[1911] | 1 | """Least squares smooting and interpolation. |
---|
| 2 | |
---|
| 3 | Implements a penalised least-squares fit and associated interpolations. |
---|
| 4 | |
---|
| 5 | The penalty term (or smoothing term) is controlled by the smoothing |
---|
| 6 | parameter alpha. |
---|
| 7 | With a value of alpha=0, the fit function will attempt |
---|
| 8 | to interpolate as closely as possible in the least-squares sense. |
---|
| 9 | With values alpha > 0, a certain amount of smoothing will be applied. |
---|
| 10 | A positive alpha is essential in cases where there are too few |
---|
| 11 | data points. |
---|
| 12 | A negative alpha is not allowed. |
---|
| 13 | A typical value of alpha is 1.0e-6 |
---|
| 14 | |
---|
| 15 | |
---|
| 16 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
---|
| 17 | Geoscience Australia, 2004. |
---|
| 18 | """ |
---|
| 19 | |
---|
| 20 | #import exceptions |
---|
| 21 | #class ShapeError(exceptions.Exception): pass |
---|
| 22 | |
---|
| 23 | #from general_mesh import General_mesh |
---|
[2608] | 24 | from numpy import zeros, take, array, Float, Int, dot, transpose, concatenate, ArrayType |
---|
| 25 | |
---|
| 26 | #FIXME (Ole): Meshes to move somewhere else |
---|
[2502] | 27 | from pyvolution.mesh import Mesh |
---|
[2503] | 28 | from utilities.sparse import Sparse, Sparse_CSR |
---|
| 29 | from utilities.cg_solve import conjugate_gradient, VectorShapeError |
---|
[2516] | 30 | from utilities.numerical_tools import ensure_numeric, mean, gradient |
---|
[1911] | 31 | |
---|
[2516] | 32 | |
---|
[1911] | 33 | from coordinate_transforms.geo_reference import Geo_reference |
---|
| 34 | |
---|
| 35 | import time |
---|
| 36 | |
---|
| 37 | |
---|
| 38 | |
---|
[2516] | 39 | |
---|
[1911] | 40 | DEFAULT_ALPHA = 0.001 |
---|
| 41 | |
---|
| 42 | def fit_to_mesh_file(mesh_file, point_file, mesh_output_file, |
---|
| 43 | alpha=DEFAULT_ALPHA, verbose= False, |
---|
| 44 | expand_search = False, |
---|
| 45 | data_origin = None, |
---|
| 46 | mesh_origin = None, |
---|
| 47 | precrop = False, |
---|
| 48 | display_errors = True): |
---|
| 49 | """ |
---|
| 50 | Given a mesh file (tsh) and a point attribute file (xya), fit |
---|
| 51 | point attributes to the mesh and write a mesh file with the |
---|
| 52 | results. |
---|
| 53 | |
---|
| 54 | |
---|
| 55 | If data_origin is not None it is assumed to be |
---|
| 56 | a 3-tuple with geo referenced |
---|
| 57 | UTM coordinates (zone, easting, northing) |
---|
| 58 | |
---|
| 59 | NOTE: Throws IOErrors, for a variety of file problems. |
---|
| 60 | |
---|
| 61 | mesh_origin is the same but refers to the input tsh file. |
---|
| 62 | FIXME: When the tsh format contains it own origin, these parameters can go. |
---|
| 63 | FIXME: And both origins should be obtained from the specified files. |
---|
| 64 | """ |
---|
| 65 | |
---|
| 66 | from load_mesh.loadASCII import import_mesh_file, \ |
---|
| 67 | import_points_file, export_mesh_file, \ |
---|
| 68 | concatinate_attributelist |
---|
| 69 | |
---|
| 70 | |
---|
| 71 | try: |
---|
| 72 | mesh_dict = import_mesh_file(mesh_file) |
---|
| 73 | except IOError,e: |
---|
| 74 | if display_errors: |
---|
| 75 | print "Could not load bad file. ", e |
---|
| 76 | raise IOError #Re-raise exception |
---|
| 77 | |
---|
| 78 | vertex_coordinates = mesh_dict['vertices'] |
---|
| 79 | triangles = mesh_dict['triangles'] |
---|
| 80 | if type(mesh_dict['vertex_attributes']) == ArrayType: |
---|
| 81 | old_point_attributes = mesh_dict['vertex_attributes'].tolist() |
---|
| 82 | else: |
---|
| 83 | old_point_attributes = mesh_dict['vertex_attributes'] |
---|
| 84 | |
---|
| 85 | if type(mesh_dict['vertex_attribute_titles']) == ArrayType: |
---|
| 86 | old_title_list = mesh_dict['vertex_attribute_titles'].tolist() |
---|
| 87 | else: |
---|
| 88 | old_title_list = mesh_dict['vertex_attribute_titles'] |
---|
| 89 | |
---|
| 90 | if verbose: print 'tsh file %s loaded' %mesh_file |
---|
| 91 | |
---|
| 92 | # load in the .pts file |
---|
| 93 | try: |
---|
| 94 | point_dict = import_points_file(point_file, verbose=verbose) |
---|
| 95 | except IOError,e: |
---|
| 96 | if display_errors: |
---|
| 97 | print "Could not load bad file. ", e |
---|
| 98 | raise IOError #Re-raise exception |
---|
| 99 | |
---|
| 100 | point_coordinates = point_dict['pointlist'] |
---|
| 101 | title_list,point_attributes = concatinate_attributelist(point_dict['attributelist']) |
---|
| 102 | |
---|
| 103 | if point_dict.has_key('geo_reference') and not point_dict['geo_reference'] is None: |
---|
| 104 | data_origin = point_dict['geo_reference'].get_origin() |
---|
| 105 | else: |
---|
| 106 | data_origin = (56, 0, 0) #FIXME(DSG-DSG) |
---|
| 107 | |
---|
| 108 | if mesh_dict.has_key('geo_reference') and not mesh_dict['geo_reference'] is None: |
---|
| 109 | mesh_origin = mesh_dict['geo_reference'].get_origin() |
---|
| 110 | else: |
---|
| 111 | mesh_origin = (56, 0, 0) #FIXME(DSG-DSG) |
---|
| 112 | |
---|
| 113 | if verbose: print "points file loaded" |
---|
[2447] | 114 | if verbose: print "fitting to mesh" |
---|
[1911] | 115 | f = fit_to_mesh(vertex_coordinates, |
---|
| 116 | triangles, |
---|
| 117 | point_coordinates, |
---|
| 118 | point_attributes, |
---|
| 119 | alpha = alpha, |
---|
| 120 | verbose = verbose, |
---|
| 121 | expand_search = expand_search, |
---|
| 122 | data_origin = data_origin, |
---|
| 123 | mesh_origin = mesh_origin, |
---|
| 124 | precrop = precrop) |
---|
| 125 | if verbose: print "finished fitting to mesh" |
---|
| 126 | |
---|
| 127 | # convert array to list of lists |
---|
| 128 | new_point_attributes = f.tolist() |
---|
| 129 | #FIXME have this overwrite attributes with the same title - DSG |
---|
| 130 | #Put the newer attributes last |
---|
| 131 | if old_title_list <> []: |
---|
| 132 | old_title_list.extend(title_list) |
---|
| 133 | #FIXME can this be done a faster way? - DSG |
---|
| 134 | for i in range(len(old_point_attributes)): |
---|
| 135 | old_point_attributes[i].extend(new_point_attributes[i]) |
---|
| 136 | mesh_dict['vertex_attributes'] = old_point_attributes |
---|
| 137 | mesh_dict['vertex_attribute_titles'] = old_title_list |
---|
| 138 | else: |
---|
| 139 | mesh_dict['vertex_attributes'] = new_point_attributes |
---|
| 140 | mesh_dict['vertex_attribute_titles'] = title_list |
---|
| 141 | |
---|
| 142 | #FIXME (Ole): Remember to output mesh_origin as well |
---|
[2447] | 143 | if verbose: print "exporting to file ", mesh_output_file |
---|
[1911] | 144 | |
---|
| 145 | try: |
---|
| 146 | export_mesh_file(mesh_output_file, mesh_dict) |
---|
| 147 | except IOError,e: |
---|
| 148 | if display_errors: |
---|
| 149 | print "Could not write file. ", e |
---|
| 150 | raise IOError |
---|
| 151 | |
---|
| 152 | def fit_to_mesh(vertex_coordinates, |
---|
| 153 | triangles, |
---|
| 154 | point_coordinates, |
---|
| 155 | point_attributes, |
---|
| 156 | alpha = DEFAULT_ALPHA, |
---|
| 157 | verbose = False, |
---|
| 158 | expand_search = False, |
---|
| 159 | data_origin = None, |
---|
| 160 | mesh_origin = None, |
---|
[2447] | 161 | precrop = False, |
---|
| 162 | use_cache = False): |
---|
[1911] | 163 | """ |
---|
| 164 | Fit a smooth surface to a triangulation, |
---|
| 165 | given data points with attributes. |
---|
| 166 | |
---|
| 167 | |
---|
| 168 | Inputs: |
---|
| 169 | |
---|
| 170 | vertex_coordinates: List of coordinate pairs [xi, eta] of points |
---|
| 171 | constituting mesh (or a an m x 2 Numeric array) |
---|
| 172 | |
---|
| 173 | triangles: List of 3-tuples (or a Numeric array) of |
---|
| 174 | integers representing indices of all vertices in the mesh. |
---|
| 175 | |
---|
| 176 | point_coordinates: List of coordinate pairs [x, y] of data points |
---|
| 177 | (or an nx2 Numeric array) |
---|
| 178 | |
---|
| 179 | alpha: Smoothing parameter. |
---|
| 180 | |
---|
| 181 | point_attributes: Vector or array of data at the point_coordinates. |
---|
| 182 | |
---|
| 183 | data_origin and mesh_origin are 3-tuples consisting of |
---|
| 184 | UTM zone, easting and northing. If specified |
---|
| 185 | point coordinates and vertex coordinates are assumed to be |
---|
| 186 | relative to their respective origins. |
---|
| 187 | |
---|
| 188 | """ |
---|
[2347] | 189 | |
---|
[2447] | 190 | if use_cache is True: |
---|
| 191 | from caching.caching import cache |
---|
| 192 | interp = cache(_interpolation, |
---|
| 193 | (vertex_coordinates, |
---|
| 194 | triangles, |
---|
| 195 | point_coordinates), |
---|
| 196 | {'alpha': alpha, |
---|
| 197 | 'verbose': verbose, |
---|
| 198 | 'expand_search': expand_search, |
---|
| 199 | 'data_origin': data_origin, |
---|
| 200 | 'mesh_origin': mesh_origin, |
---|
| 201 | 'precrop': precrop}, |
---|
| 202 | verbose = verbose) |
---|
| 203 | |
---|
| 204 | else: |
---|
| 205 | interp = Interpolation(vertex_coordinates, |
---|
| 206 | triangles, |
---|
| 207 | point_coordinates, |
---|
| 208 | alpha = alpha, |
---|
| 209 | verbose = verbose, |
---|
| 210 | expand_search = expand_search, |
---|
| 211 | data_origin = data_origin, |
---|
| 212 | mesh_origin = mesh_origin, |
---|
| 213 | precrop = precrop) |
---|
[2347] | 214 | |
---|
[1911] | 215 | vertex_attributes = interp.fit_points(point_attributes, verbose = verbose) |
---|
| 216 | return vertex_attributes |
---|
| 217 | |
---|
| 218 | |
---|
| 219 | |
---|
| 220 | def pts2rectangular(pts_name, M, N, alpha = DEFAULT_ALPHA, |
---|
| 221 | verbose = False, reduction = 1): |
---|
| 222 | """Fits attributes from pts file to MxN rectangular mesh |
---|
| 223 | |
---|
| 224 | Read pts file and create rectangular mesh of resolution MxN such that |
---|
| 225 | it covers all points specified in pts file. |
---|
| 226 | |
---|
| 227 | FIXME: This may be a temporary function until we decide on |
---|
| 228 | netcdf formats etc |
---|
| 229 | |
---|
| 230 | FIXME: Uses elevation hardwired |
---|
| 231 | """ |
---|
| 232 | |
---|
| 233 | import mesh_factory |
---|
| 234 | from load_mesh.loadASCII import import_points_file |
---|
| 235 | |
---|
| 236 | if verbose: print 'Read pts' |
---|
| 237 | points_dict = import_points_file(pts_name) |
---|
| 238 | #points, attributes = util.read_xya(pts_name) |
---|
| 239 | |
---|
| 240 | #Reduce number of points a bit |
---|
| 241 | points = points_dict['pointlist'][::reduction] |
---|
| 242 | elevation = points_dict['attributelist']['elevation'] #Must be elevation |
---|
| 243 | elevation = elevation[::reduction] |
---|
| 244 | |
---|
| 245 | if verbose: print 'Got %d data points' %len(points) |
---|
| 246 | |
---|
| 247 | if verbose: print 'Create mesh' |
---|
| 248 | #Find extent |
---|
| 249 | max_x = min_x = points[0][0] |
---|
| 250 | max_y = min_y = points[0][1] |
---|
| 251 | for point in points[1:]: |
---|
| 252 | x = point[0] |
---|
| 253 | if x > max_x: max_x = x |
---|
| 254 | if x < min_x: min_x = x |
---|
| 255 | y = point[1] |
---|
| 256 | if y > max_y: max_y = y |
---|
| 257 | if y < min_y: min_y = y |
---|
| 258 | |
---|
| 259 | #Create appropriate mesh |
---|
| 260 | vertex_coordinates, triangles, boundary =\ |
---|
| 261 | mesh_factory.rectangular(M, N, max_x-min_x, max_y-min_y, |
---|
| 262 | (min_x, min_y)) |
---|
| 263 | |
---|
| 264 | #Fit attributes to mesh |
---|
| 265 | vertex_attributes = fit_to_mesh(vertex_coordinates, |
---|
| 266 | triangles, |
---|
| 267 | points, |
---|
| 268 | elevation, alpha=alpha, verbose=verbose) |
---|
| 269 | |
---|
| 270 | |
---|
| 271 | |
---|
| 272 | return vertex_coordinates, triangles, boundary, vertex_attributes |
---|
| 273 | |
---|
| 274 | |
---|
[2447] | 275 | def _interpolation(*args, **kwargs): |
---|
| 276 | """Private function for use with caching. Reason is that classes |
---|
| 277 | may change their byte code between runs which is annoying. |
---|
| 278 | """ |
---|
| 279 | |
---|
| 280 | return Interpolation(*args, **kwargs) |
---|
[1911] | 281 | |
---|
[2447] | 282 | |
---|
[1911] | 283 | class Interpolation: |
---|
| 284 | |
---|
| 285 | def __init__(self, |
---|
| 286 | vertex_coordinates, |
---|
| 287 | triangles, |
---|
| 288 | point_coordinates = None, |
---|
| 289 | alpha = None, |
---|
| 290 | verbose = False, |
---|
| 291 | expand_search = True, |
---|
| 292 | interp_only = False, |
---|
| 293 | max_points_per_cell = 30, |
---|
| 294 | mesh_origin = None, |
---|
| 295 | data_origin = None, |
---|
| 296 | precrop = False): |
---|
| 297 | |
---|
| 298 | |
---|
| 299 | """ Build interpolation matrix mapping from |
---|
| 300 | function values at vertices to function values at data points |
---|
| 301 | |
---|
| 302 | Inputs: |
---|
| 303 | |
---|
| 304 | vertex_coordinates: List of coordinate pairs [xi, eta] of |
---|
| 305 | points constituting mesh (or a an m x 2 Numeric array) |
---|
| 306 | Points may appear multiple times |
---|
| 307 | (e.g. if vertices have discontinuities) |
---|
| 308 | |
---|
| 309 | triangles: List of 3-tuples (or a Numeric array) of |
---|
| 310 | integers representing indices of all vertices in the mesh. |
---|
| 311 | |
---|
| 312 | point_coordinates: List of coordinate pairs [x, y] of |
---|
| 313 | data points (or an nx2 Numeric array) |
---|
| 314 | If point_coordinates is absent, only smoothing matrix will |
---|
| 315 | be built |
---|
| 316 | |
---|
| 317 | alpha: Smoothing parameter |
---|
| 318 | |
---|
| 319 | data_origin and mesh_origin are 3-tuples consisting of |
---|
| 320 | UTM zone, easting and northing. If specified |
---|
| 321 | point coordinates and vertex coordinates are assumed to be |
---|
| 322 | relative to their respective origins. |
---|
| 323 | |
---|
| 324 | """ |
---|
| 325 | |
---|
| 326 | #Convert input to Numeric arrays |
---|
| 327 | triangles = ensure_numeric(triangles, Int) |
---|
| 328 | vertex_coordinates = ensure_numeric(vertex_coordinates, Float) |
---|
| 329 | |
---|
| 330 | #Build underlying mesh |
---|
| 331 | if verbose: print 'Building mesh' |
---|
| 332 | #self.mesh = General_mesh(vertex_coordinates, triangles, |
---|
| 333 | #FIXME: Trying the normal mesh while testing precrop, |
---|
| 334 | # The functionality of boundary_polygon is needed for that |
---|
| 335 | |
---|
| 336 | #FIXME - geo ref does not have to go into mesh. |
---|
| 337 | # Change the point co-ords to conform to the |
---|
| 338 | # mesh co-ords early in the code |
---|
[1979] | 339 | if mesh_origin is None: |
---|
[1911] | 340 | geo = None |
---|
| 341 | else: |
---|
| 342 | geo = Geo_reference(mesh_origin[0],mesh_origin[1],mesh_origin[2]) |
---|
[2502] | 343 | self.mesh = Mesh(vertex_coordinates, triangles, |
---|
| 344 | geo_reference = geo) |
---|
[1911] | 345 | |
---|
| 346 | self.mesh.check_integrity() |
---|
| 347 | |
---|
| 348 | self.data_origin = data_origin |
---|
| 349 | |
---|
| 350 | self.point_indices = None |
---|
| 351 | |
---|
| 352 | #Smoothing parameter |
---|
| 353 | if alpha is None: |
---|
| 354 | self.alpha = DEFAULT_ALPHA |
---|
| 355 | else: |
---|
| 356 | self.alpha = alpha |
---|
| 357 | |
---|
| 358 | |
---|
| 359 | if point_coordinates is not None: |
---|
| 360 | if verbose: print 'Building interpolation matrix' |
---|
| 361 | self.build_interpolation_matrix_A(point_coordinates, |
---|
| 362 | verbose = verbose, |
---|
| 363 | expand_search = expand_search, |
---|
| 364 | interp_only = interp_only, |
---|
| 365 | max_points_per_cell =\ |
---|
| 366 | max_points_per_cell, |
---|
| 367 | data_origin = data_origin, |
---|
| 368 | precrop = precrop) |
---|
| 369 | #Build coefficient matrices |
---|
| 370 | if interp_only == False: |
---|
| 371 | self.build_coefficient_matrix_B(point_coordinates, |
---|
| 372 | verbose = verbose, |
---|
| 373 | expand_search = expand_search, |
---|
| 374 | max_points_per_cell =\ |
---|
| 375 | max_points_per_cell, |
---|
| 376 | data_origin = data_origin, |
---|
| 377 | precrop = precrop) |
---|
| 378 | |
---|
| 379 | def set_point_coordinates(self, point_coordinates, |
---|
| 380 | data_origin = None, |
---|
| 381 | verbose = False, |
---|
| 382 | precrop = True): |
---|
| 383 | """ |
---|
| 384 | A public interface to setting the point co-ordinates. |
---|
| 385 | """ |
---|
| 386 | if point_coordinates is not None: |
---|
| 387 | if verbose: print 'Building interpolation matrix' |
---|
| 388 | self.build_interpolation_matrix_A(point_coordinates, |
---|
| 389 | verbose = verbose, |
---|
| 390 | data_origin = data_origin, |
---|
| 391 | precrop = precrop) |
---|
| 392 | self.build_coefficient_matrix_B(point_coordinates, data_origin) |
---|
| 393 | |
---|
| 394 | def build_coefficient_matrix_B(self, point_coordinates=None, |
---|
| 395 | verbose = False, expand_search = True, |
---|
| 396 | max_points_per_cell=30, |
---|
| 397 | data_origin = None, |
---|
| 398 | precrop = False): |
---|
| 399 | """Build final coefficient matrix""" |
---|
| 400 | |
---|
| 401 | |
---|
| 402 | if self.alpha <> 0: |
---|
| 403 | if verbose: print 'Building smoothing matrix' |
---|
| 404 | self.build_smoothing_matrix_D() |
---|
| 405 | |
---|
| 406 | if point_coordinates is not None: |
---|
| 407 | if self.alpha <> 0: |
---|
| 408 | self.B = self.AtA + self.alpha*self.D |
---|
| 409 | else: |
---|
| 410 | self.B = self.AtA |
---|
| 411 | |
---|
| 412 | #Convert self.B matrix to CSR format for faster matrix vector |
---|
| 413 | self.B = Sparse_CSR(self.B) |
---|
| 414 | |
---|
| 415 | def build_interpolation_matrix_A(self, point_coordinates, |
---|
| 416 | verbose = False, expand_search = True, |
---|
| 417 | max_points_per_cell=30, |
---|
| 418 | data_origin = None, |
---|
| 419 | precrop = False, |
---|
| 420 | interp_only = False): |
---|
| 421 | """Build n x m interpolation matrix, where |
---|
| 422 | n is the number of data points and |
---|
| 423 | m is the number of basis functions phi_k (one per vertex) |
---|
| 424 | |
---|
| 425 | This algorithm uses a quad tree data structure for fast binning of data points |
---|
| 426 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
---|
| 427 | If specified coordinates are assumed to be relative to this origin. |
---|
| 428 | |
---|
| 429 | This one will override any data_origin that may be specified in |
---|
| 430 | interpolation instance |
---|
| 431 | |
---|
| 432 | """ |
---|
| 433 | |
---|
| 434 | |
---|
[2347] | 435 | |
---|
[1911] | 436 | #FIXME (Ole): Check that this function is memeory efficient. |
---|
| 437 | #6 million datapoints and 300000 basis functions |
---|
| 438 | #causes out-of-memory situation |
---|
| 439 | #First thing to check is whether there is room for self.A and self.AtA |
---|
| 440 | # |
---|
| 441 | #Maybe we need some sort of blocking |
---|
| 442 | |
---|
[1941] | 443 | from pyvolution.quad import build_quadtree |
---|
[1911] | 444 | from utilities.polygon import inside_polygon |
---|
| 445 | |
---|
| 446 | |
---|
| 447 | if data_origin is None: |
---|
| 448 | data_origin = self.data_origin #Use the one from |
---|
| 449 | #interpolation instance |
---|
| 450 | |
---|
| 451 | #Convert input to Numeric arrays just in case. |
---|
| 452 | point_coordinates = ensure_numeric(point_coordinates, Float) |
---|
| 453 | |
---|
| 454 | #Keep track of discarded points (if any). |
---|
| 455 | #This is only registered if precrop is True |
---|
| 456 | self.cropped_points = False |
---|
| 457 | |
---|
| 458 | #Shift data points to same origin as mesh (if specified) |
---|
| 459 | |
---|
| 460 | #FIXME this will shift if there was no geo_ref. |
---|
| 461 | #But all this should be removed anyhow. |
---|
| 462 | #change coords before this point |
---|
| 463 | mesh_origin = self.mesh.geo_reference.get_origin() |
---|
| 464 | if point_coordinates is not None: |
---|
| 465 | if data_origin is not None: |
---|
| 466 | if mesh_origin is not None: |
---|
| 467 | |
---|
| 468 | #Transformation: |
---|
| 469 | # |
---|
| 470 | #Let x_0 be the reference point of the point coordinates |
---|
| 471 | #and xi_0 the reference point of the mesh. |
---|
| 472 | # |
---|
| 473 | #A point coordinate (x + x_0) is then made relative |
---|
| 474 | #to xi_0 by |
---|
| 475 | # |
---|
| 476 | # x_new = x + x_0 - xi_0 |
---|
| 477 | # |
---|
| 478 | #and similarly for eta |
---|
| 479 | |
---|
| 480 | x_offset = data_origin[1] - mesh_origin[1] |
---|
| 481 | y_offset = data_origin[2] - mesh_origin[2] |
---|
| 482 | else: #Shift back to a zero origin |
---|
| 483 | x_offset = data_origin[1] |
---|
| 484 | y_offset = data_origin[2] |
---|
| 485 | |
---|
| 486 | point_coordinates[:,0] += x_offset |
---|
| 487 | point_coordinates[:,1] += y_offset |
---|
| 488 | else: |
---|
| 489 | if mesh_origin is not None: |
---|
| 490 | #Use mesh origin for data points |
---|
| 491 | point_coordinates[:,0] -= mesh_origin[1] |
---|
| 492 | point_coordinates[:,1] -= mesh_origin[2] |
---|
| 493 | |
---|
| 494 | |
---|
| 495 | |
---|
| 496 | #Remove points falling outside mesh boundary |
---|
| 497 | #This reduced one example from 1356 seconds to 825 seconds |
---|
[2347] | 498 | |
---|
| 499 | |
---|
[1911] | 500 | if precrop is True: |
---|
[2608] | 501 | #from Numeric import take |
---|
[1911] | 502 | |
---|
| 503 | if verbose: print 'Getting boundary polygon' |
---|
| 504 | P = self.mesh.get_boundary_polygon() |
---|
| 505 | |
---|
| 506 | if verbose: print 'Getting indices inside mesh boundary' |
---|
| 507 | indices = inside_polygon(point_coordinates, P, verbose = verbose) |
---|
| 508 | |
---|
| 509 | |
---|
| 510 | if len(indices) != point_coordinates.shape[0]: |
---|
| 511 | self.cropped_points = True |
---|
| 512 | if verbose: |
---|
| 513 | print 'Done - %d points outside mesh have been cropped.'\ |
---|
| 514 | %(point_coordinates.shape[0] - len(indices)) |
---|
| 515 | |
---|
| 516 | point_coordinates = take(point_coordinates, indices) |
---|
| 517 | self.point_indices = indices |
---|
| 518 | |
---|
| 519 | |
---|
| 520 | |
---|
| 521 | |
---|
| 522 | #Build n x m interpolation matrix |
---|
| 523 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
| 524 | n = point_coordinates.shape[0] #Nbr of data points |
---|
| 525 | |
---|
| 526 | if verbose: print 'Number of datapoints: %d' %n |
---|
| 527 | if verbose: print 'Number of basis functions: %d' %m |
---|
| 528 | |
---|
| 529 | #FIXME (Ole): We should use CSR here since mat-mat mult is now OK. |
---|
| 530 | #However, Sparse_CSR does not have the same methods as Sparse yet |
---|
| 531 | #The tests will reveal what needs to be done |
---|
| 532 | |
---|
| 533 | # |
---|
| 534 | #self.A = Sparse_CSR(Sparse(n,m)) |
---|
| 535 | #self.AtA = Sparse_CSR(Sparse(m,m)) |
---|
| 536 | self.A = Sparse(n,m) |
---|
| 537 | self.AtA = Sparse(m,m) |
---|
| 538 | |
---|
| 539 | #Build quad tree of vertices (FIXME: Is this the right spot for that?) |
---|
| 540 | root = build_quadtree(self.mesh, |
---|
| 541 | max_points_per_cell = max_points_per_cell) |
---|
[1941] | 542 | #root.show() |
---|
| 543 | self.expanded_quad_searches = [] |
---|
[1911] | 544 | #Compute matrix elements |
---|
| 545 | for i in range(n): |
---|
| 546 | #For each data_coordinate point |
---|
| 547 | |
---|
| 548 | if verbose and i%((n+10)/10)==0: print 'Doing %d of %d' %(i, n) |
---|
| 549 | x = point_coordinates[i] |
---|
| 550 | |
---|
| 551 | #Find vertices near x |
---|
| 552 | candidate_vertices = root.search(x[0], x[1]) |
---|
| 553 | is_more_elements = True |
---|
| 554 | |
---|
| 555 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 556 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
[1941] | 557 | first_expansion = True |
---|
[1911] | 558 | while not element_found and is_more_elements and expand_search: |
---|
[1975] | 559 | #if verbose: print 'Expanding search' |
---|
[1942] | 560 | if first_expansion == True: |
---|
| 561 | self.expanded_quad_searches.append(1) |
---|
[1944] | 562 | first_expansion = False |
---|
[1941] | 563 | else: |
---|
[1944] | 564 | end = len(self.expanded_quad_searches) - 1 |
---|
[1941] | 565 | assert end >= 0 |
---|
[1942] | 566 | self.expanded_quad_searches[end] += 1 |
---|
[1911] | 567 | candidate_vertices, branch = root.expand_search() |
---|
| 568 | if branch == []: |
---|
| 569 | # Searching all the verts from the root cell that haven't |
---|
| 570 | # been searched. This is the last try |
---|
| 571 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 572 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
| 573 | is_more_elements = False |
---|
| 574 | else: |
---|
| 575 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 576 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
| 577 | |
---|
[1941] | 578 | |
---|
[1911] | 579 | #Update interpolation matrix A if necessary |
---|
| 580 | if element_found is True: |
---|
| 581 | #Assign values to matrix A |
---|
| 582 | |
---|
| 583 | j0 = self.mesh.triangles[k,0] #Global vertex id for sigma0 |
---|
| 584 | j1 = self.mesh.triangles[k,1] #Global vertex id for sigma1 |
---|
| 585 | j2 = self.mesh.triangles[k,2] #Global vertex id for sigma2 |
---|
| 586 | |
---|
| 587 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
| 588 | js = [j0,j1,j2] |
---|
| 589 | |
---|
| 590 | for j in js: |
---|
| 591 | self.A[i,j] = sigmas[j] |
---|
| 592 | for k in js: |
---|
| 593 | if interp_only == False: |
---|
| 594 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
| 595 | else: |
---|
| 596 | pass |
---|
| 597 | #Ok if there is no triangle for datapoint |
---|
| 598 | #(as in brute force version) |
---|
| 599 | #raise 'Could not find triangle for point', x |
---|
| 600 | |
---|
| 601 | |
---|
| 602 | |
---|
| 603 | def search_triangles_of_vertices(self, candidate_vertices, x): |
---|
| 604 | #Find triangle containing x: |
---|
| 605 | element_found = False |
---|
| 606 | |
---|
| 607 | # This will be returned if element_found = False |
---|
| 608 | sigma2 = -10.0 |
---|
| 609 | sigma0 = -10.0 |
---|
| 610 | sigma1 = -10.0 |
---|
| 611 | k = -10.0 |
---|
[1941] | 612 | #print "*$* candidate_vertices", candidate_vertices |
---|
[1911] | 613 | #For all vertices in same cell as point x |
---|
| 614 | for v in candidate_vertices: |
---|
[1975] | 615 | #FIXME (DSG-DSG): this catches verts with no triangle. |
---|
| 616 | #Currently pmesh is producing these. |
---|
| 617 | #this should be stopped, |
---|
[1979] | 618 | if self.mesh.vertexlist[v] is None: |
---|
[1975] | 619 | continue |
---|
[1911] | 620 | #for each triangle id (k) which has v as a vertex |
---|
| 621 | for k, _ in self.mesh.vertexlist[v]: |
---|
| 622 | |
---|
| 623 | #Get the three vertex_points of candidate triangle |
---|
| 624 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
| 625 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
| 626 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
| 627 | |
---|
| 628 | #print "PDSG - k", k |
---|
| 629 | #print "PDSG - xi0", xi0 |
---|
| 630 | #print "PDSG - xi1", xi1 |
---|
| 631 | #print "PDSG - xi2", xi2 |
---|
| 632 | #print "PDSG element %i verts((%f, %f),(%f, %f),(%f, %f))"\ |
---|
| 633 | # % (k, xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1]) |
---|
| 634 | |
---|
| 635 | #Get the three normals |
---|
| 636 | n0 = self.mesh.get_normal(k, 0) |
---|
| 637 | n1 = self.mesh.get_normal(k, 1) |
---|
| 638 | n2 = self.mesh.get_normal(k, 2) |
---|
| 639 | |
---|
| 640 | |
---|
| 641 | #Compute interpolation |
---|
| 642 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
| 643 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
| 644 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
| 645 | |
---|
| 646 | #print "PDSG - sigma0", sigma0 |
---|
| 647 | #print "PDSG - sigma1", sigma1 |
---|
| 648 | #print "PDSG - sigma2", sigma2 |
---|
| 649 | |
---|
| 650 | #FIXME: Maybe move out to test or something |
---|
| 651 | epsilon = 1.0e-6 |
---|
| 652 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
| 653 | |
---|
| 654 | #Check that this triangle contains the data point |
---|
| 655 | |
---|
| 656 | #Sigmas can get negative within |
---|
| 657 | #machine precision on some machines (e.g nautilus) |
---|
| 658 | #Hence the small eps |
---|
| 659 | eps = 1.0e-15 |
---|
| 660 | if sigma0 >= -eps and sigma1 >= -eps and sigma2 >= -eps: |
---|
| 661 | element_found = True |
---|
| 662 | break |
---|
| 663 | |
---|
| 664 | if element_found is True: |
---|
| 665 | #Don't look for any other triangle |
---|
| 666 | break |
---|
| 667 | return element_found, sigma0, sigma1, sigma2, k |
---|
| 668 | |
---|
| 669 | |
---|
| 670 | |
---|
| 671 | def build_interpolation_matrix_A_brute(self, point_coordinates): |
---|
| 672 | """Build n x m interpolation matrix, where |
---|
| 673 | n is the number of data points and |
---|
| 674 | m is the number of basis functions phi_k (one per vertex) |
---|
| 675 | |
---|
| 676 | This is the brute force which is too slow for large problems, |
---|
| 677 | but could be used for testing |
---|
| 678 | """ |
---|
| 679 | |
---|
| 680 | |
---|
| 681 | #Convert input to Numeric arrays |
---|
| 682 | point_coordinates = ensure_numeric(point_coordinates, Float) |
---|
| 683 | |
---|
| 684 | #Build n x m interpolation matrix |
---|
| 685 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
| 686 | n = point_coordinates.shape[0] #Nbr of data points |
---|
| 687 | |
---|
| 688 | self.A = Sparse(n,m) |
---|
| 689 | self.AtA = Sparse(m,m) |
---|
| 690 | |
---|
| 691 | #Compute matrix elements |
---|
| 692 | for i in range(n): |
---|
| 693 | #For each data_coordinate point |
---|
| 694 | |
---|
| 695 | x = point_coordinates[i] |
---|
| 696 | element_found = False |
---|
| 697 | k = 0 |
---|
| 698 | while not element_found and k < len(self.mesh): |
---|
| 699 | #For each triangle (brute force) |
---|
| 700 | #FIXME: Real algorithm should only visit relevant triangles |
---|
| 701 | |
---|
| 702 | #Get the three vertex_points |
---|
| 703 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
| 704 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
| 705 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
| 706 | |
---|
| 707 | #Get the three normals |
---|
| 708 | n0 = self.mesh.get_normal(k, 0) |
---|
| 709 | n1 = self.mesh.get_normal(k, 1) |
---|
| 710 | n2 = self.mesh.get_normal(k, 2) |
---|
| 711 | |
---|
| 712 | #Compute interpolation |
---|
| 713 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
| 714 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
| 715 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
| 716 | |
---|
| 717 | #FIXME: Maybe move out to test or something |
---|
| 718 | epsilon = 1.0e-6 |
---|
| 719 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
| 720 | |
---|
| 721 | #Check that this triangle contains data point |
---|
| 722 | if sigma0 >= 0 and sigma1 >= 0 and sigma2 >= 0: |
---|
| 723 | element_found = True |
---|
| 724 | #Assign values to matrix A |
---|
| 725 | |
---|
| 726 | j0 = self.mesh.triangles[k,0] #Global vertex id |
---|
| 727 | #self.A[i, j0] = sigma0 |
---|
| 728 | |
---|
| 729 | j1 = self.mesh.triangles[k,1] #Global vertex id |
---|
| 730 | #self.A[i, j1] = sigma1 |
---|
| 731 | |
---|
| 732 | j2 = self.mesh.triangles[k,2] #Global vertex id |
---|
| 733 | #self.A[i, j2] = sigma2 |
---|
| 734 | |
---|
| 735 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
| 736 | js = [j0,j1,j2] |
---|
| 737 | |
---|
| 738 | for j in js: |
---|
| 739 | self.A[i,j] = sigmas[j] |
---|
| 740 | for k in js: |
---|
| 741 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
| 742 | k = k+1 |
---|
| 743 | |
---|
| 744 | |
---|
| 745 | |
---|
| 746 | def get_A(self): |
---|
| 747 | return self.A.todense() |
---|
| 748 | |
---|
| 749 | def get_B(self): |
---|
| 750 | return self.B.todense() |
---|
| 751 | |
---|
| 752 | def get_D(self): |
---|
| 753 | return self.D.todense() |
---|
| 754 | |
---|
| 755 | #FIXME: Remember to re-introduce the 1/n factor in the |
---|
| 756 | #interpolation term |
---|
| 757 | |
---|
| 758 | def build_smoothing_matrix_D(self): |
---|
| 759 | """Build m x m smoothing matrix, where |
---|
| 760 | m is the number of basis functions phi_k (one per vertex) |
---|
| 761 | |
---|
| 762 | The smoothing matrix is defined as |
---|
| 763 | |
---|
| 764 | D = D1 + D2 |
---|
| 765 | |
---|
| 766 | where |
---|
| 767 | |
---|
| 768 | [D1]_{k,l} = \int_\Omega |
---|
| 769 | \frac{\partial \phi_k}{\partial x} |
---|
| 770 | \frac{\partial \phi_l}{\partial x}\, |
---|
| 771 | dx dy |
---|
| 772 | |
---|
| 773 | [D2]_{k,l} = \int_\Omega |
---|
| 774 | \frac{\partial \phi_k}{\partial y} |
---|
| 775 | \frac{\partial \phi_l}{\partial y}\, |
---|
| 776 | dx dy |
---|
| 777 | |
---|
| 778 | |
---|
| 779 | The derivatives \frac{\partial \phi_k}{\partial x}, |
---|
| 780 | \frac{\partial \phi_k}{\partial x} for a particular triangle |
---|
| 781 | are obtained by computing the gradient a_k, b_k for basis function k |
---|
| 782 | """ |
---|
| 783 | |
---|
| 784 | #FIXME: algorithm might be optimised by computing local 9x9 |
---|
| 785 | #"element stiffness matrices: |
---|
| 786 | |
---|
| 787 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
| 788 | |
---|
| 789 | self.D = Sparse(m,m) |
---|
| 790 | |
---|
| 791 | #For each triangle compute contributions to D = D1+D2 |
---|
| 792 | for i in range(len(self.mesh)): |
---|
| 793 | |
---|
| 794 | #Get area |
---|
| 795 | area = self.mesh.areas[i] |
---|
| 796 | |
---|
| 797 | #Get global vertex indices |
---|
| 798 | v0 = self.mesh.triangles[i,0] |
---|
| 799 | v1 = self.mesh.triangles[i,1] |
---|
| 800 | v2 = self.mesh.triangles[i,2] |
---|
| 801 | |
---|
| 802 | #Get the three vertex_points |
---|
| 803 | xi0 = self.mesh.get_vertex_coordinate(i, 0) |
---|
| 804 | xi1 = self.mesh.get_vertex_coordinate(i, 1) |
---|
| 805 | xi2 = self.mesh.get_vertex_coordinate(i, 2) |
---|
| 806 | |
---|
| 807 | #Compute gradients for each vertex |
---|
| 808 | a0, b0 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
| 809 | 1, 0, 0) |
---|
| 810 | |
---|
| 811 | a1, b1 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
| 812 | 0, 1, 0) |
---|
| 813 | |
---|
| 814 | a2, b2 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
| 815 | 0, 0, 1) |
---|
| 816 | |
---|
| 817 | #Compute diagonal contributions |
---|
| 818 | self.D[v0,v0] += (a0*a0 + b0*b0)*area |
---|
| 819 | self.D[v1,v1] += (a1*a1 + b1*b1)*area |
---|
| 820 | self.D[v2,v2] += (a2*a2 + b2*b2)*area |
---|
| 821 | |
---|
| 822 | #Compute contributions for basis functions sharing edges |
---|
| 823 | e01 = (a0*a1 + b0*b1)*area |
---|
| 824 | self.D[v0,v1] += e01 |
---|
| 825 | self.D[v1,v0] += e01 |
---|
| 826 | |
---|
| 827 | e12 = (a1*a2 + b1*b2)*area |
---|
| 828 | self.D[v1,v2] += e12 |
---|
| 829 | self.D[v2,v1] += e12 |
---|
| 830 | |
---|
| 831 | e20 = (a2*a0 + b2*b0)*area |
---|
| 832 | self.D[v2,v0] += e20 |
---|
| 833 | self.D[v0,v2] += e20 |
---|
| 834 | |
---|
| 835 | |
---|
| 836 | def fit(self, z): |
---|
| 837 | """Fit a smooth surface to given 1d array of data points z. |
---|
| 838 | |
---|
| 839 | The smooth surface is computed at each vertex in the underlying |
---|
| 840 | mesh using the formula given in the module doc string. |
---|
| 841 | |
---|
| 842 | Pre Condition: |
---|
| 843 | self.A, self.AtA and self.B have been initialised |
---|
| 844 | |
---|
| 845 | Inputs: |
---|
| 846 | z: Single 1d vector or array of data at the point_coordinates. |
---|
| 847 | """ |
---|
| 848 | |
---|
| 849 | #Convert input to Numeric arrays |
---|
| 850 | z = ensure_numeric(z, Float) |
---|
| 851 | |
---|
| 852 | if len(z.shape) > 1 : |
---|
| 853 | raise VectorShapeError, 'Can only deal with 1d data vector' |
---|
| 854 | |
---|
| 855 | if self.point_indices is not None: |
---|
| 856 | #Remove values for any points that were outside mesh |
---|
| 857 | z = take(z, self.point_indices) |
---|
| 858 | |
---|
| 859 | #Compute right hand side based on data |
---|
| 860 | #FIXME (DSG-DsG): could Sparse_CSR be used here? Use this format |
---|
| 861 | # after a matrix is built, before calcs. |
---|
| 862 | Atz = self.A.trans_mult(z) |
---|
| 863 | |
---|
| 864 | |
---|
| 865 | #Check sanity |
---|
| 866 | n, m = self.A.shape |
---|
| 867 | if n<m and self.alpha == 0.0: |
---|
| 868 | msg = 'ERROR (least_squares): Too few data points\n' |
---|
| 869 | msg += 'There are only %d data points and alpha == 0. ' %n |
---|
| 870 | msg += 'Need at least %d\n' %m |
---|
| 871 | msg += 'Alternatively, set smoothing parameter alpha to a small ' |
---|
| 872 | msg += 'positive value,\ne.g. 1.0e-3.' |
---|
| 873 | raise msg |
---|
| 874 | |
---|
| 875 | |
---|
| 876 | |
---|
| 877 | return conjugate_gradient(self.B, Atz, Atz, imax=2*len(Atz) ) |
---|
| 878 | #FIXME: Should we store the result here for later use? (ON) |
---|
| 879 | |
---|
| 880 | |
---|
| 881 | def fit_points(self, z, verbose=False): |
---|
| 882 | """Like fit, but more robust when each point has two or more attributes |
---|
| 883 | FIXME (Ole): The name fit_points doesn't carry any meaning |
---|
| 884 | for me. How about something like fit_multiple or fit_columns? |
---|
| 885 | """ |
---|
| 886 | |
---|
| 887 | try: |
---|
| 888 | if verbose: print 'Solving penalised least_squares problem' |
---|
| 889 | return self.fit(z) |
---|
| 890 | except VectorShapeError, e: |
---|
| 891 | # broadcasting is not supported. |
---|
| 892 | |
---|
| 893 | #Convert input to Numeric arrays |
---|
| 894 | z = ensure_numeric(z, Float) |
---|
| 895 | |
---|
| 896 | #Build n x m interpolation matrix |
---|
| 897 | m = self.mesh.coordinates.shape[0] #Number of vertices |
---|
| 898 | n = z.shape[1] #Number of data points |
---|
| 899 | |
---|
| 900 | f = zeros((m,n), Float) #Resulting columns |
---|
| 901 | |
---|
| 902 | for i in range(z.shape[1]): |
---|
| 903 | f[:,i] = self.fit(z[:,i]) |
---|
| 904 | |
---|
| 905 | return f |
---|
| 906 | |
---|
| 907 | |
---|
| 908 | def interpolate(self, f): |
---|
| 909 | """Evaluate smooth surface f at data points implied in self.A. |
---|
| 910 | |
---|
| 911 | The mesh values representing a smooth surface are |
---|
| 912 | assumed to be specified in f. This argument could, |
---|
| 913 | for example have been obtained from the method self.fit() |
---|
| 914 | |
---|
| 915 | Pre Condition: |
---|
| 916 | self.A has been initialised |
---|
| 917 | |
---|
| 918 | Inputs: |
---|
| 919 | f: Vector or array of data at the mesh vertices. |
---|
| 920 | If f is an array, interpolation will be done for each column as |
---|
| 921 | per underlying matrix-matrix multiplication |
---|
| 922 | |
---|
| 923 | Output: |
---|
| 924 | Interpolated values at data points implied in self.A |
---|
| 925 | |
---|
| 926 | """ |
---|
| 927 | |
---|
| 928 | return self.A * f |
---|
| 929 | |
---|
| 930 | def cull_outsiders(self, f): |
---|
| 931 | pass |
---|
| 932 | |
---|
| 933 | |
---|
| 934 | |
---|
| 935 | |
---|
| 936 | class Interpolation_function: |
---|
| 937 | """Interpolation_function - creates callable object f(t, id) or f(t,x,y) |
---|
| 938 | which is interpolated from time series defined at vertices of |
---|
| 939 | triangular mesh (such as those stored in sww files) |
---|
| 940 | |
---|
| 941 | Let m be the number of vertices, n the number of triangles |
---|
| 942 | and p the number of timesteps. |
---|
| 943 | |
---|
| 944 | Mandatory input |
---|
| 945 | time: px1 array of monotonously increasing times (Float) |
---|
| 946 | quantities: Dictionary of arrays or 1 array (Float) |
---|
| 947 | The arrays must either have dimensions pxm or mx1. |
---|
| 948 | The resulting function will be time dependent in |
---|
[1941] | 949 | the former case while it will be constan with |
---|
[1911] | 950 | respect to time in the latter case. |
---|
| 951 | |
---|
| 952 | Optional input: |
---|
| 953 | quantity_names: List of keys into the quantities dictionary |
---|
| 954 | vertex_coordinates: mx2 array of coordinates (Float) |
---|
| 955 | triangles: nx3 array of indices into vertex_coordinates (Int) |
---|
| 956 | interpolation_points: Nx2 array of coordinates to be interpolated to |
---|
| 957 | verbose: Level of reporting |
---|
| 958 | |
---|
| 959 | |
---|
| 960 | The quantities returned by the callable object are specified by |
---|
| 961 | the list quantities which must contain the names of the |
---|
| 962 | quantities to be returned and also reflect the order, e.g. for |
---|
| 963 | the shallow water wave equation, on would have |
---|
| 964 | quantities = ['stage', 'xmomentum', 'ymomentum'] |
---|
| 965 | |
---|
| 966 | The parameter interpolation_points decides at which points interpolated |
---|
| 967 | quantities are to be computed whenever object is called. |
---|
| 968 | If None, return average value |
---|
| 969 | """ |
---|
| 970 | |
---|
| 971 | |
---|
[1941] | 972 | |
---|
[1911] | 973 | def __init__(self, |
---|
| 974 | time, |
---|
| 975 | quantities, |
---|
| 976 | quantity_names = None, |
---|
| 977 | vertex_coordinates = None, |
---|
| 978 | triangles = None, |
---|
| 979 | interpolation_points = None, |
---|
| 980 | verbose = False): |
---|
| 981 | """Initialise object and build spatial interpolation if required |
---|
| 982 | """ |
---|
| 983 | |
---|
| 984 | from Numeric import array, zeros, Float, alltrue, concatenate,\ |
---|
| 985 | reshape, ArrayType |
---|
| 986 | |
---|
| 987 | |
---|
| 988 | from config import time_format |
---|
| 989 | import types |
---|
| 990 | |
---|
| 991 | |
---|
| 992 | |
---|
| 993 | #Check temporal info |
---|
| 994 | time = ensure_numeric(time) |
---|
| 995 | msg = 'Time must be a monotonuosly ' |
---|
| 996 | msg += 'increasing sequence %s' %time |
---|
| 997 | assert alltrue(time[1:] - time[:-1] >= 0 ), msg |
---|
| 998 | |
---|
| 999 | |
---|
| 1000 | #Check if quantities is a single array only |
---|
| 1001 | if type(quantities) != types.DictType: |
---|
| 1002 | quantities = ensure_numeric(quantities) |
---|
| 1003 | quantity_names = ['Attribute'] |
---|
| 1004 | |
---|
| 1005 | #Make it a dictionary |
---|
| 1006 | quantities = {quantity_names[0]: quantities} |
---|
| 1007 | |
---|
| 1008 | |
---|
| 1009 | #Use keys if no names are specified |
---|
| 1010 | if quantity_names is None: |
---|
| 1011 | quantity_names = quantities.keys() |
---|
| 1012 | |
---|
| 1013 | |
---|
| 1014 | #Check spatial info |
---|
| 1015 | if vertex_coordinates is None: |
---|
| 1016 | self.spatial = False |
---|
| 1017 | else: |
---|
| 1018 | vertex_coordinates = ensure_numeric(vertex_coordinates) |
---|
| 1019 | |
---|
| 1020 | assert triangles is not None, 'Triangles array must be specified' |
---|
| 1021 | triangles = ensure_numeric(triangles) |
---|
| 1022 | self.spatial = True |
---|
| 1023 | |
---|
| 1024 | |
---|
| 1025 | |
---|
| 1026 | #Save for use with statistics |
---|
| 1027 | self.quantity_names = quantity_names |
---|
| 1028 | self.quantities = quantities |
---|
| 1029 | self.vertex_coordinates = vertex_coordinates |
---|
| 1030 | self.interpolation_points = interpolation_points |
---|
| 1031 | self.T = time[:] # Time assumed to be relative to starttime |
---|
| 1032 | self.index = 0 # Initial time index |
---|
| 1033 | self.precomputed_values = {} |
---|
| 1034 | |
---|
| 1035 | |
---|
| 1036 | |
---|
| 1037 | #Precomputed spatial interpolation if requested |
---|
| 1038 | if interpolation_points is not None: |
---|
| 1039 | if self.spatial is False: |
---|
| 1040 | raise 'Triangles and vertex_coordinates must be specified' |
---|
| 1041 | |
---|
| 1042 | try: |
---|
| 1043 | self.interpolation_points = ensure_numeric(interpolation_points) |
---|
| 1044 | except: |
---|
| 1045 | msg = 'Interpolation points must be an N x 2 Numeric array '+\ |
---|
| 1046 | 'or a list of points\n' |
---|
| 1047 | msg += 'I got: %s.' %(str(self.interpolation_points)[:60] +\ |
---|
| 1048 | '...') |
---|
| 1049 | raise msg |
---|
| 1050 | |
---|
| 1051 | |
---|
| 1052 | m = len(self.interpolation_points) |
---|
| 1053 | p = len(self.T) |
---|
| 1054 | |
---|
| 1055 | for name in quantity_names: |
---|
| 1056 | self.precomputed_values[name] = zeros((p, m), Float) |
---|
| 1057 | |
---|
| 1058 | #Build interpolator |
---|
| 1059 | interpol = Interpolation(vertex_coordinates, |
---|
| 1060 | triangles, |
---|
| 1061 | point_coordinates = \ |
---|
| 1062 | self.interpolation_points, |
---|
| 1063 | alpha = 0, |
---|
| 1064 | precrop = False, |
---|
| 1065 | verbose = verbose) |
---|
| 1066 | |
---|
| 1067 | if verbose: print 'Interpolate' |
---|
| 1068 | for i, t in enumerate(self.T): |
---|
| 1069 | #Interpolate quantities at this timestep |
---|
| 1070 | if verbose and i%((p+10)/10)==0: |
---|
| 1071 | print ' time step %d of %d' %(i, p) |
---|
| 1072 | |
---|
| 1073 | for name in quantity_names: |
---|
| 1074 | if len(quantities[name].shape) == 2: |
---|
| 1075 | result = interpol.interpolate(quantities[name][i,:]) |
---|
| 1076 | else: |
---|
| 1077 | #Assume no time dependency |
---|
| 1078 | result = interpol.interpolate(quantities[name][:]) |
---|
| 1079 | |
---|
| 1080 | self.precomputed_values[name][i, :] = result |
---|
| 1081 | |
---|
| 1082 | |
---|
| 1083 | |
---|
| 1084 | #Report |
---|
| 1085 | if verbose: |
---|
| 1086 | print self.statistics() |
---|
| 1087 | #self.print_statistics() |
---|
| 1088 | |
---|
| 1089 | else: |
---|
| 1090 | #Store quantitites as is |
---|
| 1091 | for name in quantity_names: |
---|
| 1092 | self.precomputed_values[name] = quantities[name] |
---|
| 1093 | |
---|
| 1094 | |
---|
| 1095 | #else: |
---|
| 1096 | # #Return an average, making this a time series |
---|
| 1097 | # for name in quantity_names: |
---|
| 1098 | # self.values[name] = zeros(len(self.T), Float) |
---|
| 1099 | # |
---|
| 1100 | # if verbose: print 'Compute mean values' |
---|
| 1101 | # for i, t in enumerate(self.T): |
---|
| 1102 | # if verbose: print ' time step %d of %d' %(i, len(self.T)) |
---|
| 1103 | # for name in quantity_names: |
---|
| 1104 | # self.values[name][i] = mean(quantities[name][i,:]) |
---|
| 1105 | |
---|
| 1106 | |
---|
| 1107 | |
---|
| 1108 | |
---|
| 1109 | def __repr__(self): |
---|
| 1110 | #return 'Interpolation function (spatio-temporal)' |
---|
| 1111 | return self.statistics() |
---|
| 1112 | |
---|
| 1113 | |
---|
| 1114 | def __call__(self, t, point_id = None, x = None, y = None): |
---|
| 1115 | """Evaluate f(t), f(t, point_id) or f(t, x, y) |
---|
| 1116 | |
---|
| 1117 | Inputs: |
---|
| 1118 | t: time - Model time. Must lie within existing timesteps |
---|
| 1119 | point_id: index of one of the preprocessed points. |
---|
| 1120 | x, y: Overrides location, point_id ignored |
---|
| 1121 | |
---|
| 1122 | If spatial info is present and all of x,y,point_id |
---|
| 1123 | are None an exception is raised |
---|
| 1124 | |
---|
| 1125 | If no spatial info is present, point_id and x,y arguments are ignored |
---|
| 1126 | making f a function of time only. |
---|
| 1127 | |
---|
| 1128 | |
---|
| 1129 | FIXME: point_id could also be a slice |
---|
| 1130 | FIXME: What if x and y are vectors? |
---|
| 1131 | FIXME: What about f(x,y) without t? |
---|
| 1132 | """ |
---|
| 1133 | |
---|
| 1134 | from math import pi, cos, sin, sqrt |
---|
| 1135 | from Numeric import zeros, Float |
---|
[2526] | 1136 | from utilities.numerical_tools import mean |
---|
[1911] | 1137 | |
---|
| 1138 | if self.spatial is True: |
---|
| 1139 | if point_id is None: |
---|
| 1140 | if x is None or y is None: |
---|
| 1141 | msg = 'Either point_id or x and y must be specified' |
---|
| 1142 | raise msg |
---|
| 1143 | else: |
---|
| 1144 | if self.interpolation_points is None: |
---|
| 1145 | msg = 'Interpolation_function must be instantiated ' +\ |
---|
| 1146 | 'with a list of interpolation points before parameter ' +\ |
---|
| 1147 | 'point_id can be used' |
---|
| 1148 | raise msg |
---|
| 1149 | |
---|
| 1150 | |
---|
| 1151 | msg = 'Time interval [%s:%s]' %(self.T[0], self.T[1]) |
---|
| 1152 | msg += ' does not match model time: %s\n' %t |
---|
| 1153 | if t < self.T[0]: raise msg |
---|
| 1154 | if t > self.T[-1]: raise msg |
---|
| 1155 | |
---|
| 1156 | oldindex = self.index #Time index |
---|
| 1157 | |
---|
| 1158 | #Find current time slot |
---|
| 1159 | while t > self.T[self.index]: self.index += 1 |
---|
| 1160 | while t < self.T[self.index]: self.index -= 1 |
---|
| 1161 | |
---|
| 1162 | if t == self.T[self.index]: |
---|
| 1163 | #Protect against case where t == T[-1] (last time) |
---|
| 1164 | # - also works in general when t == T[i] |
---|
| 1165 | ratio = 0 |
---|
| 1166 | else: |
---|
| 1167 | #t is now between index and index+1 |
---|
| 1168 | ratio = (t - self.T[self.index])/\ |
---|
| 1169 | (self.T[self.index+1] - self.T[self.index]) |
---|
| 1170 | |
---|
| 1171 | #Compute interpolated values |
---|
| 1172 | q = zeros(len(self.quantity_names), Float) |
---|
| 1173 | |
---|
| 1174 | for i, name in enumerate(self.quantity_names): |
---|
| 1175 | Q = self.precomputed_values[name] |
---|
| 1176 | |
---|
| 1177 | if self.spatial is False: |
---|
| 1178 | #If there is no spatial info |
---|
| 1179 | assert len(Q.shape) == 1 |
---|
| 1180 | |
---|
| 1181 | Q0 = Q[self.index] |
---|
| 1182 | if ratio > 0: Q1 = Q[self.index+1] |
---|
| 1183 | |
---|
| 1184 | else: |
---|
| 1185 | if x is not None and y is not None: |
---|
| 1186 | #Interpolate to x, y |
---|
| 1187 | |
---|
| 1188 | raise 'x,y interpolation not yet implemented' |
---|
| 1189 | else: |
---|
| 1190 | #Use precomputed point |
---|
| 1191 | Q0 = Q[self.index, point_id] |
---|
| 1192 | if ratio > 0: Q1 = Q[self.index+1, point_id] |
---|
| 1193 | |
---|
| 1194 | #Linear temporal interpolation |
---|
| 1195 | if ratio > 0: |
---|
| 1196 | q[i] = Q0 + ratio*(Q1 - Q0) |
---|
| 1197 | else: |
---|
| 1198 | q[i] = Q0 |
---|
| 1199 | |
---|
| 1200 | |
---|
| 1201 | #Return vector of interpolated values |
---|
| 1202 | #if len(q) == 1: |
---|
| 1203 | # return q[0] |
---|
| 1204 | #else: |
---|
| 1205 | # return q |
---|
| 1206 | |
---|
| 1207 | |
---|
| 1208 | #Return vector of interpolated values |
---|
| 1209 | #FIXME: |
---|
| 1210 | if self.spatial is True: |
---|
| 1211 | return q |
---|
| 1212 | else: |
---|
| 1213 | #Replicate q according to x and y |
---|
| 1214 | #This is e.g used for Wind_stress |
---|
[1979] | 1215 | if x is None or y is None: |
---|
[1911] | 1216 | return q |
---|
| 1217 | else: |
---|
| 1218 | try: |
---|
| 1219 | N = len(x) |
---|
| 1220 | except: |
---|
| 1221 | return q |
---|
| 1222 | else: |
---|
| 1223 | from Numeric import ones, Float |
---|
| 1224 | #x is a vector - Create one constant column for each value |
---|
| 1225 | N = len(x) |
---|
| 1226 | assert len(y) == N, 'x and y must have same length' |
---|
| 1227 | res = [] |
---|
| 1228 | for col in q: |
---|
| 1229 | res.append(col*ones(N, Float)) |
---|
| 1230 | |
---|
| 1231 | return res |
---|
| 1232 | |
---|
| 1233 | |
---|
| 1234 | def statistics(self): |
---|
| 1235 | """Output statistics about interpolation_function |
---|
| 1236 | """ |
---|
| 1237 | |
---|
| 1238 | vertex_coordinates = self.vertex_coordinates |
---|
| 1239 | interpolation_points = self.interpolation_points |
---|
| 1240 | quantity_names = self.quantity_names |
---|
| 1241 | quantities = self.quantities |
---|
| 1242 | precomputed_values = self.precomputed_values |
---|
| 1243 | |
---|
| 1244 | x = vertex_coordinates[:,0] |
---|
| 1245 | y = vertex_coordinates[:,1] |
---|
| 1246 | |
---|
| 1247 | str = '------------------------------------------------\n' |
---|
| 1248 | str += 'Interpolation_function (spatio-temporal) statistics:\n' |
---|
| 1249 | str += ' Extent:\n' |
---|
| 1250 | str += ' x in [%f, %f], len(x) == %d\n'\ |
---|
| 1251 | %(min(x), max(x), len(x)) |
---|
| 1252 | str += ' y in [%f, %f], len(y) == %d\n'\ |
---|
| 1253 | %(min(y), max(y), len(y)) |
---|
| 1254 | str += ' t in [%f, %f], len(t) == %d\n'\ |
---|
| 1255 | %(min(self.T), max(self.T), len(self.T)) |
---|
| 1256 | str += ' Quantities:\n' |
---|
| 1257 | for name in quantity_names: |
---|
| 1258 | q = quantities[name][:].flat |
---|
| 1259 | str += ' %s in [%f, %f]\n' %(name, min(q), max(q)) |
---|
| 1260 | |
---|
| 1261 | if interpolation_points is not None: |
---|
| 1262 | str += ' Interpolation points (xi, eta):'\ |
---|
| 1263 | ' number of points == %d\n' %interpolation_points.shape[0] |
---|
| 1264 | str += ' xi in [%f, %f]\n' %(min(interpolation_points[:,0]), |
---|
| 1265 | max(interpolation_points[:,0])) |
---|
| 1266 | str += ' eta in [%f, %f]\n' %(min(interpolation_points[:,1]), |
---|
| 1267 | max(interpolation_points[:,1])) |
---|
| 1268 | str += ' Interpolated quantities (over all timesteps):\n' |
---|
| 1269 | |
---|
| 1270 | for name in quantity_names: |
---|
| 1271 | q = precomputed_values[name][:].flat |
---|
| 1272 | str += ' %s at interpolation points in [%f, %f]\n'\ |
---|
| 1273 | %(name, min(q), max(q)) |
---|
| 1274 | str += '------------------------------------------------\n' |
---|
| 1275 | |
---|
| 1276 | return str |
---|
| 1277 | |
---|
| 1278 | #FIXME: Delete |
---|
| 1279 | #print '------------------------------------------------' |
---|
| 1280 | #print 'Interpolation_function statistics:' |
---|
| 1281 | #print ' Extent:' |
---|
| 1282 | #print ' x in [%f, %f], len(x) == %d'\ |
---|
| 1283 | # %(min(x), max(x), len(x)) |
---|
| 1284 | #print ' y in [%f, %f], len(y) == %d'\ |
---|
| 1285 | # %(min(y), max(y), len(y)) |
---|
| 1286 | #print ' t in [%f, %f], len(t) == %d'\ |
---|
| 1287 | # %(min(self.T), max(self.T), len(self.T)) |
---|
| 1288 | #print ' Quantities:' |
---|
| 1289 | #for name in quantity_names: |
---|
| 1290 | # q = quantities[name][:].flat |
---|
| 1291 | # print ' %s in [%f, %f]' %(name, min(q), max(q)) |
---|
| 1292 | #print ' Interpolation points (xi, eta):'\ |
---|
| 1293 | # ' number of points == %d ' %interpolation_points.shape[0] |
---|
| 1294 | #print ' xi in [%f, %f]' %(min(interpolation_points[:,0]), |
---|
| 1295 | # max(interpolation_points[:,0])) |
---|
| 1296 | #print ' eta in [%f, %f]' %(min(interpolation_points[:,1]), |
---|
| 1297 | # max(interpolation_points[:,1])) |
---|
| 1298 | #print ' Interpolated quantities (over all timesteps):' |
---|
| 1299 | # |
---|
| 1300 | #for name in quantity_names: |
---|
| 1301 | # q = precomputed_values[name][:].flat |
---|
| 1302 | # print ' %s at interpolation points in [%f, %f]'\ |
---|
| 1303 | # %(name, min(q), max(q)) |
---|
| 1304 | #print '------------------------------------------------' |
---|
| 1305 | |
---|
| 1306 | |
---|
| 1307 | #------------------------------------------------------------- |
---|
| 1308 | if __name__ == "__main__": |
---|
| 1309 | """ |
---|
| 1310 | Load in a mesh and data points with attributes. |
---|
| 1311 | Fit the attributes to the mesh. |
---|
| 1312 | Save a new mesh file. |
---|
| 1313 | """ |
---|
| 1314 | import os, sys |
---|
| 1315 | usage = "usage: %s mesh_input.tsh point.xya mesh_output.tsh [expand|no_expand][vervose|non_verbose] [alpha] [display_errors|no_display_errors]"\ |
---|
| 1316 | %os.path.basename(sys.argv[0]) |
---|
| 1317 | |
---|
| 1318 | if len(sys.argv) < 4: |
---|
| 1319 | print usage |
---|
| 1320 | else: |
---|
| 1321 | mesh_file = sys.argv[1] |
---|
| 1322 | point_file = sys.argv[2] |
---|
| 1323 | mesh_output_file = sys.argv[3] |
---|
| 1324 | |
---|
| 1325 | expand_search = False |
---|
| 1326 | if len(sys.argv) > 4: |
---|
| 1327 | if sys.argv[4][0] == "e" or sys.argv[4][0] == "E": |
---|
| 1328 | expand_search = True |
---|
| 1329 | else: |
---|
| 1330 | expand_search = False |
---|
| 1331 | |
---|
| 1332 | verbose = False |
---|
| 1333 | if len(sys.argv) > 5: |
---|
| 1334 | if sys.argv[5][0] == "n" or sys.argv[5][0] == "N": |
---|
| 1335 | verbose = False |
---|
| 1336 | else: |
---|
| 1337 | verbose = True |
---|
| 1338 | |
---|
| 1339 | if len(sys.argv) > 6: |
---|
| 1340 | alpha = sys.argv[6] |
---|
| 1341 | else: |
---|
| 1342 | alpha = DEFAULT_ALPHA |
---|
| 1343 | |
---|
| 1344 | # This is used more for testing |
---|
| 1345 | if len(sys.argv) > 7: |
---|
| 1346 | if sys.argv[7][0] == "n" or sys.argv[5][0] == "N": |
---|
| 1347 | display_errors = False |
---|
| 1348 | else: |
---|
| 1349 | display_errors = True |
---|
| 1350 | |
---|
| 1351 | t0 = time.time() |
---|
| 1352 | try: |
---|
| 1353 | fit_to_mesh_file(mesh_file, |
---|
| 1354 | point_file, |
---|
| 1355 | mesh_output_file, |
---|
| 1356 | alpha, |
---|
| 1357 | verbose= verbose, |
---|
| 1358 | expand_search = expand_search, |
---|
| 1359 | display_errors = display_errors) |
---|
| 1360 | except IOError,e: |
---|
| 1361 | import sys; sys.exit(1) |
---|
| 1362 | |
---|
| 1363 | print 'That took %.2f seconds' %(time.time()-t0) |
---|
| 1364 | |
---|