| 1 | #!/usr/bin/env python |
|---|
| 2 | |
|---|
| 3 | import unittest |
|---|
| 4 | from math import sqrt |
|---|
| 5 | |
|---|
| 6 | from least_squares import * |
|---|
| 7 | from Numeric import allclose, array, transpose |
|---|
| 8 | |
|---|
| 9 | def distance(x, y): |
|---|
| 10 | return sqrt( sum( (array(x)-array(y))**2 )) |
|---|
| 11 | |
|---|
| 12 | def linear_function(point): |
|---|
| 13 | point = array(point) |
|---|
| 14 | return point[:,0]+point[:,1] |
|---|
| 15 | |
|---|
| 16 | |
|---|
| 17 | class TestCase(unittest.TestCase): |
|---|
| 18 | |
|---|
| 19 | def setUp(self): |
|---|
| 20 | pass |
|---|
| 21 | |
|---|
| 22 | def tearDown(self): |
|---|
| 23 | pass |
|---|
| 24 | |
|---|
| 25 | |
|---|
| 26 | def test_datapoint_at_centroid(self): |
|---|
| 27 | a = [0.0, 0.0] |
|---|
| 28 | b = [0.0, 2.0] |
|---|
| 29 | c = [2.0,0.0] |
|---|
| 30 | points = [a, b, c] |
|---|
| 31 | vertices = [ [1,0,2] ] #bac |
|---|
| 32 | |
|---|
| 33 | data = [ [2.0/3, 2.0/3] ] #Use centroid as one data point |
|---|
| 34 | |
|---|
| 35 | interp = Interpolation(points, vertices, data) |
|---|
| 36 | assert allclose(interp.get_A(), [[1./3, 1./3, 1./3]]) |
|---|
| 37 | |
|---|
| 38 | |
|---|
| 39 | |
|---|
| 40 | def test_datapoints_at_vertices(self): |
|---|
| 41 | """Test that data points coinciding with vertices yield a diagonal matrix |
|---|
| 42 | """ |
|---|
| 43 | print "aa" |
|---|
| 44 | a = [0.0, 0.0] |
|---|
| 45 | b = [0.0, 2.0] |
|---|
| 46 | c = [2.0,0.0] |
|---|
| 47 | points = [a, b, c] |
|---|
| 48 | vertices = [ [1,0,2] ] #bac |
|---|
| 49 | |
|---|
| 50 | data = points #Use data at vertices |
|---|
| 51 | |
|---|
| 52 | interp = Interpolation(points, vertices, data) |
|---|
| 53 | assert allclose(interp.get_A(), [[1., 0., 0.], |
|---|
| 54 | [0., 1., 0.], |
|---|
| 55 | [0., 0., 1.]]) |
|---|
| 56 | |
|---|
| 57 | |
|---|
| 58 | |
|---|
| 59 | def test_datapoints_on_edge_midpoints(self): |
|---|
| 60 | """Try datapoints midway on edges - |
|---|
| 61 | each point should affect two matrix entries equally |
|---|
| 62 | """ |
|---|
| 63 | print "bb" |
|---|
| 64 | |
|---|
| 65 | a = [0.0, 0.0] |
|---|
| 66 | b = [0.0, 2.0] |
|---|
| 67 | c = [2.0,0.0] |
|---|
| 68 | points = [a, b, c] |
|---|
| 69 | vertices = [ [1,0,2] ] #bac |
|---|
| 70 | |
|---|
| 71 | data = [ [0., 1.], [1., 0.], [1., 1.] ] |
|---|
| 72 | |
|---|
| 73 | interp = Interpolation(points, vertices, data) |
|---|
| 74 | |
|---|
| 75 | assert allclose(interp.get_A(), [[0.5, 0.5, 0.0], #Affects vertex 1 and 0 |
|---|
| 76 | [0.5, 0.0, 0.5], #Affects vertex 0 and 2 |
|---|
| 77 | [0.0, 0.5, 0.5]]) #Affects vertex 1 and 2 |
|---|
| 78 | |
|---|
| 79 | |
|---|
| 80 | def test_datapoints_on_edges(self): |
|---|
| 81 | """Try datapoints on edges - |
|---|
| 82 | each point should affect two matrix entries in proportion |
|---|
| 83 | """ |
|---|
| 84 | print "cc" |
|---|
| 85 | |
|---|
| 86 | a = [0.0, 0.0] |
|---|
| 87 | b = [0.0, 2.0] |
|---|
| 88 | c = [2.0,0.0] |
|---|
| 89 | points = [a, b, c] |
|---|
| 90 | vertices = [ [1,0,2] ] #bac |
|---|
| 91 | |
|---|
| 92 | data = [ [0., 1.5], [1.5, 0.], [1.5, 0.5] ] |
|---|
| 93 | |
|---|
| 94 | interp = Interpolation(points, vertices, data) |
|---|
| 95 | |
|---|
| 96 | assert allclose(interp.get_A(), [[0.25, 0.75, 0.0], #Affects vertex 1 and 0 |
|---|
| 97 | [0.25, 0.0, 0.75], #Affects vertex 0 and 2 |
|---|
| 98 | [0.0, 0.25, 0.75]]) #Affects vertex 1 and 2 |
|---|
| 99 | |
|---|
| 100 | def test_arbitrary_datapoints(self): |
|---|
| 101 | """Try arbitrary datapoints |
|---|
| 102 | """ |
|---|
| 103 | |
|---|
| 104 | from Numeric import sum |
|---|
| 105 | |
|---|
| 106 | a = [0.0, 0.0] |
|---|
| 107 | b = [0.0, 2.0] |
|---|
| 108 | c = [2.0,0.0] |
|---|
| 109 | points = [a, b, c] |
|---|
| 110 | vertices = [ [1,0,2] ] #bac |
|---|
| 111 | |
|---|
| 112 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44] ] |
|---|
| 113 | |
|---|
| 114 | interp = Interpolation(points, vertices, data) |
|---|
| 115 | |
|---|
| 116 | assert allclose(sum(interp.get_A(), axis=1), 1.0) |
|---|
| 117 | |
|---|
| 118 | |
|---|
| 119 | # this causes a memory error in scipy.sparce |
|---|
| 120 | def bad_test_more_triangles(self): |
|---|
| 121 | print "dd" |
|---|
| 122 | a = [-1.0, 0.0] |
|---|
| 123 | b = [3.0, 4.0] |
|---|
| 124 | c = [4.0,1.0] |
|---|
| 125 | d = [-3.0, 2.0] #3 |
|---|
| 126 | e = [-1.0,-2.0] |
|---|
| 127 | f = [1.0, -2.0] #5 |
|---|
| 128 | |
|---|
| 129 | points = [a, b, c, d,e,f] |
|---|
| 130 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 131 | |
|---|
| 132 | #Data points |
|---|
| 133 | data_points = [ [-3., 1.9], [-2, 1], [0.0, 1], [0, 3], [2, 3], [-1.0/3,-4./3] ] |
|---|
| 134 | interp = Interpolation(points, triangles, data_points) |
|---|
| 135 | |
|---|
| 136 | answer = [[0.0, 0.0, 0.0, 1.0, 0.0, 0.0], #Affects point d |
|---|
| 137 | [0.5, 0.0, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
|---|
| 138 | [0.75, 0.25, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
|---|
| 139 | [0.0, 0.5, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
|---|
| 140 | [0.25, 0.75, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
|---|
| 141 | [1./3, 0.0, 0.0, 0.0, 1./3, 1./3]] #Affects points a,e and f |
|---|
| 142 | |
|---|
| 143 | assert allclose(interp.get_A(), answer) |
|---|
| 144 | |
|---|
| 145 | |
|---|
| 146 | |
|---|
| 147 | |
|---|
| 148 | def test_smooth_attributes_to_mesh(self): |
|---|
| 149 | print "ee" |
|---|
| 150 | a = [0.0, 0.0] |
|---|
| 151 | b = [0.0, 5.0] |
|---|
| 152 | c = [5.0, 0.0] |
|---|
| 153 | points = [a, b, c] |
|---|
| 154 | triangles = [ [1,0,2] ] #bac |
|---|
| 155 | |
|---|
| 156 | d1 = [1.0, 1.0] |
|---|
| 157 | d2 = [1.0, 3.0] |
|---|
| 158 | d3 = [3.0,1.0] |
|---|
| 159 | z1 = 2 |
|---|
| 160 | z2 = 4 |
|---|
| 161 | z3 = 4 |
|---|
| 162 | data_coords = [d1, d2, d3] |
|---|
| 163 | |
|---|
| 164 | interp = Interpolation(points, triangles, data_coords, alpha=5.0e-7) |
|---|
| 165 | z = [z1, z2, z3] |
|---|
| 166 | f = interp.fit(z) |
|---|
| 167 | answer = [0, 5., 5.] |
|---|
| 168 | assert allclose(f, answer) |
|---|
| 169 | |
|---|
| 170 | |
|---|
| 171 | def test_smooth_att_to_meshII(self): |
|---|
| 172 | print "ff" |
|---|
| 173 | a = [0.0, 0.0] |
|---|
| 174 | b = [0.0, 5.0] |
|---|
| 175 | c = [5.0, 0.0] |
|---|
| 176 | points = [a, b, c] |
|---|
| 177 | triangles = [ [1,0,2] ] #bac |
|---|
| 178 | |
|---|
| 179 | d1 = [1.0, 1.0] |
|---|
| 180 | d2 = [1.0, 2.0] |
|---|
| 181 | d3 = [3.0,1.0] |
|---|
| 182 | data_coords = [d1, d2, d3] |
|---|
| 183 | z = linear_function(data_coords) |
|---|
| 184 | interp = Interpolation(points, triangles, data_coords, alpha=0.0) |
|---|
| 185 | f = interp.fit(z) |
|---|
| 186 | answer = linear_function(points) |
|---|
| 187 | |
|---|
| 188 | assert allclose(f, answer) |
|---|
| 189 | |
|---|
| 190 | def test_smooth_attributes_to_meshIII(self): |
|---|
| 191 | print "gg" |
|---|
| 192 | a = [-1.0, 0.0] |
|---|
| 193 | b = [3.0, 4.0] |
|---|
| 194 | c = [4.0,1.0] |
|---|
| 195 | d = [-3.0, 2.0] #3 |
|---|
| 196 | e = [-1.0,-2.0] |
|---|
| 197 | f = [1.0, -2.0] #5 |
|---|
| 198 | |
|---|
| 199 | vertices = [a, b, c, d,e,f] |
|---|
| 200 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 201 | |
|---|
| 202 | point_coords = [[-2.0, 2.0], |
|---|
| 203 | [-1.0, 1.0], |
|---|
| 204 | [0.0,2.0], |
|---|
| 205 | [1.0, 1.0], |
|---|
| 206 | [2.0, 1.0], |
|---|
| 207 | [0.0,0.0], |
|---|
| 208 | [1.0, 0.0], |
|---|
| 209 | [0.0, -1.0], |
|---|
| 210 | [-0.2,-0.5], |
|---|
| 211 | [-0.9, -1.5], |
|---|
| 212 | [0.5, -1.9], |
|---|
| 213 | [3.0,1.0]] |
|---|
| 214 | |
|---|
| 215 | z = linear_function(point_coords) |
|---|
| 216 | interp = Interpolation(vertices, triangles, point_coords, alpha=0.0) |
|---|
| 217 | f = interp.fit(z) |
|---|
| 218 | answer = linear_function(vertices) |
|---|
| 219 | assert allclose(f, answer) |
|---|
| 220 | |
|---|
| 221 | |
|---|
| 222 | def test_smooth_attributes_to_meshIV(self): |
|---|
| 223 | print "hh" |
|---|
| 224 | """ Testing 2 attributes smoothed to the mesh |
|---|
| 225 | """ |
|---|
| 226 | print "test_smooth_attributes_to_meshIV" |
|---|
| 227 | a = [0.0, 0.0] |
|---|
| 228 | b = [0.0, 5.0] |
|---|
| 229 | c = [5.0, 0.0] |
|---|
| 230 | points = [a, b, c] |
|---|
| 231 | triangles = [ [1,0,2] ] #bac |
|---|
| 232 | |
|---|
| 233 | d1 = [1.0, 1.0] |
|---|
| 234 | d2 = [1.0, 3.0] |
|---|
| 235 | d3 = [3.0,1.0] |
|---|
| 236 | z1 = [2,4] |
|---|
| 237 | z2 = [4,8] |
|---|
| 238 | z3 = [4,8] |
|---|
| 239 | data_coords = [ d1, d2, d3] |
|---|
| 240 | |
|---|
| 241 | interp = Interpolation(points, triangles, data_coords, alpha=0.0) |
|---|
| 242 | z = [z1, z2, z3] |
|---|
| 243 | f = interp.fit(z) |
|---|
| 244 | answer = [[0,0], [5., 10.], [5., 10.]] |
|---|
| 245 | assert allclose(f, answer) |
|---|
| 246 | |
|---|
| 247 | def test_interpolate_attributes_to_points(self): |
|---|
| 248 | v0 = [0.0, 0.0] |
|---|
| 249 | v1 = [0.0, 5.0] |
|---|
| 250 | v2 = [5.0, 0.0] |
|---|
| 251 | |
|---|
| 252 | vertices = [v0, v1, v2] |
|---|
| 253 | triangles = [ [1,0,2] ] #bac |
|---|
| 254 | |
|---|
| 255 | d0 = [1.0, 1.0] |
|---|
| 256 | d1 = [1.0, 2.0] |
|---|
| 257 | d2 = [3.0,1.0] |
|---|
| 258 | point_coords = [ d0, d1, d2] |
|---|
| 259 | |
|---|
| 260 | interp = Interpolation(vertices, triangles, point_coords) |
|---|
| 261 | f = linear_function(vertices) |
|---|
| 262 | z = interp.interpolate(f) |
|---|
| 263 | answer = linear_function(point_coords) |
|---|
| 264 | |
|---|
| 265 | |
|---|
| 266 | assert allclose(z, answer) |
|---|
| 267 | |
|---|
| 268 | |
|---|
| 269 | def test_interpolate_attributes_to_pointsII(self): |
|---|
| 270 | a = [-1.0, 0.0] |
|---|
| 271 | b = [3.0, 4.0] |
|---|
| 272 | c = [4.0,1.0] |
|---|
| 273 | d = [-3.0, 2.0] #3 |
|---|
| 274 | e = [-1.0,-2.0] |
|---|
| 275 | f = [1.0, -2.0] #5 |
|---|
| 276 | |
|---|
| 277 | vertices = [a, b, c, d,e,f] |
|---|
| 278 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 279 | |
|---|
| 280 | |
|---|
| 281 | point_coords = [[-2.0, 2.0], |
|---|
| 282 | [-1.0, 1.0], |
|---|
| 283 | [0.0,2.0], |
|---|
| 284 | [1.0, 1.0], |
|---|
| 285 | [2.0, 1.0], |
|---|
| 286 | [0.0,0.0], |
|---|
| 287 | [1.0, 0.0], |
|---|
| 288 | [0.0, -1.0], |
|---|
| 289 | [-0.2,-0.5], |
|---|
| 290 | [-0.9, -1.5], |
|---|
| 291 | [0.5, -1.9], |
|---|
| 292 | [3.0,1.0]] |
|---|
| 293 | |
|---|
| 294 | interp = Interpolation(vertices, triangles, point_coords) |
|---|
| 295 | f = linear_function(vertices) |
|---|
| 296 | z = interp.interpolate(f) |
|---|
| 297 | answer = linear_function(point_coords) |
|---|
| 298 | #print "z",z |
|---|
| 299 | #print "answer",answer |
|---|
| 300 | assert allclose(z, answer) |
|---|
| 301 | |
|---|
| 302 | def test_interpolate_attributes_to_pointsIII(self): |
|---|
| 303 | v0 = [0.0, 0.0] |
|---|
| 304 | v1 = [0.0, 5.0] |
|---|
| 305 | v2 = [5.0, 0.0] |
|---|
| 306 | |
|---|
| 307 | vertices = [v0, v1, v2] |
|---|
| 308 | triangles = [ [1,0,2] ] #bac |
|---|
| 309 | |
|---|
| 310 | d0 = [1.0, 1.0] |
|---|
| 311 | d1 = [1.0, 2.0] |
|---|
| 312 | d2 = [3.0,1.0] |
|---|
| 313 | point_coords = [ d0, d1, d2] |
|---|
| 314 | |
|---|
| 315 | interp = Interpolation(vertices, triangles, point_coords) |
|---|
| 316 | f = [ [0., 0.], [5., 10.], [5., 10.]] #linear_function(vertices) |
|---|
| 317 | #print "f",f |
|---|
| 318 | |
|---|
| 319 | z = interp.interpolate(f) |
|---|
| 320 | answer = [ [2., 4.], [3., 6.], [4., 8.]] |
|---|
| 321 | |
|---|
| 322 | #print "***********" |
|---|
| 323 | #print "z",z |
|---|
| 324 | #print "answer",answer |
|---|
| 325 | #print "***********" |
|---|
| 326 | |
|---|
| 327 | assert allclose(z, answer) |
|---|
| 328 | |
|---|
| 329 | def test_interpolate_attributes_to_pointsIV(self): |
|---|
| 330 | a = [-1.0, 0.0] |
|---|
| 331 | b = [3.0, 4.0] |
|---|
| 332 | c = [4.0,1.0] |
|---|
| 333 | d = [-3.0, 2.0] #3 |
|---|
| 334 | e = [-1.0,-2.0] |
|---|
| 335 | f = [1.0, -2.0] #5 |
|---|
| 336 | |
|---|
| 337 | vertices = [a, b, c, d,e,f] |
|---|
| 338 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 339 | |
|---|
| 340 | |
|---|
| 341 | point_coords = [[-2.0, 2.0], |
|---|
| 342 | [-1.0, 1.0], |
|---|
| 343 | [0.0,2.0], |
|---|
| 344 | [1.0, 1.0], |
|---|
| 345 | [2.0, 1.0], |
|---|
| 346 | [0.0,0.0], |
|---|
| 347 | [1.0, 0.0], |
|---|
| 348 | [0.0, -1.0], |
|---|
| 349 | [-0.2,-0.5], |
|---|
| 350 | [-0.9, -1.5], |
|---|
| 351 | [0.5, -1.9], |
|---|
| 352 | [3.0,1.0]] |
|---|
| 353 | |
|---|
| 354 | interp = Interpolation(vertices, triangles, point_coords) |
|---|
| 355 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 356 | f = transpose(f) |
|---|
| 357 | #print "f",f |
|---|
| 358 | z = interp.interpolate(f) |
|---|
| 359 | answer = [linear_function(point_coords), |
|---|
| 360 | |
|---|
| 361 | 2*linear_function(point_coords) ] |
|---|
| 362 | answer = transpose(answer) |
|---|
| 363 | #print "z",z |
|---|
| 364 | #print "answer",answer |
|---|
| 365 | assert allclose(z, answer) |
|---|
| 366 | |
|---|
| 367 | def test_smooth_attributes_to_mesh_function(self): |
|---|
| 368 | """ Testing 2 attributes smoothed to the mesh |
|---|
| 369 | """ |
|---|
| 370 | """Test multiple attributes |
|---|
| 371 | """ |
|---|
| 372 | |
|---|
| 373 | a = [0.0, 0.0] |
|---|
| 374 | b = [0.0, 5.0] |
|---|
| 375 | c = [5.0, 0.0] |
|---|
| 376 | points = [a, b, c] |
|---|
| 377 | triangles = [ [1,0,2] ] #bac |
|---|
| 378 | |
|---|
| 379 | d1 = [1.0, 1.0] |
|---|
| 380 | d2 = [1.0, 3.0] |
|---|
| 381 | d3 = [3.0,1.0] |
|---|
| 382 | z1 = [2,4] |
|---|
| 383 | z2 = [4,8] |
|---|
| 384 | z3 = [4,8] |
|---|
| 385 | data_coords = [ d1, d2, d3] |
|---|
| 386 | z = [z1, z2, z3] |
|---|
| 387 | |
|---|
| 388 | f = fit_to_mesh(points, triangles, data_coords, z, alpha=0.0) |
|---|
| 389 | answer = [[0, 0], [5., 10.], [5., 10.]] |
|---|
| 390 | |
|---|
| 391 | assert allclose(f, answer) |
|---|
| 392 | |
|---|
| 393 | |
|---|
| 394 | |
|---|
| 395 | #Tests of smoothing matrix |
|---|
| 396 | def test_smoothing_matrix_one_triangle(self): |
|---|
| 397 | from Numeric import dot |
|---|
| 398 | a = [0.0, 0.0] |
|---|
| 399 | b = [0.0, 2.0] |
|---|
| 400 | c = [2.0,0.0] |
|---|
| 401 | points = [a, b, c] |
|---|
| 402 | |
|---|
| 403 | vertices = [ [1,0,2] ] #bac |
|---|
| 404 | |
|---|
| 405 | interp = Interpolation(points, vertices) |
|---|
| 406 | |
|---|
| 407 | assert allclose(interp.get_D(), [[1, -0.5, -0.5], |
|---|
| 408 | [-0.5, 0.5, 0], |
|---|
| 409 | [-0.5, 0, 0.5]]) |
|---|
| 410 | |
|---|
| 411 | #Define f(x,y) = x |
|---|
| 412 | f = array([0,0,2]) #Value at global vertex 2 |
|---|
| 413 | |
|---|
| 414 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
|---|
| 415 | # int 1 dx dy = area = 2 |
|---|
| 416 | assert dot(dot(f, interp.get_D()), f) == 2 |
|---|
| 417 | |
|---|
| 418 | #Define f(x,y) = y |
|---|
| 419 | f = array([0,2,0]) #Value at global vertex 1 |
|---|
| 420 | |
|---|
| 421 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
|---|
| 422 | # int 1 dx dy = area = 2 |
|---|
| 423 | assert dot(dot(f, interp.get_D()), f) == 2 |
|---|
| 424 | |
|---|
| 425 | #Define f(x,y) = x+y |
|---|
| 426 | f = array([0,2,2]) #Values at global vertex 1 and 2 |
|---|
| 427 | |
|---|
| 428 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
|---|
| 429 | # int 2 dx dy = 2*area = 4 |
|---|
| 430 | assert dot(dot(f, interp.get_D()), f) == 4 |
|---|
| 431 | |
|---|
| 432 | |
|---|
| 433 | |
|---|
| 434 | def test_smoothing_matrix_more_triangles(self): |
|---|
| 435 | from Numeric import dot |
|---|
| 436 | |
|---|
| 437 | a = [0.0, 0.0] |
|---|
| 438 | b = [0.0, 2.0] |
|---|
| 439 | c = [2.0,0.0] |
|---|
| 440 | d = [0.0, 4.0] |
|---|
| 441 | e = [2.0, 2.0] |
|---|
| 442 | f = [4.0,0.0] |
|---|
| 443 | |
|---|
| 444 | points = [a, b, c, d, e, f] |
|---|
| 445 | #bac, bce, ecf, dbe, daf, dae |
|---|
| 446 | vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
|---|
| 447 | |
|---|
| 448 | interp = Interpolation(points, vertices) |
|---|
| 449 | |
|---|
| 450 | |
|---|
| 451 | #assert allclose(interp.get_D(), [[1, -0.5, -0.5], |
|---|
| 452 | # [-0.5, 0.5, 0], |
|---|
| 453 | # [-0.5, 0, 0.5]]) |
|---|
| 454 | |
|---|
| 455 | #Define f(x,y) = x |
|---|
| 456 | f = array([0,0,2,0,2,4]) #f evaluated at points a-f |
|---|
| 457 | |
|---|
| 458 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
|---|
| 459 | # int 1 dx dy = total area = 8 |
|---|
| 460 | assert dot(dot(f, interp.get_D()), f) == 8 |
|---|
| 461 | |
|---|
| 462 | #Define f(x,y) = y |
|---|
| 463 | f = array([0,2,0,4,2,0]) #f evaluated at points a-f |
|---|
| 464 | |
|---|
| 465 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
|---|
| 466 | # int 1 dx dy = area = 8 |
|---|
| 467 | assert dot(dot(f, interp.get_D()), f) == 8 |
|---|
| 468 | |
|---|
| 469 | #Define f(x,y) = x+y |
|---|
| 470 | f = array([0,2,2,4,4,4]) #f evaluated at points a-f |
|---|
| 471 | |
|---|
| 472 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
|---|
| 473 | # int 2 dx dy = 2*area = 16 |
|---|
| 474 | assert dot(dot(f, interp.get_D()), f) == 16 |
|---|
| 475 | |
|---|
| 476 | |
|---|
| 477 | def test_fit_and_interpolation(self): |
|---|
| 478 | from mesh import Mesh |
|---|
| 479 | |
|---|
| 480 | a = [0.0, 0.0] |
|---|
| 481 | b = [0.0, 2.0] |
|---|
| 482 | c = [2.0, 0.0] |
|---|
| 483 | d = [0.0, 4.0] |
|---|
| 484 | e = [2.0, 2.0] |
|---|
| 485 | f = [4.0, 0.0] |
|---|
| 486 | |
|---|
| 487 | points = [a, b, c, d, e, f] |
|---|
| 488 | #bac, bce, ecf, dbe, daf, dae |
|---|
| 489 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
|---|
| 490 | |
|---|
| 491 | #Get (enough) datapoints |
|---|
| 492 | data_points = [[ 0.66666667, 0.66666667], |
|---|
| 493 | [ 1.33333333, 1.33333333], |
|---|
| 494 | [ 2.66666667, 0.66666667], |
|---|
| 495 | [ 0.66666667, 2.66666667], |
|---|
| 496 | [ 0.0, 1.0], |
|---|
| 497 | [ 0.0, 3.0], |
|---|
| 498 | [ 1.0, 0.0], |
|---|
| 499 | [ 1.0, 1.0], |
|---|
| 500 | [ 1.0, 2.0], |
|---|
| 501 | [ 1.0, 3.0], |
|---|
| 502 | [ 2.0, 1.0], |
|---|
| 503 | [ 3.0, 0.0], |
|---|
| 504 | [ 3.0, 1.0]] |
|---|
| 505 | |
|---|
| 506 | interp = Interpolation(points, triangles, data_points, alpha=0.0) |
|---|
| 507 | |
|---|
| 508 | z = linear_function(data_points) |
|---|
| 509 | answer = linear_function(points) |
|---|
| 510 | |
|---|
| 511 | f = interp.fit(z) |
|---|
| 512 | |
|---|
| 513 | assert allclose(f, answer) |
|---|
| 514 | |
|---|
| 515 | #Map back |
|---|
| 516 | z1 = interp.interpolate(f) |
|---|
| 517 | assert allclose(z, z1) |
|---|
| 518 | |
|---|
| 519 | |
|---|
| 520 | def test_smoothing_and_interpolation(self): |
|---|
| 521 | |
|---|
| 522 | a = [0.0, 0.0] |
|---|
| 523 | b = [0.0, 2.0] |
|---|
| 524 | c = [2.0, 0.0] |
|---|
| 525 | d = [0.0, 4.0] |
|---|
| 526 | e = [2.0, 2.0] |
|---|
| 527 | f = [4.0, 0.0] |
|---|
| 528 | |
|---|
| 529 | points = [a, b, c, d, e, f] |
|---|
| 530 | #bac, bce, ecf, dbe, daf, dae |
|---|
| 531 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
|---|
| 532 | |
|---|
| 533 | #Get (too few!) datapoints |
|---|
| 534 | data_points = [[ 0.66666667, 0.66666667], |
|---|
| 535 | [ 1.33333333, 1.33333333], |
|---|
| 536 | [ 2.66666667, 0.66666667], |
|---|
| 537 | [ 0.66666667, 2.66666667]] |
|---|
| 538 | |
|---|
| 539 | z = linear_function(data_points) |
|---|
| 540 | answer = linear_function(points) |
|---|
| 541 | |
|---|
| 542 | #Make interpolator with too few data points and no smoothing |
|---|
| 543 | interp = Interpolation(points, triangles, data_points, alpha=0.0) |
|---|
| 544 | #Must raise an exception |
|---|
| 545 | try: |
|---|
| 546 | f = interp.fit(z) |
|---|
| 547 | except: |
|---|
| 548 | pass |
|---|
| 549 | |
|---|
| 550 | #Now try with smoothing parameter |
|---|
| 551 | interp = Interpolation(points, triangles, data_points, alpha=1.0e-13) |
|---|
| 552 | |
|---|
| 553 | f = interp.fit(z) |
|---|
| 554 | |
|---|
| 555 | #f will be different from answerr due to smoothing |
|---|
| 556 | #assert allclose(f, answer) |
|---|
| 557 | |
|---|
| 558 | #Map back |
|---|
| 559 | z1 = interp.interpolate(f) |
|---|
| 560 | assert allclose(z, z1) |
|---|
| 561 | |
|---|
| 562 | def test_fit_to_mesh_file(self): |
|---|
| 563 | from load_mesh.loadASCII import mesh_file_to_mesh_dictionary, \ |
|---|
| 564 | export_trianglulation_file |
|---|
| 565 | import tempfile |
|---|
| 566 | import os |
|---|
| 567 | |
|---|
| 568 | # create a .tsh file, no user outline |
|---|
| 569 | mesh_dic = {} |
|---|
| 570 | mesh_dic['generatedpointlist'] = [[0.0, 0.0], |
|---|
| 571 | [0.0, 5.0], |
|---|
| 572 | [5.0, 0.0]] |
|---|
| 573 | mesh_dic['generatedtrianglelist'] = [[0, 2, 1]] |
|---|
| 574 | mesh_dic['generatedsegmentlist'] = [[0, 1], [2, 0], [1, 2]] |
|---|
| 575 | mesh_dic['generatedtriangleattributelist'] = [['']] |
|---|
| 576 | mesh_dic['generatedpointattributelist'] = [[], [], []] |
|---|
| 577 | mesh_dic['generatedpointattributetitlelist'] = [] |
|---|
| 578 | mesh_dic['generatedtriangleneighborlist'] = [[-1, -1, -1]] |
|---|
| 579 | mesh_dic['generatedsegmentmarkerlist'] = ['external', |
|---|
| 580 | 'external', |
|---|
| 581 | 'external'] |
|---|
| 582 | mesh_file = tempfile.mktemp(".tsh") |
|---|
| 583 | export_trianglulation_file(mesh_file,mesh_dic) |
|---|
| 584 | |
|---|
| 585 | # create an .xya file |
|---|
| 586 | point_file = tempfile.mktemp(".xya") |
|---|
| 587 | fd = open(point_file,'w') |
|---|
| 588 | fd.write("elevation, stage \n 1.0, 1.0,2.,4 \n 1.0, 3.0,4,8 \n 3.0,1.0,4.,8 \n") |
|---|
| 589 | fd.close() |
|---|
| 590 | |
|---|
| 591 | mesh_output_file = "new_trianlge.tsh" |
|---|
| 592 | fit_to_mesh_file(mesh_file, |
|---|
| 593 | point_file, |
|---|
| 594 | mesh_output_file, |
|---|
| 595 | alpha = 0.0) |
|---|
| 596 | # load in the .tsh file we just wrote |
|---|
| 597 | mesh_dic = mesh_file_to_mesh_dictionary(mesh_output_file) |
|---|
| 598 | |
|---|
| 599 | assert allclose(mesh_dic['generatedpointattributelist'], |
|---|
| 600 | [[0.0, 0.0], |
|---|
| 601 | [5.0, 10.0], |
|---|
| 602 | [5.0,10.0]]) |
|---|
| 603 | |
|---|
| 604 | self.failUnless(mesh_dic['generatedpointattributetitlelist'] == |
|---|
| 605 | ['elevation','stage'], |
|---|
| 606 | 'test_fit_to_mesh_file failed') |
|---|
| 607 | |
|---|
| 608 | #clean up |
|---|
| 609 | os.remove(mesh_file) |
|---|
| 610 | os.remove(point_file) |
|---|
| 611 | |
|---|
| 612 | def test_fit_to_mesh_fileII(self): |
|---|
| 613 | from load_mesh.loadASCII import mesh_file_to_mesh_dictionary, \ |
|---|
| 614 | export_trianglulation_file |
|---|
| 615 | import tempfile |
|---|
| 616 | import os |
|---|
| 617 | |
|---|
| 618 | # create a .tsh file, no user outline |
|---|
| 619 | mesh_dic = {} |
|---|
| 620 | mesh_dic['generatedpointlist'] = [[0.0, 0.0], |
|---|
| 621 | [0.0, 5.0], |
|---|
| 622 | [5.0, 0.0]] |
|---|
| 623 | mesh_dic['generatedtrianglelist'] = [[0, 2, 1]] |
|---|
| 624 | mesh_dic['generatedsegmentlist'] = [[0, 1], [2, 0], [1, 2]] |
|---|
| 625 | mesh_dic['generatedtriangleattributelist'] = [['']] |
|---|
| 626 | mesh_dic['generatedpointattributelist'] = [[1,2], [1,2], [1,2]] |
|---|
| 627 | mesh_dic['generatedpointattributetitlelist'] = ['density', 'temp'] |
|---|
| 628 | mesh_dic['generatedtriangleneighborlist'] = [[-1, -1, -1]] |
|---|
| 629 | mesh_dic['generatedsegmentmarkerlist'] = ['external', |
|---|
| 630 | 'external', |
|---|
| 631 | 'external'] |
|---|
| 632 | mesh_file = tempfile.mktemp(".tsh") |
|---|
| 633 | export_trianglulation_file(mesh_file,mesh_dic) |
|---|
| 634 | |
|---|
| 635 | # create an .xya file |
|---|
| 636 | point_file = tempfile.mktemp(".xya") |
|---|
| 637 | fd = open(point_file,'w') |
|---|
| 638 | fd.write("elevation, stage \n 1.0, 1.0,2.,4 \n 1.0, 3.0,4,8 \n 3.0,1.0,4.,8 \n") |
|---|
| 639 | fd.close() |
|---|
| 640 | |
|---|
| 641 | mesh_output_file = "new_trianlge.tsh" |
|---|
| 642 | fit_to_mesh_file(mesh_file, |
|---|
| 643 | point_file, |
|---|
| 644 | mesh_output_file, |
|---|
| 645 | alpha = 0.0) |
|---|
| 646 | # load in the .tsh file we just wrote |
|---|
| 647 | mesh_dic = mesh_file_to_mesh_dictionary(mesh_output_file) |
|---|
| 648 | |
|---|
| 649 | assert allclose(mesh_dic['generatedpointattributelist'], |
|---|
| 650 | [[1.0, 2.0,0.0, 0.0], |
|---|
| 651 | [1.0, 2.0,5.0, 10.0], |
|---|
| 652 | [1.0, 2.0,5.0,10.0]]) |
|---|
| 653 | |
|---|
| 654 | self.failUnless(mesh_dic['generatedpointattributetitlelist'] == |
|---|
| 655 | ['density', 'temp','elevation','stage'], |
|---|
| 656 | 'test_fit_to_mesh_file failed') |
|---|
| 657 | |
|---|
| 658 | #clean up |
|---|
| 659 | os.remove(mesh_file) |
|---|
| 660 | os.remove(point_file) |
|---|
| 661 | |
|---|
| 662 | #------------------------------------------------------------- |
|---|
| 663 | if __name__ == "__main__": |
|---|
| 664 | suite = unittest.makeSuite(TestCase,'test') |
|---|
| 665 | runner = unittest.TextTestRunner() |
|---|
| 666 | runner.run(suite) |
|---|
| 667 | |
|---|
| 668 | |
|---|
| 669 | |
|---|
| 670 | |
|---|
| 671 | |
|---|
| 672 | |
|---|
