1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
|
{-# OPTIONS_GHC -fglasgow-exts #-}
-----------------------------------------------------------------------------
{- |
Module : Numeric.GSL.Minimization
Copyright : (c) Alberto Ruiz 2006
License : GPL-style
Maintainer : Alberto Ruiz (aruiz at um dot es)
Stability : provisional
Portability : uses ffi
Minimization of a multidimensional function Minimization of a multidimensional function using some of the algorithms described in:
<http://www.gnu.org/software/gsl/manual/html_node/Multidimensional-Minimization.html>
-}
-----------------------------------------------------------------------------
module Numeric.GSL.Minimization (
minimizeConjugateGradient,
minimizeNMSimplex
) where
import Data.Packed.Internal
import Data.Packed.Matrix
import Foreign
import Foreign.C.Types(CInt)
-------------------------------------------------------------------------
{- | 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:
@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
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"
let it = round (rawpath @@> (maxit-1,0))
path = takeRows it rawpath
[sol] = toLists $ dropRows (it-1) path
freeHaskellFunPtr fp
return (drop 3 sol, path)
foreign import ccall "gsl-aux.h minimize"
c_minimizeNMSimplex:: 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 istep minimpar tol maxit f df xi = unsafePerformIO $ do
let xiv = fromList xi
n = dim xiv
f' = f . toList
df' = (fromList . df . toList)
fp <- mkVecfun (iv f')
dfp <- mkVecVecfun (aux_vTov df')
rawpath <- withVector xiv $ \xiv' ->
createMIO maxit (n+2)
(c_minimizeConjugateGradient fp dfp istep minimpar tol (fi maxit) // xiv')
"minimizeDerivV"
let it = round (rawpath @@> (maxit-1,0))
path = takeRows it rawpath
sol = toList $ cdat $ dropColumns 2 $ dropRows (it-1) path
freeHaskellFunPtr fp
freeHaskellFunPtr dfp
return (sol,path)
foreign import ccall "gsl-aux.h minimizeWithDeriv"
c_minimizeConjugateGradient :: FunPtr (CInt -> Ptr Double -> Double)
-> FunPtr (CInt -> Ptr Double -> Ptr Double -> IO ())
-> Double -> Double -> Double -> CInt
-> TVM
---------------------------------------------------------------------
iv :: (Vector Double -> Double) -> (CInt -> Ptr Double -> Double)
iv f n p = f (createV (fromIntegral n) copy "iv") where
copy n' q = do
copyArray q p (fromIntegral n')
return 0
-- | conversion of Haskell functions into function pointers that can be used in the C side
foreign import ccall "wrapper"
mkVecfun :: (CInt -> Ptr Double -> Double)
-> IO( FunPtr (CInt -> Ptr Double -> Double))
-- | another required conversion
foreign import ccall "wrapper"
mkVecVecfun :: (CInt -> Ptr Double -> Ptr Double -> IO ())
-> IO (FunPtr (CInt -> Ptr Double -> Ptr Double->IO()))
aux_vTov :: (Vector Double -> Vector Double) -> (CInt -> Ptr Double -> Ptr Double -> IO())
aux_vTov f n p r = g where
V {fptr = pr} = f x
x = createV (fromIntegral n) copy "aux_vTov"
copy n' q = do
copyArray q p (fromIntegral n')
return 0
g = withForeignPtr pr $ \p' -> copyArray r p' (fromIntegral n)
--------------------------------------------------------------------
createV n fun msg = unsafePerformIO $ do
r <- createVector n
app1 fun vec r msg
return r
createMIO r c fun msg = do
res <- createMatrix RowMajor r c
app1 fun mat res msg
return res
|
