lagrangian 0.1.0.0 → 0.2.0.0

raw patch · 4 files changed

+35/−10 lines, 4 filesdep ~ad

Dependency ranges changed: ad

Files

• lagrangian.cabal +28/−4
• src/Numeric/AD/Lagrangian.hs +1/−1
• src/Numeric/AD/Lagrangian/Internal.hs +4/−3
• tests/Main.hs +2/−2

@@ -10,14 +10,38 @@ -- PVP summary:      +-+------- breaking API changes --                   | | +----- non-breaking API additions --                   | | | +--- code changes with no API change-version:             0.1.0.0+version:             0.2.0.0  -- A short (one-line) description of the package. synopsis:            Solve lagrangian multiplier problems  -- A longer description of the package.--- description:         -+description:      + Numerically solve convex lagrange multiplier problems with conjugate gradient descent. + .+ Convexity is key, otherwise the descent algorithm can return the wrong answer.+ .+ Convexity can be tested by assuring that the hessian of the lagrangian is positive+ definite over region the function is defined in. + .+ I have provided test that the hessian is positive definite at a point, which is something,+ but not enough to ensure that the whole function is convex.+ .+ Be that as it may, if you know what the your lagrangian is convex you can use 'solve' to + find the minimum.+ .+ For example, find the maximum entropy with the constraint that the probabilities add+ up to one. + .+ @ +    solve 0.00001 (negate . sum . map (\x -> x * log x), [(sum, 1)]) 3+ @+ .+ Gives the answer ([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.+ . -- URL for the project homepage or repository. homepage:            http://github.com/jfischoff/lagrangian @@ -56,7 +80,7 @@   build-depends:    base ==4.6.*,                      nonlinear-optimization ==0.3.*,                      vector ==0.10.*, -                    ad ==3.3.*,+                    ad ==3.4.*,                     hmatrix == 0.14.*      -- Directories containing source files.

@@ -15,7 +15,7 @@ --  up to one.  --   --  @ ---     solve (negate . sum . map (\x -> x * log x), [(sum, 1)]) 3+--     solve 0.00001 (negate . sum . map (\x -> x * log x), [(sum, 1)]) 3 --  @ --   --  Gives the answer ([0.33, 0.33, 0.33], [-0.09])

@@ -48,10 +48,11 @@ -- | This is the lagrangrain multiplier solver. It is assumed that the  --   objective function and all of the constraints take in the  --   same about of arguments.-solve :: (forall a. Floating a => ([a] -> a, [Constraint a])) -- ^ A pair of the function to minimize and the constraints+solve :: Double+      -> (forall a. Floating a => ([a] -> a, [Constraint a])) -- ^ A pair of the function to minimize and the constraints       -> Int -- ^ The arity of the objective function and the constraints.       -> Either (Result, Statistics) ([Double], [Double]) -- ^ Either an explaination of why the gradient descent failed or a pair of the arguments at the minimum and the lagrange multipliers-solve params argCount = result where+solve tolerance params argCount = result where     obj :: Floating a => [a] -> a     obj argsAndLams = squaredGrad lang argsAndLams @@ -63,7 +64,7 @@     guess = U.fromList $ replicate (argCount + constraintCount) (1.0 :: Double)       result = case unsafePerformIO (optimize (defaultParameters { printFinal = False }) -                    0.00001 guess (toFunction obj) (toGradient obj)+                    tolerance guess (toFunction obj) (toGradient obj)                        Nothing) of                 (vs, ToleranceStatisfied, _) -> Right (take argCount . S.toList $ vs, 

@@ -15,7 +15,7 @@           noConstraints = (fst <$> actual) @?= Right expected where-    actual    = solve (f, []) 1+    actual    = solve 0.00001 (f, []) 1     expected  = [1]     f [x] = -(x - 1) ^2     @@ -24,7 +24,7 @@   entropyTest = (sum . map abs $ zipWith (-) actual expected) < 0.02 @?= True  where-    Right actual = fst <$> solve (f, [(\xs -> sum xs, 1.0)]) 3+    Right actual = fst <$> solve 0.00001 (f, [(\xs -> sum xs, 1.0)]) 3     expected  = [0.33, 0.33, 0.33]     f :: Floating a => [a] -> a     f = negate . sum . map (\x -> x * log x)