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+{- |
+Module      :  Numeric.GSL.Interpolation
+Copyright   :  (c) Matthew Peddie 2015
+License     :  GPL
+Maintainer  :  Alberto Ruiz
+Stability   :  provisional
+
+Simulated annealing routines.
+
+<https://www.gnu.org/software/gsl/manual/html_node/Simulated-Annealing.html#Simulated-Annealing>
+
+Here is a translation of the simple example given in
+<https://www.gnu.org/software/gsl/manual/html_node/Trivial-example.html#Trivial-example the GSL manual>:
+
+> import Numeric.GSL.SimulatedAnnealing
+> import Numeric.LinearAlgebra.HMatrix
+>
+> main = print $ simanSolve 0 1 exampleParams 15.5 exampleE exampleM exampleS (Just show)
+>
+> exampleParams = SimulatedAnnealingParams 200 1000 1.0 1.0 0.008 1.003 2.0e-6
+>
+> exampleE x = exp (-(x - 1)**2) * sin (8 * x)
+>
+> exampleM x y = abs $ x - y
+>
+> exampleS rands stepSize current = (rands ! 0) * 2 * stepSize - stepSize + current
+
+The manual states:
+
+>     The first example, in one dimensional Cartesian space, sets up an
+>     energy function which is a damped sine wave; this has many local
+>     minima, but only one global minimum, somewhere between 1.0 and
+>     1.5. The initial guess given is 15.5, which is several local minima
+>     away from the global minimum.
+
+This global minimum is around 1.36.
+
+-}
+{-# OPTIONS_GHC -Wall #-}
+
+module Numeric.GSL.SimulatedAnnealing (
+  -- * Searching for minima
+  simanSolve
+  -- * Configuring the annealing process
+  , SimulatedAnnealingParams(..)
+  ) where
+
+import Numeric.GSL.Internal
+import Numeric.LinearAlgebra.HMatrix hiding(step)
+
+import Data.Vector.Storable(generateM)
+import Foreign.Storable(Storable(..))
+import Foreign.Marshal.Utils(with)
+import Foreign.Ptr(Ptr, FunPtr, nullFunPtr)
+import Foreign.StablePtr(StablePtr, newStablePtr, deRefStablePtr, freeStablePtr)
+import Foreign.C.Types
+import System.IO.Unsafe(unsafePerformIO)
+
+import System.IO (hFlush, stdout)
+
+import Data.IORef (IORef, newIORef, writeIORef, readIORef, modifyIORef')
+
+-- | 'SimulatedAnnealingParams' is a translation of the
+-- @gsl_siman_params_t@ structure documented in
+-- <https://www.gnu.org/software/gsl/manual/html_node/Simulated-Annealing-functions.html#Simulated-Annealing-functions the GSL manual>,
+-- which controls the simulated annealing algorithm.
+--
+-- The annealing process is parameterized by the Boltzmann
+-- distribution and the /cooling schedule/.  For more details, see
+-- <https://www.gnu.org/software/gsl/manual/html_node/Simulated-Annealing-algorithm.html#Simulated-Annealing-algorithm the relevant section of the manual>.
+data SimulatedAnnealingParams = SimulatedAnnealingParams {
+  n_tries :: CInt  -- ^ The number of points to try for each step.
+  , iters_fixed_T :: CInt  -- ^ The number of iterations at each temperature
+  , step_size :: Double    -- ^ The maximum step size in the random walk
+  , boltzmann_k :: Double  -- ^ Boltzmann distribution parameter
+  , cooling_t_initial :: Double -- ^ Initial temperature
+  , cooling_mu_t :: Double      -- ^ Cooling rate parameter
+  , cooling_t_min :: Double     -- ^ Final temperature
+  } deriving (Eq, Show, Read)
+
+instance Storable SimulatedAnnealingParams where
+  sizeOf p = sizeOf (n_tries p) +
+             sizeOf (iters_fixed_T p) +
+             sizeOf (step_size p) +
+             sizeOf (boltzmann_k p) +
+             sizeOf (cooling_t_initial p) +
+             sizeOf (cooling_mu_t p) +
+             sizeOf (cooling_t_min p)
+  -- TODO(MP): is this safe?
+  alignment p = alignment (step_size p)
+  -- TODO(MP): Is there a more automatic way to write these?
+  peek ptr = SimulatedAnnealingParams <$>
+             peekByteOff ptr 0 <*>
+             peekByteOff ptr i <*>
+             peekByteOff ptr (2*i) <*>
+             peekByteOff ptr (2*i + d) <*>
+             peekByteOff ptr (2*i + 2*d) <*>
+             peekByteOff ptr (2*i + 3*d) <*>
+             peekByteOff ptr (2*i + 4*d)
+    where
+      i = sizeOf (0 :: CInt)
+      d = sizeOf (0 :: Double)
+  poke ptr sap = do
+    pokeByteOff ptr 0 (n_tries sap)
+    pokeByteOff ptr i (iters_fixed_T sap)
+    pokeByteOff ptr (2*i) (step_size sap)
+    pokeByteOff ptr (2*i + d) (boltzmann_k sap)
+    pokeByteOff ptr (2*i + 2*d) (cooling_t_initial sap)
+    pokeByteOff ptr (2*i + 3*d) (cooling_mu_t sap)
+    pokeByteOff ptr (2*i + 4*d) (cooling_t_min sap)
+    where
+      i = sizeOf (0 :: CInt)
+      d = sizeOf (0 :: Double)
+
+-- We use a StablePtr to an IORef so that we can keep hold of
+-- StablePtr values but mutate their contents.  A simple 'StablePtr a'
+-- won't work, since we'd have no way to write 'copyConfig'.
+type P a = StablePtr (IORef a)
+
+copyConfig :: P a -> P a -> IO ()
+copyConfig src' dest' = do
+  dest <- deRefStablePtr dest'
+  src <- deRefStablePtr src'
+  readIORef src >>= writeIORef dest
+
+copyConstructConfig :: P a -> IO (P a)
+copyConstructConfig x = do
+  conf <- deRefRead x
+  newconf <- newIORef conf
+  newStablePtr newconf
+
+destroyConfig :: P a -> IO ()
+destroyConfig p = do
+  freeStablePtr p
+
+deRefRead :: P a -> IO a
+deRefRead p = deRefStablePtr p >>= readIORef
+
+wrapEnergy :: (a -> Double) -> P a -> Double
+wrapEnergy f p = unsafePerformIO $ f <$> deRefRead p
+
+wrapMetric :: (a -> a -> Double) -> P a -> P a -> Double
+wrapMetric f x y = unsafePerformIO $ f <$> deRefRead x <*> deRefRead y
+
+wrapStep :: Int
+         -> (Vector Double -> Double -> a -> a)
+         -> GSLRNG
+         -> P a
+         -> Double
+         -> IO ()
+wrapStep nrand f (GSLRNG rng) confptr stepSize = do
+  v <- generateM nrand (\_ -> gslRngUniform rng)
+  conf <- deRefStablePtr confptr
+  modifyIORef' conf $ f v stepSize
+
+wrapPrint :: (a -> String) -> P a -> IO ()
+wrapPrint pf ptr = deRefRead ptr >>= putStr . pf >> hFlush stdout
+
+foreign import ccall safe "wrapper"
+  mkEnergyFun :: (P a -> Double) -> IO (FunPtr (P a -> Double))
+
+foreign import ccall safe "wrapper"
+  mkMetricFun :: (P a -> P a -> Double) -> IO (FunPtr (P a -> P a -> Double))
+
+foreign import ccall safe "wrapper"
+  mkStepFun :: (GSLRNG -> P a -> Double -> IO ())
+            -> IO (FunPtr (GSLRNG -> P a -> Double -> IO ()))
+
+foreign import ccall safe "wrapper"
+  mkCopyFun :: (P a -> P a -> IO ()) -> IO (FunPtr (P a -> P a -> IO ()))
+
+foreign import ccall safe "wrapper"
+  mkCopyConstructorFun :: (P a -> IO (P a)) -> IO (FunPtr (P a -> IO (P a)))
+
+foreign import ccall safe "wrapper"
+  mkDestructFun :: (P a -> IO ()) -> IO (FunPtr (P a -> IO ()))
+
+newtype GSLRNG = GSLRNG (Ptr GSLRNG)
+
+foreign import ccall safe "gsl_rng.h gsl_rng_uniform"
+  gslRngUniform :: Ptr GSLRNG -> IO Double
+
+foreign import ccall safe "gsl-aux.h siman"
+  siman :: CInt     -- ^ RNG seed (for repeatability)
+        -> Ptr SimulatedAnnealingParams    -- ^ params
+        -> P a                             -- ^ Configuration
+        -> FunPtr (P a -> Double)          -- ^ Energy functional
+        -> FunPtr (P a -> P a -> Double) -- ^ Metric definition
+        -> FunPtr (GSLRNG -> P a -> Double -> IO ())  -- ^ Step evaluation
+        -> FunPtr (P a -> P a -> IO ())  -- ^ Copy config
+        -> FunPtr (P a -> IO (P a))      -- ^ Copy constructor for config
+        -> FunPtr (P a -> IO ())           -- ^ Destructor for config
+        -> FunPtr (P a -> IO ())           -- ^ Print function
+        -> IO CInt
+
+-- |
+-- Calling
+--
+-- > simanSolve seed nrand params x0 e m step print
+--
+-- performs a simulated annealing search through a given space. So
+-- that any configuration type may be used, the space is specified by
+-- providing the functions @e@ (the energy functional) and @m@ (the
+-- metric definition).  @x0@ is the initial configuration of the
+-- system.  The simulated annealing steps are generated using the
+-- user-provided function @step@, which should randomly construct a
+-- new system configuration.
+--
+-- If 'Nothing' is passed instead of a printing function, no
+-- incremental output will be generated.  Otherwise, the GSL-formatted
+-- output, including the configuration description the user function
+-- generates, will be printed to stdout.
+--
+-- Each time the step function is called, it is supplied with a random
+-- vector containing @nrand@ 'Double' values, uniformly distributed in
+-- @[0, 1)@.  It should use these values to generate its new
+-- configuration.
+simanSolve :: Int   -- ^ Seed for the random number generator
+           -> Int   -- ^ @nrand@, the number of random 'Double's the
+                    -- step function requires
+           -> SimulatedAnnealingParams  -- ^ Parameters to configure the solver
+           -> a                    -- ^ Initial configuration @x0@
+           -> (a -> Double)        -- ^ Energy functional @e@
+           -> (a -> a -> Double)   -- ^ Metric definition @m@
+           -> (Vector Double -> Double -> a -> a)  -- ^ Stepping function @step@
+           -> Maybe (a -> String)  -- ^ Optional printing function
+           -> a          -- ^ Best configuration the solver has found
+simanSolve seed nrand params conf e m step printfun =
+  unsafePerformIO $ with params $ \paramptr -> do
+    ewrap <- mkEnergyFun $ wrapEnergy e
+    mwrap <- mkMetricFun $ wrapMetric m
+    stepwrap <- mkStepFun $ wrapStep nrand step
+    confptr <- newIORef conf >>= newStablePtr
+    cpwrap <- mkCopyFun copyConfig
+    ccwrap <- mkCopyConstructorFun copyConstructConfig
+    dwrap <- mkDestructFun destroyConfig
+    pwrap <- case printfun of
+      Nothing -> return nullFunPtr
+      Just pf -> mkDestructFun $ wrapPrint pf
+    siman (fromIntegral seed)
+      paramptr confptr
+      ewrap mwrap stepwrap cpwrap ccwrap dwrap pwrap // check "siman"
+    result <- deRefRead confptr
+    freeStablePtr confptr
+    return result