included all GSL minimization methods

4 files changed, 109 insertions, 136 deletions

diff --git a/lib/Numeric/GSL/Minimization.hs b/lib/Numeric/GSL/Minimization.hs
index b95765f..048c717 100644
--- a/lib/Numeric/GSL/Minimization.hs
+++ b/lib/Numeric/GSL/Minimization.hs
@@ -13,12 +13,49 @@ Minimization of a multidimensional function using some of the algorithms describ
 
 <http://www.gnu.org/software/gsl/manual/html_node/Multidimensional-Minimization.html>
 
+The example in the GSL manual:
+
+@
+
+f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30
+
+main = do
+    let (s,p) = minimize NMSimplex2 1E-2 30 [1,1] f [5,7]
+    print s
+    print p
+
+\> main
+[0.9920430849306288,1.9969168063253182]
+ 0.000  512.500  1.130  6.500  5.000
+ 1.000  290.625  1.409  5.250  4.000
+ 2.000  290.625  1.409  5.250  4.000
+ 3.000  252.500  1.409  5.500  1.000
+ ...
+22.000   30.001  0.013  0.992  1.997
+23.000   30.001  0.008  0.992  1.997
+@
+
+The path to the solution can be graphically shown by means of:
+
+@'Graphics.Plot.mplot' $ drop 3 ('toColumns' p)@
+
+Taken from the GSL manual:
+
+The vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is a quasi-Newton method which builds up an approximation to the second derivatives of the function f using the difference between successive gradient vectors. By combining the first and second derivatives the algorithm is able to take Newton-type steps towards the function minimum, assuming quadratic behavior in that region.
+
+The bfgs2 version of this minimizer is the most efficient version available, and is a faithful implementation of the line minimization scheme described in Fletcher's Practical Methods of Optimization, Algorithms 2.6.2 and 2.6.4. It supercedes the original bfgs routine and requires substantially fewer function and gradient evaluations. The user-supplied tolerance tol corresponds to the parameter \sigma used by Fletcher. A value of 0.1 is recommended for typical use (larger values correspond to less accurate line searches).
+
+The nmsimplex2 version is a new O(N) implementation of the earlier O(N^2) nmsimplex minimiser. It calculates the size of simplex as the rms distance of each vertex from the center rather than the mean distance, which has the advantage of allowing a linear update.
+
 -}
+
 -----------------------------------------------------------------------------
 module Numeric.GSL.Minimization (
+    minimize, MinimizeMethod(..),
+    minimizeD, MinimizeMethodD(..),
+    minimizeNMSimplex,
     minimizeConjugateGradient,
-    minimizeVectorBFGS2,
-    minimizeNMSimplex
+    minimizeVectorBFGS2
 ) where
 
 
@@ -27,68 +64,67 @@ import Data.Packed.Matrix
 import Foreign
 import Foreign.C.Types(CInt)
 
+------------------------------------------------------------------------
+
+{-# DEPRECATED minimizeNMSimplex "use minimize NMSimplex2 eps maxit sizes f xi" #-}
+minimizeNMSimplex f xi szs eps maxit = minimize NMSimplex eps maxit szs f xi
+
+{-# DEPRECATED minimizeConjugateGradient "use minimizeD ConjugateFR eps maxit step tol f g xi" #-}
+minimizeConjugateGradient step tol eps maxit f g xi = minimizeD ConjugateFR eps maxit step tol f g xi
+
+{-# DEPRECATED minimizeVectorBFGS2 "use minimizeD VectorBFGS2 eps maxit step tol f g xi" #-}
+minimizeVectorBFGS2 step tol eps maxit f g xi = minimizeD VectorBFGS2 eps maxit step tol f g xi
+
 -------------------------------------------------------------------------
 
-{- | The method of Nelder and Mead, implemented by /gsl_multimin_fminimizer_nmsimplex/. The gradient of the function is not required. This is the example in the GSL manual:
+data MinimizeMethod = NMSimplex
+                    | NMSimplex2
+                    deriving (Enum,Eq,Show)
+
+-- | Minimization without derivatives.
+minimize :: MinimizeMethod
+         -> Double              -- ^ desired precision of the solution (size test)
+         -> Int                 -- ^ maximum number of iterations allowed
+         -> [Double]            -- ^ sizes of the initial search box
+         -> ([Double] -> Double) -- ^ function to minimize
+         -> [Double]            -- ^ starting point
+         -> ([Double], Matrix Double) -- ^ solution vector and optimization path
+
+minimize method = minimizeGen (fi (fromEnum method))
+
+data MinimizeMethodD = ConjugateFR
+                     | ConjugatePR
+                     | VectorBFGS
+                     | VectorBFGS2
+                     | SteepestDescent
+                     deriving (Enum,Eq,Show)
+
+-- | Minimization with derivatives.
+minimizeD :: MinimizeMethodD
+    -> Double                 -- ^ desired precision of the solution (gradient test)
+    -> Int                    -- ^ maximum number of iterations allowed
+    -> Double                 -- ^ size of the first trial step
+    -> Double                 -- ^ tol (precise meaning depends on method)
+    -> ([Double] -> Double)   -- ^ function to minimize
+    -> ([Double] -> [Double]) -- ^ gradient
+    -> [Double]               -- ^ starting point
+    -> ([Double], Matrix Double) -- ^ solution vector and optimization path
+
+minimizeD method = minimizeDGen (fi (fromEnum method))
 
-@minimize f xi = minimizeNMSimplex f xi (replicate (length xi) 1) 1e-2 100
-\  -- 
-f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30
-\  --
-main = do
-    let (s,p) = minimize f [5,7]
-    print s
-    print p
-\  --
-\> main
-[0.9920430849306285,1.9969168063253164]
-0. 512.500    1.082 6.500    5.
- 1. 290.625    1.372 5.250    4.
- 2. 290.625    1.372 5.250    4.
- 3. 252.500    1.372 5.500    1.
- 4. 101.406    1.823 2.625 3.500
- 5. 101.406    1.823 2.625 3.500
- 6.     60.    1.823    0.    3.
- 7.  42.275    1.303 2.094 1.875
- 8.  42.275    1.303 2.094 1.875
- 9.  35.684    1.026 0.258 1.906
-10.  35.664    0.804 0.588 2.445
-11.  30.680    0.467 1.258 2.025
-12.  30.680    0.356 1.258 2.025
-13.  30.539    0.285 1.093 1.849
-14.  30.137    0.168 0.883 2.004
-15.  30.137    0.123 0.883 2.004
-16.  30.090    0.100 0.958 2.060
-17.  30.005 6.051e-2 1.022 2.004
-18.  30.005 4.249e-2 1.022 2.004
-19.  30.005 4.249e-2 1.022 2.004
-20.  30.005 2.742e-2 1.022 2.004
-21.  30.005 2.119e-2 1.022 2.004
-22.  30.001 1.530e-2 0.992 1.997
-23.  30.001 1.259e-2 0.992 1.997
-24.  30.001 7.663e-3 0.992 1.997@
+-------------------------------------------------------------------------
 
-The path to the solution can be graphically shown by means of:
 
-@'Graphics.Plot.mplot' $ drop 3 ('toColumns' p)@
 
--}
-minimizeNMSimplex :: ([Double] -> Double) -- ^ function to minimize
-          -> [Double]            -- ^ starting point
-          -> [Double]            -- ^ sizes of the initial search box
-          -> Double              -- ^ desired precision of the solution
-          -> Int                 -- ^ maximum number of iterations allowed
-          -> ([Double], Matrix Double)
-          -- ^ solution vector, and the optimization trajectory followed by the algorithm
-minimizeNMSimplex f xi sz tol maxit = unsafePerformIO $ do
+minimizeGen method eps maxit sz f xi = unsafePerformIO $ do
     let xiv = fromList xi
         szv = fromList sz
         n   = dim xiv
     fp <- mkVecfun (iv (f.toList))
     rawpath <- ww2 withVector xiv withVector szv $ \xiv' szv' ->
                    createMIO maxit (n+3)
-                         (c_minimizeNMSimplex fp tol (fi maxit) // xiv' // szv')
-                         "minimizeNMSimplex"
+                         (c_minimize method fp eps (fi maxit) // xiv' // szv')
+                         "minimize"
     let it = round (rawpath @@> (maxit-1,0))
         path = takeRows it rawpath
         [sol] = toLists $ dropRows (it-1) path
@@ -97,73 +133,13 @@ minimizeNMSimplex f xi sz tol maxit = unsafePerformIO $ do
 
 
 foreign import ccall "gsl-aux.h minimize"
-    c_minimizeNMSimplex:: FunPtr (CInt -> Ptr Double -> Double) -> Double -> CInt -> TVVM
+    c_minimize:: CInt -> FunPtr (CInt -> Ptr Double -> Double) -> Double -> CInt -> TVVM
 
 ----------------------------------------------------------------------------------
 
-{- | The Fletcher-Reeves conjugate gradient algorithm /gsl_multimin_fminimizer_conjugate_fr/. This is the example in the GSL manual:
 
-@minimize = minimizeConjugateGradient 1E-2 1E-4 1E-3 30
-f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30
-\  --
-df [x,y] = [20*(x-1), 40*(y-2)]
-\   --
-main = do
-    let (s,p) = minimize f df [5,7]
-    print s
-    print p
-\  --
-\> main
-[1.0,2.0]
- 0. 687.848 4.996 6.991
- 1. 683.555 4.989 6.972
- 2. 675.013 4.974 6.935
- 3. 658.108 4.944 6.861
- 4. 625.013 4.885 6.712
- 5. 561.684 4.766 6.415
- 6. 446.467 4.528 5.821
- 7. 261.794 4.053 4.632
- 8.  75.498 3.102 2.255
- 9.  67.037 2.852 1.630
-10.  45.316 2.191 1.762
-11.  30.186 0.869 2.026
-12.     30.    1.    2.@
-
-The path to the solution can be graphically shown by means of:
-
-@'Graphics.Plot.mplot' $ drop 2 ('toColumns' p)@
 
--}
-minimizeConjugateGradient ::
-       Double        -- ^ initial step size
-    -> Double        -- ^ minimization parameter   
-    -> Double        -- ^ desired precision of the solution (gradient test)
-    -> Int           -- ^ maximum number of iterations allowed
-    -> ([Double] -> Double) -- ^ function to minimize
-    -> ([Double] -> [Double])      -- ^ gradient
-    -> [Double]             -- ^ starting point
-    -> ([Double], Matrix Double)        -- ^ solution vector, and the optimization trajectory followed by the algorithm
-minimizeConjugateGradient = minimizeWithDeriv 0
-
-{- | Taken from the GSL manual:
-
-The vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. This is a quasi-Newton method which builds up an approximation to the second derivatives of the function f using the difference between successive gradient vectors. By combining the first and second derivatives the algorithm is able to take Newton-type steps towards the function minimum, assuming quadratic behavior in that region.
-
-The bfgs2 version of this minimizer is the most efficient version available, and is a faithful implementation of the line minimization scheme described in Fletcher's Practical Methods of Optimization, Algorithms 2.6.2 and 2.6.4. It supercedes the original bfgs routine and requires substantially fewer function and gradient evaluations. The user-supplied tolerance tol corresponds to the parameter \sigma used by Fletcher. A value of 0.1 is recommended for typical use (larger values correspond to less accurate line searches).
--}
-minimizeVectorBFGS2 ::
-       Double        -- ^ initial step size
-    -> Double        -- ^ minimization parameter tol
-    -> Double        -- ^ desired precision of the solution (gradient test)
-    -> Int           -- ^ maximum number of iterations allowed
-    -> ([Double] -> Double) -- ^ function to minimize
-    -> ([Double] -> [Double])      -- ^ gradient
-    -> [Double]             -- ^ starting point
-    -> ([Double], Matrix Double)        -- ^ solution vector, and the optimization trajectory followed by the algorithm
-minimizeVectorBFGS2 = minimizeWithDeriv 1
-
-
-minimizeWithDeriv method istep minimpar tol maxit f df xi = unsafePerformIO $ do
+minimizeDGen method eps maxit istep tol f df xi = unsafePerformIO $ do
     let xiv = fromList xi
         n = dim xiv
         f' = f . toList
@@ -172,7 +148,7 @@ minimizeWithDeriv method istep minimpar tol maxit f df xi = unsafePerformIO $ do
     dfp <- mkVecVecfun (aux_vTov df')
     rawpath <- withVector xiv $ \xiv' ->
                     createMIO maxit (n+2)
-                         (c_minimizeWithDeriv method fp dfp istep minimpar tol (fi maxit) // xiv')
+                         (c_minimizeWithDeriv method fp dfp istep tol eps (fi maxit) // xiv')
                          "minimizeDerivV"
     let it = round (rawpath @@> (maxit-1,0))
         path = takeRows it rawpath
@@ -181,7 +157,7 @@ minimizeWithDeriv method istep minimpar tol maxit f df xi = unsafePerformIO $ do
     freeHaskellFunPtr dfp
     return (sol,path)
 
-foreign import ccall "gsl-aux.h minimizeWithDeriv"
+foreign import ccall "gsl-aux.h minimizeD"
     c_minimizeWithDeriv :: CInt -> FunPtr (CInt -> Ptr Double -> Double)
                                 -> FunPtr (CInt -> Ptr Double -> Ptr Double -> IO ())
                                 -> Double -> Double -> Double -> CInt
diff --git a/lib/Numeric/GSL/gsl-aux.c b/lib/Numeric/GSL/gsl-aux.c
index c6b052f..2ecfb51 100644
--- a/lib/Numeric/GSL/gsl-aux.c
+++ b/lib/Numeric/GSL/gsl-aux.c
@@ -369,7 +369,7 @@ double only_f_aux_min(const gsl_vector*x, void *pars) {
 }
 
 // this version returns info about intermediate steps
-int minimize(double f(int, double*), double tolsize, int maxit, 
+int minimize(int method, double f(int, double*), double tolsize, int maxit, 
                  KRVEC(xi), KRVEC(sz), RMAT(sol)) {
     REQUIRES(xin==szn && solr == maxit && solc == 3+xin,BAD_SIZE);
     DEBUGMSG("minimizeList (nmsimplex)");
@@ -388,7 +388,11 @@ int minimize(double f(int, double*), double tolsize, int maxit,
     // Starting point
     KDVVIEW(xi);
     // Minimizer nmsimplex, without derivatives
-    T = gsl_multimin_fminimizer_nmsimplex;
+    switch(method) {
+        case 0 : {T = gsl_multimin_fminimizer_nmsimplex; break; }
+        case 1 : {T = gsl_multimin_fminimizer_nmsimplex2; break; }
+        default: ERROR(BAD_CODE);
+    }
     s = gsl_multimin_fminimizer_alloc (T, my_func.n);
     gsl_multimin_fminimizer_set (s, &my_func, V(xi), V(sz));
     do {
@@ -458,9 +462,9 @@ void fdf_aux_min(const gsl_vector * x, void * pars, double * f, gsl_vector * g)
 }
 
 
-int minimizeWithDeriv(int method, double f(int, double*), void df(int, double*, double*), 
-                      double initstep, double minimpar, double tolgrad, int maxit, 
-                      KRVEC(xi), RMAT(sol)) {
+int minimizeD(int method, double f(int, double*), void df(int, double*, double*), 
+              double initstep, double minimpar, double tolgrad, int maxit, 
+              KRVEC(xi), RMAT(sol)) {
     REQUIRES(solr == maxit && solc == 2+xin,BAD_SIZE);
     DEBUGMSG("minimizeWithDeriv (conjugate_fr)");
     gsl_multimin_function_fdf my_func;
@@ -482,7 +486,10 @@ int minimizeWithDeriv(int method, double f(int, double*), void df(int, double*,
     // conjugate gradient fr
     switch(method) {
         case 0 : {T = gsl_multimin_fdfminimizer_conjugate_fr; break; }
-        case 1 : {T = gsl_multimin_fdfminimizer_vector_bfgs2; break; }
+        case 1 : {T = gsl_multimin_fdfminimizer_conjugate_pr; break; }
+        case 2 : {T = gsl_multimin_fdfminimizer_vector_bfgs; break; }
+        case 3 : {T = gsl_multimin_fdfminimizer_vector_bfgs2; break; }
+        case 4 : {T = gsl_multimin_fdfminimizer_steepest_descent; break; }
         default: ERROR(BAD_CODE);
     }
     s = gsl_multimin_fdfminimizer_alloc (T, my_func.n);
diff --git a/lib/Numeric/GSL/gsl-aux.h b/lib/Numeric/GSL/gsl-aux.h
index c9fd546..881d0d0 100644
--- a/lib/Numeric/GSL/gsl-aux.h
+++ b/lib/Numeric/GSL/gsl-aux.h
@@ -38,13 +38,3 @@ int integrate_qags(double f(double,void*), double a, double b, double prec, int
 
 int polySolve(KRVEC(a), CVEC(z));
 
-int minimize(double f(int, double*), double tolsize, int maxit, 
-                 KRVEC(xi), KRVEC(sz), RMAT(sol));
-
-int minimizeWithDeriv(int method, double f(int, double*), void df(int, double*, double*),
-                      double initstep, double minimpar, double tolgrad, int maxit, 
-                      KRVEC(xi), RMAT(sol));
-
-int root(int method, void f(int, double*, int, double*),
-         double epsabs, int maxit,
-         KRVEC(xi), RMAT(sol));
diff --git a/lib/Numeric/LinearAlgebra/Tests.hs b/lib/Numeric/LinearAlgebra/Tests.hs
index 83f581f..464ed27 100644
--- a/lib/Numeric/LinearAlgebra/Tests.hs
+++ b/lib/Numeric/LinearAlgebra/Tests.hs
@@ -109,13 +109,13 @@ expmTest2 = expm nd2 :~15~: (2><2)
 
 ---------------------------------------------------------------------
 
-minimizationTest = TestList [ utest "minimization conj grad" (minim1 f df [5,7] ~~ [1,2])
-                            , utest "minimization bg2"       (minim2 f df [5,7] ~~ [1,2])
+minimizationTest = TestList [ utest "minimization conjugatefr" (minim1 f df [5,7] ~~ [1,2])
+                            , utest "minimization nmsimplex2"       (minim2 f [5,7] == 24)
                             ]
     where f [x,y] = 10*(x-1)^2 + 20*(y-2)^2 + 30
           df [x,y] = [20*(x-1), 40*(y-2)]
-          minim1 g dg ini = fst $ minimizeConjugateGradient 1E-2 1E-4 1E-3 30 g dg ini
-          minim2 g dg ini = fst $ minimizeVectorBFGS2 1E-2 1E-2 1E-3 30 g dg ini
+          minim1 g dg ini = fst $ minimizeD ConjugateFR 1E-3 30 1E-2 1E-4 g dg ini
+          minim2 g ini = rows $ snd $ minimize NMSimplex2 1E-2 30 [1,1] g ini
 
 ---------------------------------------------------------------------