From 302a220b636d510ccf654e3671e8a93391c13523 Mon Sep 17 00:00:00 2001 From: Alberto Ruiz Date: Thu, 12 Jun 2014 14:13:05 +0200 Subject: add L1 and LInf solvers --- packages/glpk/lib/Numeric/LinearProgramming.hs | 264 ------------------------- 1 file changed, 264 deletions(-) delete mode 100644 packages/glpk/lib/Numeric/LinearProgramming.hs (limited to 'packages/glpk/lib/Numeric/LinearProgramming.hs') diff --git a/packages/glpk/lib/Numeric/LinearProgramming.hs b/packages/glpk/lib/Numeric/LinearProgramming.hs deleted file mode 100644 index 25cdab2..0000000 --- a/packages/glpk/lib/Numeric/LinearProgramming.hs +++ /dev/null @@ -1,264 +0,0 @@ -{-# LANGUAGE ForeignFunctionInterface #-} - -{- | -Module : Numeric.LinearProgramming -Copyright : (c) Alberto Ruiz 2010 -License : GPL - -Maintainer : Alberto Ruiz -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 Data.Packed -import Data.Packed.Development -import Foreign(Ptr) -import System.IO.Unsafe(unsafePerformIO) -import Foreign.C.Types -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 unsafe "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) - 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 ] - --} - -- cgit v1.2.3