diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,2 @@ +Copyright Alberto Ruiz 2010 +GPL license diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,4 @@ +#! /usr/bin/env runhaskell + +> import Distribution.Simple +> main = defaultMain diff --git a/examples/simplex1.hs b/examples/simplex1.hs new file mode 100644 --- /dev/null +++ b/examples/simplex1.hs @@ -0,0 +1,20 @@ +-- first example in glpk manual + +import Numeric.LinearProgramming + +objFun = Maximize [10, 6, 4] + +constr = Dense [ [1,1,1] :<: 100 + , [10,4,5] :<: 600 + , [2,2,6] :<: 300 ] + +-- default bounds +bnds = [ 1 :>: 0 + , 2 :>: 0 + , 3 :>: 0 ] + +main = do + print $ simplex objFun constr [] + print $ simplex objFun constr bnds + print $ simplex objFun constr [Free 3] + print $ simplex objFun constr [ 2 :<: 50 ] diff --git a/examples/simplex2.hs b/examples/simplex2.hs new file mode 100644 --- /dev/null +++ b/examples/simplex2.hs @@ -0,0 +1,18 @@ +import Numeric.LinearProgramming + +prob = Maximize [4, -3, 2] + +constr1 = Sparse [ [2#1, 1#2] :<: 10 + , [1#2, 5#3] :<: 20 + ] + +constr2 = Dense [ [2,1,0] :<: 10 + , [0,1,5] :<: 20 + ] + +main = do + print $ simplex prob constr1 [] + print $ simplex prob constr2 [] + print $ simplex prob constr2 [ 2 :>: 1, 3 :&: (2,7)] + print $ simplex prob constr2 [ Free 2 ] + diff --git a/examples/simplex3.hs b/examples/simplex3.hs new file mode 100644 --- /dev/null +++ b/examples/simplex3.hs @@ -0,0 +1,25 @@ +-- compare with +-- $ glpsol --cpxlp /usr/share/doc/glpk-utils/examples/plan.lp -o result.txt + +import Numeric.LinearProgramming + +prob = Minimize [0.03, 0.08, 0.17, 0.12, 0.15, 0.21, 0.38] + +constr = Dense + [ [1,1,1,1,1,1,1] :==: 2000 + , [0.15, 0.04, 0.02, 0.04, 0.2,0.01, 0.03] :<: 60 + , [0.03, 0.05, 0.08, 0.02, 0.06, 0.01, 0] :<: 100 + , [0.02, 0.04, 0.01, 0.02, 0.02, 0, 0] :<: 40 + , [0.02, 0.03, 0, 0, 0.01, 0, 0] :<: 30 + , [0.7, 0.75, 0.8, 0.75, 0.8, 0.97, 0] :>: 1500 + , [0.02, 0.06, 0.08, 0.12, 0.02, 0.01, 0.97] :&: (250,300) + ] + +bounds = [ 1 :&: (0,200) + , 2 :&: (0,2500) + , 3 :&: (400,800) + , 4 :&: (100,700) + , 5 :&: (0,1500) ] + +main = print $ simplex prob constr bounds + diff --git a/examples/simplex4.hs b/examples/simplex4.hs new file mode 100644 --- /dev/null +++ b/examples/simplex4.hs @@ -0,0 +1,25 @@ +-- compare with +-- $ glpsol --cpxlp /usr/share/doc/glpk-utils/examples/plan.lp -o result.txt + +import Numeric.LinearProgramming + +prob = Minimize [0.03, 0.08, 0.17, 0.12, 0.15, 0.21, 0.38] + +constr = Sparse + [ [1#1,1#2,1#3,1#4,1#5,1#6,1#7] :==: 2000 + , [0.15#1, 0.04#2, 0.02#3, 0.04#4, 0.2#5,0.01#6, 0.03#7] :<: 60 + , [0.03#1, 0.05#2, 0.08#3, 0.02#4, 0.06#5, 0.01#6] :<: 100 + , [0.02#1, 0.04#2, 0.01#3, 0.02#4, 0.02#5] :<: 40 + , [0.02#1, 0.03#2, 0.01#5] :<: 30 + , [0.7#1, 0.75#2, 0.8#3, 0.75#4, 0.8#5, 0.97#6] :>: 1500 + , [0.02#1, 0.06#2, 0.08#3, 0.12#4, 0.02#5, 0.01#6, 0.97#7] :&: (250,300) + ] + +bounds = [ 1 :&: (0,200) + , 2 :&: (0,2500) + , 3 :&: (400,800) + , 4 :&: (100,700) + , 5 :&: (0,1500) ] + +main = print $ simplex prob constr bounds + diff --git a/hmatrix-glpk.cabal b/hmatrix-glpk.cabal new file mode 100644 --- /dev/null +++ b/hmatrix-glpk.cabal @@ -0,0 +1,35 @@ +Name: hmatrix-glpk +Version: 0.1.0 +License: GPL +License-file: LICENSE +Author: Alberto Ruiz +Maintainer: Alberto Ruiz +Stability: experimental +Homepage: http://code.haskell.org/hmatrix +Synopsis: Linear Programming based on GLPK +Description: + Simple interface to linear programming functions provided by GLPK. + +Category: Math +tested-with: GHC ==6.10.4 + +cabal-version: >=1.2 +build-type: Simple + +extra-source-files: examples/simplex1.hs + examples/simplex2.hs + examples/simplex3.hs + examples/simplex4.hs + +library + Build-Depends: base >= 3 && < 5, hmatrix >= 0.8.3 && < 0.9 + + hs-source-dirs: lib + + Exposed-modules: Numeric.LinearProgramming + + c-sources: lib/Numeric/LinearProgramming/glpk.c + + ghc-options: -Wall + + extra-libraries: glpk diff --git a/lib/Numeric/LinearProgramming.hs b/lib/Numeric/LinearProgramming.hs new file mode 100644 --- /dev/null +++ b/lib/Numeric/LinearProgramming.hs @@ -0,0 +1,264 @@ +{-# LANGUAGE ForeignFunctionInterface #-} + +{- | +Module : Numeric.LinearProgramming +Copyright : (c) Alberto Ruiz 2010 +License : GPL + +Maintainer : Alberto Ruiz (aruiz at um dot es) +Stability : provisional + +This module provides an interface to the standard simplex algorithm. + +For example, the following LP problem + +@maximize 4 x_1 - 3 x_2 + 2 x_3 +subject to + +2 x_1 + x_2 <= 10 + x_3 + 5 x_4 <= 20 + +and + +x_i >= 0@ + +can be solved as follows: + +@import Numeric.LinearProgramming + +prob = Maximize [4, -3, 2] + +constr1 = Sparse [ [2\#1, 1\#2] :<: 10 + , [1\#2, 5\#3] :<: 20 + ] + +\> simplex prob constr1 [] +Optimal (28.0,[5.0,0.0,4.0])@ + +The coefficients of the constraint matrix can also be given in dense format: + +@constr2 = Dense [ [2,1,0] :<: 10 + , [0,1,5] :<: 20 + ]@ + +By default all variables are bounded as @x_i >= 0@, but this can be +changed: + +@\> simplex prob constr2 [ 2 :>: 1, 3 :&: (2,7)] +Optimal (22.6,[4.5,1.0,3.8]) + +\> simplex prob constr2 [Free 2] +Unbounded@ + +The given bound for a variable completely replaces the default, +so @0 <= x_i <= b@ must be explicitly given as @i :&: (0,b)@. +Multiple bounds for a variable are not allowed, instead of +@[i :>: a, i:<: b]@ use @i :&: (a,b)@. + +-} + +module Numeric.LinearProgramming( + simplex, + Optimization(..), + Constraints(..), + Bounds, + Bound(..), + (#), + Solution(..) +) where + +import Numeric.LinearAlgebra hiding (i) +import Data.Packed.Development +import Foreign(Ptr,unsafePerformIO) +import Foreign.C.Types(CInt) +import Data.List((\\),sortBy,nub) +import Data.Function(on) + +--import Debug.Trace +--debug x = trace (show x) x + +----------------------------------------------------- + +-- | Coefficient of a variable for a sparse representation of constraints. +(#) :: Double -> Int -> (Double,Int) +infixl 5 # +(#) = (,) + +data Bound x = x :<: Double + | x :>: Double + | x :&: (Double,Double) + | x :==: Double + | Free x + deriving Show + +data Solution = Undefined + | Feasible (Double, [Double]) + | Infeasible (Double, [Double]) + | NoFeasible + | Optimal (Double, [Double]) + | Unbounded + deriving Show + +data Constraints = Dense [ Bound [Double] ] + | Sparse [ Bound [(Double,Int)] ] + +data Optimization = Maximize [Double] + | Minimize [Double] + +type Bounds = [Bound Int] + +simplex :: Optimization -> Constraints -> Bounds -> Solution + +simplex opt (Dense []) bnds = simplex opt (Sparse []) bnds +simplex opt (Sparse []) bnds = simplex opt (Sparse [Free [0#1]]) bnds + +simplex opt (Dense constr) bnds = extract sg sol where + sol = simplexSparse m n (mkConstrD sz objfun constr) (mkBounds sz constr bnds) + n = length objfun + m = length constr + (sz, sg, objfun) = adapt opt + +simplex opt (Sparse constr) bnds = extract sg sol where + sol = simplexSparse m n (mkConstrS sz objfun constr) (mkBounds sz constr bnds) + n = length objfun + m = length constr + (sz, sg, objfun) = adapt opt + +adapt :: Optimization -> (Int, Double, [Double]) +adapt opt = case opt of + Maximize x -> (size x, 1 ,x) + Minimize x -> (size x, -1, (map negate x)) + where size x | null x = error "simplex: objective function with zero variables" + | otherwise = length x + +extract :: Double -> Vector Double -> Solution +extract sg sol = r where + z = sg * (sol@>1) + v = toList $ subVector 2 (dim sol -2) sol + r = case round(sol@>0)::Int of + 1 -> Undefined + 2 -> Feasible (z,v) + 3 -> Infeasible (z,v) + 4 -> NoFeasible + 5 -> Optimal (z,v) + 6 -> Unbounded + _ -> error "simplex: solution type unknown" + +----------------------------------------------------- + +obj :: Bound t -> t +obj (x :<: _) = x +obj (x :>: _) = x +obj (x :&: _) = x +obj (x :==: _) = x +obj (Free x) = x + +tb :: Bound t -> Double +tb (_ :<: _) = glpUP +tb (_ :>: _) = glpLO +tb (_ :&: _) = glpDB +tb (_ :==: _) = glpFX +tb (Free _) = glpFR + +lb :: Bound t -> Double +lb (_ :<: _) = 0 +lb (_ :>: a) = a +lb (_ :&: (a,_)) = a +lb (_ :==: a) = a +lb (Free _) = 0 + +ub :: Bound t -> Double +ub (_ :<: a) = a +ub (_ :>: _) = 0 +ub (_ :&: (_,a)) = a +ub (_ :==: a) = a +ub (Free _) = 0 + +mkBound1 :: Bound t -> [Double] +mkBound1 b = [tb b, lb b, ub b] + +mkBound2 :: Bound t -> (t, [Double]) +mkBound2 b = (obj b, mkBound1 b) + +mkBounds :: Int -> [Bound [a]] -> [Bound Int] -> Matrix Double +mkBounds n b1 b2 = fromLists (cb++vb) where + gv' = map obj b2 + gv | nub gv' == gv' = gv' + | otherwise = error $ "simplex: duplicate bounds for vars " ++ show (gv'\\nub gv') + rv | null gv || minimum gv >= 0 && maximum gv <= n = [1..n] \\ gv + | otherwise = error $ "simplex: bounds: variables "++show gv++" not in 1.."++show n + vb = map snd $ sortBy (compare `on` fst) $ map (mkBound2 . (:>: 0)) rv ++ map mkBound2 b2 + cb = map mkBound1 b1 + +mkConstrD :: Int -> [Double] -> [Bound [Double]] -> Matrix Double +mkConstrD n f b1 | ok = fromLists (ob ++ co) + | otherwise = error $ "simplex: dense constraints require "++show n + ++" variables, given " ++ show ls + where + cs = map obj b1 + ls = map length cs + ok = all (==n) ls + den = fromLists cs + ob = map (([0,0]++).return) f + co = [[fromIntegral i, fromIntegral j,den@@>(i-1,j-1)]| i<-[1 ..rows den], j<-[1 .. cols den]] + +mkConstrS :: Int -> [Double] -> [Bound [(Double, Int)]] -> Matrix Double +mkConstrS n objfun b1 = fromLists (ob ++ co) where + ob = map (([0,0]++).return) objfun + co = concat $ zipWith f [1::Int ..] cs + cs = map obj b1 + f k = map (g k) + g k (c,v) | v >=1 && v<= n = [fromIntegral k, fromIntegral v,c] + | otherwise = error $ "simplex: sparse constraints: variable "++show v++" not in 1.."++show n + +----------------------------------------------------- + +foreign import ccall "c_simplex_sparse" c_simplex_sparse + :: CInt -> CInt -- rows and cols + -> CInt -> CInt -> Ptr Double -- coeffs + -> CInt -> CInt -> Ptr Double -- bounds + -> CInt -> Ptr Double -- result + -> IO CInt -- exit code + +simplexSparse :: Int -> Int -> Matrix Double -> Matrix Double -> Vector Double +simplexSparse m n c b = unsafePerformIO $ do + s <- createVector (2+n) + let fi = fromIntegral + app3 (c_simplex_sparse (fi m) (fi n)) mat (cmat c) mat (cmat b) vec s "c_simplex_sparse" + return s + +glpFR, glpLO, glpUP, glpDB, glpFX :: Double +glpFR = 0 +glpLO = 1 +glpUP = 2 +glpDB = 3 +glpFX = 4 + +{- Raw format of coeffs + +simplexSparse + +(12><3) + [ 0.0, 0.0, 10.0 + , 0.0, 0.0, 6.0 + , 0.0, 0.0, 4.0 + , 1.0, 1.0, 1.0 + , 1.0, 2.0, 1.0 + , 1.0, 3.0, 1.0 + , 2.0, 1.0, 10.0 + , 2.0, 2.0, 4.0 + , 2.0, 3.0, 5.0 + , 3.0, 1.0, 2.0 + , 3.0, 2.0, 2.0 + , 3.0, 3.0, 6.0 ] + +bounds = (6><3) + [ glpUP,0,100 + , glpUP,0,600 + , glpUP,0,300 + , glpLO,0,0 + , glpLO,0,0 + , glpLO,0,0 ] + +-} + diff --git a/lib/Numeric/LinearProgramming/glpk.c b/lib/Numeric/LinearProgramming/glpk.c new file mode 100644 --- /dev/null +++ b/lib/Numeric/LinearProgramming/glpk.c @@ -0,0 +1,76 @@ +#define DVEC(A) int A##n, double*A##p +#define DMAT(A) int A##r, int A##c, double*A##p + +#define AT(M,r,co) (M##p[(r)*M##c+(co)]) + +#include +#include +#include +#include + +/*-----------------------------------------------------*/ + +int c_simplex_sparse(int m, int n, DMAT(c), DMAT(b), DVEC(s)) { + glp_prob *lp; + lp = glp_create_prob(); + glp_set_obj_dir(lp, GLP_MAX); + int i,j,k; + int tot = cr - n; + glp_add_rows(lp, m); + glp_add_cols(lp, n); + + //printf("%d %d\n",m,n); + + // the first n values + for (k=1;k<=n;k++) { + glp_set_obj_coef(lp, k, AT(c, k-1, 2)); + //printf("%d %f\n",k,AT(c, k-1, 2)); + } + + int * ia = malloc((1+tot)*sizeof(int)); + int * ja = malloc((1+tot)*sizeof(int)); + double * ar = malloc((1+tot)*sizeof(double)); + + for (k=1; k<= tot; k++) { + ia[k] = rint(AT(c,k-1+n,0)); + ja[k] = rint(AT(c,k-1+n,1)); + ar[k] = AT(c,k-1+n,2); + //printf("%d %d %f\n",ia[k],ja[k],ar[k]); + } + glp_load_matrix(lp, tot, ia, ja, ar); + + int t; + for (i=1;i<=m;i++) { + switch((int)rint(AT(b,i-1,0))) { + case 0: { t = GLP_FR; break; } + case 1: { t = GLP_LO; break; } + case 2: { t = GLP_UP; break; } + case 3: { t = GLP_DB; break; } + default: { t = GLP_FX; break; } + } + glp_set_row_bnds(lp, i, t , AT(b,i-1,1), AT(b,i-1,2)); + } + for (j=1;j<=n;j++) { + switch((int)rint(AT(b,m+j-1,0))) { + case 0: { t = GLP_FR; break; } + case 1: { t = GLP_LO; break; } + case 2: { t = GLP_UP; break; } + case 3: { t = GLP_DB; break; } + default: { t = GLP_FX; break; } + } + glp_set_col_bnds(lp, j, t , AT(b,m+j-1,1), AT(b,m+j-1,2)); + } + glp_term_out(0); + glp_simplex(lp, NULL); + sp[0] = glp_get_status(lp); + sp[1] = glp_get_obj_val(lp); + for (k=1; k<=n; k++) { + sp[k+1] = glp_get_col_prim(lp, k); + } + glp_delete_prob(lp); + free(ia); + free(ja); + free(ar); + + return 0; +}