lagrangian 0.3.0.1 → 0.4.0.0

raw patch · 4 files changed

+42/−12 lines, 4 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• lagrangian.cabal +17/−4
• src/Numeric/AD/Lagrangian.hs +4/−3
• src/Numeric/AD/Lagrangian/Internal.hs +19/−3
• tests/Main.hs +2/−2

@@ -10,25 +10,38 @@ -- PVP summary:      +-+------- breaking API changes --                   | | +----- non-breaking API additions --                   | | | +--- code changes with no API change-version:             0.3.0.1+version:             0.4.0.0  -- A short (one-line) description of the package. synopsis:            Solve lagrange multiplier problems  -- A longer description of the package. description:      - Numerically solve convex lagrange multiplier problems with conjugate gradient descent. + Numerically solve convex Lagrange multiplier problems with conjugate gradient descent.   .+ For some background on the method of Lagrange multipliers checkout the wikipedia page+ <http://en.wikipedia.org/wiki/Lagrange_multiplier>+ .+ Here is an example from the Wikipedia page on Lagrange multipliers+ Maximize f(x, y) = x + y, subject to the constraint x^2 + y^2 = 1 + .+ @+   \> maximize 0.00001 (\[x, y] -> x + y) [(\[x, y] -> x^2 + y^2) <=> 1] 2+   Right ([0.707,0.707], [-0.707])+ @+ .+ For more information look here: <http://en.wikipedia.org/wiki/Lagrange_multiplier#Example_1>+ .  For example, find the maximum entropy with the constraint that the probabilities sum  to one.   .  @-   \> solve 0.00001 (negate . sum . map (\x -> x * log x)) [sum \<=\> 1] 3+   \> maximize 0.00001 (negate . sum . map (\\x -> x * log x)) [sum \<=\> 1] 3    Right ([0.33, 0.33, 0.33], [-0.09])  @  .  The first elements of the result pair are the arguments for the - objective function at the minimum. The second elements are the lagrange multipliers.+ objective function at the maximum. The second elements are the Lagrange multipliers.  . -- URL for the project homepage or repository. homepage:            http://github.com/jfischoff/lagrangian

@@ -3,7 +3,7 @@ --  Here is an example from the Wikipedia page on Lagrange multipliers. --  Maximize f(x, y) = x + y, subject to the constraint x^2 + y^2 = 1  --  ---  >>> solve 0.00001 (\[x, y] -> x + y) [\[x, y] -> x^2 + y^2 <=> 1] 2+--  >>> maximize 0.00001 (\[x, y] -> x + y) [(\[x, y] -> x^2 + y^2) <=> 1] 2 --  Right ([0.707,0.707], [-0.707]) --   --  The first elements of the result pair are the arguments for the objective function at the minimum. @@ -14,7 +14,8 @@     (<=>),     Constraint,     -- ** Solver-    solve,+    maximize,+    minimize,     -- *** Experimental features     feasible) where-import Numeric.AD.Lagrangian.Internal (AD2, (<=>), solve, feasible, Constraint)+import Numeric.AD.Lagrangian.Internal (AD2, (<=>), maximize, minimize, feasible, Constraint)

@@ -27,7 +27,7 @@ -- | This is the lagrangian multiplier solver. It is assumed that the  --   objective function and all of the constraints take in the  --   same amount of arguments.-solve :: Double+minimize :: Double       -> (forall s r. (Mode s, Mode r) => [AD2 s r Double] -> AD2 s r Double)          -- ^ The function to minimize       -> (forall s r. (Mode s, Mode r) => [Constraint (AD2 s r Double)] ) @@ -39,7 +39,7 @@       -> Either (Result, Statistics) (S.Vector Double, S.Vector Double)        -- ^ Either an explanation of why the gradient descent failed or a pair        --   containing the arguments at the minimum and the lagrange multipliers-solve tolerance toMin constraints argCount = result where+minimize tolerance toMin constraints argCount = result where     -- The function to minimize for the langrangian is the squared gradient     obj argsAndLams =          squaredGrad (lagrangian toMin constraints argCount) argsAndLams@@ -61,6 +61,22 @@        (vs, ToleranceStatisfied, _) -> Right (S.take argCount vs,                                                S.drop argCount vs)         (_, x, y) -> Left (x, y)+       +-- | Finding the maximum is the same as the minimum with the objective function inverted+maximize :: Double+      -> (forall s r. (Mode s, Mode r) => [AD2 s r Double] -> AD2 s r Double) +        -- ^ The function to maximize+      -> (forall s r. (Mode s, Mode r) => [Constraint (AD2 s r Double)] ) +      -- ^ The constraints as pairs @g \<=\> c@ which represent equations +      --   of the form @g(x, y, ...) = c@+      -> Int +      -- ^ The arity of the objective function which should equal the arity of +      --   the constraints.+      -> Either (Result, Statistics) (S.Vector Double, S.Vector Double) +      -- ^ Either an explanation of why the gradient descent failed or a pair +      --   containing the arguments at the minimum and the lagrange multipliers+maximize tolerance toMax constraints argCount = +    minimize tolerance (negate1 . toMax) constraints argCount  lagrangian :: Num a             => ([a] -> a)@@ -72,7 +88,7 @@     args = take argCount argsAndLams     lams = drop argCount argsAndLams     -    -- (g, c) <=> g(x, y, ...) = c <=> g(x, y, ...) - c = 0+    -- g(x, y, ...) = c <=> g(x, y, ...) - c = 0     appliedConstraints = fmap (\(f, c) -> f args - c) constraints          -- L(x, y, ..., lam0, ...) = f(x, y, ...) + lam0 * (g0 - c0) ... 

@@ -16,7 +16,7 @@           noConstraints = (fst <$> actual) @?= Right expected where-    actual    = solve 0.00001 f [] 1+    actual    = minimize 0.00001 f [] 1     expected  = S.fromList [1]     f [x] = -(x - 1) ^2     @@ -24,7 +24,7 @@ --    x =~= y :: a -> a -> Bool  entropyTest = (S.sum . S.map abs $ S.zipWith (-) actual expected) < 0.02 @?= True  where-    Right actual = fst <$> solve 0.00001 f [(\xs -> sum xs, 1)] 3+    Right actual = fst <$> maximize 0.00001 f [(\xs -> sum xs, 1)] 3     expected  = S.fromList [0.33, 0.33, 0.33]     f :: Floating a => [a] -> a     f = negate . sum . map (\x -> x * log x)