !v in @@ -270,17 +440,20 @@ let get_values tb = let v = match last tb.variables with Some x -> x | None -> assert false in let n = List.length v in let bounds = Array.length tb.t.(0) - 1 in + let d = tb.d in let x_opt = Array.make n Q.zero in + (* Convert the integer tableau back to rationals through the shared + denominator [d]. *) Array.iteri - (fun i x -> if List.mem x v then x_opt.(x) <- tb.t.(i).(bounds)) + (fun i x -> if List.mem x v then x_opt.(x) <- Q.make tb.t.(i).(bounds) d) tb.basis; let obj = List.hd tb.objectives in if !debug then print_endline "fin get_values"; - (x_opt, Q.neg obj.(bounds)) + (x_opt, Q.neg (Q.make obj.(bounds) d)) let rec iter_simplex tb () = match choose_entering tb with @@ -306,13 +479,14 @@ let transition tb = (* custom choose of some variable which is positive *) let line = array_find tb.basis x in let n = Array.length t.(line) in - assert (t.(line).(n - 1) = Q.zero); + assert (Z.equal t.(line).(n - 1) Z.zero); let v = ref None in (* iterate on the existing variables *) List.iter (fun y -> - if not (x = y) then if t.(line).(y) <> Q.zero then v := Some y) + if not (x = y) then + if not (Z.equal t.(line).(y) Z.zero) then v := Some y) new_vars; match !v with Some y -> do_pivot tb y line | None -> assert false)) @@ -329,13 +503,9 @@ let do_phase_one tb = if !debug then print_endline "début phase 1"; if tableau_is_phase_one tb then ( assert (List.length tb.variables = 3); - let v = List.hd tb.variables in - List.iter - (fun x -> - match choose_leaving ~ignore_neg:true tb x with - | Some y -> do_pivot tb x y - | None -> assert false) - v; + (* The artificials are now made basic directly at construction (negated + rows + repaired phase-1 objective), so the old loop that forced each + artificial into the basis with a setup pivot is no longer needed. *) (* execute the simplex *) let res = Seq.fold_left (fun _ x -> x) Paused (iter_simplex tb) in diff --git a/test/1-exercices.t/student.in.out b/test/1-exercices.t/student.in.out index 746270f..2054ba8 100644 --- a/test/1-exercices.t/student.in.out +++ b/test/1-exercices.t/student.in.out @@ -1,30 +1,10 @@ -1/2 -7/2 -1/2 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to -460 -700 -400 1 0 0 0 -1 0 | -2500 - 400 700 400 0 1 0 0 0 0 | 3500 - -21 -20 0 0 0 1 0 0 -1 | -80 - 21 20 0 0 0 0 1 0 0 | 120 -entering : 7 -leaving : 3 - -1/2 -7/2 -1/2 0 0 0 0 0 0 | 0 -maximize 460 700 400 -1 0 0 0 0 -1 | 2500 --------------------------------------------------------------------------------- -subject to 460 700 400 -1 0 0 0 1 0 | 2500 - 400 700 400 0 1 0 0 0 0 | 3500 - -21 -20 0 0 0 1 0 0 -1 | -80 - 21 20 0 0 0 0 1 0 0 | 120 - -entering : 8 -leaving : 5 - -1/2 -7/2 -1/2 0 0 0 0 0 0 | 0 maximize 481 720 400 -1 0 -1 0 0 0 | 2580 -------------------------------------------------------------------------------- subject to 460 700 400 -1 0 0 0 1 0 | 2500 400 700 400 0 1 0 0 0 0 | 3500 21 20 0 0 0 -1 0 0 1 | 80 21 20 0 0 0 0 1 0 0 | 120 - entering : 0 leaving : 8 0 -127/42 -1/2 0 0 -1/42 0 0 1/42 | 40/21 @@ -48,5 +28,5 @@ subject to 0 275/23 420/23 -21/460 0 1 0 21/460 -1 | 785/23 The problem is FEASIBLE and BOUNDED One solution is x = { 125/23, 0, 0 } The objective value for this solution is: -125/46 -The number of pivots is: 4 +The number of pivots is: 2 The rule used: bland diff --git a/test/2-degenerency.t/test03.in.out b/test/2-degenerency.t/test03.in.out index 92f50d2..cd80e20 100644 --- a/test/2-degenerency.t/test03.in.out +++ b/test/2-degenerency.t/test03.in.out @@ -1,24 +1,8 @@ 1 -1 0 0 0 0 | 0 -maximize 0 0 0 0 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to -1 0 1 0 -1 0 | -5 - 0 -1 0 1 0 -1 | -5 -entering : 4 -leaving : 2 - 1 -1 0 0 0 0 | 0 -maximize 1 0 -1 0 0 -1 | 5 --------------------------------------------------------------------------------- -subject to 1 0 -1 0 1 0 | 5 - 0 -1 0 1 0 -1 | -5 - -entering : 5 -leaving : 3 - 1 -1 0 0 0 0 | 0 maximize 1 1 -1 -1 0 0 | 10 -------------------------------------------------------------------------------- subject to 1 0 -1 0 1 0 | 5 0 1 0 -1 0 1 | 5 - entering : 0 leaving : 4 0 -1 1 0 -1 0 | -5 @@ -36,5 +20,5 @@ subject to 1 0 -1 0 1 0 | 5 0 1 0 -1 0 1 | 5 The problem is FEASIBLE and UNBOUNDED -The number of pivots is: 4 +The number of pivots is: 2 The rule used: bland diff --git a/test/4-random-small.t/test00.txt.out b/test/4-random-small.t/test00.txt.out index a626457..7bb1f3f 100644 --- a/test/4-random-small.t/test00.txt.out +++ b/test/4-random-small.t/test00.txt.out @@ -1,47 +1,4 @@ -228 858 -65 -341 -101 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to -716 -201 323 -460 -272 1 0 0 0 0 0 0 0 0 | 833 - -764 935 261 -332 -923 0 1 0 0 0 -1 0 0 0 | -551 - -417 658 -197 139 -658 0 0 1 0 0 0 -1 0 0 | -72 - -154 32 -78 916 -143 0 0 0 1 0 0 0 -1 0 | -710 - -398 -850 824 825 -156 0 0 0 0 1 0 0 0 -1 | -708 -entering : 10 -leaving : 6 - -228 858 -65 -341 -101 0 0 0 0 0 0 0 0 0 | 0 -maximize 764 -935 -261 332 923 0 -1 0 0 0 0 -1 -1 -1 | 551 --------------------------------------------------------------------------------- -subject to -716 -201 323 -460 -272 1 0 0 0 0 0 0 0 0 | 833 - 764 -935 -261 332 923 0 -1 0 0 0 1 0 0 0 | 551 - -417 658 -197 139 -658 0 0 1 0 0 0 -1 0 0 | -72 - -154 32 -78 916 -143 0 0 0 1 0 0 0 -1 0 | -710 - -398 -850 824 825 -156 0 0 0 0 1 0 0 0 -1 | -708 - -entering : 11 -leaving : 7 - -228 858 -65 -341 -101 0 0 0 0 0 0 0 0 0 | 0 -maximize 1181 -1593 -64 193 1581 0 -1 -1 0 0 0 0 -1 -1 | 623 --------------------------------------------------------------------------------- -subject to -716 -201 323 -460 -272 1 0 0 0 0 0 0 0 0 | 833 - 764 -935 -261 332 923 0 -1 0 0 0 1 0 0 0 | 551 - 417 -658 197 -139 658 0 0 -1 0 0 0 1 0 0 | 72 - -154 32 -78 916 -143 0 0 0 1 0 0 0 -1 0 | -710 - -398 -850 824 825 -156 0 0 0 0 1 0 0 0 -1 | -708 - -entering : 12 -leaving : 8 - -228 858 -65 -341 -101 0 0 0 0 0 0 0 0 0 | 0 -maximize 1335 -1625 14 -723 1724 0 -1 -1 -1 0 0 0 0 -1 | 1333 --------------------------------------------------------------------------------- -subject to -716 -201 323 -460 -272 1 0 0 0 0 0 0 0 0 | 833 - 764 -935 -261 332 923 0 -1 0 0 0 1 0 0 0 | 551 - 417 -658 197 -139 658 0 0 -1 0 0 0 1 0 0 | 72 - 154 -32 78 -916 143 0 0 0 -1 0 0 0 1 0 | 710 - -398 -850 824 825 -156 0 0 0 0 1 0 0 0 -1 | -708 - -entering : 13 -leaving : 9 - -228 858 -65 -341 -101 0 0 0 0 0 0 0 0 0 | 0 maximize 1733 -775 -810 -1548 1880 0 -1 -1 -1 -1 0 0 0 0 | 2041 -------------------------------------------------------------------------------- subject to -716 -201 323 -460 -272 1 0 0 0 0 0 0 0 0 | 833 @@ -49,7 +6,6 @@ subject to -716 -201 323 -460 -272 1 0 0 0 0 0 0 0 0 | 833 417 -658 197 -139 658 0 0 -1 0 0 0 1 0 0 | 72 154 -32 78 -916 143 0 0 0 -1 0 0 0 1 0 | 710 398 850 -824 -825 156 0 0 0 0 -1 0 0 0 1 | 708 - entering : 0 leaving : 11 0 69254/139 5937/139 -417 35969/139 0 0 -76/139 0 0 0 76/139 0 0 | 5472/139 @@ -105,5 +61,5 @@ subject to 0 0 15273558/21997 -270658363/43994 19980571/87988 1 0 26933/4 0 0 13828592/21997 -74584363/43994 13578543/87988 0 1 -59771/43994 -112817/87988 0 -1 59771/43994 112817/87988 0 | 20112853/43994 The problem is FEASIBLE and UNBOUNDED -The number of pivots is: 9 +The number of pivots is: 5 The rule used: bland diff --git a/test/4-random-small.t/test01.txt.out b/test/4-random-small.t/test01.txt.out index 52d1531..ff1b207 100644 --- a/test/4-random-small.t/test01.txt.out +++ b/test/4-random-small.t/test01.txt.out @@ -1,63 +1,4 @@ -416 -971 607 -924 848 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to 679 -224 400 509 -152 1 0 0 0 0 0 -1 0 0 0 0 | -827 - -362 -763 -922 -2 593 0 1 0 0 0 0 0 -1 0 0 0 | -610 - 574 973 -14 135 852 0 0 1 0 0 0 0 0 0 0 0 | 40 - -858 774 -636 971 398 0 0 0 1 0 0 0 0 -1 0 0 | -795 - 802 204 563 -586 779 0 0 0 0 1 0 0 0 0 -1 0 | -816 - 339 -905 -630 -984 -621 0 0 0 0 0 1 0 0 0 0 -1 | -840 -entering : 11 -leaving : 5 - -416 -971 607 -924 848 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -679 224 -400 -509 152 -1 0 0 0 0 0 0 -1 -1 -1 -1 | 827 --------------------------------------------------------------------------------- -subject to -679 224 -400 -509 152 -1 0 0 0 0 0 1 0 0 0 0 | 827 - -362 -763 -922 -2 593 0 1 0 0 0 0 0 -1 0 0 0 | -610 - 574 973 -14 135 852 0 0 1 0 0 0 0 0 0 0 0 | 40 - -858 774 -636 971 398 0 0 0 1 0 0 0 0 -1 0 0 | -795 - 802 204 563 -586 779 0 0 0 0 1 0 0 0 0 -1 0 | -816 - 339 -905 -630 -984 -621 0 0 0 0 0 1 0 0 0 0 -1 | -840 - -entering : 12 -leaving : 6 - -416 -971 607 -924 848 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -317 987 522 -507 -441 -1 -1 0 0 0 0 0 0 -1 -1 -1 | 1437 --------------------------------------------------------------------------------- -subject to -679 224 -400 -509 152 -1 0 0 0 0 0 1 0 0 0 0 | 827 - 362 763 922 2 -593 0 -1 0 0 0 0 0 1 0 0 0 | 610 - 574 973 -14 135 852 0 0 1 0 0 0 0 0 0 0 0 | 40 - -858 774 -636 971 398 0 0 0 1 0 0 0 0 -1 0 0 | -795 - 802 204 563 -586 779 0 0 0 0 1 0 0 0 0 -1 0 | -816 - 339 -905 -630 -984 -621 0 0 0 0 0 1 0 0 0 0 -1 | -840 - -entering : 13 -leaving : 8 - -416 -971 607 -924 848 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 541 213 1158 -1478 -839 -1 -1 0 -1 0 0 0 0 0 -1 -1 | 2232 --------------------------------------------------------------------------------- -subject to -679 224 -400 -509 152 -1 0 0 0 0 0 1 0 0 0 0 | 827 - 362 763 922 2 -593 0 -1 0 0 0 0 0 1 0 0 0 | 610 - 574 973 -14 135 852 0 0 1 0 0 0 0 0 0 0 0 | 40 - 858 -774 636 -971 -398 0 0 0 -1 0 0 0 0 1 0 0 | 795 - 802 204 563 -586 779 0 0 0 0 1 0 0 0 0 -1 0 | -816 - 339 -905 -630 -984 -621 0 0 0 0 0 1 0 0 0 0 -1 | -840 - -entering : 14 -leaving : 9 - -416 -971 607 -924 848 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -261 9 595 -892 -1618 -1 -1 0 -1 -1 0 0 0 0 0 -1 | 3048 --------------------------------------------------------------------------------- -subject to -679 224 -400 -509 152 -1 0 0 0 0 0 1 0 0 0 0 | 827 - 362 763 922 2 -593 0 -1 0 0 0 0 0 1 0 0 0 | 610 - 574 973 -14 135 852 0 0 1 0 0 0 0 0 0 0 0 | 40 - 858 -774 636 -971 -398 0 0 0 -1 0 0 0 0 1 0 0 | 795 - -802 -204 -563 586 -779 0 0 0 0 -1 0 0 0 0 1 0 | 816 - 339 -905 -630 -984 -621 0 0 0 0 0 1 0 0 0 0 -1 | -840 - -entering : 15 -leaving : 10 - -416 -971 607 -924 848 0 0 0 0 0 0 0 0 0 0 0 | 0 maximize -600 914 1225 92 -997 -1 -1 0 -1 -1 -1 0 0 0 0 0 | 3888 -------------------------------------------------------------------------------- subject to -679 224 -400 -509 152 -1 0 0 0 0 0 1 0 0 0 0 | 827 @@ -66,7 +7,6 @@ subject to -679 224 -400 -509 152 -1 0 0 0 0 0 1 0 0 0 0 | 827 858 -774 636 -971 -398 0 0 0 -1 0 0 0 0 1 0 0 | 795 -802 -204 -563 586 -779 0 0 0 0 -1 0 0 0 0 1 0 | 816 -339 905 630 984 621 0 0 0 0 0 -1 0 0 0 0 1 | 840 - entering : 1 leaving : 7 21798/139 0 82431/139 -767967/973 1652396/973 0 0 971/973 0 0 0 0 0 0 0 0 | 38840/973 @@ -116,5 +56,5 @@ subject to -3613489/11075 0 0 -54077281/66450 2036128/33225 -1 0 0 -6289 -5081379/11075 0 0 104265643/132900 38569108/33225 0 1 0 -8843/26580 0 -24977/22150 0 -1 8843/26580 0 24977/22150 | 5331067/8860 The problem is UNFEASIBLE -The number of pivots is: 9 +The number of pivots is: 4 The rule used: bland diff --git a/test/4-random-small.t/test02.txt.out b/test/4-random-small.t/test02.txt.out index 9e5d833..76b2d14 100644 --- a/test/4-random-small.t/test02.txt.out +++ b/test/4-random-small.t/test02.txt.out @@ -1,16 +1,4 @@ 139 500 -607 184 959 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 -1 | 0 --------------------------------------------------------------------------------- -subject to 217 619 -475 745 31 1 0 0 0 0 0 0 0 | 473 - 238 810 -403 305 -438 0 1 0 0 0 0 0 0 | 950 - 48 -567 376 -185 -232 0 0 1 0 0 0 0 0 | 704 - -340 -8 -219 -75 941 0 0 0 1 0 0 0 -1 | -657 - -25 62 -694 46 277 0 0 0 0 1 0 0 0 | 927 - -521 -98 707 441 488 0 0 0 0 0 1 0 0 | 94 - 30 589 861 -902 -518 0 0 0 0 0 0 1 0 | 130 -entering : 12 -leaving : 8 - 139 500 -607 184 959 0 0 0 0 0 0 0 0 | 0 maximize 340 8 219 75 -941 0 0 0 -1 0 0 0 0 | 657 -------------------------------------------------------------------------------- subject to 217 619 -475 745 31 1 0 0 0 0 0 0 0 | 473 @@ -20,7 +8,6 @@ subject to 217 619 -475 745 31 1 0 0 0 0 0 0 0 | 473 -25 62 -694 46 277 0 0 0 0 1 0 0 0 | 927 -521 -98 707 441 488 0 0 0 0 0 1 0 0 | 94 30 589 861 -902 -518 0 0 0 0 0 0 1 0 | 130 - entering : 0 leaving : 12 0 42222/85 -236821/340 10427/68 456859/340 0 0 0 139/340 0 0 0 -139/340 | -91323/340 @@ -85,5 +72,5 @@ subject to 0 298645081/89820223 0 9576379/89820223 1 286170/89820223 0 0 The problem is FEASIBLE and BOUNDED One solution is x = { 242672324/89820223, 0, 23406028/89820223, 0, 30417241/89820223 } The objective value for this solution is: 48694128159/89820223 -The number of pivots is: 6 +The number of pivots is: 5 The rule used: bland diff --git a/test/4-random-small.t/test03.txt.out b/test/4-random-small.t/test03.txt.out index 3dc07ed..bc441b3 100644 --- a/test/4-random-small.t/test03.txt.out +++ b/test/4-random-small.t/test03.txt.out @@ -1,73 +1,4 @@ 893 287 671 -68 623 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to 390 -630 48 230 932 1 0 0 0 0 0 0 0 -1 0 0 0 0 | -521 - -120 781 478 478 -918 0 1 0 0 0 0 0 0 0 -1 0 0 0 | -957 - 524 -377 74 -168 876 0 0 1 0 0 0 0 0 0 0 0 0 0 | 447 - 283 -614 -939 -79 211 0 0 0 1 0 0 0 0 0 0 -1 0 0 | -857 - -283 994 -399 -299 -253 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -219 - -723 36 46 -511 -214 0 0 0 0 0 1 0 0 0 0 0 0 0 | 951 - -960 -997 8 -767 -519 0 0 0 0 0 0 1 0 0 0 0 0 0 | 745 - 410 -231 -362 462 171 0 0 0 0 0 0 0 1 0 0 0 0 -1 | -586 -entering : 13 -leaving : 5 - 893 287 671 -68 623 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 0 -1 -1 -1 -1 | 521 --------------------------------------------------------------------------------- -subject to -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 1 0 0 0 0 | 521 - -120 781 478 478 -918 0 1 0 0 0 0 0 0 0 -1 0 0 0 | -957 - 524 -377 74 -168 876 0 0 1 0 0 0 0 0 0 0 0 0 0 | 447 - 283 -614 -939 -79 211 0 0 0 1 0 0 0 0 0 0 -1 0 0 | -857 - -283 994 -399 -299 -253 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -219 - -723 36 46 -511 -214 0 0 0 0 0 1 0 0 0 0 0 0 0 | 951 - -960 -997 8 -767 -519 0 0 0 0 0 0 1 0 0 0 0 0 0 | 745 - 410 -231 -362 462 171 0 0 0 0 0 0 0 1 0 0 0 0 -1 | -586 - -entering : 14 -leaving : 6 - 893 287 671 -68 623 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -270 -151 -526 -708 -14 -1 -1 0 0 0 0 0 0 0 0 -1 -1 -1 | 1478 --------------------------------------------------------------------------------- -subject to -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 1 0 0 0 0 | 521 - 120 -781 -478 -478 918 0 -1 0 0 0 0 0 0 0 1 0 0 0 | 957 - 524 -377 74 -168 876 0 0 1 0 0 0 0 0 0 0 0 0 0 | 447 - 283 -614 -939 -79 211 0 0 0 1 0 0 0 0 0 0 -1 0 0 | -857 - -283 994 -399 -299 -253 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -219 - -723 36 46 -511 -214 0 0 0 0 0 1 0 0 0 0 0 0 0 | 951 - -960 -997 8 -767 -519 0 0 0 0 0 0 1 0 0 0 0 0 0 | 745 - 410 -231 -362 462 171 0 0 0 0 0 0 0 1 0 0 0 0 -1 | -586 - -entering : 15 -leaving : 8 - 893 287 671 -68 623 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -553 463 413 -629 -225 -1 -1 0 -1 0 0 0 0 0 0 0 -1 -1 | 2335 --------------------------------------------------------------------------------- -subject to -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 1 0 0 0 0 | 521 - 120 -781 -478 -478 918 0 -1 0 0 0 0 0 0 0 1 0 0 0 | 957 - 524 -377 74 -168 876 0 0 1 0 0 0 0 0 0 0 0 0 0 | 447 - -283 614 939 79 -211 0 0 0 -1 0 0 0 0 0 0 1 0 0 | 857 - -283 994 -399 -299 -253 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -219 - -723 36 46 -511 -214 0 0 0 0 0 1 0 0 0 0 0 0 0 | 951 - -960 -997 8 -767 -519 0 0 0 0 0 0 1 0 0 0 0 0 0 | 745 - 410 -231 -362 462 171 0 0 0 0 0 0 0 1 0 0 0 0 -1 | -586 - -entering : 16 -leaving : 9 - 893 287 671 -68 623 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -270 -531 812 -330 28 -1 -1 0 -1 -1 0 0 0 0 0 0 0 -1 | 2554 --------------------------------------------------------------------------------- -subject to -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 1 0 0 0 0 | 521 - 120 -781 -478 -478 918 0 -1 0 0 0 0 0 0 0 1 0 0 0 | 957 - 524 -377 74 -168 876 0 0 1 0 0 0 0 0 0 0 0 0 0 | 447 - -283 614 939 79 -211 0 0 0 -1 0 0 0 0 0 0 1 0 0 | 857 - 283 -994 399 299 253 0 0 0 0 -1 0 0 0 0 0 0 1 0 | 219 - -723 36 46 -511 -214 0 0 0 0 0 1 0 0 0 0 0 0 0 | 951 - -960 -997 8 -767 -519 0 0 0 0 0 0 1 0 0 0 0 0 0 | 745 - 410 -231 -362 462 171 0 0 0 0 0 0 0 1 0 0 0 0 -1 | -586 - -entering : 17 -leaving : 12 - 893 287 671 -68 623 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 maximize -680 -300 1174 -792 -143 -1 -1 0 -1 -1 0 0 -1 0 0 0 0 0 | 3140 -------------------------------------------------------------------------------- subject to -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 1 0 0 0 0 | 521 @@ -78,7 +9,6 @@ subject to -390 630 -48 -230 -932 -1 0 0 0 0 0 0 0 1 0 0 0 0 | -723 36 46 -511 -214 0 0 0 0 0 1 0 0 0 0 0 0 0 | 951 -960 -997 8 -767 -519 0 0 0 0 0 0 1 0 0 0 0 0 0 | 745 -410 231 362 -462 -171 0 0 0 0 0 0 0 -1 0 0 0 0 1 | 586 - entering : 2 leaving : 16 166414/399 111641/57 0 -227761/399 78814/399 0 0 0 0 671/399 0 0 0 0 0 0 -671/399 0 | -48983/133 @@ -122,5 +52,5 @@ subject to -18847265/98196 0 0 -2112883/24549 -37422025/49098 -1 0 0 484 -178362883/589176 0 0 -72713591/147294 -26870663/294588 0 0 0 64571/168336 5359/1178352 0 0 -1 0 0 -64571/168336 -5359/1178352 1 | 150989611/589176 The problem is UNFEASIBLE -The number of pivots is: 8 +The number of pivots is: 3 The rule used: bland diff --git a/test/4-random-small.t/test04.txt.out b/test/4-random-small.t/test04.txt.out index f1a0ab9..85b7a84 100644 --- a/test/4-random-small.t/test04.txt.out +++ b/test/4-random-small.t/test04.txt.out @@ -1,78 +1,4 @@ -987 -630 -777 -548 930 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to -213 734 -418 -110 -602 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 | -881 - 532 259 541 233 -229 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 | -195 - 710 -126 -403 143 153 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 177 - 230 -402 568 -308 365 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 201 - -545 136 -244 -874 719 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 | -271 - 100 -215 650 777 280 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -733 - 737 -237 -782 -116 -630 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 | -219 - -942 -46 314 -943 -336 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 8 - -673 -457 269 -220 187 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 132 -entering : 14 -leaving : 5 - -987 -630 -777 -548 930 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 | 881 --------------------------------------------------------------------------------- -subject to 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 | 881 - 532 259 541 233 -229 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 | -195 - 710 -126 -403 143 153 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 177 - 230 -402 568 -308 365 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 201 - -545 136 -244 -874 719 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 | -271 - 100 -215 650 777 280 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -733 - 737 -237 -782 -116 -630 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 | -219 - -942 -46 314 -943 -336 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 8 - -673 -457 269 -220 187 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 132 - -entering : 15 -leaving : 6 - -987 -630 -777 -548 930 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -319 -993 -123 -123 831 -1 -1 0 0 0 0 0 0 0 0 0 -1 -1 -1 | 1076 --------------------------------------------------------------------------------- -subject to 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 | 881 - -532 -259 -541 -233 229 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 | 195 - 710 -126 -403 143 153 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 177 - 230 -402 568 -308 365 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 201 - -545 136 -244 -874 719 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 | -271 - 100 -215 650 777 280 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -733 - 737 -237 -782 -116 -630 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 | -219 - -942 -46 314 -943 -336 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 8 - -673 -457 269 -220 187 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 132 - -entering : 16 -leaving : 9 - -987 -630 -777 -548 930 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 226 -1129 121 751 112 -1 -1 0 0 -1 0 0 0 0 0 0 0 -1 -1 | 1347 --------------------------------------------------------------------------------- -subject to 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 | 881 - -532 -259 -541 -233 229 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 | 195 - 710 -126 -403 143 153 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 177 - 230 -402 568 -308 365 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 201 - 545 -136 244 874 -719 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 | 271 - 100 -215 650 777 280 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 | -733 - 737 -237 -782 -116 -630 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 | -219 - -942 -46 314 -943 -336 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 8 - -673 -457 269 -220 187 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 132 - -entering : 17 -leaving : 10 - -987 -630 -777 -548 930 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 126 -914 -529 -26 -168 -1 -1 0 0 -1 -1 0 0 0 0 0 0 0 -1 | 2080 --------------------------------------------------------------------------------- -subject to 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 | 881 - -532 -259 -541 -233 229 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 | 195 - 710 -126 -403 143 153 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 177 - 230 -402 568 -308 365 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 201 - 545 -136 244 874 -719 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 | 271 - -100 215 -650 -777 -280 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 | 733 - 737 -237 -782 -116 -630 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 | -219 - -942 -46 314 -943 -336 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 8 - -673 -457 269 -220 187 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 132 - -entering : 18 -leaving : 11 - -987 -630 -777 -548 930 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 maximize -611 -677 253 90 462 -1 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0 | 2299 -------------------------------------------------------------------------------- subject to 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 | 881 @@ -84,7 +10,6 @@ subject to 213 -734 418 110 602 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 -737 237 782 116 630 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 | 219 -942 -46 314 -943 -336 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 8 -673 -457 269 -220 187 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 132 - entering : 2 leaving : 12 -3318 -116781/157 0 -904783/314 15474/157 0 0 0 0 0 0 0 777/314 0 0 0 0 0 0 | 3108/157 @@ -176,5 +101,5 @@ subject to 290698729/317012 -304443687/317012 -52036069/158506 0 0 -1 0 0 -167731933/317012 -156397413/317012 51387987/158506 0 0 0 0 0 0 -40073/158506 0 2629/317012 0 1 0 0 40073/158506 0 -2629/317012 | 62989399/317012 The problem is UNFEASIBLE -The number of pivots is: 11 +The number of pivots is: 6 The rule used: bland diff --git a/test/4-random-small.t/test05.txt.out b/test/4-random-small.t/test05.txt.out index 03fd618..7037e1a 100644 --- a/test/4-random-small.t/test05.txt.out +++ b/test/4-random-small.t/test05.txt.out @@ -1,131 +1,4 @@ 534 426 494 -177 -645 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to -653 950 -775 911 58 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 | -378 - 858 304 984 610 47 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 | -272 - -971 -461 602 -153 -420 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 406 - 863 -109 -380 930 -276 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 | -955 - 5 -146 693 138 480 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 | -929 - 35 606 -185 697 520 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 | -132 - 549 716 -344 860 781 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 | -955 - -193 892 825 730 930 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 | -318 - -121 168 861 -298 -306 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 | -860 - -128 -804 380 -254 209 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 691 -entering : 15 -leaving : 5 - 534 426 494 -177 -645 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 653 -950 775 -911 -58 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 | 378 --------------------------------------------------------------------------------- -subject to 653 -950 775 -911 -58 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 378 - 858 304 984 610 47 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 | -272 - -971 -461 602 -153 -420 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 406 - 863 -109 -380 930 -276 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 | -955 - 5 -146 693 138 480 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 | -929 - 35 606 -185 697 520 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 | -132 - 549 716 -344 860 781 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 | -955 - -193 892 825 730 930 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 | -318 - -121 168 861 -298 -306 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 | -860 - -128 -804 380 -254 209 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 691 - -entering : 16 -leaving : 6 - 534 426 494 -177 -645 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize -205 -1254 -209 -1521 -105 -1 -1 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 | 650 --------------------------------------------------------------------------------- -subject to 653 -950 775 -911 -58 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | 378 - -858 -304 -984 -610 -47 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 272 - -971 -461 602 -153 -420 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 406 - 863 -109 -380 930 -276 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 | -955 - 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entering : 0 leaving : 10 0 684793/731 -363985/731 -560627/731 -22864/731 0 0 0 0 0 -383/731 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | -21831/731 @@ -194,5 +50,5 @@ subject to 0 0 894707879/687801 -398596236/229267 5640907/229267 -1 861649 0 0 289715691/229267 -164519954/229267 -233150488/229267 0 -7509/229267 0 0 0 238066/229267 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 | 113756899/229267 The problem is UNFEASIBLE -The number of pivots is: 10 +The number of pivots is: 2 The rule used: bland diff --git a/test/4-random-small.t/test08.txt.out b/test/4-random-small.t/test08.txt.out index b052186..7f8b730 100644 --- a/test/4-random-small.t/test08.txt.out +++ b/test/4-random-small.t/test08.txt.out @@ -1,136 +1,4 @@ 150 -95 -357 -645 857 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to 836 -78 -423 944 -423 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 | -907 - 75 -372 871 -634 866 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 342 - 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entering : 2 leaving : 6 157425/871 -215549/871 0 -788133/871 1055609/871 0 357/871 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 122094/871 @@ -167,5 +34,5 @@ subject to -759881/871 225294/871 0 -554042/871 2115/871 -1 -423/871 0 0 -324058/871 -774056/871 0 553950/871 -207353/871 0 11/871 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 | 453198/871 The problem is UNFEASIBLE -The number of pivots is: 8 +The number of pivots is: 1 The rule used: bland diff --git a/test/4-random-small.t/test09.txt.out b/test/4-random-small.t/test09.txt.out index 7669f85..3c7a093 100644 --- a/test/4-random-small.t/test09.txt.out +++ b/test/4-random-small.t/test09.txt.out @@ -1,183 +1,4 @@ -137 -616 -178 -135 -725 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 | 0 --------------------------------------------------------------------------------- -subject to 501 -100 216 -44 913 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 | -556 - -775 739 -861 240 37 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 409 - 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entering : 1 leaving : 16 229387/965 0 406654/965 435213/965 -93481/965 0 0 0 0 0 0 0 0 0 0 0 616/965 0 0 0 0 0 0 0 0 0 0 0 | 15400/193 @@ -216,5 +36,5 @@ subject to -108433/193 0 -60468/193 -9868/193 -195889/193 -1 0 0 0 0 0 -646654/965 0 -1150328/965 109849/965 -781318/965 0 0 0 0 0 0 0 0 0 0 0 -592/965 0 1 0 0 0 0 0 0 0 0 0 | 100421/193 The problem is UNFEASIBLE -The number of pivots is: 10 +The number of pivots is: 1 The rule used: bland diff --git a/test/5-random-medium.t/test00.txt.out b/test/5-random-medium.t/test00.txt.out index 2097610..f978036 100644 --- a/test/5-random-medium.t/test00.txt.out +++ b/test/5-random-medium.t/test00.txt.out @@ -1,26 +1,26 @@ -503 -164 -695 -577 269 -995 728 -564 -451 -489 544 -420 -312 -240 100 -761 -473 -70 795 743 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 | 0 +maximize -731 3649 3600 795 4126 -3222 1989 -168 47 1897 589 766 -2342 -1639 3731 -1104 2091 -2752 1185 -173 -1 -1 0 -1 0 -1 -1 0 0 0 0 -1 -1 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 | 4685 -------------------------------------------------------------------------------- -subject to -369 -923 -376 778 -141 957 -785 -144 -102 -268 344 480 245 -205 -734 -581 -657 -132 456 -450 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 | -312 - 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978 528 -504 -899 359 -213 -751 278 -704 49 -17 -163 -129 691 868 428 43 924 -724 -444 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 | -662 - -423 109 547 -827 -972 900 717 776 238 658 -765 332 -527 -294 -975 973 -235 -129 -246 -912 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 | -877 + -978 -528 504 899 -359 213 751 -278 704 -49 17 163 129 -691 -868 -428 -43 -924 724 444 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | 662 + 423 -109 -547 827 972 -900 -717 -776 -238 -658 765 -332 527 294 975 -973 235 129 246 912 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | 877 671 -656 115 -316 -358 521 323 700 804 -727 258 856 28 -159 -798 -924 215 -243 799 -719 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 947 717 545 -462 996 574 650 593 -986 175 133 -5 686 355 178 947 595 -250 -787 -165 -921 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 356 987 -237 -930 -129 -309 -934 618 -914 664 471 284 -795 -31 15 822 -18 -886 763 -583 193 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 263 879 -440 -725 59 414 493 940 841 -639 -742 230 -394 -466 -369 603 671 883 245 288 262 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 459 - -874 -190 -518 -854 -544 149 -99 -724 455 -1 -398 851 936 617 -338 516 117 -348 -392 -678 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 | -58 - 259 -749 -322 174 -954 986 -765 -167 660 -584 -756 -808 243 411 -814 -804 771 796 -374 -54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 | -259 - 379 -976 -877 357 147 607 194 -881 25 -304 799 -380 237 -402 -166 -129 -469 -917 812 -330 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 | -66 + 874 190 518 854 544 -149 99 724 -455 1 398 -851 -936 -617 338 -516 -117 348 392 678 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 | 58 + -259 749 322 -174 954 -986 765 167 -660 584 756 808 -243 -411 814 804 -771 -796 374 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 | 259 + -379 976 877 -357 -147 -607 -194 881 -25 304 -799 380 -237 402 166 129 469 917 -812 330 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 | 66 The problem is UNFEASIBLE -The number of pivots is: 56 +The number of pivots is: 46 The rule used: bland diff --git a/test/5-random-medium.t/test01.txt.out b/test/5-random-medium.t/test01.txt.out index 7ec1303..cc2f257 100644 --- a/test/5-random-medium.t/test01.txt.out +++ b/test/5-random-medium.t/test01.txt.out @@ -1,30 +1,30 @@ -50 -583 -133 774 -879 -680 720 52 247 -227 305 -581 -884 246 -488 -164 -66 -668 949 984 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 | 0 +maximize 3164 1018 715 262 799 -3999 353 -2855 1242 -4644 1038 -3073 -2874 5181 4187 2094 -262 -2260 1437 343 -1 -1 0 0 0 0 -1 -1 -1 -1 -1 0 -1 -1 -1 -1 0 -1 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5805 -------------------------------------------------------------------------------- -subject to -518 117 809 -472 117 -424 74 -965 -610 -60 -614 829 895 369 -496 356 -43 845 -571 27 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | -235 - 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-64 -351 692 573 -599 437 255 -150 -187 821 196 347 614 -386 -471 445 351 -810 915 -457 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 | -25 - -378 -503 -463 -778 -870 -472 -779 509 842 -97 -705 129 722 -789 -816 -995 -650 607 138 -320 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 | -431 - -655 91 77 815 -83 354 -757 -595 -174 776 -817 949 -926 -82 -752 -395 776 345 -236 559 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 | -418 + 64 351 -692 -573 599 -437 -255 150 187 -821 -196 -347 -614 386 471 -445 -351 810 -915 457 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | 25 + 378 503 463 778 870 472 779 -509 -842 97 705 -129 -722 789 816 995 650 -607 -138 320 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | 431 + 655 -91 -77 -815 83 -354 757 595 174 -776 817 -949 926 82 752 395 -776 -345 236 -559 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | 418 -302 471 566 -372 783 982 -647 694 921 210 -673 -587 44 444 714 802 -434 698 -223 -462 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 945 -708 126 -400 277 -751 183 500 -553 855 -547 16 -672 839 -425 503 -116 198 -717 -463 447 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 46 - -740 -802 -707 921 -436 577 898 218 886 -213 -187 303 -989 -647 961 -695 992 -295 -94 -64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 | -386 + 740 802 707 -921 436 -577 -898 -218 -886 213 187 -303 989 647 -961 695 -992 295 94 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | 386 708 -155 -136 190 -885 935 936 614 -517 341 -64 -708 808 -989 870 -835 -546 799 -504 -57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 957 The problem is FEASIBLE and UNBOUNDED -The number of pivots is: 91 +The number of pivots is: 76 The rule used: bland diff --git a/test/5-random-medium.t/test02.txt.out b/test/5-random-medium.t/test02.txt.out index 76f7b8e..c866002 100644 --- a/test/5-random-medium.t/test02.txt.out +++ b/test/5-random-medium.t/test02.txt.out @@ -1,36 +1,36 @@ -682 297 -178 895 -258 -973 919 910 -774 552 658 -49 -951 -235 85 -871 -170 -290 -408 -114 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 -maximize 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 | 0 +maximize -482 2366 -1134 1189 791 -283 883 -1848 960 -319 1752 2076 -716 -1204 270 -94 153 1482 1889 -591 0 0 0 -1 -1 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 | 4928 -------------------------------------------------------------------------------- subject to 197 -810 143 810 535 -751 297 975 957 -748 893 -680 -196 580 847 670 709 -757 437 -864 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 120 -938 -518 985 588 -88 590 640 763 125 -627 -194 -244 -534 457 -765 7 541 900 172 -899 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 662 -34 -402 870 101 552 -986 504 498 -617 678 24 -453 962 25 684 790 230 -368 -1000 -849 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 893 - 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