{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ScopedTypeVariables #-}
--------------------------------------------------------------------------------
-- |
-- Module : LevMar
-- Copyright : (c) 2009 Roel van Dijk & Bas van Dijk
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : vandijk.roel@gmail.com, v.dijk.bas@gmail.com
-- Stability : Experimental
--
--
--
-- For additional documentation see the documentation of the levmar C
-- library which this library is based on:
--
--
--------------------------------------------------------------------------------
module LevMar
( -- * Model & Jacobian.
Model
, Jacobian
-- * Levenberg-Marquardt algorithm.
, LMA_I.LevMarable
, levmar
, LinearConstraints
, noLinearConstraints
, Matrix
-- * Minimization options.
, LMA_I.Options(..)
, LMA_I.defaultOpts
-- * Output
, LMA_I.Info(..)
, LMA_I.StopReason(..)
, CovarMatrix
, LMA_I.LevMarError(..)
-- *Type-level machinery
, Z, S, Nat
, SizedList(..)
, NFunction
)
where
import qualified LevMar.Intermediate as LMA_I
import LevMar.Utils ( LinearConstraints
, noLinearConstraints
, Matrix
, CovarMatrix
, convertLinearConstraints
, convertResult
)
import TypeLevelNat ( Z, S, Nat )
import SizedList ( SizedList(..), toList, unsafeFromList )
import NFunction ( NFunction, ($*) )
import Data.Either
--------------------------------------------------------------------------------
-- Model & Jacobian.
--------------------------------------------------------------------------------
{- | A functional relation describing measurements represented as a function
from @m@ parameters to @n@ expected measurements.
An example from /Demo.hs/:
@
type N4 = 'S' ('S' ('S' ('S' 'Z')))
hatfldc :: Model N4 N4 Double
hatfldc p0 p1 p2 p3 = p0 - 1.0
::: p0 - sqrt p1
::: p1 - sqrt p2
::: p3 - 1.0
::: Nil
@
-}
type Model m n r = NFunction m r (SizedList n r)
{- | The jacobian of the 'Model' function. Expressed as a function
from @m@ parameters to a @n@/x/@m@ matrix which for each of the @n@
expected measurement describes the @m@ partial derivatives of the
parameters.
See:
For example the jacobian of the above @hatfldc@ model is:
@
type N4 = 'S' ('S' ('S' ('S' 'Z')))
hatfldc_jac :: Jacobian N4 N4 Double
hatfldc_jac _ p1 p2 _ = (1.0 ::: 0.0 ::: 0.0 ::: 0.0 ::: Nil)
::: (1.0 ::: -0.5 / sqrt p1 ::: 0.0 ::: 0.0 ::: Nil)
::: (0.0 ::: 1.0 ::: -0.5 / sqrt p2 ::: 0.0 ::: Nil)
::: (0.0 ::: 0.0 ::: 0.0 ::: 1.0 ::: Nil)
::: Nil
@
-}
type Jacobian m n r = NFunction m r (Matrix n m r)
--------------------------------------------------------------------------------
-- Levenberg-Marquardt algorithm.
--------------------------------------------------------------------------------
-- | The Levenberg-Marquardt algorithm.
levmar :: forall m n k r. (Nat m, Nat n, Nat k, LMA_I.LevMarable r)
=> (Model m n r) -- ^ Model
-> Maybe (Jacobian m n r) -- ^ Optional jacobian
-> SizedList m r -- ^ Initial parameters
-> SizedList n r -- ^ Samples
-> Integer -- ^ Maximum number of iterations
-> LMA_I.Options r -- ^ Minimization options
-> Maybe (SizedList m r) -- ^ Optional lower bounds
-> Maybe (SizedList m r) -- ^ Optional upper bounds
-> Maybe (LinearConstraints k m r) -- ^ Optional linear constraints
-> Maybe (SizedList m r) -- ^ Optional weights
-> Either LMA_I.LevMarError (SizedList m r, LMA_I.Info r, CovarMatrix m r)
levmar model mJac params ys itMax opts mLowBs mUpBs mLinC mWghts =
fmap convertResult $ LMA_I.levmar (convertModel model)
(fmap convertJacob mJac)
(toList params)
(toList ys)
itMax
opts
(fmap toList mLowBs)
(fmap toList mUpBs)
(fmap convertLinearConstraints mLinC)
(fmap toList mWghts)
where
convertModel f = \ps -> toList (f $* (unsafeFromList ps :: SizedList m r) :: SizedList n r)
convertJacob f = \ps -> toList (fmap toList (f $* (unsafeFromList ps :: SizedList m r) :: Matrix n m r))
-- The End ---------------------------------------------------------------------