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-rw-r--r--packages/glpk/src/Numeric/LinearProgramming.hs75
1 files changed, 70 insertions, 5 deletions
diff --git a/packages/glpk/src/Numeric/LinearProgramming.hs b/packages/glpk/src/Numeric/LinearProgramming.hs
index b0537cc..6a0c47d 100644
--- a/packages/glpk/src/Numeric/LinearProgramming.hs
+++ b/packages/glpk/src/Numeric/LinearProgramming.hs
@@ -49,6 +49,14 @@ constr2 = Dense [ [2,1,0] :<=: 10
49 ] 49 ]
50@ 50@
51 51
52Note that when using sparse constraints, coefficients cannot appear more than once in each constraint. You can alternatively use General which will automatically sum any duplicate coefficients when necessary.
53
54@
55constr3 = General [ [1\#1, 1\#1, 1\#2] :<=: 10
56 , [1\#2, 5\#3] :<=: 20
57 ]
58@
59
52By default all variables are bounded as @x_i >= 0@, but this can be 60By default all variables are bounded as @x_i >= 0@, but this can be
53changed: 61changed:
54 62
@@ -67,6 +75,8 @@ Multiple bounds for a variable are not allowed, instead of
67 75
68module Numeric.LinearProgramming( 76module Numeric.LinearProgramming(
69 simplex, 77 simplex,
78 exact,
79 sparseOfGeneral,
70 Optimization(..), 80 Optimization(..),
71 Constraints(..), 81 Constraints(..),
72 Bounds, 82 Bounds,
@@ -82,13 +92,14 @@ import System.IO.Unsafe(unsafePerformIO)
82import Foreign.C.Types 92import Foreign.C.Types
83import Data.List((\\),sortBy,nub) 93import Data.List((\\),sortBy,nub)
84import Data.Function(on) 94import Data.Function(on)
95import qualified Data.Map.Strict as Map
85 96
86--import Debug.Trace 97--import Debug.Trace
87--debug x = trace (show x) x 98--debug x = trace (show x) x
88 99
89----------------------------------------------------- 100-----------------------------------------------------
90 101
91-- | Coefficient of a variable for a sparse representation of constraints. 102-- | Coefficient of a variable for a sparse and general representations of constraints.
92(#) :: Double -> Int -> (Double,Int) 103(#) :: Double -> Int -> (Double,Int)
93infixl 5 # 104infixl 5 #
94(#) = (,) 105(#) = (,)
@@ -108,18 +119,29 @@ data Solution = Undefined
108 | Unbounded 119 | Unbounded
109 deriving Show 120 deriving Show
110 121
111data Constraints = Dense [ Bound [Double] ] 122data Constraints = Dense [ Bound [Double] ]
112 | Sparse [ Bound [(Double,Int)] ] 123 | Sparse [ Bound [(Double,Int)] ]
124 | General [ Bound [(Double,Int)] ]
113 125
114data Optimization = Maximize [Double] 126data Optimization = Maximize [Double]
115 | Minimize [Double] 127 | Minimize [Double]
116 128
117type Bounds = [Bound Int] 129type Bounds = [Bound Int]
118 130
131-- | Convert a system of General constraints to one with unique coefficients.
132sparseOfGeneral :: Constraints -> Constraints
133sparseOfGeneral (General cs) =
134 Sparse $ map (\bl ->
135 let cl = obj bl in
136 let cl_unique = foldr (\(c,t) m -> Map.insertWith (+) t c m) Map.empty cl in
137 withObj bl (Map.foldrWithKey' (\t c l -> (c#t) : l) [] cl_unique)) cs
138sparseOfGeneral _ = error "sparseOfGeneral: a general system of constraints was expected"
139
119simplex :: Optimization -> Constraints -> Bounds -> Solution 140simplex :: Optimization -> Constraints -> Bounds -> Solution
120 141
121simplex opt (Dense []) bnds = simplex opt (Sparse []) bnds 142simplex opt (Dense []) bnds = simplex opt (Sparse []) bnds
122simplex opt (Sparse []) bnds = simplex opt (Sparse [Free [0#1]]) bnds 143simplex opt (Sparse []) bnds = simplex opt (Sparse [Free [0#1]]) bnds
144simplex opt (General []) bnds = simplex opt (Sparse [Free [0#1]]) bnds
123 145
124simplex opt (Dense constr) bnds = extract sg sol where 146simplex opt (Dense constr) bnds = extract sg sol where
125 sol = simplexSparse m n (mkConstrD sz objfun constr) (mkBounds sz constr bnds) 147 sol = simplexSparse m n (mkConstrD sz objfun constr) (mkBounds sz constr bnds)
@@ -133,6 +155,29 @@ simplex opt (Sparse constr) bnds = extract sg sol where
133 m = length constr 155 m = length constr
134 (sz, sg, objfun) = adapt opt 156 (sz, sg, objfun) = adapt opt
135 157
158simplex opt constr@(General _) bnds = simplex opt (sparseOfGeneral constr) bnds
159
160-- | Simplex method with exact internal arithmetic. See glp_exact in glpk documentation for more information.
161exact :: Optimization -> Constraints -> Bounds -> Solution
162
163exact opt (Dense []) bnds = exact opt (Sparse []) bnds
164exact opt (Sparse []) bnds = exact opt (Sparse [Free [0#1]]) bnds
165exact opt (General []) bnds = exact opt (Sparse [Free [0#1]]) bnds
166
167exact opt (Dense constr) bnds = extract sg sol where
168 sol = exactSparse m n (mkConstrD sz objfun constr) (mkBounds sz constr bnds)
169 n = length objfun
170 m = length constr
171 (sz, sg, objfun) = adapt opt
172
173exact opt (Sparse constr) bnds = extract sg sol where
174 sol = exactSparse m n (mkConstrS sz objfun constr) (mkBounds sz constr bnds)
175 n = length objfun
176 m = length constr
177 (sz, sg, objfun) = adapt opt
178
179exact opt constr@(General _) bnds = exact opt (sparseOfGeneral constr) bnds
180
136adapt :: Optimization -> (Int, Double, [Double]) 181adapt :: Optimization -> (Int, Double, [Double])
137adapt opt = case opt of 182adapt opt = case opt of
138 Maximize x -> (size x, 1 ,x) 183 Maximize x -> (size x, 1 ,x)
@@ -162,6 +207,13 @@ obj (x :&: _) = x
162obj (x :==: _) = x 207obj (x :==: _) = x
163obj (Free x) = x 208obj (Free x) = x
164 209
210withObj :: Bound t -> t -> Bound t
211withObj (_ :<=: b) x = (x :<=: b)
212withObj (_ :>=: b) x = (x :>=: b)
213withObj (_ :&: b) x = (x :&: b)
214withObj (_ :==: b) x = (x :==: b)
215withObj (Free _) x = Free x
216
165tb :: Bound t -> Double 217tb :: Bound t -> Double
166tb (_ :<=: _) = glpUP 218tb (_ :<=: _) = glpUP
167tb (_ :>=: _) = glpLO 219tb (_ :>=: _) = glpLO
@@ -235,6 +287,19 @@ simplexSparse m n c b = unsafePerformIO $ do
235 app3 (c_simplex_sparse (fi m) (fi n)) mat (cmat c) mat (cmat b) vec s "c_simplex_sparse" 287 app3 (c_simplex_sparse (fi m) (fi n)) mat (cmat c) mat (cmat b) vec s "c_simplex_sparse"
236 return s 288 return s
237 289
290foreign import ccall unsafe "c_exact_sparse" c_exact_sparse
291 :: CInt -> CInt -- rows and cols
292 -> CInt -> CInt -> Ptr Double -- coeffs
293 -> CInt -> CInt -> Ptr Double -- bounds
294 -> CInt -> Ptr Double -- result
295 -> IO CInt -- exit code
296
297exactSparse :: Int -> Int -> Matrix Double -> Matrix Double -> Vector Double
298exactSparse m n c b = unsafePerformIO $ do
299 s <- createVector (2+n)
300 app3 (c_exact_sparse (fi m) (fi n)) mat (cmat c) mat (cmat b) vec s "c_exact_sparse"
301 return s
302
238glpFR, glpLO, glpUP, glpDB, glpFX :: Double 303glpFR, glpLO, glpUP, glpDB, glpFX :: Double
239glpFR = 0 304glpFR = 0
240glpLO = 1 305glpLO = 1