snobfit.tests.test

1 """ Unit tests for Snobfit 2 Author: Ziwen Fu 3 Nov 2008 4 """ 5 6 import unittest 7 import numpy 8 try: 9 from snobfit.snobfit import snobfit 10 except: 11 from snobfit import snobfit 12

13 -def ros(x):

14 f = 100*( x[0]**2 - x[1] ) **2 + (x[0] - 1) **2 15 return f

16 17

18 -def bra(x):

19 20 a=1 21 b=5.1/(4*numpy.pi*numpy.pi) 22 c=5/numpy.pi 23 d=6 24 h=10 25 ff=1/(8*numpy.pi) 26 27 x1 = x[0] 28 x2 = x[1] 29 30 f = a * (x2-b * x1 **2 + c*x1-d )**2 + \ 31 h* (1-ff) * numpy.cos(x1) + h 32 33 return f

34

35 -def cam(x):

36 f = ( 4- 2.1 * x[0]**2 + x[0]**4 /3 ) * x[0]**2 + \ 37 x[0] * x[1] + \ 38 (-4 + 4.0 * x[1]**2 ) * x[1]**2 39 return f

40

41 -def gpr(x,y=None):

42 if y == None: 43 x1 = x[0] 44 x2 = x[1] 45 else: 46 x1 = x 47 x2 = y 48 49 f =( 1+ (x1+x2+1)**2 *(19-14*x1+3*x1**2 - 14*x2 + 6*x1*x2 + 3*x2**22) ) * \ 50 ( 30+(2*x1-3*x2)**2 * (18-32*x1 + 12*x1**2 + 48*x2 - \ 51 36*x1*x2 + 27*x2**2) ) 52 53 return f

54 55

56 -def sh5(x):

57 a = numpy.array( [[4.0, 1.0, 8.0, 6.0, 3.0], 58 [4.0, 1.0, 8.0, 6.0, 7.0], 59 [4.0, 1.0, 8.0, 6.0, 3.0], 60 [4.0, 1.0, 8.0, 6.0, 7.0]]) 61 c = numpy.array( [0.1, 0.2, 0.2, 0.4, 0.4] ) 62 d = numpy.zeros(5) 63 for i in xrange(5): 64 b = ( x - a[:,i] ) ** 2 65 d[i] = sum(b) 66 67 f = -sum( (c+d) ** (-1) ) 68 69 return f

70 71

72 -def sh7(x):

73 a = numpy.array( [[4, 1, 8, 6, 3, 2, 5], 74 [4, 1, 8, 6, 7, 9, 5], 75 [4, 1, 8, 6, 3, 2, 3], 76 [4, 1, 8, 6, 7, 9, 3]] 77 ) 78 c = numpy.array([0.1, 0.2, 0.2, 0.4, 0.4, 0.6, 0.3]) 79 d = numpy.zeros(a.shape[1]) 80 for i in xrange(7): 81 b = ( x - a[:,i] ) **2 82 d[i] = sum(b) 83 84 f = -sum( (c+d)**(-1) ) 85 return f

86 87

88 -def sh10(x):

89 a = numpy.array([[4, 1, 8, 6, 3, 2, 5, 8, 6, 7], 90 [4, 1, 8, 6, 7, 9, 5, 1, 2, 3.6], 91 [4, 1, 8, 6, 3, 2, 3, 8, 6, 7], 92 [4, 1, 8, 6, 7, 9, 3, 1, 2, 3.6]]) 93 c = numpy.array( [0.1, 0.2, 0.2, 0.4, 0.4, 0.6, 0.3, 0.7, 0.5, 0.5] ) 94 95 d = numpy.zeros(10) 96 for i in xrange(10): 97 b = ( x - a[:,i] ) ** 2 98 d[i] = numpy.sum(b) 99 100 f = -numpy.sum( (c+d)**(-1) ) 101 102 return f

103 104

105 -def hm3(x):

106 a = numpy.array([[3.0, 0.1, 3.0, 0.1], 107 [10.0, 10.0, 10.0, 10.0], 108 [30.0, 35.0, 30.0, 35.0]]) 109 110 p = numpy.array( [[ 0.36890, 0.46990, 0.10910, 0.03815], 111 [ 0.11700, 0.43870, 0.87320, 0.57430], 112 [ 0.26730, 0.74700, 0.55470, 0.88280]]) 113 114 c = numpy.array( [1.0, 1.2, 3.0, 3.2] ) 115 d = numpy.zeros(4) 116 for i in xrange(4): 117 d[i] = sum( a[:,i] * ( x - p[:,i]) **2 ) 118 119 f = -sum( c * numpy.exp( -d ) ) 120 121 return f

122 123

124 -def hm6(x):

125 a = numpy.array([[ 10.00, 0.05, 3.00, 17.00], 126 [ 3.00, 10.00, 3.50, 8.00], 127 [ 17.00, 17.00, 1.70, 0.05], 128 [ 3.50, 0.10, 10.00, 10.00], 129 [ 1.70, 8.00, 17.00, 0.10], 130 [ 8.00, 14.00, 8.00, 14.00]]) 131 132 p = numpy.array([[ 0.1312, 0.2329, 0.2348, 0.4047], 133 [ 0.1696, 0.4135, 0.1451, 0.8828], 134 [ 0.5569, 0.8307, 0.3522, 0.8732], 135 [ 0.0124, 0.3736, 0.2883, 0.5743], 136 [ 0.8283, 0.1004, 0.3047, 0.1091], 137 [ 0.5886, 0.9991, 0.6650, 0.0381]]) 138 139 c = numpy.array( [1.0, 1.2, 3.0, 3.2] ) 140 141 d = numpy.zeros(4) 142 for i in xrange(4): 143 d[i] = numpy.sum( a[:,i] * ( x - p[:,i] ) **2 ) 144 145 f = -numpy.sum( c*numpy.exp(-d)); 146 147 return f

148

149 -def shu(x):

150 # Shubert function 151 sum1 = 0 152 sum2 = 0 153 for i in range(1,6): 154 sum1 += i * numpy.cos( (i+1) * x[0] + i ) 155 sum2 += i * numpy.cos( (i+1) * x[1] + i ); 156 157 f = sum1*sum2 158 return f

159 160 161 # ---------------------------------------------------------------------

162 -class test_Snobfit(unittest.TestCase):

163

164 - def setUp(self):

165 pass

166

167 - def test_bra(self):

168 u = numpy.array( [-5, 0]) 169 v = numpy.array( [10, 15] ) 170 x0 = numpy.array( [2,3] ) 171 fglob = 0.397887357729739 172 xglob = numpy.array( [[9.42477796, -3.14159265, 3.14159265], 173 [2.47499998, 12.27500000, 2.27500000]] ) 174 175 xbest, fbest, ncall = snobfit(bra, x0, (u, v), fglob=fglob) 176 assert abs(fbest-fglob) < 1.0e-6

177

178 - def test_ros(self):

179 """ Rosenbrock """ 180 x0 = numpy.array([2, 3]) 181 u = -5.12*numpy.ones(2) 182 v = -u 183 fglob = 0 184 xglob = numpy.array([1, 1]) 185 xbest, fbest, ncall = snobfit(ros, x0, (u, v)) 186 # print 'optimize:',xbest, fbest, ncall 187 188 assert abs(fbest) < 1.0e-6

189

190 - def test_cam(self):

191 # six-hump camel 192 u = numpy.array([-3, -2]) 193 v = numpy.array([3, 2] ) 194 x0 = numpy.array([1, 1]) 195 fglob = -1.0316284535 196 xglob = numpy.array([ 0.08984201, -0.08984201, 197 -0.71265640, 0.71265640]) 198 xbest, fbest, ncall = snobfit(cam, x0, (u, v), fglob=fglob) 199 200 assert abs(fbest-fglob) < 1.0e-6

201 202

203 - def test_sh5(self):

204 # Shekel 5 205 u = numpy.array([0, 0, 0, 0]) 206 v = numpy.array([10, 10, 10, 10] ) 207 x0 = numpy.array([5, 5,5,5]) 208 fglob = -10.1531996790582 209 xglob = numpy.array([4, 4, 4, 4]) 210 xbest, fbest, ncall = snobfit(sh5, x0, (u, v), fglob=fglob) 211 212 assert abs(fbest-fglob) < 1.0e-6

213 214 215

216 - def test_sh7(self):

217 #Shekel 7 218 u = numpy.array([0, 0, 0, 0]) 219 v = numpy.array([10, 10, 10, 10]) 220 x0 = numpy.array([5, 5,5,5]) 221 fglob = -10.4029405668187 222 xglob = numpy.array([4, 4, 4, 4]) 223 xbest, fbest, ncall = snobfit(sh7, x0, (u, v), fglob=fglob) 224 225 assert abs(fbest-fglob) < 1.0e-6

226 227

228 - def test_sh10(self):

229 #Shekel 7 230 u = numpy.array([0, 0, 0, 0]) 231 v = numpy.array([10, 10, 10, 10]) 232 x0 = numpy.array([5, 5,5,5]) 233 fglob = -10.5364098166920 234 xglob = numpy.array([4, 4, 4, 4]) 235 xbest, fbest, ncall = snobfit(sh10, x0, (u, v), fglob=fglob) 236 237 assert abs(fbest-fglob) < 1.0e-6

238 239

240 - def test_hm3(self):

241 # Hartman 3 242 u = numpy.array([0, 0, 0]) 243 v = numpy.array([1, 1, 1]) 244 x0 = numpy.array([0.5, 0.5,0.5]) 245 fglob = -3.86278214782076 246 xglob = numpy.array([0.1, 0.55592003, 0.85218259]) 247 xbest, fbest, ncall = snobfit(hm3, x0, (u, v), fglob=fglob) 248 249 assert abs(fbest-fglob) < 1.0e-6

250 251

252 - def test_hm6(self):

253 # Hartman 6 254 u = numpy.array([0, 0, 0, 0, 0, 0]) 255 v = numpy.array([1, 1, 1, 1, 1, 1]) 256 x0 = numpy.array([0.5, 0.5,0.5,0.5,0.5,0.5]) 257 fglob = -3.32236801141551 258 xglob = numpy.array([0.20168952, 0.15001069, 0.47687398, 259 0.27533243, 0.31165162, 0.65730054]) 260 xbest, fbest, ncall = snobfit(hm6, x0, (u, v), fglob=fglob) 261 262 assert abs( (fbest-fglob)/fglob ) < 1.0e-6

263

264 - def test_shu(self):

265 # Shubert 266 u = numpy.array([-10, -10]) 267 v = numpy.array([10, 10]) 268 x0 = numpy.array([1, 1]) 269 fglob = -186.730908831024 270 xglob = numpy.array([[ -7.08350658, 5.48286415, 4.85805691, 271 4.85805691, -7.08350658, -7.70831382, 272 -1.42512845, -0.80032121, -1.42512844, 273 -7.08350639, -7.70831354, 5.48286415, 274 5.48286415, 4.85805691, -7.70831354, 275 -0.80032121, -1.42512845, -0.80032121], 276 [4.85805691, 4.85805681, -7.08350658, 277 5.48286415, -7.70831382, -7.08350658, 278 -0.80032121, -1.42512845, -7.08350639, 279 -1.42512844, 5.48286415, -7.70831354, 280 4.85805691, 5.48286415, -0.80032121, 281 -7.70831354, -0.80032121, -1.42512845]]) 282 283 xbest, fbest, ncall = snobfit(shu, x0, (u, v), fglob=fglob) 284 assert abs( (fbest-fglob)/fglob ) < 1.0e-6

285 286 287 288 #--------------------------------------------- 289 if __name__ == '__main__': 290 unittest.main() 291

Source Code for Module snobfit.tests.test_Snobfit