[1018] | 1 | #!/usr/bin/env python |
---|
| 2 | |
---|
| 3 | #TEST |
---|
| 4 | |
---|
| 5 | import unittest |
---|
| 6 | from math import sqrt |
---|
| 7 | |
---|
| 8 | |
---|
| 9 | from least_squares import * |
---|
| 10 | from Numeric import allclose, array, transpose |
---|
| 11 | |
---|
[1097] | 12 | from coordinate_transforms.geo_reference import Geo_reference |
---|
| 13 | |
---|
[1018] | 14 | def distance(x, y): |
---|
| 15 | return sqrt( sum( (array(x)-array(y))**2 )) |
---|
| 16 | |
---|
| 17 | def linear_function(point): |
---|
| 18 | point = array(point) |
---|
| 19 | return point[:,0]+point[:,1] |
---|
| 20 | |
---|
| 21 | |
---|
| 22 | class Test_Least_Squares(unittest.TestCase): |
---|
| 23 | |
---|
| 24 | def setUp(self): |
---|
| 25 | pass |
---|
| 26 | |
---|
| 27 | def tearDown(self): |
---|
| 28 | pass |
---|
| 29 | |
---|
| 30 | def test_datapoint_at_centroid(self): |
---|
| 31 | a = [0.0, 0.0] |
---|
| 32 | b = [0.0, 2.0] |
---|
| 33 | c = [2.0,0.0] |
---|
| 34 | points = [a, b, c] |
---|
| 35 | vertices = [ [1,0,2] ] #bac |
---|
| 36 | |
---|
| 37 | data = [ [2.0/3, 2.0/3] ] #Use centroid as one data point |
---|
| 38 | |
---|
| 39 | interp = Interpolation(points, vertices, data) |
---|
| 40 | assert allclose(interp.get_A(), [[1./3, 1./3, 1./3]]) |
---|
| 41 | |
---|
| 42 | |
---|
| 43 | def test_quad_tree(self): |
---|
| 44 | p0 = [-10.0, -10.0] |
---|
| 45 | p1 = [20.0, -10.0] |
---|
| 46 | p2 = [-10.0, 20.0] |
---|
| 47 | p3 = [10.0, 50.0] |
---|
| 48 | p4 = [30.0, 30.0] |
---|
| 49 | p5 = [50.0, 10.0] |
---|
| 50 | p6 = [40.0, 60.0] |
---|
| 51 | p7 = [60.0, 40.0] |
---|
| 52 | p8 = [-66.0, 20.0] |
---|
| 53 | p9 = [10.0, -66.0] |
---|
| 54 | |
---|
| 55 | points = [p0, p1, p2, p3, p4, p5, p6, p7, p8, p9] |
---|
| 56 | triangles = [ [0, 1, 2], |
---|
| 57 | [3, 2, 4], |
---|
| 58 | [4, 2, 1], |
---|
| 59 | [4, 1, 5], |
---|
| 60 | [3, 4, 6], |
---|
| 61 | [6, 4, 7], |
---|
| 62 | [7, 4, 5], |
---|
| 63 | [8, 0, 2], |
---|
| 64 | [0, 9, 1]] |
---|
| 65 | |
---|
| 66 | data = [ [4,4] ] |
---|
| 67 | interp = Interpolation(points, triangles, data, alpha = 0.0, |
---|
| 68 | max_points_per_cell = 4) |
---|
| 69 | #print "PDSG - interp.get_A()", interp.get_A() |
---|
| 70 | answer = [ [ 0.06666667, 0.46666667, 0.46666667, 0., |
---|
| 71 | 0., 0. , 0., 0., 0., 0.]] |
---|
| 72 | assert allclose(interp.get_A(), answer) |
---|
| 73 | interp.set_point_coordinates([[-30, -30]]) #point outside of mesh |
---|
| 74 | #print "PDSG - interp.get_A()", interp.get_A() |
---|
| 75 | answer = [ [ 0.0, 0.0, 0.0, 0., |
---|
| 76 | 0., 0. , 0., 0., 0., 0.]] |
---|
| 77 | assert allclose(interp.get_A(), answer) |
---|
| 78 | |
---|
| 79 | |
---|
| 80 | #point outside of quad tree root cell |
---|
| 81 | interp.set_point_coordinates([[-70, -70]]) |
---|
| 82 | #print "PDSG - interp.get_A()", interp.get_A() |
---|
| 83 | answer = [ [ 0.0, 0.0, 0.0, 0., |
---|
| 84 | 0., 0. , 0., 0., 0., 0.]] |
---|
| 85 | assert allclose(interp.get_A(), answer) |
---|
| 86 | |
---|
| 87 | def test_expand_search(self): |
---|
| 88 | p0 = [-10.0, -10.0] |
---|
| 89 | p1 = [20.0, -10.0] |
---|
| 90 | p2 = [-10.0, 20.0] |
---|
| 91 | p3 = [10.0, 50.0] |
---|
| 92 | p4 = [30.0, 30.0] |
---|
| 93 | p5 = [50.0, 10.0] |
---|
| 94 | p6 = [40.0, 60.0] |
---|
| 95 | p7 = [60.0, 40.0] |
---|
| 96 | p8 = [-66.0, 20.0] |
---|
| 97 | p9 = [10.0, -66.0] |
---|
| 98 | |
---|
| 99 | points = [p0, p1, p2, p3, p4, p5, p6, p7, p8, p9] |
---|
| 100 | triangles = [ [0, 1, 2], |
---|
| 101 | [3, 2, 4], |
---|
| 102 | [4, 2, 1], |
---|
| 103 | [4, 1, 5], |
---|
| 104 | [3, 4, 6], |
---|
| 105 | [6, 4, 7], |
---|
| 106 | [7, 4, 5], |
---|
| 107 | [8, 0, 2], |
---|
| 108 | [0, 9, 1]] |
---|
| 109 | |
---|
| 110 | data = [ [4,4], |
---|
| 111 | [-30,10], |
---|
| 112 | [-20,0], |
---|
| 113 | [-20,10], |
---|
| 114 | [0,30], |
---|
| 115 | [10,-40], |
---|
| 116 | [10,-30], |
---|
| 117 | [10,-20], |
---|
| 118 | [10,10], |
---|
| 119 | [10,20], |
---|
| 120 | [10,30], |
---|
| 121 | [10,40], |
---|
| 122 | [20,10], |
---|
| 123 | [25,45], |
---|
| 124 | [30,0], |
---|
| 125 | [30,10], |
---|
| 126 | [30,30], |
---|
| 127 | [30,40], |
---|
| 128 | [30,50], |
---|
| 129 | [40,10], |
---|
| 130 | [40,30], |
---|
| 131 | [40,40], |
---|
| 132 | [40,50], |
---|
| 133 | [50,20], |
---|
| 134 | [50,30], |
---|
| 135 | [50,40], |
---|
| 136 | [50,50], |
---|
| 137 | [30,0], |
---|
| 138 | [-20,-20]] |
---|
| 139 | point_attributes = [ -400000, |
---|
| 140 | 10, |
---|
| 141 | 10, |
---|
| 142 | 10, |
---|
| 143 | 10, |
---|
| 144 | 10, |
---|
| 145 | 10, |
---|
| 146 | 10, |
---|
| 147 | 10, |
---|
| 148 | 10, |
---|
| 149 | 10, |
---|
| 150 | 10, |
---|
| 151 | 10, |
---|
| 152 | 10, |
---|
| 153 | 10, |
---|
| 154 | 10, |
---|
| 155 | 10, |
---|
| 156 | 10, |
---|
| 157 | 10, |
---|
| 158 | 10, |
---|
| 159 | 10, |
---|
| 160 | 10, |
---|
| 161 | 10, |
---|
| 162 | 10, |
---|
| 163 | 10, |
---|
| 164 | 10, |
---|
| 165 | 10, |
---|
| 166 | 10, |
---|
| 167 | 99] |
---|
| 168 | |
---|
| 169 | interp = Interpolation(points, triangles, data, |
---|
| 170 | alpha=0.0, expand_search=False, #verbose = True, #False, |
---|
| 171 | max_points_per_cell = 4) |
---|
| 172 | calc = interp.fit_points(point_attributes, ) |
---|
| 173 | #print "calc",calc |
---|
| 174 | |
---|
| 175 | # the point at 4,4 is ignored. An expanded search has to be done |
---|
| 176 | # to fine which triangel it's in. |
---|
| 177 | # An expanded search isn't done to find that the last point |
---|
| 178 | # isn't in the mesh. But this isn't tested. |
---|
| 179 | answer= [ 10, |
---|
| 180 | 10, |
---|
| 181 | 10, |
---|
| 182 | 10, |
---|
| 183 | 10, |
---|
| 184 | 10, |
---|
| 185 | 10, |
---|
| 186 | 10, |
---|
| 187 | 10, |
---|
| 188 | 10] |
---|
| 189 | assert allclose(calc, answer) |
---|
| 190 | |
---|
| 191 | def test_quad_treeII(self): |
---|
| 192 | p0 = [-66.0, 14.0] |
---|
| 193 | p1 = [14.0, -66.0] |
---|
| 194 | p2 = [14.0, 14.0] |
---|
| 195 | p3 = [60.0, 20.0] |
---|
| 196 | p4 = [10.0, 60.0] |
---|
| 197 | p5 = [60.0, 60.0] |
---|
| 198 | |
---|
| 199 | points = [p0, p1, p2, p3, p4, p5] |
---|
| 200 | triangles = [ [0, 1, 2], |
---|
| 201 | [3, 2, 1], |
---|
| 202 | [0, 2, 4], |
---|
| 203 | [4, 2, 5], |
---|
| 204 | [5, 2, 3]] |
---|
| 205 | |
---|
| 206 | data = [ [-26.0,-26.0] ] |
---|
| 207 | interp = Interpolation(points, triangles, data, alpha = 0.0, |
---|
| 208 | max_points_per_cell = 4) |
---|
| 209 | #print "PDSG - interp.get_A()", interp.get_A() |
---|
| 210 | answer = [ [ 0.5, 0.5, 0.0, 0., |
---|
| 211 | 0., 0.]] |
---|
| 212 | assert allclose(interp.get_A(), answer) |
---|
| 213 | interp.set_point_coordinates([[-30, -30]]) #point outside of mesh |
---|
| 214 | #print "PDSG -30,-30 - interp.get_A()", interp.get_A() |
---|
| 215 | answer = [ [ 0.0, 0.0, 0.0, 0., |
---|
| 216 | 0., 0.]] |
---|
| 217 | assert allclose(interp.get_A(), answer) |
---|
| 218 | |
---|
| 219 | |
---|
| 220 | #point outside of quad tree root cell |
---|
| 221 | interp.set_point_coordinates([[-70, -70]]) |
---|
| 222 | #print "PDSG -70,-70 interp.get_A()", interp.get_A() |
---|
| 223 | answer = [ [ 0.0, 0.0, 0.0, 0., |
---|
| 224 | 0., 0. ]] |
---|
| 225 | assert allclose(interp.get_A(), answer) |
---|
| 226 | |
---|
| 227 | |
---|
| 228 | def test_datapoints_at_vertices(self): |
---|
| 229 | """Test that data points coinciding with vertices yield a diagonal matrix |
---|
| 230 | """ |
---|
| 231 | |
---|
| 232 | a = [0.0, 0.0] |
---|
| 233 | b = [0.0, 2.0] |
---|
| 234 | c = [2.0,0.0] |
---|
| 235 | points = [a, b, c] |
---|
| 236 | vertices = [ [1,0,2] ] #bac |
---|
| 237 | |
---|
| 238 | data = points #Use data at vertices |
---|
| 239 | |
---|
| 240 | interp = Interpolation(points, vertices, data) |
---|
| 241 | assert allclose(interp.get_A(), [[1., 0., 0.], |
---|
| 242 | [0., 1., 0.], |
---|
| 243 | [0., 0., 1.]]) |
---|
| 244 | |
---|
| 245 | |
---|
| 246 | |
---|
| 247 | def test_datapoints_on_edge_midpoints(self): |
---|
| 248 | """Try datapoints midway on edges - |
---|
| 249 | each point should affect two matrix entries equally |
---|
| 250 | """ |
---|
| 251 | |
---|
| 252 | a = [0.0, 0.0] |
---|
| 253 | b = [0.0, 2.0] |
---|
| 254 | c = [2.0,0.0] |
---|
| 255 | points = [a, b, c] |
---|
| 256 | vertices = [ [1,0,2] ] #bac |
---|
| 257 | |
---|
| 258 | data = [ [0., 1.], [1., 0.], [1., 1.] ] |
---|
| 259 | |
---|
| 260 | interp = Interpolation(points, vertices, data) |
---|
| 261 | |
---|
| 262 | assert allclose(interp.get_A(), [[0.5, 0.5, 0.0], #Affects vertex 1 and 0 |
---|
| 263 | [0.5, 0.0, 0.5], #Affects vertex 0 and 2 |
---|
| 264 | [0.0, 0.5, 0.5]]) #Affects vertex 1 and 2 |
---|
| 265 | |
---|
| 266 | |
---|
| 267 | def test_datapoints_on_edges(self): |
---|
| 268 | """Try datapoints on edges - |
---|
| 269 | each point should affect two matrix entries in proportion |
---|
| 270 | """ |
---|
| 271 | |
---|
| 272 | a = [0.0, 0.0] |
---|
| 273 | b = [0.0, 2.0] |
---|
| 274 | c = [2.0,0.0] |
---|
| 275 | points = [a, b, c] |
---|
| 276 | vertices = [ [1,0,2] ] #bac |
---|
| 277 | |
---|
| 278 | data = [ [0., 1.5], [1.5, 0.], [1.5, 0.5] ] |
---|
| 279 | |
---|
| 280 | interp = Interpolation(points, vertices, data) |
---|
| 281 | |
---|
| 282 | assert allclose(interp.get_A(), [[0.25, 0.75, 0.0], #Affects vertex 1 and 0 |
---|
| 283 | [0.25, 0.0, 0.75], #Affects vertex 0 and 2 |
---|
| 284 | [0.0, 0.25, 0.75]]) #Affects vertex 1 and 2 |
---|
| 285 | |
---|
| 286 | def test_arbitrary_datapoints(self): |
---|
| 287 | """Try arbitrary datapoints |
---|
| 288 | """ |
---|
| 289 | |
---|
| 290 | from Numeric import sum |
---|
| 291 | |
---|
| 292 | a = [0.0, 0.0] |
---|
| 293 | b = [0.0, 2.0] |
---|
| 294 | c = [2.0,0.0] |
---|
| 295 | points = [a, b, c] |
---|
| 296 | vertices = [ [1,0,2] ] #bac |
---|
| 297 | |
---|
| 298 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44] ] |
---|
| 299 | |
---|
| 300 | interp = Interpolation(points, vertices, data) |
---|
| 301 | #print "interp.get_A()", interp.get_A() |
---|
| 302 | assert allclose(sum(interp.get_A(), axis=1), 1.0) |
---|
| 303 | |
---|
| 304 | def test_arbitrary_datapoints_some_outside(self): |
---|
| 305 | """Try arbitrary datapoints one outside the triangle. |
---|
| 306 | That one should be ignored |
---|
| 307 | """ |
---|
| 308 | |
---|
| 309 | from Numeric import sum |
---|
| 310 | |
---|
| 311 | a = [0.0, 0.0] |
---|
| 312 | b = [0.0, 2.0] |
---|
| 313 | c = [2.0,0.0] |
---|
| 314 | points = [a, b, c] |
---|
| 315 | vertices = [ [1,0,2] ] #bac |
---|
| 316 | |
---|
| 317 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44], [5.0, 7.0]] |
---|
| 318 | |
---|
| 319 | |
---|
| 320 | interp = Interpolation(points, vertices, data, precrop = True) |
---|
| 321 | assert allclose(sum(interp.get_A(), axis=1), 1.0) |
---|
| 322 | |
---|
| 323 | interp = Interpolation(points, vertices, data, precrop = False) |
---|
| 324 | assert allclose(sum(interp.get_A(), axis=1), [1,1,1,0]) |
---|
| 325 | |
---|
| 326 | |
---|
| 327 | |
---|
| 328 | # this causes a memory error in scipy.sparse |
---|
| 329 | def test_more_triangles(self): |
---|
| 330 | |
---|
| 331 | a = [-1.0, 0.0] |
---|
| 332 | b = [3.0, 4.0] |
---|
| 333 | c = [4.0,1.0] |
---|
| 334 | d = [-3.0, 2.0] #3 |
---|
| 335 | e = [-1.0,-2.0] |
---|
| 336 | f = [1.0, -2.0] #5 |
---|
| 337 | |
---|
| 338 | points = [a, b, c, d,e,f] |
---|
| 339 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
---|
| 340 | |
---|
| 341 | #Data points |
---|
| 342 | data_points = [ [-3., 2.0], [-2, 1], [0.0, 1], [0, 3], [2, 3], [-1.0/3,-4./3] ] |
---|
| 343 | interp = Interpolation(points, triangles, data_points) |
---|
| 344 | |
---|
| 345 | answer = [[0.0, 0.0, 0.0, 1.0, 0.0, 0.0], #Affects point d |
---|
| 346 | [0.5, 0.0, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
---|
| 347 | [0.75, 0.25, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
---|
| 348 | [0.0, 0.5, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
---|
| 349 | [0.25, 0.75, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
---|
| 350 | [1./3, 0.0, 0.0, 0.0, 1./3, 1./3]] #Affects points a, e and f |
---|
| 351 | |
---|
| 352 | |
---|
| 353 | A = interp.get_A() |
---|
| 354 | for i in range(A.shape[0]): |
---|
| 355 | for j in range(A.shape[1]): |
---|
| 356 | if not allclose(A[i,j], answer[i][j]): |
---|
| 357 | print i,j,':',A[i,j], answer[i][j] |
---|
| 358 | |
---|
| 359 | |
---|
| 360 | assert allclose(interp.get_A(), answer) |
---|
| 361 | |
---|
| 362 | |
---|
| 363 | |
---|
| 364 | |
---|
| 365 | def test_smooth_attributes_to_mesh(self): |
---|
| 366 | a = [0.0, 0.0] |
---|
| 367 | b = [0.0, 5.0] |
---|
| 368 | c = [5.0, 0.0] |
---|
| 369 | points = [a, b, c] |
---|
| 370 | triangles = [ [1,0,2] ] #bac |
---|
| 371 | |
---|
| 372 | d1 = [1.0, 1.0] |
---|
| 373 | d2 = [1.0, 3.0] |
---|
| 374 | d3 = [3.0,1.0] |
---|
| 375 | z1 = 2 |
---|
| 376 | z2 = 4 |
---|
| 377 | z3 = 4 |
---|
| 378 | data_coords = [d1, d2, d3] |
---|
| 379 | |
---|
| 380 | interp = Interpolation(points, triangles, data_coords, alpha=5.0e-20) |
---|
| 381 | z = [z1, z2, z3] |
---|
| 382 | f = interp.fit(z) |
---|
| 383 | answer = [0, 5., 5.] |
---|
| 384 | |
---|
| 385 | #print "f\n",f |
---|
| 386 | #print "answer\n",answer |
---|
| 387 | |
---|
| 388 | assert allclose(f, answer, atol=1e-7) |
---|
| 389 | |
---|
| 390 | |
---|
| 391 | def test_smooth_att_to_meshII(self): |
---|
| 392 | |
---|
| 393 | a = [0.0, 0.0] |
---|
| 394 | b = [0.0, 5.0] |
---|
| 395 | c = [5.0, 0.0] |
---|
| 396 | points = [a, b, c] |
---|
| 397 | triangles = [ [1,0,2] ] #bac |
---|
| 398 | |
---|
| 399 | d1 = [1.0, 1.0] |
---|
| 400 | d2 = [1.0, 2.0] |
---|
| 401 | d3 = [3.0,1.0] |
---|
| 402 | data_coords = [d1, d2, d3] |
---|
| 403 | z = linear_function(data_coords) |
---|
| 404 | interp = Interpolation(points, triangles, data_coords, alpha=0.0) |
---|
| 405 | f = interp.fit(z) |
---|
| 406 | answer = linear_function(points) |
---|
| 407 | |
---|
| 408 | assert allclose(f, answer) |
---|
| 409 | |
---|
| 410 | def test_smooth_attributes_to_meshIII(self): |
---|
| 411 | |
---|
| 412 | a = [-1.0, 0.0] |
---|
| 413 | b = [3.0, 4.0] |
---|
| 414 | c = [4.0,1.0] |
---|
| 415 | d = [-3.0, 2.0] #3 |
---|
| 416 | e = [-1.0,-2.0] |
---|
| 417 | f = [1.0, -2.0] #5 |
---|
| 418 | |
---|
| 419 | vertices = [a, b, c, d,e,f] |
---|
| 420 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
---|
| 421 | |
---|
| 422 | point_coords = [[-2.0, 2.0], |
---|
| 423 | [-1.0, 1.0], |
---|
| 424 | [0.0,2.0], |
---|
| 425 | [1.0, 1.0], |
---|
| 426 | [2.0, 1.0], |
---|
| 427 | [0.0,0.0], |
---|
| 428 | [1.0, 0.0], |
---|
| 429 | [0.0, -1.0], |
---|
| 430 | [-0.2,-0.5], |
---|
| 431 | [-0.9, -1.5], |
---|
| 432 | [0.5, -1.9], |
---|
| 433 | [3.0,1.0]] |
---|
| 434 | |
---|
| 435 | z = linear_function(point_coords) |
---|
| 436 | interp = Interpolation(vertices, triangles, point_coords, alpha=0.0) |
---|
| 437 | |
---|
| 438 | #print 'z',z |
---|
| 439 | f = interp.fit(z) |
---|
| 440 | answer = linear_function(vertices) |
---|
| 441 | #print "f\n",f |
---|
| 442 | #print "answer\n",answer |
---|
| 443 | assert allclose(f, answer) |
---|
| 444 | |
---|
| 445 | |
---|
| 446 | def test_smooth_attributes_to_meshIV(self): |
---|
| 447 | """ Testing 2 attributes smoothed to the mesh |
---|
| 448 | """ |
---|
| 449 | |
---|
| 450 | a = [0.0, 0.0] |
---|
| 451 | b = [0.0, 5.0] |
---|
| 452 | c = [5.0, 0.0] |
---|
| 453 | points = [a, b, c] |
---|
| 454 | triangles = [ [1,0,2] ] #bac |
---|
| 455 | |
---|
| 456 | d1 = [1.0, 1.0] |
---|
| 457 | d2 = [1.0, 3.0] |
---|
| 458 | d3 = [3.0, 1.0] |
---|
| 459 | z1 = [2, 4] |
---|
| 460 | z2 = [4, 8] |
---|
| 461 | z3 = [4, 8] |
---|
| 462 | data_coords = [d1, d2, d3] |
---|
| 463 | |
---|
| 464 | interp = Interpolation(points, triangles, data_coords, alpha=0.0) |
---|
| 465 | z = [z1, z2, z3] |
---|
| 466 | f = interp.fit_points(z) |
---|
| 467 | answer = [[0,0], [5., 10.], [5., 10.]] |
---|
| 468 | assert allclose(f, answer) |
---|
| 469 | |
---|
| 470 | def test_interpolate_attributes_to_points(self): |
---|
| 471 | v0 = [0.0, 0.0] |
---|
| 472 | v1 = [0.0, 5.0] |
---|
| 473 | v2 = [5.0, 0.0] |
---|
| 474 | |
---|
| 475 | vertices = [v0, v1, v2] |
---|
| 476 | triangles = [ [1,0,2] ] #bac |
---|
| 477 | |
---|
| 478 | d0 = [1.0, 1.0] |
---|
| 479 | d1 = [1.0, 2.0] |
---|
| 480 | d2 = [3.0, 1.0] |
---|
| 481 | point_coords = [ d0, d1, d2] |
---|
| 482 | |
---|
| 483 | interp = Interpolation(vertices, triangles, point_coords) |
---|
| 484 | f = linear_function(vertices) |
---|
| 485 | z = interp.interpolate(f) |
---|
| 486 | answer = linear_function(point_coords) |
---|
| 487 | |
---|
| 488 | |
---|
| 489 | assert allclose(z, answer) |
---|
| 490 | |
---|
| 491 | |
---|
| 492 | def test_interpolate_attributes_to_pointsII(self): |
---|
| 493 | a = [-1.0, 0.0] |
---|
| 494 | b = [3.0, 4.0] |
---|
| 495 | c = [4.0, 1.0] |
---|
| 496 | d = [-3.0, 2.0] #3 |
---|
| 497 | e = [-1.0, -2.0] |
---|
| 498 | f = [1.0, -2.0] #5 |
---|
| 499 | |
---|
| 500 | vertices = [a, b, c, d,e,f] |
---|
| 501 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
---|
| 502 | |
---|
| 503 | |
---|
| 504 | point_coords = [[-2.0, 2.0], |
---|
| 505 | [-1.0, 1.0], |
---|
| 506 | [0.0, 2.0], |
---|
| 507 | [1.0, 1.0], |
---|
| 508 | [2.0, 1.0], |
---|
| 509 | [0.0, 0.0], |
---|
| 510 | [1.0, 0.0], |
---|
| 511 | [0.0, -1.0], |
---|
| 512 | [-0.2, -0.5], |
---|
| 513 | [-0.9, -1.5], |
---|
| 514 | [0.5, -1.9], |
---|
| 515 | [3.0, 1.0]] |
---|
| 516 | |
---|
| 517 | interp = Interpolation(vertices, triangles, point_coords) |
---|
| 518 | f = linear_function(vertices) |
---|
| 519 | z = interp.interpolate(f) |
---|
| 520 | answer = linear_function(point_coords) |
---|
| 521 | #print "z",z |
---|
| 522 | #print "answer",answer |
---|
| 523 | assert allclose(z, answer) |
---|
| 524 | |
---|
| 525 | def test_interpolate_attributes_to_pointsIII(self): |
---|
| 526 | """Test linear interpolation of known values at vertices to |
---|
| 527 | new points inside a triangle |
---|
| 528 | """ |
---|
| 529 | a = [0.0, 0.0] |
---|
| 530 | b = [0.0, 5.0] |
---|
| 531 | c = [5.0, 0.0] |
---|
| 532 | d = [5.0, 5.0] |
---|
| 533 | |
---|
| 534 | vertices = [a, b, c, d] |
---|
[1158] | 535 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
---|
[1018] | 536 | |
---|
| 537 | #Points within triangle 1 |
---|
| 538 | d0 = [1.0, 1.0] |
---|
| 539 | d1 = [1.0, 2.0] |
---|
| 540 | d2 = [3.0, 1.0] |
---|
| 541 | |
---|
| 542 | #Point within triangle 2 |
---|
| 543 | d3 = [4.0, 3.0] |
---|
| 544 | |
---|
| 545 | #Points on common edge |
---|
| 546 | d4 = [2.5, 2.5] |
---|
| 547 | d5 = [4.0, 1.0] |
---|
| 548 | |
---|
| 549 | #Point on common vertex |
---|
| 550 | d6 = [0., 5.] |
---|
| 551 | |
---|
| 552 | |
---|
| 553 | point_coords = [d0, d1, d2, d3, d4, d5, d6] |
---|
| 554 | |
---|
| 555 | interp = Interpolation(vertices, triangles, point_coords) |
---|
| 556 | |
---|
| 557 | #Known values at vertices |
---|
| 558 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
---|
| 559 | f = [ [0., 0., 0., -5.], # (0,0) |
---|
| 560 | [5., 10., 5., -10.], # (0,5) |
---|
| 561 | [5., 5., 10.0, 0.], # (5,0) |
---|
| 562 | [10., 15., 15., -5.]] # (5,5) |
---|
| 563 | |
---|
| 564 | z = interp.interpolate(f) |
---|
| 565 | answer = [ [2., 3., 3., -5.], # (1,1) |
---|
| 566 | [3., 5., 4., -6.], # (1,2) |
---|
| 567 | [4., 5., 7., -3.], # (3,1) |
---|
| 568 | [7., 10., 11., -4.], # (4,3) |
---|
| 569 | [5., 7.5, 7.5, -5.], # (2.5, 2.5) |
---|
| 570 | [5., 6., 9., -2.], # (4,1) |
---|
| 571 | [5., 10., 5., -10.]] # (0,5) |
---|
| 572 | |
---|
| 573 | #print "***********" |
---|
| 574 | #print "z",z |
---|
| 575 | #print "answer",answer |
---|
| 576 | #print "***********" |
---|
| 577 | |
---|
| 578 | assert allclose(z, answer) |
---|
| 579 | |
---|
| 580 | def test_interpolate_attributes_to_pointsIV(self): |
---|
| 581 | a = [-1.0, 0.0] |
---|
| 582 | b = [3.0, 4.0] |
---|
| 583 | c = [4.0, 1.0] |
---|
| 584 | d = [-3.0, 2.0] #3 |
---|
| 585 | e = [-1.0, -2.0] |
---|
| 586 | f = [1.0, -2.0] #5 |
---|
| 587 | |
---|
| 588 | vertices = [a, b, c, d,e,f] |
---|
| 589 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
---|
| 590 | |
---|
| 591 | |
---|
| 592 | point_coords = [[-2.0, 2.0], |
---|
| 593 | [-1.0, 1.0], |
---|
| 594 | [0.0, 2.0], |
---|
| 595 | [1.0, 1.0], |
---|
| 596 | [2.0, 1.0], |
---|
| 597 | [0.0, 0.0], |
---|
| 598 | [1.0, 0.0], |
---|
| 599 | [0.0, -1.0], |
---|
| 600 | [-0.2, -0.5], |
---|
| 601 | [-0.9, -1.5], |
---|
| 602 | [0.5, -1.9], |
---|
| 603 | [3.0, 1.0]] |
---|
| 604 | |
---|
| 605 | interp = Interpolation(vertices, triangles, point_coords) |
---|
| 606 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
---|
| 607 | f = transpose(f) |
---|
| 608 | #print "f",f |
---|
| 609 | z = interp.interpolate(f) |
---|
| 610 | answer = [linear_function(point_coords), |
---|
| 611 | 2*linear_function(point_coords) ] |
---|
| 612 | answer = transpose(answer) |
---|
| 613 | #print "z",z |
---|
| 614 | #print "answer",answer |
---|
| 615 | assert allclose(z, answer) |
---|
| 616 | |
---|
| 617 | def test_smooth_attributes_to_mesh_function(self): |
---|
| 618 | """ Testing 2 attributes smoothed to the mesh |
---|
| 619 | """ |
---|
| 620 | |
---|
| 621 | a = [0.0, 0.0] |
---|
| 622 | b = [0.0, 5.0] |
---|
| 623 | c = [5.0, 0.0] |
---|
| 624 | points = [a, b, c] |
---|
| 625 | triangles = [ [1,0,2] ] #bac |
---|
| 626 | |
---|
| 627 | d1 = [1.0, 1.0] |
---|
| 628 | d2 = [1.0, 3.0] |
---|
| 629 | d3 = [3.0, 1.0] |
---|
| 630 | z1 = [2, 4] |
---|
| 631 | z2 = [4, 8] |
---|
| 632 | z3 = [4, 8] |
---|
| 633 | data_coords = [d1, d2, d3] |
---|
| 634 | z = [z1, z2, z3] |
---|
| 635 | |
---|
| 636 | f = fit_to_mesh(points, triangles, data_coords, z, alpha=0.0) |
---|
| 637 | answer = [[0, 0], [5., 10.], [5., 10.]] |
---|
| 638 | |
---|
| 639 | assert allclose(f, answer) |
---|
| 640 | |
---|
| 641 | |
---|
| 642 | |
---|
| 643 | def test_pts2rectangular(self): |
---|
| 644 | |
---|
| 645 | import time, os |
---|
| 646 | FN = 'xyatest' + str(time.time()) + '.xya' |
---|
| 647 | fid = open(FN, 'w') |
---|
| 648 | fid.write(' %s \n' %('elevation')) |
---|
| 649 | fid.write('%f %f %f\n' %(1,1,2) ) |
---|
| 650 | fid.write('%f %f %f\n' %(1,3,4) ) |
---|
| 651 | fid.write('%f %f %f\n' %(3,1,4) ) |
---|
| 652 | fid.close() |
---|
| 653 | |
---|
| 654 | points, triangles, boundary, attributes =\ |
---|
| 655 | pts2rectangular(FN, 4, 4, format = 'asc') |
---|
| 656 | |
---|
| 657 | |
---|
| 658 | data_coords = [ [1,1], [1,3], [3,1] ] |
---|
| 659 | z = [2, 4, 4] |
---|
| 660 | |
---|
| 661 | ref = fit_to_mesh(points, triangles, data_coords, z) |
---|
| 662 | |
---|
| 663 | #print attributes |
---|
| 664 | #print ref |
---|
| 665 | assert allclose(attributes, ref) |
---|
| 666 | |
---|
| 667 | os.remove(FN) |
---|
| 668 | |
---|
| 669 | |
---|
| 670 | #Tests of smoothing matrix |
---|
| 671 | def test_smoothing_matrix_one_triangle(self): |
---|
| 672 | from Numeric import dot |
---|
| 673 | a = [0.0, 0.0] |
---|
| 674 | b = [0.0, 2.0] |
---|
| 675 | c = [2.0,0.0] |
---|
| 676 | points = [a, b, c] |
---|
| 677 | |
---|
| 678 | vertices = [ [1,0,2] ] #bac |
---|
| 679 | |
---|
| 680 | interp = Interpolation(points, vertices) |
---|
| 681 | |
---|
| 682 | assert allclose(interp.get_D(), [[1, -0.5, -0.5], |
---|
| 683 | [-0.5, 0.5, 0], |
---|
| 684 | [-0.5, 0, 0.5]]) |
---|
| 685 | |
---|
| 686 | #Define f(x,y) = x |
---|
| 687 | f = array([0,0,2]) #Value at global vertex 2 |
---|
| 688 | |
---|
| 689 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
---|
| 690 | # int 1 dx dy = area = 2 |
---|
| 691 | assert dot(dot(f, interp.get_D()), f) == 2 |
---|
| 692 | |
---|
| 693 | #Define f(x,y) = y |
---|
| 694 | f = array([0,2,0]) #Value at global vertex 1 |
---|
| 695 | |
---|
| 696 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
---|
| 697 | # int 1 dx dy = area = 2 |
---|
| 698 | assert dot(dot(f, interp.get_D()), f) == 2 |
---|
| 699 | |
---|
| 700 | #Define f(x,y) = x+y |
---|
| 701 | f = array([0,2,2]) #Values at global vertex 1 and 2 |
---|
| 702 | |
---|
| 703 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
---|
| 704 | # int 2 dx dy = 2*area = 4 |
---|
| 705 | assert dot(dot(f, interp.get_D()), f) == 4 |
---|
| 706 | |
---|
| 707 | |
---|
| 708 | |
---|
| 709 | def test_smoothing_matrix_more_triangles(self): |
---|
| 710 | from Numeric import dot |
---|
| 711 | |
---|
| 712 | a = [0.0, 0.0] |
---|
| 713 | b = [0.0, 2.0] |
---|
| 714 | c = [2.0,0.0] |
---|
| 715 | d = [0.0, 4.0] |
---|
| 716 | e = [2.0, 2.0] |
---|
| 717 | f = [4.0,0.0] |
---|
| 718 | |
---|
| 719 | points = [a, b, c, d, e, f] |
---|
| 720 | #bac, bce, ecf, dbe, daf, dae |
---|
| 721 | vertices = [ [1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
---|
| 722 | |
---|
| 723 | interp = Interpolation(points, vertices) |
---|
| 724 | |
---|
| 725 | |
---|
| 726 | #assert allclose(interp.get_D(), [[1, -0.5, -0.5], |
---|
| 727 | # [-0.5, 0.5, 0], |
---|
| 728 | # [-0.5, 0, 0.5]]) |
---|
| 729 | |
---|
| 730 | #Define f(x,y) = x |
---|
| 731 | f = array([0,0,2,0,2,4]) #f evaluated at points a-f |
---|
| 732 | |
---|
| 733 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
---|
| 734 | # int 1 dx dy = total area = 8 |
---|
| 735 | assert dot(dot(f, interp.get_D()), f) == 8 |
---|
| 736 | |
---|
| 737 | #Define f(x,y) = y |
---|
| 738 | f = array([0,2,0,4,2,0]) #f evaluated at points a-f |
---|
| 739 | |
---|
| 740 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
---|
| 741 | # int 1 dx dy = area = 8 |
---|
| 742 | assert dot(dot(f, interp.get_D()), f) == 8 |
---|
| 743 | |
---|
| 744 | #Define f(x,y) = x+y |
---|
| 745 | f = array([0,2,2,4,4,4]) #f evaluated at points a-f |
---|
| 746 | |
---|
| 747 | #Check that int (df/dx)**2 + (df/dy)**2 dx dy = |
---|
| 748 | # int 2 dx dy = 2*area = 16 |
---|
| 749 | assert dot(dot(f, interp.get_D()), f) == 16 |
---|
| 750 | |
---|
| 751 | |
---|
| 752 | def test_fit_and_interpolation(self): |
---|
| 753 | from mesh import Mesh |
---|
| 754 | |
---|
| 755 | a = [0.0, 0.0] |
---|
| 756 | b = [0.0, 2.0] |
---|
| 757 | c = [2.0, 0.0] |
---|
| 758 | d = [0.0, 4.0] |
---|
| 759 | e = [2.0, 2.0] |
---|
| 760 | f = [4.0, 0.0] |
---|
| 761 | |
---|
| 762 | points = [a, b, c, d, e, f] |
---|
| 763 | #bac, bce, ecf, dbe, daf, dae |
---|
| 764 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
---|
| 765 | |
---|
| 766 | #Get (enough) datapoints |
---|
| 767 | data_points = [[ 0.66666667, 0.66666667], |
---|
| 768 | [ 1.33333333, 1.33333333], |
---|
| 769 | [ 2.66666667, 0.66666667], |
---|
| 770 | [ 0.66666667, 2.66666667], |
---|
| 771 | [ 0.0, 1.0], |
---|
| 772 | [ 0.0, 3.0], |
---|
| 773 | [ 1.0, 0.0], |
---|
| 774 | [ 1.0, 1.0], |
---|
| 775 | [ 1.0, 2.0], |
---|
| 776 | [ 1.0, 3.0], |
---|
| 777 | [ 2.0, 1.0], |
---|
| 778 | [ 3.0, 0.0], |
---|
| 779 | [ 3.0, 1.0]] |
---|
| 780 | |
---|
| 781 | interp = Interpolation(points, triangles, data_points, alpha=0.0) |
---|
| 782 | |
---|
| 783 | z = linear_function(data_points) |
---|
| 784 | answer = linear_function(points) |
---|
| 785 | |
---|
| 786 | f = interp.fit(z) |
---|
| 787 | |
---|
| 788 | #print "f",f |
---|
| 789 | #print "answer",answer |
---|
| 790 | assert allclose(f, answer) |
---|
| 791 | |
---|
| 792 | #Map back |
---|
| 793 | z1 = interp.interpolate(f) |
---|
| 794 | #print "z1\n", z1 |
---|
| 795 | #print "z\n",z |
---|
| 796 | assert allclose(z, z1) |
---|
| 797 | |
---|
| 798 | |
---|
| 799 | def test_smoothing_and_interpolation(self): |
---|
| 800 | |
---|
| 801 | a = [0.0, 0.0] |
---|
| 802 | b = [0.0, 2.0] |
---|
| 803 | c = [2.0, 0.0] |
---|
| 804 | d = [0.0, 4.0] |
---|
| 805 | e = [2.0, 2.0] |
---|
| 806 | f = [4.0, 0.0] |
---|
| 807 | |
---|
| 808 | points = [a, b, c, d, e, f] |
---|
| 809 | #bac, bce, ecf, dbe, daf, dae |
---|
| 810 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
---|
| 811 | |
---|
| 812 | #Get (too few!) datapoints |
---|
| 813 | data_points = [[ 0.66666667, 0.66666667], |
---|
| 814 | [ 1.33333333, 1.33333333], |
---|
| 815 | [ 2.66666667, 0.66666667], |
---|
| 816 | [ 0.66666667, 2.66666667]] |
---|
| 817 | |
---|
| 818 | z = linear_function(data_points) |
---|
| 819 | answer = linear_function(points) |
---|
| 820 | |
---|
| 821 | #Make interpolator with too few data points and no smoothing |
---|
| 822 | interp = Interpolation(points, triangles, data_points, alpha=0.0) |
---|
| 823 | #Must raise an exception |
---|
| 824 | try: |
---|
| 825 | f = interp.fit(z) |
---|
| 826 | except: |
---|
| 827 | pass |
---|
| 828 | |
---|
| 829 | #Now try with smoothing parameter |
---|
| 830 | interp = Interpolation(points, triangles, data_points, alpha=1.0e-13) |
---|
| 831 | |
---|
| 832 | f = interp.fit(z) |
---|
| 833 | #f will be different from answerr due to smoothing |
---|
| 834 | assert allclose(f, answer,atol=5) |
---|
| 835 | |
---|
| 836 | #Map back |
---|
| 837 | z1 = interp.interpolate(f) |
---|
| 838 | assert allclose(z, z1) |
---|
| 839 | |
---|
| 840 | |
---|
| 841 | |
---|
| 842 | def test_fit_and_interpolation_with_new_points(self): |
---|
| 843 | """Fit a surface to one set of points. Then interpolate that surface |
---|
| 844 | using another set of points. |
---|
| 845 | """ |
---|
| 846 | from mesh import Mesh |
---|
| 847 | |
---|
| 848 | |
---|
| 849 | #Setup mesh used to represent fitted function |
---|
| 850 | a = [0.0, 0.0] |
---|
| 851 | b = [0.0, 2.0] |
---|
| 852 | c = [2.0, 0.0] |
---|
| 853 | d = [0.0, 4.0] |
---|
| 854 | e = [2.0, 2.0] |
---|
| 855 | f = [4.0, 0.0] |
---|
| 856 | |
---|
| 857 | points = [a, b, c, d, e, f] |
---|
| 858 | #bac, bce, ecf, dbe, daf, dae |
---|
| 859 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
---|
| 860 | |
---|
| 861 | #Datapoints to fit from |
---|
| 862 | data_points1 = [[ 0.66666667, 0.66666667], |
---|
| 863 | [ 1.33333333, 1.33333333], |
---|
| 864 | [ 2.66666667, 0.66666667], |
---|
| 865 | [ 0.66666667, 2.66666667], |
---|
| 866 | [ 0.0, 1.0], |
---|
| 867 | [ 0.0, 3.0], |
---|
| 868 | [ 1.0, 0.0], |
---|
| 869 | [ 1.0, 1.0], |
---|
| 870 | [ 15, -17], #Outside mesh |
---|
| 871 | [ 1.0, 2.0], |
---|
| 872 | [ 1.0, 3.0], |
---|
| 873 | [ 2.0, 1.0], |
---|
| 874 | [ 3.0, 0.0], |
---|
| 875 | [ 3.0, 1.0]] |
---|
| 876 | |
---|
| 877 | #Fit surface to mesh |
---|
| 878 | interp = Interpolation(points, triangles, data_points1, alpha=0.0, |
---|
| 879 | precrop = True) |
---|
| 880 | z = linear_function(data_points1) #Example z-values |
---|
| 881 | f = interp.fit(z) #Fitted values at vertices |
---|
| 882 | |
---|
| 883 | |
---|
| 884 | |
---|
| 885 | #New datapoints where interpolated values are sought |
---|
| 886 | data_points2 = [[ 0.0, 0.0], |
---|
| 887 | [ 0.5, 0.5], |
---|
| 888 | [ 0.7, 0.7], |
---|
| 889 | [-13, 65], #Outside |
---|
| 890 | [ 1.0, 0.5], |
---|
| 891 | [ 2.0, 0.4], |
---|
| 892 | [ 2.8, 1.2]] |
---|
| 893 | |
---|
| 894 | |
---|
| 895 | |
---|
| 896 | #Build new A matrix based on new points (without precrop) |
---|
| 897 | interp.build_interpolation_matrix_A(data_points2, precrop = False) |
---|
| 898 | |
---|
| 899 | #Interpolate using fitted surface |
---|
| 900 | z1 = interp.interpolate(f) |
---|
| 901 | |
---|
| 902 | #import Numeric |
---|
| 903 | #data_points2 = Numeric.take(data_points2, interp.point_indices) |
---|
| 904 | |
---|
| 905 | #Desired result (OK for points inside) |
---|
| 906 | |
---|
| 907 | answer = linear_function(data_points2) |
---|
| 908 | import Numeric |
---|
| 909 | z1 = Numeric.take(z1, [0,1,2,4,5,6]) |
---|
| 910 | answer = Numeric.take(answer, [0,1,2,4,5,6]) |
---|
| 911 | assert allclose(z1, answer) |
---|
| 912 | |
---|
| 913 | #Build new A matrix based on new points (with precrop) |
---|
| 914 | interp.build_interpolation_matrix_A(data_points2, precrop = True) |
---|
| 915 | |
---|
| 916 | #Interpolate using fitted surface |
---|
| 917 | z1 = interp.interpolate(f) |
---|
| 918 | |
---|
| 919 | import Numeric |
---|
| 920 | data_points2 = Numeric.take(data_points2, interp.point_indices) |
---|
| 921 | |
---|
| 922 | #Desired result |
---|
| 923 | answer = linear_function(data_points2) |
---|
| 924 | assert allclose(z1, answer) |
---|
| 925 | |
---|
| 926 | |
---|
| 927 | |
---|
| 928 | def test_fit_and_interpolation_with_different_origins(self): |
---|
| 929 | """Fit a surface to one set of points. Then interpolate that surface |
---|
| 930 | using another set of points. |
---|
| 931 | This test tests situtaion where points and mesh belong to a different |
---|
| 932 | coordinate system as defined by origin. |
---|
| 933 | """ |
---|
| 934 | from mesh import Mesh |
---|
| 935 | |
---|
| 936 | #Setup mesh used to represent fitted function |
---|
| 937 | a = [0.0, 0.0] |
---|
| 938 | b = [0.0, 2.0] |
---|
| 939 | c = [2.0, 0.0] |
---|
| 940 | d = [0.0, 4.0] |
---|
| 941 | e = [2.0, 2.0] |
---|
| 942 | f = [4.0, 0.0] |
---|
| 943 | |
---|
| 944 | points = [a, b, c, d, e, f] |
---|
| 945 | #bac, bce, ecf, dbe, daf, dae |
---|
| 946 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
---|
| 947 | |
---|
| 948 | #Datapoints to fit from |
---|
| 949 | data_points1 = [[ 0.66666667, 0.66666667], |
---|
| 950 | [ 1.33333333, 1.33333333], |
---|
| 951 | [ 2.66666667, 0.66666667], |
---|
| 952 | [ 0.66666667, 2.66666667], |
---|
| 953 | [ 0.0, 1.0], |
---|
| 954 | [ 0.0, 3.0], |
---|
| 955 | [ 1.0, 0.0], |
---|
| 956 | [ 1.0, 1.0], |
---|
| 957 | [ 1.0, 2.0], |
---|
| 958 | [ 1.0, 3.0], |
---|
| 959 | [ 2.0, 1.0], |
---|
| 960 | [ 3.0, 0.0], |
---|
| 961 | [ 3.0, 1.0]] |
---|
| 962 | |
---|
| 963 | |
---|
| 964 | #First check that things are OK when using same origin |
---|
| 965 | mesh_origin = (56, 290000, 618000) #zone, easting, northing |
---|
| 966 | data_origin = (56, 290000, 618000) #zone, easting, northing |
---|
| 967 | |
---|
| 968 | |
---|
| 969 | #Fit surface to mesh |
---|
| 970 | interp = Interpolation(points, triangles, data_points1, |
---|
| 971 | alpha=0.0, |
---|
| 972 | data_origin = data_origin, |
---|
| 973 | mesh_origin = mesh_origin) |
---|
| 974 | |
---|
| 975 | z = linear_function(data_points1) #Example z-values |
---|
| 976 | f = interp.fit(z) #Fitted values at vertices |
---|
| 977 | |
---|
| 978 | |
---|
| 979 | #New datapoints where interpolated values are sought |
---|
| 980 | data_points2 = [[ 0.0, 0.0], |
---|
| 981 | [ 0.5, 0.5], |
---|
| 982 | [ 0.7, 0.7], |
---|
| 983 | [ 1.0, 0.5], |
---|
| 984 | [ 2.0, 0.4], |
---|
| 985 | [ 2.8, 1.2]] |
---|
| 986 | |
---|
| 987 | |
---|
| 988 | #Build new A matrix based on new points |
---|
| 989 | interp.build_interpolation_matrix_A(data_points2) |
---|
| 990 | |
---|
| 991 | #Interpolate using fitted surface |
---|
| 992 | z1 = interp.interpolate(f) |
---|
| 993 | |
---|
| 994 | #Desired result |
---|
| 995 | answer = linear_function(data_points2) |
---|
| 996 | assert allclose(z1, answer) |
---|
| 997 | |
---|
| 998 | |
---|
| 999 | ############################################## |
---|
| 1000 | |
---|
[1096] | 1001 | #Then check situation where points are relative to a different |
---|
[1018] | 1002 | #origin (same zone, though, until we figure that out (FIXME)) |
---|
| 1003 | |
---|
| 1004 | mesh_origin = (56, 290000, 618000) #zone, easting, northing |
---|
| 1005 | data_origin = (56, 10000, 10000) #zone, easting, northing |
---|
| 1006 | |
---|
| 1007 | #Shift datapoints according to new origin |
---|
| 1008 | |
---|
| 1009 | for k in range(len(data_points1)): |
---|
| 1010 | data_points1[k][0] += mesh_origin[1] - data_origin[1] |
---|
| 1011 | data_points1[k][1] += mesh_origin[2] - data_origin[2] |
---|
| 1012 | |
---|
| 1013 | for k in range(len(data_points2)): |
---|
| 1014 | data_points2[k][0] += mesh_origin[1] - data_origin[1] |
---|
| 1015 | data_points2[k][1] += mesh_origin[2] - data_origin[2] |
---|
| 1016 | |
---|
| 1017 | |
---|
| 1018 | |
---|
| 1019 | #Fit surface to mesh |
---|
| 1020 | interp = Interpolation(points, triangles, data_points1, |
---|
| 1021 | alpha=0.0, |
---|
| 1022 | data_origin = data_origin, |
---|
| 1023 | mesh_origin = mesh_origin) |
---|
| 1024 | |
---|
| 1025 | f1 = interp.fit(z) #Fitted values at vertices (using same z as before) |
---|
| 1026 | |
---|
| 1027 | assert allclose(f,f1), 'Fit should have been unaltered' |
---|
| 1028 | |
---|
| 1029 | |
---|
| 1030 | #Build new A matrix based on new points |
---|
| 1031 | interp.build_interpolation_matrix_A(data_points2) |
---|
| 1032 | |
---|
| 1033 | #Interpolate using fitted surface |
---|
| 1034 | z1 = interp.interpolate(f) |
---|
| 1035 | assert allclose(z1, answer) |
---|
| 1036 | |
---|
| 1037 | |
---|
| 1038 | ######################################################### |
---|
| 1039 | #Finally try to relate data_points2 to new origin without |
---|
| 1040 | #rebuilding matrix |
---|
| 1041 | |
---|
| 1042 | data_origin = (56, 2000, 2000) #zone, easting, northing |
---|
| 1043 | for k in range(len(data_points2)): |
---|
| 1044 | data_points2[k][0] += 8000 |
---|
| 1045 | data_points2[k][1] += 8000 |
---|
| 1046 | |
---|
| 1047 | #Build new A matrix based on new points |
---|
| 1048 | interp.build_interpolation_matrix_A(data_points2, |
---|
| 1049 | data_origin = data_origin) |
---|
| 1050 | |
---|
| 1051 | #Interpolate using fitted surface |
---|
| 1052 | z1 = interp.interpolate(f) |
---|
| 1053 | assert allclose(z1, answer) |
---|
| 1054 | |
---|
| 1055 | |
---|
| 1056 | def test_fit_to_mesh_file(self): |
---|
[1423] | 1057 | from load_mesh.loadASCII import import_mesh_file, \ |
---|
[1018] | 1058 | export_mesh_file |
---|
| 1059 | import tempfile |
---|
| 1060 | import os |
---|
| 1061 | |
---|
| 1062 | # create a .tsh file, no user outline |
---|
| 1063 | mesh_dic = {} |
---|
| 1064 | mesh_dic['vertices'] = [[0.0, 0.0], |
---|
| 1065 | [0.0, 5.0], |
---|
| 1066 | [5.0, 0.0]] |
---|
| 1067 | mesh_dic['triangles'] = [[0, 2, 1]] |
---|
| 1068 | mesh_dic['segments'] = [[0, 1], [2, 0], [1, 2]] |
---|
[1183] | 1069 | mesh_dic['triangle_tags'] = [''] |
---|
[1018] | 1070 | mesh_dic['vertex_attributes'] = [[], [], []] |
---|
| 1071 | mesh_dic['vertiex_attribute_titles'] = [] |
---|
| 1072 | mesh_dic['triangle_neighbors'] = [[-1, -1, -1]] |
---|
| 1073 | mesh_dic['segment_tags'] = ['external', |
---|
| 1074 | 'external', |
---|
| 1075 | 'external'] |
---|
| 1076 | mesh_file = tempfile.mktemp(".tsh") |
---|
| 1077 | export_mesh_file(mesh_file,mesh_dic) |
---|
| 1078 | |
---|
| 1079 | # create an .xya file |
---|
| 1080 | point_file = tempfile.mktemp(".xya") |
---|
| 1081 | fd = open(point_file,'w') |
---|
| 1082 | 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") |
---|
| 1083 | fd.close() |
---|
| 1084 | |
---|
| 1085 | mesh_output_file = "new_trianlge.tsh" |
---|
| 1086 | fit_to_mesh_file(mesh_file, |
---|
| 1087 | point_file, |
---|
| 1088 | mesh_output_file, |
---|
| 1089 | alpha = 0.0) |
---|
| 1090 | # load in the .tsh file we just wrote |
---|
[1423] | 1091 | mesh_dic = import_mesh_file(mesh_output_file) |
---|
[1018] | 1092 | #print "mesh_dic",mesh_dic |
---|
| 1093 | ans =[[0.0, 0.0], |
---|
| 1094 | [5.0, 10.0], |
---|
| 1095 | [5.0,10.0]] |
---|
| 1096 | assert allclose(mesh_dic['vertex_attributes'],ans) |
---|
| 1097 | |
---|
| 1098 | self.failUnless(mesh_dic['vertex_attribute_titles'] == |
---|
| 1099 | ['elevation','stage'], |
---|
| 1100 | 'test_fit_to_mesh_file failed') |
---|
| 1101 | |
---|
| 1102 | #clean up |
---|
| 1103 | os.remove(mesh_file) |
---|
| 1104 | os.remove(point_file) |
---|
| 1105 | os.remove(mesh_output_file) |
---|
| 1106 | |
---|
[1097] | 1107 | def test_fit_to_mesh_file3(self): |
---|
[1423] | 1108 | from load_mesh.loadASCII import import_mesh_file, \ |
---|
[1097] | 1109 | export_mesh_file |
---|
| 1110 | import tempfile |
---|
| 1111 | import os |
---|
| 1112 | |
---|
| 1113 | # create a .tsh file, no user outline |
---|
| 1114 | mesh_dic = {} |
---|
| 1115 | mesh_dic['vertices'] = [[0.76, 0.76], |
---|
| 1116 | [0.76, 5.76], |
---|
| 1117 | [5.76, 0.76]] |
---|
| 1118 | mesh_dic['triangles'] = [[0, 2, 1]] |
---|
| 1119 | mesh_dic['segments'] = [[0, 1], [2, 0], [1, 2]] |
---|
[1183] | 1120 | mesh_dic['triangle_tags'] = [''] |
---|
[1097] | 1121 | mesh_dic['vertex_attributes'] = [[], [], []] |
---|
| 1122 | mesh_dic['vertiex_attribute_titles'] = [] |
---|
| 1123 | mesh_dic['triangle_neighbors'] = [[-1, -1, -1]] |
---|
| 1124 | mesh_dic['segment_tags'] = ['external', |
---|
| 1125 | 'external', |
---|
| 1126 | 'external'] |
---|
| 1127 | mesh_dic['geo_reference'] = Geo_reference(56,-0.76,-0.76) |
---|
| 1128 | mesh_file = tempfile.mktemp(".tsh") |
---|
| 1129 | export_mesh_file(mesh_file,mesh_dic) |
---|
| 1130 | |
---|
| 1131 | #FIXME - make this test the georef in the points file as well. |
---|
| 1132 | # create an .xya file |
---|
| 1133 | point_file = tempfile.mktemp(".xya") |
---|
| 1134 | fd = open(point_file,'w') |
---|
| 1135 | 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") |
---|
| 1136 | fd.close() |
---|
| 1137 | |
---|
| 1138 | mesh_output_file = "new_trianlge.tsh" |
---|
| 1139 | fit_to_mesh_file(mesh_file, |
---|
| 1140 | point_file, |
---|
| 1141 | mesh_output_file, |
---|
| 1142 | alpha = 0.0) |
---|
| 1143 | # load in the .tsh file we just wrote |
---|
[1423] | 1144 | mesh_dic = import_mesh_file(mesh_output_file) |
---|
[1097] | 1145 | #print "mesh_dic",mesh_dic |
---|
| 1146 | ans =[[0.0, 0.0], |
---|
| 1147 | [5.0, 10.0], |
---|
| 1148 | [5.0,10.0]] |
---|
| 1149 | assert allclose(mesh_dic['vertex_attributes'],ans) |
---|
| 1150 | |
---|
| 1151 | self.failUnless(mesh_dic['vertex_attribute_titles'] == |
---|
| 1152 | ['elevation','stage'], |
---|
| 1153 | 'test_fit_to_mesh_file failed') |
---|
| 1154 | |
---|
| 1155 | #clean up |
---|
| 1156 | os.remove(mesh_file) |
---|
| 1157 | os.remove(point_file) |
---|
| 1158 | os.remove(mesh_output_file) |
---|
| 1159 | |
---|
[1018] | 1160 | def test_fit_to_mesh_fileII(self): |
---|
[1423] | 1161 | from load_mesh.loadASCII import import_mesh_file, \ |
---|
[1018] | 1162 | export_mesh_file |
---|
| 1163 | import tempfile |
---|
| 1164 | import os |
---|
| 1165 | |
---|
| 1166 | # create a .tsh file, no user outline |
---|
| 1167 | mesh_dic = {} |
---|
| 1168 | mesh_dic['vertices'] = [[0.0, 0.0], |
---|
| 1169 | [0.0, 5.0], |
---|
| 1170 | [5.0, 0.0]] |
---|
| 1171 | mesh_dic['triangles'] = [[0, 2, 1]] |
---|
| 1172 | mesh_dic['segments'] = [[0, 1], [2, 0], [1, 2]] |
---|
[1183] | 1173 | mesh_dic['triangle_tags'] = [''] |
---|
[1018] | 1174 | mesh_dic['vertex_attributes'] = [[1,2], [1,2], [1,2]] |
---|
| 1175 | mesh_dic['vertex_attribute_titles'] = ['density', 'temp'] |
---|
| 1176 | mesh_dic['triangle_neighbors'] = [[-1, -1, -1]] |
---|
| 1177 | mesh_dic['segment_tags'] = ['external', |
---|
| 1178 | 'external', |
---|
| 1179 | 'external'] |
---|
| 1180 | mesh_file = tempfile.mktemp(".tsh") |
---|
| 1181 | export_mesh_file(mesh_file,mesh_dic) |
---|
| 1182 | |
---|
| 1183 | # create an .xya file |
---|
| 1184 | point_file = tempfile.mktemp(".xya") |
---|
| 1185 | fd = open(point_file,'w') |
---|
| 1186 | 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") |
---|
| 1187 | fd.close() |
---|
| 1188 | |
---|
| 1189 | mesh_output_file = "new_triangle.tsh" |
---|
| 1190 | fit_to_mesh_file(mesh_file, |
---|
| 1191 | point_file, |
---|
| 1192 | mesh_output_file, |
---|
| 1193 | alpha = 0.0) |
---|
| 1194 | # load in the .tsh file we just wrote |
---|
[1423] | 1195 | mesh_dic = import_mesh_file(mesh_output_file) |
---|
[1018] | 1196 | |
---|
| 1197 | assert allclose(mesh_dic['vertex_attributes'], |
---|
| 1198 | [[1.0, 2.0,0.0, 0.0], |
---|
| 1199 | [1.0, 2.0,5.0, 10.0], |
---|
| 1200 | [1.0, 2.0,5.0,10.0]]) |
---|
| 1201 | |
---|
| 1202 | self.failUnless(mesh_dic['vertex_attribute_titles'] == |
---|
| 1203 | ['density', 'temp','elevation','stage'], |
---|
| 1204 | 'test_fit_to_mesh_file failed') |
---|
| 1205 | |
---|
| 1206 | #clean up |
---|
| 1207 | os.remove(mesh_file) |
---|
| 1208 | os.remove(mesh_output_file) |
---|
| 1209 | os.remove(point_file) |
---|
| 1210 | |
---|
| 1211 | def test_fit_to_msh_netcdf_fileII(self): |
---|
[1423] | 1212 | from load_mesh.loadASCII import import_mesh_file,export_mesh_file |
---|
[1018] | 1213 | import tempfile |
---|
| 1214 | import os |
---|
| 1215 | |
---|
| 1216 | # create a .tsh file, no user outline |
---|
| 1217 | mesh_dic = {} |
---|
| 1218 | mesh_dic['vertices'] = [[0.0, 0.0], |
---|
| 1219 | [0.0, 5.0], |
---|
| 1220 | [5.0, 0.0]] |
---|
| 1221 | mesh_dic['triangles'] = [[0, 2, 1]] |
---|
| 1222 | mesh_dic['segments'] = [[0, 1], [2, 0], [1, 2]] |
---|
[1183] | 1223 | mesh_dic['triangle_tags'] = [''] |
---|
[1018] | 1224 | mesh_dic['vertex_attributes'] = [[1,2], [1,2], [1,2]] |
---|
| 1225 | mesh_dic['vertex_attribute_titles'] = ['density', 'temp'] |
---|
| 1226 | mesh_dic['triangle_neighbors'] = [[-1, -1, -1]] |
---|
| 1227 | mesh_dic['segment_tags'] = ['external', |
---|
| 1228 | 'external', |
---|
| 1229 | 'external'] |
---|
| 1230 | mesh_file = tempfile.mktemp(".msh") |
---|
| 1231 | export_mesh_file(mesh_file,mesh_dic) |
---|
| 1232 | |
---|
| 1233 | # create an .xya file |
---|
| 1234 | point_file = tempfile.mktemp(".xya") |
---|
| 1235 | fd = open(point_file,'w') |
---|
| 1236 | 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") |
---|
| 1237 | fd.close() |
---|
| 1238 | |
---|
| 1239 | mesh_output_file = "new_triangle.msh" |
---|
| 1240 | fit_to_mesh_file(mesh_file, |
---|
| 1241 | point_file, |
---|
| 1242 | mesh_output_file, |
---|
| 1243 | alpha = 0.0) |
---|
| 1244 | # load in the .tsh file we just wrote |
---|
[1423] | 1245 | mesh_dic = import_mesh_file(mesh_output_file) |
---|
[1018] | 1246 | |
---|
| 1247 | assert allclose(mesh_dic['vertex_attributes'], |
---|
| 1248 | [[1.0, 2.0,0.0, 0.0], |
---|
| 1249 | [1.0, 2.0,5.0, 10.0], |
---|
| 1250 | [1.0, 2.0,5.0,10.0]]) |
---|
| 1251 | |
---|
| 1252 | self.failUnless(mesh_dic['vertex_attribute_titles'] == |
---|
| 1253 | ['density', 'temp','elevation','stage'], |
---|
| 1254 | 'test_fit_to_mesh_file failed') |
---|
| 1255 | |
---|
| 1256 | #clean up |
---|
| 1257 | os.remove(mesh_file) |
---|
| 1258 | os.remove(mesh_output_file) |
---|
| 1259 | os.remove(point_file) |
---|
| 1260 | |
---|
| 1261 | #------------------------------------------------------------- |
---|
| 1262 | if __name__ == "__main__": |
---|
| 1263 | suite = unittest.makeSuite(Test_Least_Squares,'test') |
---|
| 1264 | |
---|
| 1265 | #suite = unittest.makeSuite(Test_Least_Squares,'test_fit_to_msh_netcdf_fileII') |
---|
| 1266 | #suite = unittest.makeSuite(Test_Least_Squares,'test_fit_to_mesh_fileII') |
---|
| 1267 | runner = unittest.TextTestRunner(verbosity=1) |
---|
| 1268 | runner.run(suite) |
---|
| 1269 | |
---|
| 1270 | |
---|
| 1271 | |
---|
| 1272 | |
---|
| 1273 | |
---|