| 1 | #!/usr/bin/env python |
|---|
| 2 | |
|---|
| 3 | #TEST |
|---|
| 4 | |
|---|
| 5 | #import time, os |
|---|
| 6 | |
|---|
| 7 | |
|---|
| 8 | import sys |
|---|
| 9 | import os |
|---|
| 10 | import unittest |
|---|
| 11 | from math import sqrt |
|---|
| 12 | import tempfile |
|---|
| 13 | |
|---|
| 14 | from Scientific.IO.NetCDF import NetCDFFile |
|---|
| 15 | from Numeric import allclose, array, transpose, zeros, Float |
|---|
| 16 | |
|---|
| 17 | |
|---|
| 18 | # ANUGA code imports |
|---|
| 19 | from interpolate import * |
|---|
| 20 | from coordinate_transforms.geo_reference import Geo_reference |
|---|
| 21 | from shallow_water import Domain, Transmissive_boundary |
|---|
| 22 | from utilities.numerical_tools import mean, INF |
|---|
| 23 | from data_manager import get_dataobject |
|---|
| 24 | from geospatial_data.geospatial_data import Geospatial_data |
|---|
| 25 | |
|---|
| 26 | def distance(x, y): |
|---|
| 27 | return sqrt( sum( (array(x)-array(y))**2 )) |
|---|
| 28 | |
|---|
| 29 | def linear_function(point): |
|---|
| 30 | point = array(point) |
|---|
| 31 | return point[:,0]+point[:,1] |
|---|
| 32 | |
|---|
| 33 | |
|---|
| 34 | class Test_Interpolate(unittest.TestCase): |
|---|
| 35 | |
|---|
| 36 | def setUp(self): |
|---|
| 37 | |
|---|
| 38 | import time |
|---|
| 39 | from mesh_factory import rectangular |
|---|
| 40 | |
|---|
| 41 | |
|---|
| 42 | #Create basic mesh |
|---|
| 43 | points, vertices, boundary = rectangular(2, 2) |
|---|
| 44 | |
|---|
| 45 | #Create shallow water domain |
|---|
| 46 | domain = Domain(points, vertices, boundary) |
|---|
| 47 | domain.default_order=2 |
|---|
| 48 | domain.beta_h = 0 |
|---|
| 49 | |
|---|
| 50 | |
|---|
| 51 | #Set some field values |
|---|
| 52 | domain.set_quantity('elevation', lambda x,y: -x) |
|---|
| 53 | domain.set_quantity('friction', 0.03) |
|---|
| 54 | |
|---|
| 55 | |
|---|
| 56 | ###################### |
|---|
| 57 | # Boundary conditions |
|---|
| 58 | B = Transmissive_boundary(domain) |
|---|
| 59 | domain.set_boundary( {'left': B, 'right': B, 'top': B, 'bottom': B}) |
|---|
| 60 | |
|---|
| 61 | |
|---|
| 62 | ###################### |
|---|
| 63 | #Initial condition - with jumps |
|---|
| 64 | |
|---|
| 65 | bed = domain.quantities['elevation'].vertex_values |
|---|
| 66 | stage = zeros(bed.shape, Float) |
|---|
| 67 | |
|---|
| 68 | h = 0.3 |
|---|
| 69 | for i in range(stage.shape[0]): |
|---|
| 70 | if i % 2 == 0: |
|---|
| 71 | stage[i,:] = bed[i,:] + h |
|---|
| 72 | else: |
|---|
| 73 | stage[i,:] = bed[i,:] |
|---|
| 74 | |
|---|
| 75 | domain.set_quantity('stage', stage) |
|---|
| 76 | |
|---|
| 77 | domain.distribute_to_vertices_and_edges() |
|---|
| 78 | |
|---|
| 79 | |
|---|
| 80 | self.domain = domain |
|---|
| 81 | |
|---|
| 82 | C = domain.get_vertex_coordinates() |
|---|
| 83 | self.X = C[:,0:6:2].copy() |
|---|
| 84 | self.Y = C[:,1:6:2].copy() |
|---|
| 85 | |
|---|
| 86 | self.F = bed |
|---|
| 87 | |
|---|
| 88 | |
|---|
| 89 | |
|---|
| 90 | def tearDown(self): |
|---|
| 91 | pass |
|---|
| 92 | |
|---|
| 93 | def test_datapoint_at_centroid(self): |
|---|
| 94 | a = [0.0, 0.0] |
|---|
| 95 | b = [0.0, 2.0] |
|---|
| 96 | c = [2.0,0.0] |
|---|
| 97 | points = [a, b, c] |
|---|
| 98 | vertices = [ [1,0,2] ] #bac |
|---|
| 99 | |
|---|
| 100 | data = [ [2.0/3, 2.0/3] ] #Use centroid as one data point |
|---|
| 101 | |
|---|
| 102 | interp = Interpolate(points, vertices) |
|---|
| 103 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 104 | [[1./3, 1./3, 1./3]]) |
|---|
| 105 | |
|---|
| 106 | def test_quad_tree(self): |
|---|
| 107 | p0 = [-10.0, -10.0] |
|---|
| 108 | p1 = [20.0, -10.0] |
|---|
| 109 | p2 = [-10.0, 20.0] |
|---|
| 110 | p3 = [10.0, 50.0] |
|---|
| 111 | p4 = [30.0, 30.0] |
|---|
| 112 | p5 = [50.0, 10.0] |
|---|
| 113 | p6 = [40.0, 60.0] |
|---|
| 114 | p7 = [60.0, 40.0] |
|---|
| 115 | p8 = [-66.0, 20.0] |
|---|
| 116 | p9 = [10.0, -66.0] |
|---|
| 117 | |
|---|
| 118 | points = [p0, p1, p2, p3, p4, p5, p6, p7, p8, p9] |
|---|
| 119 | triangles = [ [0, 1, 2], |
|---|
| 120 | [3, 2, 4], |
|---|
| 121 | [4, 2, 1], |
|---|
| 122 | [4, 1, 5], |
|---|
| 123 | [3, 4, 6], |
|---|
| 124 | [6, 4, 7], |
|---|
| 125 | [7, 4, 5], |
|---|
| 126 | [8, 0, 2], |
|---|
| 127 | [0, 9, 1]] |
|---|
| 128 | |
|---|
| 129 | data = [ [4,4] ] |
|---|
| 130 | interp = Interpolate(points, triangles, |
|---|
| 131 | max_vertices_per_cell = 4) |
|---|
| 132 | #print "PDSG - interp.get_A()", interp.get_A() |
|---|
| 133 | answer = [ [ 0.06666667, 0.46666667, 0.46666667, 0., |
|---|
| 134 | 0., 0. , 0., 0., 0., 0.]] |
|---|
| 135 | |
|---|
| 136 | |
|---|
| 137 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 138 | answer) |
|---|
| 139 | #interp.set_point_coordinates([[-30, -30]]) #point outside of mesh |
|---|
| 140 | #print "PDSG - interp.get_A()", interp.get_A() |
|---|
| 141 | data = [[-30, -30]] |
|---|
| 142 | answer = [ [ 0.0, 0.0, 0.0, 0., |
|---|
| 143 | 0., 0. , 0., 0., 0., 0.]] |
|---|
| 144 | |
|---|
| 145 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 146 | answer) |
|---|
| 147 | |
|---|
| 148 | |
|---|
| 149 | #point outside of quad tree root cell |
|---|
| 150 | #interp.set_point_coordinates([[-70, -70]]) |
|---|
| 151 | #print "PDSG - interp.get_A()", interp.get_A() |
|---|
| 152 | data = [[-70, -70]] |
|---|
| 153 | answer = [ [ 0.0, 0.0, 0.0, 0., |
|---|
| 154 | 0., 0. , 0., 0., 0., 0.]] |
|---|
| 155 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 156 | answer) |
|---|
| 157 | |
|---|
| 158 | def test_datapoints_at_vertices(self): |
|---|
| 159 | """Test that data points coinciding with vertices yield a diagonal matrix |
|---|
| 160 | """ |
|---|
| 161 | |
|---|
| 162 | a = [0.0, 0.0] |
|---|
| 163 | b = [0.0, 2.0] |
|---|
| 164 | c = [2.0,0.0] |
|---|
| 165 | points = [a, b, c] |
|---|
| 166 | vertices = [ [1,0,2] ] #bac |
|---|
| 167 | |
|---|
| 168 | data = points #Use data at vertices |
|---|
| 169 | |
|---|
| 170 | interp = Interpolate(points, vertices) |
|---|
| 171 | answer = [[1., 0., 0.], |
|---|
| 172 | [0., 1., 0.], |
|---|
| 173 | [0., 0., 1.]] |
|---|
| 174 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 175 | answer) |
|---|
| 176 | |
|---|
| 177 | |
|---|
| 178 | def test_datapoints_on_edge_midpoints(self): |
|---|
| 179 | """Try datapoints midway on edges - |
|---|
| 180 | each point should affect two matrix entries equally |
|---|
| 181 | """ |
|---|
| 182 | |
|---|
| 183 | a = [0.0, 0.0] |
|---|
| 184 | b = [0.0, 2.0] |
|---|
| 185 | c = [2.0,0.0] |
|---|
| 186 | points = [a, b, c] |
|---|
| 187 | vertices = [ [1,0,2] ] #bac |
|---|
| 188 | |
|---|
| 189 | data = [ [0., 1.], [1., 0.], [1., 1.] ] |
|---|
| 190 | answer = [[0.5, 0.5, 0.0], #Affects vertex 1 and 0 |
|---|
| 191 | [0.5, 0.0, 0.5], #Affects vertex 0 and 2 |
|---|
| 192 | [0.0, 0.5, 0.5]] |
|---|
| 193 | interp = Interpolate(points, vertices) |
|---|
| 194 | |
|---|
| 195 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 196 | answer) |
|---|
| 197 | |
|---|
| 198 | def test_datapoints_on_edges(self): |
|---|
| 199 | """Try datapoints on edges - |
|---|
| 200 | each point should affect two matrix entries in proportion |
|---|
| 201 | """ |
|---|
| 202 | |
|---|
| 203 | a = [0.0, 0.0] |
|---|
| 204 | b = [0.0, 2.0] |
|---|
| 205 | c = [2.0,0.0] |
|---|
| 206 | points = [a, b, c] |
|---|
| 207 | vertices = [ [1,0,2] ] #bac |
|---|
| 208 | |
|---|
| 209 | data = [ [0., 1.5], [1.5, 0.], [1.5, 0.5] ] |
|---|
| 210 | answer = [[0.25, 0.75, 0.0], #Affects vertex 1 and 0 |
|---|
| 211 | [0.25, 0.0, 0.75], #Affects vertex 0 and 2 |
|---|
| 212 | [0.0, 0.25, 0.75]] |
|---|
| 213 | |
|---|
| 214 | interp = Interpolate(points, vertices) |
|---|
| 215 | |
|---|
| 216 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
|---|
| 217 | answer) |
|---|
| 218 | |
|---|
| 219 | |
|---|
| 220 | def test_arbitrary_datapoints(self): |
|---|
| 221 | """Try arbitrary datapoints |
|---|
| 222 | """ |
|---|
| 223 | |
|---|
| 224 | from Numeric import sum |
|---|
| 225 | |
|---|
| 226 | a = [0.0, 0.0] |
|---|
| 227 | b = [0.0, 2.0] |
|---|
| 228 | c = [2.0,0.0] |
|---|
| 229 | points = [a, b, c] |
|---|
| 230 | vertices = [ [1,0,2] ] #bac |
|---|
| 231 | |
|---|
| 232 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44] ] |
|---|
| 233 | |
|---|
| 234 | interp = Interpolate(points, vertices) |
|---|
| 235 | #print "interp.get_A()", interp.get_A() |
|---|
| 236 | results = interp._build_interpolation_matrix_A(data).todense() |
|---|
| 237 | assert allclose(sum(results, axis=1), 1.0) |
|---|
| 238 | |
|---|
| 239 | def test_arbitrary_datapoints_some_outside(self): |
|---|
| 240 | """Try arbitrary datapoints one outside the triangle. |
|---|
| 241 | That one should be ignored |
|---|
| 242 | """ |
|---|
| 243 | |
|---|
| 244 | from Numeric import sum |
|---|
| 245 | |
|---|
| 246 | a = [0.0, 0.0] |
|---|
| 247 | b = [0.0, 2.0] |
|---|
| 248 | c = [2.0,0.0] |
|---|
| 249 | points = [a, b, c] |
|---|
| 250 | vertices = [ [1,0,2] ] #bac |
|---|
| 251 | |
|---|
| 252 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44], [5.0, 7.0]] |
|---|
| 253 | |
|---|
| 254 | interp = Interpolate(points, vertices) |
|---|
| 255 | results = interp._build_interpolation_matrix_A(data).todense() |
|---|
| 256 | assert allclose(sum(results, axis=1), [1,1,1,0]) |
|---|
| 257 | |
|---|
| 258 | |
|---|
| 259 | |
|---|
| 260 | # this causes a memory error in scipy.sparse |
|---|
| 261 | def test_more_triangles(self): |
|---|
| 262 | |
|---|
| 263 | a = [-1.0, 0.0] |
|---|
| 264 | b = [3.0, 4.0] |
|---|
| 265 | c = [4.0,1.0] |
|---|
| 266 | d = [-3.0, 2.0] #3 |
|---|
| 267 | e = [-1.0,-2.0] |
|---|
| 268 | f = [1.0, -2.0] #5 |
|---|
| 269 | |
|---|
| 270 | points = [a, b, c, d,e,f] |
|---|
| 271 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 272 | |
|---|
| 273 | #Data points |
|---|
| 274 | data = [ [-3., 2.0], [-2, 1], [0.0, 1], [0, 3], [2, 3], [-1.0/3,-4./3] ] |
|---|
| 275 | interp = Interpolate(points, triangles) |
|---|
| 276 | |
|---|
| 277 | answer = [[0.0, 0.0, 0.0, 1.0, 0.0, 0.0], #Affects point d |
|---|
| 278 | [0.5, 0.0, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
|---|
| 279 | [0.75, 0.25, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
|---|
| 280 | [0.0, 0.5, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
|---|
| 281 | [0.25, 0.75, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
|---|
| 282 | [1./3, 0.0, 0.0, 0.0, 1./3, 1./3]] #Affects points a, e and f |
|---|
| 283 | |
|---|
| 284 | |
|---|
| 285 | A = interp._build_interpolation_matrix_A(data).todense() |
|---|
| 286 | for i in range(A.shape[0]): |
|---|
| 287 | for j in range(A.shape[1]): |
|---|
| 288 | if not allclose(A[i,j], answer[i][j]): |
|---|
| 289 | print i,j,':',A[i,j], answer[i][j] |
|---|
| 290 | |
|---|
| 291 | |
|---|
| 292 | #results = interp._build_interpolation_matrix_A(data).todense() |
|---|
| 293 | |
|---|
| 294 | assert allclose(A, answer) |
|---|
| 295 | |
|---|
| 296 | def test_geo_ref(self): |
|---|
| 297 | v0 = [0.0, 0.0] |
|---|
| 298 | v1 = [0.0, 5.0] |
|---|
| 299 | v2 = [5.0, 0.0] |
|---|
| 300 | |
|---|
| 301 | vertices_absolute = [v0, v1, v2] |
|---|
| 302 | triangles = [ [1,0,2] ] #bac |
|---|
| 303 | |
|---|
| 304 | geo = Geo_reference(57,100, 500) |
|---|
| 305 | |
|---|
| 306 | vertices = geo.change_points_geo_ref(vertices_absolute) |
|---|
| 307 | #print "vertices",vertices |
|---|
| 308 | |
|---|
| 309 | d0 = [1.0, 1.0] |
|---|
| 310 | d1 = [1.0, 2.0] |
|---|
| 311 | d2 = [3.0, 1.0] |
|---|
| 312 | point_coords = [ d0, d1, d2] |
|---|
| 313 | |
|---|
| 314 | interp = Interpolate(vertices, triangles, mesh_origin=geo) |
|---|
| 315 | f = linear_function(vertices_absolute) |
|---|
| 316 | z = interp.interpolate(f, point_coords) |
|---|
| 317 | answer = linear_function(point_coords) |
|---|
| 318 | |
|---|
| 319 | #print "z",z |
|---|
| 320 | #print "answer",answer |
|---|
| 321 | assert allclose(z, answer) |
|---|
| 322 | |
|---|
| 323 | |
|---|
| 324 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 325 | answer = linear_function(point_coords) |
|---|
| 326 | |
|---|
| 327 | #print "z",z |
|---|
| 328 | #print "answer",answer |
|---|
| 329 | assert allclose(z, answer) |
|---|
| 330 | |
|---|
| 331 | |
|---|
| 332 | def test_Geospatial_verts(self): |
|---|
| 333 | v0 = [0.0, 0.0] |
|---|
| 334 | v1 = [0.0, 5.0] |
|---|
| 335 | v2 = [5.0, 0.0] |
|---|
| 336 | |
|---|
| 337 | vertices_absolute = [v0, v1, v2] |
|---|
| 338 | triangles = [ [1,0,2] ] #bac |
|---|
| 339 | |
|---|
| 340 | geo = Geo_reference(57,100, 500) |
|---|
| 341 | vertices = geo.change_points_geo_ref(vertices_absolute) |
|---|
| 342 | geopoints = Geospatial_data(vertices,geo_reference = geo) |
|---|
| 343 | #print "vertices",vertices |
|---|
| 344 | |
|---|
| 345 | d0 = [1.0, 1.0] |
|---|
| 346 | d1 = [1.0, 2.0] |
|---|
| 347 | d2 = [3.0, 1.0] |
|---|
| 348 | point_coords = [ d0, d1, d2] |
|---|
| 349 | |
|---|
| 350 | interp = Interpolate(geopoints, triangles) |
|---|
| 351 | f = linear_function(vertices_absolute) |
|---|
| 352 | z = interp.interpolate(f, point_coords) |
|---|
| 353 | answer = linear_function(point_coords) |
|---|
| 354 | |
|---|
| 355 | #print "z",z |
|---|
| 356 | #print "answer",answer |
|---|
| 357 | assert allclose(z, answer) |
|---|
| 358 | |
|---|
| 359 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 360 | answer = linear_function(point_coords) |
|---|
| 361 | |
|---|
| 362 | #print "z",z |
|---|
| 363 | #print "answer",answer |
|---|
| 364 | assert allclose(z, answer) |
|---|
| 365 | |
|---|
| 366 | def test_interpolate_attributes_to_points(self): |
|---|
| 367 | v0 = [0.0, 0.0] |
|---|
| 368 | v1 = [0.0, 5.0] |
|---|
| 369 | v2 = [5.0, 0.0] |
|---|
| 370 | |
|---|
| 371 | vertices = [v0, v1, v2] |
|---|
| 372 | triangles = [ [1,0,2] ] #bac |
|---|
| 373 | |
|---|
| 374 | d0 = [1.0, 1.0] |
|---|
| 375 | d1 = [1.0, 2.0] |
|---|
| 376 | d2 = [3.0, 1.0] |
|---|
| 377 | point_coords = [ d0, d1, d2] |
|---|
| 378 | |
|---|
| 379 | interp = Interpolate(vertices, triangles) |
|---|
| 380 | f = linear_function(vertices) |
|---|
| 381 | z = interp.interpolate(f, point_coords) |
|---|
| 382 | answer = linear_function(point_coords) |
|---|
| 383 | |
|---|
| 384 | #print "z",z |
|---|
| 385 | #print "answer",answer |
|---|
| 386 | assert allclose(z, answer) |
|---|
| 387 | |
|---|
| 388 | |
|---|
| 389 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 390 | answer = linear_function(point_coords) |
|---|
| 391 | |
|---|
| 392 | #print "z",z |
|---|
| 393 | #print "answer",answer |
|---|
| 394 | assert allclose(z, answer) |
|---|
| 395 | |
|---|
| 396 | def test_interpolate_attributes_to_pointsII(self): |
|---|
| 397 | a = [-1.0, 0.0] |
|---|
| 398 | b = [3.0, 4.0] |
|---|
| 399 | c = [4.0, 1.0] |
|---|
| 400 | d = [-3.0, 2.0] #3 |
|---|
| 401 | e = [-1.0, -2.0] |
|---|
| 402 | f = [1.0, -2.0] #5 |
|---|
| 403 | |
|---|
| 404 | vertices = [a, b, c, d,e,f] |
|---|
| 405 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 406 | |
|---|
| 407 | |
|---|
| 408 | point_coords = [[-2.0, 2.0], |
|---|
| 409 | [-1.0, 1.0], |
|---|
| 410 | [0.0, 2.0], |
|---|
| 411 | [1.0, 1.0], |
|---|
| 412 | [2.0, 1.0], |
|---|
| 413 | [0.0, 0.0], |
|---|
| 414 | [1.0, 0.0], |
|---|
| 415 | [0.0, -1.0], |
|---|
| 416 | [-0.2, -0.5], |
|---|
| 417 | [-0.9, -1.5], |
|---|
| 418 | [0.5, -1.9], |
|---|
| 419 | [3.0, 1.0]] |
|---|
| 420 | |
|---|
| 421 | interp = Interpolate(vertices, triangles) |
|---|
| 422 | f = linear_function(vertices) |
|---|
| 423 | z = interp.interpolate(f, point_coords) |
|---|
| 424 | answer = linear_function(point_coords) |
|---|
| 425 | #print "z",z |
|---|
| 426 | #print "answer",answer |
|---|
| 427 | assert allclose(z, answer) |
|---|
| 428 | |
|---|
| 429 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 430 | answer = linear_function(point_coords) |
|---|
| 431 | |
|---|
| 432 | #print "z",z |
|---|
| 433 | #print "answer",answer |
|---|
| 434 | assert allclose(z, answer) |
|---|
| 435 | |
|---|
| 436 | def test_interpolate_attributes_to_pointsIII(self): |
|---|
| 437 | """Test linear interpolation of known values at vertices to |
|---|
| 438 | new points inside a triangle |
|---|
| 439 | """ |
|---|
| 440 | a = [0.0, 0.0] |
|---|
| 441 | b = [0.0, 5.0] |
|---|
| 442 | c = [5.0, 0.0] |
|---|
| 443 | d = [5.0, 5.0] |
|---|
| 444 | |
|---|
| 445 | vertices = [a, b, c, d] |
|---|
| 446 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
|---|
| 447 | |
|---|
| 448 | #Points within triangle 1 |
|---|
| 449 | d0 = [1.0, 1.0] |
|---|
| 450 | d1 = [1.0, 2.0] |
|---|
| 451 | d2 = [3.0, 1.0] |
|---|
| 452 | |
|---|
| 453 | #Point within triangle 2 |
|---|
| 454 | d3 = [4.0, 3.0] |
|---|
| 455 | |
|---|
| 456 | #Points on common edge |
|---|
| 457 | d4 = [2.5, 2.5] |
|---|
| 458 | d5 = [4.0, 1.0] |
|---|
| 459 | |
|---|
| 460 | #Point on common vertex |
|---|
| 461 | d6 = [0., 5.] |
|---|
| 462 | |
|---|
| 463 | point_coords = [d0, d1, d2, d3, d4, d5, d6] |
|---|
| 464 | |
|---|
| 465 | interp = Interpolate(vertices, triangles) |
|---|
| 466 | |
|---|
| 467 | #Known values at vertices |
|---|
| 468 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
|---|
| 469 | f = [ [0., 0., 0., -5.], # (0,0) |
|---|
| 470 | [5., 10., 5., -10.], # (0,5) |
|---|
| 471 | [5., 5., 10.0, 0.], # (5,0) |
|---|
| 472 | [10., 15., 15., -5.]] # (5,5) |
|---|
| 473 | |
|---|
| 474 | z = interp.interpolate(f, point_coords) |
|---|
| 475 | answer = [ [2., 3., 3., -5.], # (1,1) |
|---|
| 476 | [3., 5., 4., -6.], # (1,2) |
|---|
| 477 | [4., 5., 7., -3.], # (3,1) |
|---|
| 478 | [7., 10., 11., -4.], # (4,3) |
|---|
| 479 | [5., 7.5, 7.5, -5.], # (2.5, 2.5) |
|---|
| 480 | [5., 6., 9., -2.], # (4,1) |
|---|
| 481 | [5., 10., 5., -10.]] # (0,5) |
|---|
| 482 | |
|---|
| 483 | #print "***********" |
|---|
| 484 | #print "z",z |
|---|
| 485 | #print "answer",answer |
|---|
| 486 | #print "***********" |
|---|
| 487 | |
|---|
| 488 | #Should an error message be returned if points are outside |
|---|
| 489 | # of the mesh? Not currently. |
|---|
| 490 | |
|---|
| 491 | assert allclose(z, answer) |
|---|
| 492 | |
|---|
| 493 | |
|---|
| 494 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 495 | |
|---|
| 496 | #print "z",z |
|---|
| 497 | #print "answer",answer |
|---|
| 498 | assert allclose(z, answer) |
|---|
| 499 | |
|---|
| 500 | def test_interpolate_point_outside_of_mesh(self): |
|---|
| 501 | """Test linear interpolation of known values at vertices to |
|---|
| 502 | new points inside a triangle |
|---|
| 503 | """ |
|---|
| 504 | a = [0.0, 0.0] |
|---|
| 505 | b = [0.0, 5.0] |
|---|
| 506 | c = [5.0, 0.0] |
|---|
| 507 | d = [5.0, 5.0] |
|---|
| 508 | |
|---|
| 509 | vertices = [a, b, c, d] |
|---|
| 510 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
|---|
| 511 | |
|---|
| 512 | #Far away point |
|---|
| 513 | d7 = [-1., -1.] |
|---|
| 514 | |
|---|
| 515 | point_coords = [ d7] |
|---|
| 516 | interp = Interpolate(vertices, triangles) |
|---|
| 517 | |
|---|
| 518 | #Known values at vertices |
|---|
| 519 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
|---|
| 520 | f = [ [0., 0., 0., -5.], # (0,0) |
|---|
| 521 | [5., 10., 5., -10.], # (0,5) |
|---|
| 522 | [5., 5., 10.0, 0.], # (5,0) |
|---|
| 523 | [10., 15., 15., -5.]] # (5,5) |
|---|
| 524 | |
|---|
| 525 | z = interp.interpolate(f, point_coords) |
|---|
| 526 | answer = array([ [INF, INF, INF, INF]]) # (-1,-1) |
|---|
| 527 | |
|---|
| 528 | #print "***********" |
|---|
| 529 | #print "z",z |
|---|
| 530 | #print "answer",answer |
|---|
| 531 | #print "***********" |
|---|
| 532 | |
|---|
| 533 | #Should an error message be returned if points are outside |
|---|
| 534 | # of the mesh? Not currently. |
|---|
| 535 | |
|---|
| 536 | for i in range(4): |
|---|
| 537 | self.failUnless( z[0,i] == answer[0,i], 'Fail!') |
|---|
| 538 | |
|---|
| 539 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 540 | |
|---|
| 541 | #print "z",z |
|---|
| 542 | #print "answer",answer |
|---|
| 543 | |
|---|
| 544 | for i in range(4): |
|---|
| 545 | self.failUnless( z[0,i] == answer[0,i], 'Fail!') |
|---|
| 546 | |
|---|
| 547 | |
|---|
| 548 | def test_interpolate_attributes_to_pointsIV(self): |
|---|
| 549 | a = [-1.0, 0.0] |
|---|
| 550 | b = [3.0, 4.0] |
|---|
| 551 | c = [4.0, 1.0] |
|---|
| 552 | d = [-3.0, 2.0] #3 |
|---|
| 553 | e = [-1.0, -2.0] |
|---|
| 554 | f = [1.0, -2.0] #5 |
|---|
| 555 | |
|---|
| 556 | vertices = [a, b, c, d,e,f] |
|---|
| 557 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 558 | |
|---|
| 559 | |
|---|
| 560 | point_coords = [[-2.0, 2.0], |
|---|
| 561 | [-1.0, 1.0], |
|---|
| 562 | [0.0, 2.0], |
|---|
| 563 | [1.0, 1.0], |
|---|
| 564 | [2.0, 1.0], |
|---|
| 565 | [0.0, 0.0], |
|---|
| 566 | [1.0, 0.0], |
|---|
| 567 | [0.0, -1.0], |
|---|
| 568 | [-0.2, -0.5], |
|---|
| 569 | [-0.9, -1.5], |
|---|
| 570 | [0.5, -1.9], |
|---|
| 571 | [3.0, 1.0]] |
|---|
| 572 | |
|---|
| 573 | interp = Interpolate(vertices, triangles) |
|---|
| 574 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 575 | f = transpose(f) |
|---|
| 576 | #print "f",f |
|---|
| 577 | z = interp.interpolate(f, point_coords) |
|---|
| 578 | answer = [linear_function(point_coords), |
|---|
| 579 | 2*linear_function(point_coords) ] |
|---|
| 580 | answer = transpose(answer) |
|---|
| 581 | #print "z",z |
|---|
| 582 | #print "answer",answer |
|---|
| 583 | assert allclose(z, answer) |
|---|
| 584 | |
|---|
| 585 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 586 | |
|---|
| 587 | #print "z",z |
|---|
| 588 | #print "answer",answer |
|---|
| 589 | assert allclose(z, answer) |
|---|
| 590 | |
|---|
| 591 | def test_interpolate_blocking(self): |
|---|
| 592 | a = [-1.0, 0.0] |
|---|
| 593 | b = [3.0, 4.0] |
|---|
| 594 | c = [4.0, 1.0] |
|---|
| 595 | d = [-3.0, 2.0] #3 |
|---|
| 596 | e = [-1.0, -2.0] |
|---|
| 597 | f = [1.0, -2.0] #5 |
|---|
| 598 | |
|---|
| 599 | vertices = [a, b, c, d,e,f] |
|---|
| 600 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 601 | |
|---|
| 602 | |
|---|
| 603 | point_coords = [[-2.0, 2.0], |
|---|
| 604 | [-1.0, 1.0], |
|---|
| 605 | [0.0, 2.0], |
|---|
| 606 | [1.0, 1.0], |
|---|
| 607 | [2.0, 1.0], |
|---|
| 608 | [0.0, 0.0], |
|---|
| 609 | [1.0, 0.0], |
|---|
| 610 | [0.0, -1.0], |
|---|
| 611 | [-0.2, -0.5], |
|---|
| 612 | [-0.9, -1.5], |
|---|
| 613 | [0.5, -1.9], |
|---|
| 614 | [3.0, 1.0]] |
|---|
| 615 | |
|---|
| 616 | interp = Interpolate(vertices, triangles) |
|---|
| 617 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 618 | f = transpose(f) |
|---|
| 619 | #print "f",f |
|---|
| 620 | for blocking_max in range(len(point_coords)+2): |
|---|
| 621 | #if True: |
|---|
| 622 | # blocking_max = 5 |
|---|
| 623 | z = interp.interpolate(f, point_coords, |
|---|
| 624 | start_blocking_len=blocking_max) |
|---|
| 625 | answer = [linear_function(point_coords), |
|---|
| 626 | 2*linear_function(point_coords) ] |
|---|
| 627 | answer = transpose(answer) |
|---|
| 628 | #print "z",z |
|---|
| 629 | #print "answer",answer |
|---|
| 630 | assert allclose(z, answer) |
|---|
| 631 | |
|---|
| 632 | f = array([linear_function(vertices),2*linear_function(vertices), |
|---|
| 633 | 2*linear_function(vertices) - 100 ]) |
|---|
| 634 | f = transpose(f) |
|---|
| 635 | #print "f",f |
|---|
| 636 | for blocking_max in range(len(point_coords)+2): |
|---|
| 637 | #if True: |
|---|
| 638 | # blocking_max = 5 |
|---|
| 639 | z = interp.interpolate(f, point_coords, |
|---|
| 640 | start_blocking_len=blocking_max) |
|---|
| 641 | answer = array([linear_function(point_coords), |
|---|
| 642 | 2*linear_function(point_coords) , |
|---|
| 643 | 2*linear_function(point_coords)-100 ]) |
|---|
| 644 | z = transpose(z) |
|---|
| 645 | #print "z",z |
|---|
| 646 | #print "answer",answer |
|---|
| 647 | assert allclose(z, answer) |
|---|
| 648 | |
|---|
| 649 | def test_interpolate_geo_spatial(self): |
|---|
| 650 | a = [-1.0, 0.0] |
|---|
| 651 | b = [3.0, 4.0] |
|---|
| 652 | c = [4.0, 1.0] |
|---|
| 653 | d = [-3.0, 2.0] #3 |
|---|
| 654 | e = [-1.0, -2.0] |
|---|
| 655 | f = [1.0, -2.0] #5 |
|---|
| 656 | |
|---|
| 657 | vertices = [a, b, c, d,e,f] |
|---|
| 658 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 659 | |
|---|
| 660 | |
|---|
| 661 | point_coords_absolute = [[-2.0, 2.0], |
|---|
| 662 | [-1.0, 1.0], |
|---|
| 663 | [0.0, 2.0], |
|---|
| 664 | [1.0, 1.0], |
|---|
| 665 | [2.0, 1.0], |
|---|
| 666 | [0.0, 0.0], |
|---|
| 667 | [1.0, 0.0], |
|---|
| 668 | [0.0, -1.0], |
|---|
| 669 | [-0.2, -0.5], |
|---|
| 670 | [-0.9, -1.5], |
|---|
| 671 | [0.5, -1.9], |
|---|
| 672 | [3.0, 1.0]] |
|---|
| 673 | |
|---|
| 674 | geo = Geo_reference(57,100, 500) |
|---|
| 675 | point_coords = geo.change_points_geo_ref(point_coords_absolute) |
|---|
| 676 | point_coords = Geospatial_data(point_coords,geo_reference = geo) |
|---|
| 677 | |
|---|
| 678 | interp = Interpolate(vertices, triangles) |
|---|
| 679 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 680 | f = transpose(f) |
|---|
| 681 | #print "f",f |
|---|
| 682 | for blocking_max in range(14): |
|---|
| 683 | #if True: |
|---|
| 684 | # blocking_max = 5 |
|---|
| 685 | z = interp.interpolate(f, point_coords, |
|---|
| 686 | start_blocking_len=blocking_max) |
|---|
| 687 | answer = [linear_function(point_coords.get_data_points( \ |
|---|
| 688 | absolute = True)), |
|---|
| 689 | 2*linear_function(point_coords.get_data_points( \ |
|---|
| 690 | absolute = True)) ] |
|---|
| 691 | answer = transpose(answer) |
|---|
| 692 | #print "z",z |
|---|
| 693 | #print "answer",answer |
|---|
| 694 | assert allclose(z, answer) |
|---|
| 695 | |
|---|
| 696 | f = array([linear_function(vertices),2*linear_function(vertices), |
|---|
| 697 | 2*linear_function(vertices) - 100 ]) |
|---|
| 698 | f = transpose(f) |
|---|
| 699 | #print "f",f |
|---|
| 700 | for blocking_max in range(14): |
|---|
| 701 | #if True: |
|---|
| 702 | # blocking_max = 5 |
|---|
| 703 | z = interp.interpolate(f, point_coords, |
|---|
| 704 | start_blocking_len=blocking_max) |
|---|
| 705 | answer = array([linear_function(point_coords.get_data_points( \ |
|---|
| 706 | absolute = True)), |
|---|
| 707 | 2*linear_function(point_coords.get_data_points( \ |
|---|
| 708 | absolute = True)) , |
|---|
| 709 | 2*linear_function(point_coords.get_data_points( \ |
|---|
| 710 | absolute = True))-100 ]) |
|---|
| 711 | z = transpose(z) |
|---|
| 712 | #print "z",z |
|---|
| 713 | #print "answer",answer |
|---|
| 714 | assert allclose(z, answer) |
|---|
| 715 | |
|---|
| 716 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 717 | |
|---|
| 718 | #print "z",z |
|---|
| 719 | #print "answer",answer |
|---|
| 720 | assert allclose(z, answer) |
|---|
| 721 | |
|---|
| 722 | def test_interpolate_geo_spatial(self): |
|---|
| 723 | a = [-1.0, 0.0] |
|---|
| 724 | b = [3.0, 4.0] |
|---|
| 725 | c = [4.0, 1.0] |
|---|
| 726 | d = [-3.0, 2.0] #3 |
|---|
| 727 | e = [-1.0, -2.0] |
|---|
| 728 | f = [1.0, -2.0] #5 |
|---|
| 729 | |
|---|
| 730 | vertices = [a, b, c, d,e,f] |
|---|
| 731 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 732 | |
|---|
| 733 | |
|---|
| 734 | point_coords_absolute = [[-2.0, 2.0], |
|---|
| 735 | [-1.0, 1.0], |
|---|
| 736 | [0.0, 2.0], |
|---|
| 737 | [1.0, 1.0], |
|---|
| 738 | [2.0, 1.0], |
|---|
| 739 | [0.0, 0.0], |
|---|
| 740 | [1.0, 0.0], |
|---|
| 741 | [0.0, -1.0], |
|---|
| 742 | [-0.2, -0.5], |
|---|
| 743 | [-0.9, -1.5], |
|---|
| 744 | [0.5, -1.9], |
|---|
| 745 | [3.0, 1.0]] |
|---|
| 746 | |
|---|
| 747 | geo = Geo_reference(57,100, 500) |
|---|
| 748 | point_coords = geo.change_points_geo_ref(point_coords_absolute) |
|---|
| 749 | point_coords = Geospatial_data(point_coords,geo_reference = geo) |
|---|
| 750 | |
|---|
| 751 | interp = Interpolate(vertices, triangles) |
|---|
| 752 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 753 | f = transpose(f) |
|---|
| 754 | #print "f",f |
|---|
| 755 | z = interp.interpolate_block(f, point_coords) |
|---|
| 756 | answer = [linear_function(point_coords.get_data_points( \ |
|---|
| 757 | absolute = True)), |
|---|
| 758 | 2*linear_function(point_coords.get_data_points( \ |
|---|
| 759 | absolute = True)) ] |
|---|
| 760 | answer = transpose(answer) |
|---|
| 761 | #print "z",z |
|---|
| 762 | #print "answer",answer |
|---|
| 763 | assert allclose(z, answer) |
|---|
| 764 | |
|---|
| 765 | z = interp.interpolate(f, point_coords, start_blocking_len = 2) |
|---|
| 766 | |
|---|
| 767 | #print "z",z |
|---|
| 768 | #print "answer",answer |
|---|
| 769 | assert allclose(z, answer) |
|---|
| 770 | |
|---|
| 771 | |
|---|
| 772 | def test_interpolate_reuse(self): |
|---|
| 773 | a = [-1.0, 0.0] |
|---|
| 774 | b = [3.0, 4.0] |
|---|
| 775 | c = [4.0, 1.0] |
|---|
| 776 | d = [-3.0, 2.0] #3 |
|---|
| 777 | e = [-1.0, -2.0] |
|---|
| 778 | f = [1.0, -2.0] #5 |
|---|
| 779 | |
|---|
| 780 | vertices = [a, b, c, d,e,f] |
|---|
| 781 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 782 | |
|---|
| 783 | |
|---|
| 784 | point_coords = [[-2.0, 2.0], |
|---|
| 785 | [-1.0, 1.0], |
|---|
| 786 | [0.0, 2.0], |
|---|
| 787 | [1.0, 1.0], |
|---|
| 788 | [2.0, 1.0], |
|---|
| 789 | [0.0, 0.0], |
|---|
| 790 | [1.0, 0.0], |
|---|
| 791 | [0.0, -1.0], |
|---|
| 792 | [-0.2, -0.5], |
|---|
| 793 | [-0.9, -1.5], |
|---|
| 794 | [0.5, -1.9], |
|---|
| 795 | [3.0, 1.0]] |
|---|
| 796 | |
|---|
| 797 | interp = Interpolate(vertices, triangles) |
|---|
| 798 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 799 | f = transpose(f) |
|---|
| 800 | z = interp.interpolate(f, point_coords, |
|---|
| 801 | start_blocking_len=20) |
|---|
| 802 | answer = [linear_function(point_coords), |
|---|
| 803 | 2*linear_function(point_coords) ] |
|---|
| 804 | answer = transpose(answer) |
|---|
| 805 | #print "z",z |
|---|
| 806 | #print "answer",answer |
|---|
| 807 | assert allclose(z, answer) |
|---|
| 808 | assert allclose(interp._A_can_be_reused, True) |
|---|
| 809 | |
|---|
| 810 | z = interp.interpolate(f) |
|---|
| 811 | assert allclose(z, answer) |
|---|
| 812 | |
|---|
| 813 | # This causes blocking to occur. |
|---|
| 814 | z = interp.interpolate(f, start_blocking_len=10) |
|---|
| 815 | assert allclose(z, answer) |
|---|
| 816 | assert allclose(interp._A_can_be_reused, False) |
|---|
| 817 | |
|---|
| 818 | #A is recalculated |
|---|
| 819 | z = interp.interpolate(f) |
|---|
| 820 | assert allclose(z, answer) |
|---|
| 821 | assert allclose(interp._A_can_be_reused, True) |
|---|
| 822 | |
|---|
| 823 | interp = Interpolate(vertices, triangles) |
|---|
| 824 | #Must raise an exception, no points specified |
|---|
| 825 | try: |
|---|
| 826 | z = interp.interpolate(f) |
|---|
| 827 | except: |
|---|
| 828 | pass |
|---|
| 829 | |
|---|
| 830 | |
|---|
| 831 | |
|---|
| 832 | def test_interpolation_interface_time_only(self): |
|---|
| 833 | |
|---|
| 834 | # Test spatio-temporal interpolation |
|---|
| 835 | # Test that spatio temporal function performs the correct |
|---|
| 836 | # interpolations in both time and space |
|---|
| 837 | |
|---|
| 838 | |
|---|
| 839 | |
|---|
| 840 | #Three timesteps |
|---|
| 841 | time = [1.0, 5.0, 6.0] |
|---|
| 842 | |
|---|
| 843 | |
|---|
| 844 | #One quantity |
|---|
| 845 | Q = zeros( (3,6), Float ) |
|---|
| 846 | |
|---|
| 847 | #Linear in time and space |
|---|
| 848 | a = [0.0, 0.0] |
|---|
| 849 | b = [0.0, 2.0] |
|---|
| 850 | c = [2.0, 0.0] |
|---|
| 851 | d = [0.0, 4.0] |
|---|
| 852 | e = [2.0, 2.0] |
|---|
| 853 | f = [4.0, 0.0] |
|---|
| 854 | |
|---|
| 855 | points = [a, b, c, d, e, f] |
|---|
| 856 | |
|---|
| 857 | for i, t in enumerate(time): |
|---|
| 858 | Q[i, :] = t*linear_function(points) |
|---|
| 859 | |
|---|
| 860 | |
|---|
| 861 | #Check basic interpolation of one quantity using averaging |
|---|
| 862 | #(no interpolation points or spatial info) |
|---|
| 863 | I = Interpolation_function(time, [mean(Q[0,:]), |
|---|
| 864 | mean(Q[1,:]), |
|---|
| 865 | mean(Q[2,:])]) |
|---|
| 866 | |
|---|
| 867 | |
|---|
| 868 | |
|---|
| 869 | #Check temporal interpolation |
|---|
| 870 | for i in [0,1,2]: |
|---|
| 871 | assert allclose(I(time[i]), mean(Q[i,:])) |
|---|
| 872 | |
|---|
| 873 | #Midway |
|---|
| 874 | assert allclose(I( (time[0] + time[1])/2 ), |
|---|
| 875 | (I(time[0]) + I(time[1]))/2 ) |
|---|
| 876 | |
|---|
| 877 | assert allclose(I( (time[1] + time[2])/2 ), |
|---|
| 878 | (I(time[1]) + I(time[2]))/2 ) |
|---|
| 879 | |
|---|
| 880 | assert allclose(I( (time[0] + time[2])/2 ), |
|---|
| 881 | (I(time[0]) + I(time[2]))/2 ) |
|---|
| 882 | |
|---|
| 883 | #1/3 |
|---|
| 884 | assert allclose(I( (time[0] + time[2])/3 ), |
|---|
| 885 | (I(time[0]) + I(time[2]))/3 ) |
|---|
| 886 | |
|---|
| 887 | |
|---|
| 888 | #Out of bounds checks |
|---|
| 889 | try: |
|---|
| 890 | I(time[0]-1) |
|---|
| 891 | except: |
|---|
| 892 | pass |
|---|
| 893 | else: |
|---|
| 894 | raise 'Should raise exception' |
|---|
| 895 | |
|---|
| 896 | try: |
|---|
| 897 | I(time[-1]+1) |
|---|
| 898 | except: |
|---|
| 899 | pass |
|---|
| 900 | else: |
|---|
| 901 | raise 'Should raise exception' |
|---|
| 902 | |
|---|
| 903 | |
|---|
| 904 | |
|---|
| 905 | |
|---|
| 906 | def test_interpolation_interface_spatial_only(self): |
|---|
| 907 | # Test spatio-temporal interpolation with constant time |
|---|
| 908 | |
|---|
| 909 | #Three timesteps |
|---|
| 910 | time = [1.0, 5.0, 6.0] |
|---|
| 911 | |
|---|
| 912 | |
|---|
| 913 | #Setup mesh used to represent fitted function |
|---|
| 914 | a = [0.0, 0.0] |
|---|
| 915 | b = [0.0, 2.0] |
|---|
| 916 | c = [2.0, 0.0] |
|---|
| 917 | d = [0.0, 4.0] |
|---|
| 918 | e = [2.0, 2.0] |
|---|
| 919 | f = [4.0, 0.0] |
|---|
| 920 | |
|---|
| 921 | points = [a, b, c, d, e, f] |
|---|
| 922 | #bac, bce, ecf, dbe |
|---|
| 923 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
|---|
| 924 | |
|---|
| 925 | |
|---|
| 926 | #New datapoints where interpolated values are sought |
|---|
| 927 | interpolation_points = [[ 0.0, 0.0], |
|---|
| 928 | [ 0.5, 0.5], |
|---|
| 929 | [ 0.7, 0.7], |
|---|
| 930 | [ 1.0, 0.5], |
|---|
| 931 | [ 2.0, 0.4], |
|---|
| 932 | [ 2.8, 1.2]] |
|---|
| 933 | |
|---|
| 934 | |
|---|
| 935 | #One quantity linear in space |
|---|
| 936 | Q = linear_function(points) |
|---|
| 937 | |
|---|
| 938 | |
|---|
| 939 | #Check interpolation of one quantity using interpolaton points |
|---|
| 940 | I = Interpolation_function(time, Q, |
|---|
| 941 | vertex_coordinates = points, |
|---|
| 942 | triangles = triangles, |
|---|
| 943 | interpolation_points = interpolation_points, |
|---|
| 944 | verbose = False) |
|---|
| 945 | |
|---|
| 946 | |
|---|
| 947 | answer = linear_function(interpolation_points) |
|---|
| 948 | |
|---|
| 949 | t = time[0] |
|---|
| 950 | for j in range(50): #t in [1, 6] |
|---|
| 951 | for id in range(len(interpolation_points)): |
|---|
| 952 | assert allclose(I(t, id), answer[id]) |
|---|
| 953 | |
|---|
| 954 | t += 0.1 |
|---|
| 955 | |
|---|
| 956 | |
|---|
| 957 | try: |
|---|
| 958 | I(1) |
|---|
| 959 | except: |
|---|
| 960 | pass |
|---|
| 961 | else: |
|---|
| 962 | raise 'Should raise exception' |
|---|
| 963 | |
|---|
| 964 | |
|---|
| 965 | |
|---|
| 966 | def test_interpolation_interface(self): |
|---|
| 967 | # Test spatio-temporal interpolation |
|---|
| 968 | # Test that spatio temporal function performs the correct |
|---|
| 969 | # interpolations in both time and space |
|---|
| 970 | |
|---|
| 971 | #Three timesteps |
|---|
| 972 | time = [1.0, 5.0, 6.0] |
|---|
| 973 | |
|---|
| 974 | #Setup mesh used to represent fitted function |
|---|
| 975 | a = [0.0, 0.0] |
|---|
| 976 | b = [0.0, 2.0] |
|---|
| 977 | c = [2.0, 0.0] |
|---|
| 978 | d = [0.0, 4.0] |
|---|
| 979 | e = [2.0, 2.0] |
|---|
| 980 | f = [4.0, 0.0] |
|---|
| 981 | |
|---|
| 982 | points = [a, b, c, d, e, f] |
|---|
| 983 | #bac, bce, ecf, dbe |
|---|
| 984 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
|---|
| 985 | |
|---|
| 986 | |
|---|
| 987 | #New datapoints where interpolated values are sought |
|---|
| 988 | interpolation_points = [[ 0.0, 0.0], |
|---|
| 989 | [ 0.5, 0.5], |
|---|
| 990 | [ 0.7, 0.7], |
|---|
| 991 | [ 1.0, 0.5], |
|---|
| 992 | [ 2.0, 0.4], |
|---|
| 993 | [ 2.8, 1.2]] |
|---|
| 994 | |
|---|
| 995 | #One quantity |
|---|
| 996 | Q = zeros( (3,6), Float ) |
|---|
| 997 | |
|---|
| 998 | #Linear in time and space |
|---|
| 999 | for i, t in enumerate(time): |
|---|
| 1000 | Q[i, :] = t*linear_function(points) |
|---|
| 1001 | |
|---|
| 1002 | #Check interpolation of one quantity using interpolaton points) |
|---|
| 1003 | I = Interpolation_function(time, Q, |
|---|
| 1004 | vertex_coordinates = points, |
|---|
| 1005 | triangles = triangles, |
|---|
| 1006 | interpolation_points = interpolation_points, |
|---|
| 1007 | verbose = False) |
|---|
| 1008 | |
|---|
| 1009 | answer = linear_function(interpolation_points) |
|---|
| 1010 | |
|---|
| 1011 | t = time[0] |
|---|
| 1012 | for j in range(50): #t in [1, 6] |
|---|
| 1013 | for id in range(len(interpolation_points)): |
|---|
| 1014 | assert allclose(I(t, id), t*answer[id]) |
|---|
| 1015 | t += 0.1 |
|---|
| 1016 | |
|---|
| 1017 | try: |
|---|
| 1018 | I(1) |
|---|
| 1019 | except: |
|---|
| 1020 | pass |
|---|
| 1021 | else: |
|---|
| 1022 | raise 'Should raise exception' |
|---|
| 1023 | |
|---|
| 1024 | |
|---|
| 1025 | def test_interpolation_precompute_points(self): |
|---|
| 1026 | # looking at a discrete mesh |
|---|
| 1027 | # |
|---|
| 1028 | |
|---|
| 1029 | #Three timesteps |
|---|
| 1030 | time = [0.0, 60.0] |
|---|
| 1031 | |
|---|
| 1032 | #Setup mesh used to represent fitted function |
|---|
| 1033 | points = [[ 15., -20.], |
|---|
| 1034 | [ 15., 10.], |
|---|
| 1035 | [ 0., -20.], |
|---|
| 1036 | [ 0., 10.], |
|---|
| 1037 | [ 0., -20.], |
|---|
| 1038 | [ 15., 10.]] |
|---|
| 1039 | |
|---|
| 1040 | triangles = [[0, 1, 2], |
|---|
| 1041 | [3, 4, 5]] |
|---|
| 1042 | |
|---|
| 1043 | #New datapoints where interpolated values are sought |
|---|
| 1044 | interpolation_points = [[ 1., 0.], [0.,1.]] |
|---|
| 1045 | |
|---|
| 1046 | #One quantity |
|---|
| 1047 | Q = zeros( (2,6), Float ) |
|---|
| 1048 | |
|---|
| 1049 | #Linear in time and space |
|---|
| 1050 | for i, t in enumerate(time): |
|---|
| 1051 | Q[i, :] = t*linear_function(points) |
|---|
| 1052 | #print "Q", Q |
|---|
| 1053 | |
|---|
| 1054 | |
|---|
| 1055 | |
|---|
| 1056 | interp = Interpolate(points, triangles) |
|---|
| 1057 | f = array([linear_function(points),2*linear_function(points) ]) |
|---|
| 1058 | f = transpose(f) |
|---|
| 1059 | #print "f",f |
|---|
| 1060 | z = interp.interpolate(f, interpolation_points) |
|---|
| 1061 | answer = [linear_function(interpolation_points), |
|---|
| 1062 | 2*linear_function(interpolation_points) ] |
|---|
| 1063 | answer = transpose(answer) |
|---|
| 1064 | #print "z",z |
|---|
| 1065 | #print "answer",answer |
|---|
| 1066 | assert allclose(z, answer) |
|---|
| 1067 | |
|---|
| 1068 | |
|---|
| 1069 | #Check interpolation of one quantity using interpolaton points) |
|---|
| 1070 | I = Interpolation_function(time, Q, |
|---|
| 1071 | vertex_coordinates = points, |
|---|
| 1072 | triangles = triangles, |
|---|
| 1073 | interpolation_points = interpolation_points, |
|---|
| 1074 | verbose = False) |
|---|
| 1075 | |
|---|
| 1076 | #print "I.precomputed_values", I.precomputed_values |
|---|
| 1077 | |
|---|
| 1078 | msg = 'Interpolation failed' |
|---|
| 1079 | assert allclose(I.precomputed_values['Attribute'][1], [60, 60]), msg |
|---|
| 1080 | #self.failUnless( I.precomputed_values['Attribute'][1] == 60.0, |
|---|
| 1081 | # ' failed') |
|---|
| 1082 | |
|---|
| 1083 | def test_interpolation_function_outside_point(self): |
|---|
| 1084 | # Test spatio-temporal interpolation |
|---|
| 1085 | # Test that spatio temporal function performs the correct |
|---|
| 1086 | # interpolations in both time and space |
|---|
| 1087 | |
|---|
| 1088 | #Three timesteps |
|---|
| 1089 | time = [1.0, 5.0, 6.0] |
|---|
| 1090 | |
|---|
| 1091 | #Setup mesh used to represent fitted function |
|---|
| 1092 | a = [0.0, 0.0] |
|---|
| 1093 | b = [0.0, 2.0] |
|---|
| 1094 | c = [2.0, 0.0] |
|---|
| 1095 | d = [0.0, 4.0] |
|---|
| 1096 | e = [2.0, 2.0] |
|---|
| 1097 | f = [4.0, 0.0] |
|---|
| 1098 | |
|---|
| 1099 | points = [a, b, c, d, e, f] |
|---|
| 1100 | #bac, bce, ecf, dbe |
|---|
| 1101 | triangles = [[1,0,2], [1,2,4], [4,2,5], [3,1,4]] |
|---|
| 1102 | |
|---|
| 1103 | |
|---|
| 1104 | #New datapoints where interpolated values are sought |
|---|
| 1105 | interpolation_points = [[ 0.0, 0.0], |
|---|
| 1106 | [ 0.5, 0.5], |
|---|
| 1107 | [ 0.7, 0.7], |
|---|
| 1108 | [ 1.0, 0.5], |
|---|
| 1109 | [ 2.0, 0.4], |
|---|
| 1110 | [ 545354534, 4354354353]] # outside the mesh |
|---|
| 1111 | |
|---|
| 1112 | #One quantity |
|---|
| 1113 | Q = zeros( (3,6), Float ) |
|---|
| 1114 | |
|---|
| 1115 | #Linear in time and space |
|---|
| 1116 | for i, t in enumerate(time): |
|---|
| 1117 | Q[i, :] = t*linear_function(points) |
|---|
| 1118 | |
|---|
| 1119 | #Check interpolation of one quantity using interpolaton points) |
|---|
| 1120 | I = Interpolation_function(time, Q, |
|---|
| 1121 | vertex_coordinates = points, |
|---|
| 1122 | triangles = triangles, |
|---|
| 1123 | interpolation_points = interpolation_points, |
|---|
| 1124 | verbose = False) |
|---|
| 1125 | |
|---|
| 1126 | answer = linear_function(interpolation_points) |
|---|
| 1127 | |
|---|
| 1128 | t = time[0] |
|---|
| 1129 | for j in range(50): #t in [1, 6] |
|---|
| 1130 | for id in range(len(interpolation_points)-1): |
|---|
| 1131 | assert allclose(I(t, id), t*answer[id]) |
|---|
| 1132 | t += 0.1 |
|---|
| 1133 | |
|---|
| 1134 | # Now test the point outside the mesh |
|---|
| 1135 | t = time[0] |
|---|
| 1136 | for j in range(50): #t in [1, 6] |
|---|
| 1137 | self.failUnless(I(t, 5) == INF, 'Fail!') |
|---|
| 1138 | t += 0.1 |
|---|
| 1139 | |
|---|
| 1140 | try: |
|---|
| 1141 | I(1) |
|---|
| 1142 | except: |
|---|
| 1143 | pass |
|---|
| 1144 | else: |
|---|
| 1145 | raise 'Should raise exception' |
|---|
| 1146 | |
|---|
| 1147 | def test_points_outside_the_polygon(self): |
|---|
| 1148 | a = [-1.0, 0.0] |
|---|
| 1149 | b = [3.0, 4.0] |
|---|
| 1150 | c = [4.0, 1.0] |
|---|
| 1151 | d = [-3.0, 2.0] #3 |
|---|
| 1152 | e = [-1.0, -2.0] |
|---|
| 1153 | f = [1.0, -2.0] #5 |
|---|
| 1154 | |
|---|
| 1155 | vertices = [a, b, c, d,e,f] |
|---|
| 1156 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
|---|
| 1157 | |
|---|
| 1158 | point_coords = [[-2.0, 2.0], |
|---|
| 1159 | [-1.0, 1.0], |
|---|
| 1160 | [9999.0, 9999.0], # point Outside poly |
|---|
| 1161 | [-9999.0, 1.0], # point Outside poly |
|---|
| 1162 | [2.0, 1.0], |
|---|
| 1163 | [0.0, 0.0], |
|---|
| 1164 | [1.0, 0.0], |
|---|
| 1165 | [0.0, -1.0], |
|---|
| 1166 | [-0.2, -0.5], |
|---|
| 1167 | [-0.9, -1.5], |
|---|
| 1168 | [0.5, -1.9], |
|---|
| 1169 | [999999, 9999999]] # point Outside poly |
|---|
| 1170 | geo_data = Geospatial_data(data_points = point_coords) |
|---|
| 1171 | |
|---|
| 1172 | interp = Interpolate(vertices, triangles) |
|---|
| 1173 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
|---|
| 1174 | f = transpose(f) |
|---|
| 1175 | #print "f",f |
|---|
| 1176 | z = interp.interpolate(f, geo_data) |
|---|
| 1177 | #z = interp.interpolate(f, point_coords) |
|---|
| 1178 | answer = [linear_function(point_coords), |
|---|
| 1179 | 2*linear_function(point_coords) ] |
|---|
| 1180 | answer = transpose(answer) |
|---|
| 1181 | answer[2,:] = [INF, INF] |
|---|
| 1182 | answer[3,:] = [INF, INF] |
|---|
| 1183 | answer[11,:] = [INF, INF] |
|---|
| 1184 | #print "z",z |
|---|
| 1185 | #print "answer _ fixed",answer |
|---|
| 1186 | assert allclose(z[0:1], answer[0:1]) |
|---|
| 1187 | assert allclose(z[4:10], answer[4:10]) |
|---|
| 1188 | for i in [2,3,11]: |
|---|
| 1189 | self.failUnless( z[i,1] == answer[11,1], 'Fail!') |
|---|
| 1190 | self.failUnless( z[i,0] == answer[11,0], 'Fail!') |
|---|
| 1191 | |
|---|
| 1192 | #------------------------------------------------------------- |
|---|
| 1193 | if __name__ == "__main__": |
|---|
| 1194 | |
|---|
| 1195 | suite = unittest.makeSuite(Test_Interpolate,'test') |
|---|
| 1196 | #suite = unittest.makeSuite(Test_Interpolate,'test_interpolation_precompute_points') |
|---|
| 1197 | runner = unittest.TextTestRunner(verbosity=1) |
|---|
| 1198 | runner.run(suite) |
|---|
| 1199 | |
|---|
| 1200 | |
|---|
| 1201 | |
|---|
| 1202 | |
|---|
| 1203 | |
|---|
