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 | class FittingError(exceptions.Exception): pass |
---|
23 | |
---|
24 | |
---|
25 | #from general_mesh import General_mesh |
---|
26 | from Numeric import zeros, array, Float, Int, dot, transpose, concatenate, ArrayType, NewAxis |
---|
27 | from pyvolution.mesh import Mesh |
---|
28 | |
---|
29 | from Numeric import zeros, take, compress, array, Float, Int, dot, transpose, concatenate, ArrayType |
---|
30 | from utilities.sparse import Sparse, Sparse_CSR |
---|
31 | from utilities.cg_solve import conjugate_gradient, VectorShapeError |
---|
32 | from utilities.numerical_tools import ensure_numeric, mean, gradient |
---|
33 | |
---|
34 | |
---|
35 | from coordinate_transforms.geo_reference import Geo_reference |
---|
36 | |
---|
37 | import time |
---|
38 | |
---|
39 | |
---|
40 | |
---|
41 | DEFAULT_ALPHA = 0.001 |
---|
42 | |
---|
43 | def fit_to_mesh_file(mesh_file, point_file, mesh_output_file, |
---|
44 | alpha=DEFAULT_ALPHA, verbose= False, |
---|
45 | expand_search = False, |
---|
46 | data_origin = None, |
---|
47 | mesh_origin = None, |
---|
48 | precrop = False, |
---|
49 | display_errors = True): |
---|
50 | """ |
---|
51 | Given a mesh file (tsh) and a point attribute file (xya), fit |
---|
52 | point attributes to the mesh and write a mesh file with the |
---|
53 | results. |
---|
54 | |
---|
55 | |
---|
56 | If data_origin is not None it is assumed to be |
---|
57 | a 3-tuple with geo referenced |
---|
58 | UTM coordinates (zone, easting, northing) |
---|
59 | |
---|
60 | NOTE: Throws IOErrors, for a variety of file problems. |
---|
61 | |
---|
62 | mesh_origin is the same but refers to the input tsh file. |
---|
63 | FIXME: When the tsh format contains it own origin, these parameters can go. |
---|
64 | FIXME: And both origins should be obtained from the specified files. |
---|
65 | """ |
---|
66 | |
---|
67 | from load_mesh.loadASCII import import_mesh_file, \ |
---|
68 | import_points_file, export_mesh_file, \ |
---|
69 | concatinate_attributelist |
---|
70 | |
---|
71 | |
---|
72 | try: |
---|
73 | mesh_dict = import_mesh_file(mesh_file) |
---|
74 | except IOError,e: |
---|
75 | if display_errors: |
---|
76 | print "Could not load bad file. ", e |
---|
77 | raise IOError #Re-raise exception |
---|
78 | |
---|
79 | vertex_coordinates = mesh_dict['vertices'] |
---|
80 | triangles = mesh_dict['triangles'] |
---|
81 | if type(mesh_dict['vertex_attributes']) == ArrayType: |
---|
82 | old_point_attributes = mesh_dict['vertex_attributes'].tolist() |
---|
83 | else: |
---|
84 | old_point_attributes = mesh_dict['vertex_attributes'] |
---|
85 | |
---|
86 | if type(mesh_dict['vertex_attribute_titles']) == ArrayType: |
---|
87 | old_title_list = mesh_dict['vertex_attribute_titles'].tolist() |
---|
88 | else: |
---|
89 | old_title_list = mesh_dict['vertex_attribute_titles'] |
---|
90 | |
---|
91 | if verbose: print 'tsh file %s loaded' %mesh_file |
---|
92 | |
---|
93 | # load in the .pts file |
---|
94 | try: |
---|
95 | point_dict = import_points_file(point_file, verbose=verbose) |
---|
96 | except IOError,e: |
---|
97 | if display_errors: |
---|
98 | print "Could not load bad file. ", e |
---|
99 | raise IOError #Re-raise exception |
---|
100 | |
---|
101 | point_coordinates = point_dict['pointlist'] |
---|
102 | title_list,point_attributes = concatinate_attributelist(point_dict['attributelist']) |
---|
103 | |
---|
104 | if point_dict.has_key('geo_reference') and not point_dict['geo_reference'] is None: |
---|
105 | data_origin = point_dict['geo_reference'].get_origin() |
---|
106 | else: |
---|
107 | data_origin = (56, 0, 0) #FIXME(DSG-DSG) |
---|
108 | |
---|
109 | if mesh_dict.has_key('geo_reference') and not mesh_dict['geo_reference'] is None: |
---|
110 | mesh_origin = mesh_dict['geo_reference'].get_origin() |
---|
111 | else: |
---|
112 | mesh_origin = (56, 0, 0) #FIXME(DSG-DSG) |
---|
113 | |
---|
114 | if verbose: print "points file loaded" |
---|
115 | if verbose: print "fitting to mesh" |
---|
116 | f = fit_to_mesh(vertex_coordinates, |
---|
117 | triangles, |
---|
118 | point_coordinates, |
---|
119 | point_attributes, |
---|
120 | alpha = alpha, |
---|
121 | verbose = verbose, |
---|
122 | expand_search = expand_search, |
---|
123 | data_origin = data_origin, |
---|
124 | mesh_origin = mesh_origin, |
---|
125 | precrop = precrop) |
---|
126 | if verbose: print "finished fitting to mesh" |
---|
127 | |
---|
128 | # convert array to list of lists |
---|
129 | new_point_attributes = f.tolist() |
---|
130 | #FIXME have this overwrite attributes with the same title - DSG |
---|
131 | #Put the newer attributes last |
---|
132 | if old_title_list <> []: |
---|
133 | old_title_list.extend(title_list) |
---|
134 | #FIXME can this be done a faster way? - DSG |
---|
135 | for i in range(len(old_point_attributes)): |
---|
136 | old_point_attributes[i].extend(new_point_attributes[i]) |
---|
137 | mesh_dict['vertex_attributes'] = old_point_attributes |
---|
138 | mesh_dict['vertex_attribute_titles'] = old_title_list |
---|
139 | else: |
---|
140 | mesh_dict['vertex_attributes'] = new_point_attributes |
---|
141 | mesh_dict['vertex_attribute_titles'] = title_list |
---|
142 | |
---|
143 | #FIXME (Ole): Remember to output mesh_origin as well |
---|
144 | if verbose: print "exporting to file ", mesh_output_file |
---|
145 | |
---|
146 | try: |
---|
147 | export_mesh_file(mesh_output_file, mesh_dict) |
---|
148 | except IOError,e: |
---|
149 | if display_errors: |
---|
150 | print "Could not write file. ", e |
---|
151 | raise IOError |
---|
152 | |
---|
153 | def fit_to_mesh(vertex_coordinates, |
---|
154 | triangles, |
---|
155 | point_coordinates, |
---|
156 | point_attributes, |
---|
157 | alpha = DEFAULT_ALPHA, |
---|
158 | verbose = False, |
---|
159 | acceptable_overshoot = 1.01, |
---|
160 | expand_search = False, |
---|
161 | data_origin = None, |
---|
162 | mesh_origin = None, |
---|
163 | precrop = False, |
---|
164 | use_cache = False): |
---|
165 | """ |
---|
166 | Fit a smooth surface to a triangulation, |
---|
167 | given data points with attributes. |
---|
168 | |
---|
169 | |
---|
170 | Inputs: |
---|
171 | |
---|
172 | vertex_coordinates: List of coordinate pairs [xi, eta] of points |
---|
173 | constituting mesh (or a an m x 2 Numeric array) |
---|
174 | |
---|
175 | triangles: List of 3-tuples (or a Numeric array) of |
---|
176 | integers representing indices of all vertices in the mesh. |
---|
177 | |
---|
178 | point_coordinates: List of coordinate pairs [x, y] of data points |
---|
179 | (or an nx2 Numeric array) |
---|
180 | |
---|
181 | alpha: Smoothing parameter. |
---|
182 | |
---|
183 | acceptable overshoot: controls the allowed factor by which fitted values |
---|
184 | may exceed the value of input data. The lower limit is defined |
---|
185 | as min(z) - acceptable_overshoot*delta z and upper limit |
---|
186 | as max(z) + acceptable_overshoot*delta z |
---|
187 | |
---|
188 | |
---|
189 | point_attributes: Vector or array of data at the point_coordinates. |
---|
190 | |
---|
191 | data_origin and mesh_origin are 3-tuples consisting of |
---|
192 | UTM zone, easting and northing. If specified |
---|
193 | point coordinates and vertex coordinates are assumed to be |
---|
194 | relative to their respective origins. |
---|
195 | |
---|
196 | """ |
---|
197 | |
---|
198 | if use_cache is True: |
---|
199 | from caching.caching import cache |
---|
200 | interp = cache(_interpolation, |
---|
201 | (vertex_coordinates, |
---|
202 | triangles, |
---|
203 | point_coordinates), |
---|
204 | {'alpha': alpha, |
---|
205 | 'verbose': verbose, |
---|
206 | 'expand_search': expand_search, |
---|
207 | 'data_origin': data_origin, |
---|
208 | 'mesh_origin': mesh_origin, |
---|
209 | 'precrop': precrop}, |
---|
210 | verbose = verbose) |
---|
211 | |
---|
212 | else: |
---|
213 | interp = Interpolation(vertex_coordinates, |
---|
214 | triangles, |
---|
215 | point_coordinates, |
---|
216 | alpha = alpha, |
---|
217 | verbose = verbose, |
---|
218 | expand_search = expand_search, |
---|
219 | data_origin = data_origin, |
---|
220 | mesh_origin = mesh_origin, |
---|
221 | precrop = precrop) |
---|
222 | |
---|
223 | vertex_attributes = interp.fit_points(point_attributes, verbose = verbose) |
---|
224 | |
---|
225 | |
---|
226 | #Sanity check |
---|
227 | point_coordinates = ensure_numeric(point_coordinates) |
---|
228 | vertex_coordinates = ensure_numeric(vertex_coordinates) |
---|
229 | |
---|
230 | #Data points |
---|
231 | X = point_coordinates[:,0] |
---|
232 | Y = point_coordinates[:,1] |
---|
233 | Z = ensure_numeric(point_attributes) |
---|
234 | if len(Z.shape) == 1: |
---|
235 | Z = Z[:, NewAxis] |
---|
236 | |
---|
237 | |
---|
238 | #Data points inside mesh boundary |
---|
239 | indices = interp.point_indices |
---|
240 | if indices is not None: |
---|
241 | Xc = take(X, indices) |
---|
242 | Yc = take(Y, indices) |
---|
243 | Zc = take(Z, indices) |
---|
244 | else: |
---|
245 | Xc = X |
---|
246 | Yc = Y |
---|
247 | Zc = Z |
---|
248 | |
---|
249 | #Vertex coordinates |
---|
250 | Xi = vertex_coordinates[:,0] |
---|
251 | Eta = vertex_coordinates[:,1] |
---|
252 | Zeta = ensure_numeric(vertex_attributes) |
---|
253 | if len(Zeta.shape) == 1: |
---|
254 | Zeta = Zeta[:, NewAxis] |
---|
255 | |
---|
256 | for i in range(Zeta.shape[1]): #For each attribute |
---|
257 | zeta = Zeta[:,i] |
---|
258 | z = Z[:,i] |
---|
259 | zc = Zc[:,i] |
---|
260 | |
---|
261 | max_zc = max(zc) |
---|
262 | min_zc = min(zc) |
---|
263 | delta_zc = max_zc-min_zc |
---|
264 | upper_limit = max_zc + delta_zc*acceptable_overshoot |
---|
265 | lower_limit = min_zc - delta_zc*acceptable_overshoot |
---|
266 | |
---|
267 | |
---|
268 | if max(zeta) > upper_limit or min(zeta) < lower_limit: |
---|
269 | msg = 'Least sqares produced values outside the allowed ' |
---|
270 | msg += 'range [%f, %f].\n' %(lower_limit, upper_limit) |
---|
271 | msg += 'z in [%f, %f], zeta in [%f, %f].\n' %(min_zc, max_zc, |
---|
272 | min(zeta), max(zeta)) |
---|
273 | msg += 'If greater range is needed, increase the value of ' |
---|
274 | msg += 'acceptable_fit_overshoot (currently %.2f).\n' %(acceptable_overshoot) |
---|
275 | |
---|
276 | |
---|
277 | offending_vertices = (zeta > upper_limit or zeta < lower_limit) |
---|
278 | Xi_c = compress(offending_vertices, Xi) |
---|
279 | Eta_c = compress(offending_vertices, Eta) |
---|
280 | offending_coordinates = concatenate((Xi_c[:, NewAxis], |
---|
281 | Eta_c[:, NewAxis]), |
---|
282 | axis=1) |
---|
283 | |
---|
284 | msg += 'Offending locations:\n %s' %(offending_coordinates) |
---|
285 | |
---|
286 | raise FittingError, msg |
---|
287 | |
---|
288 | |
---|
289 | |
---|
290 | if verbose: |
---|
291 | print '+------------------------------------------------' |
---|
292 | print 'Least squares statistics' |
---|
293 | print '+------------------------------------------------' |
---|
294 | print 'points: %d points' %(len(z)) |
---|
295 | print ' x in [%f, %f]'%(min(X), max(X)) |
---|
296 | print ' y in [%f, %f]'%(min(Y), max(Y)) |
---|
297 | print ' z in [%f, %f]'%(min(z), max(z)) |
---|
298 | print |
---|
299 | |
---|
300 | if indices is not None: |
---|
301 | print 'Cropped points: %d points' %(len(zc)) |
---|
302 | print ' x in [%f, %f]'%(min(Xc), max(Xc)) |
---|
303 | print ' y in [%f, %f]'%(min(Yc), max(Yc)) |
---|
304 | print ' z in [%f, %f]'%(min(zc), max(zc)) |
---|
305 | print |
---|
306 | |
---|
307 | |
---|
308 | print 'Mesh: %d vertices' %(len(zeta)) |
---|
309 | print ' xi in [%f, %f]'%(min(Xi), max(Xi)) |
---|
310 | print ' eta in [%f, %f]'%(min(Eta), max(Eta)) |
---|
311 | print ' zeta in [%f, %f]'%(min(zeta), max(zeta)) |
---|
312 | print '+------------------------------------------------' |
---|
313 | |
---|
314 | return vertex_attributes |
---|
315 | |
---|
316 | |
---|
317 | |
---|
318 | def pts2rectangular(pts_name, M, N, alpha = DEFAULT_ALPHA, |
---|
319 | verbose = False, reduction = 1): |
---|
320 | """Fits attributes from pts file to MxN rectangular mesh |
---|
321 | |
---|
322 | Read pts file and create rectangular mesh of resolution MxN such that |
---|
323 | it covers all points specified in pts file. |
---|
324 | |
---|
325 | FIXME: This may be a temporary function until we decide on |
---|
326 | netcdf formats etc |
---|
327 | |
---|
328 | FIXME: Uses elevation hardwired |
---|
329 | """ |
---|
330 | |
---|
331 | import mesh_factory |
---|
332 | from load_mesh.loadASCII import import_points_file |
---|
333 | |
---|
334 | if verbose: print 'Read pts' |
---|
335 | points_dict = import_points_file(pts_name) |
---|
336 | #points, attributes = util.read_xya(pts_name) |
---|
337 | |
---|
338 | #Reduce number of points a bit |
---|
339 | points = points_dict['pointlist'][::reduction] |
---|
340 | elevation = points_dict['attributelist']['elevation'] #Must be elevation |
---|
341 | elevation = elevation[::reduction] |
---|
342 | |
---|
343 | if verbose: print 'Got %d data points' %len(points) |
---|
344 | |
---|
345 | if verbose: print 'Create mesh' |
---|
346 | #Find extent |
---|
347 | max_x = min_x = points[0][0] |
---|
348 | max_y = min_y = points[0][1] |
---|
349 | for point in points[1:]: |
---|
350 | x = point[0] |
---|
351 | if x > max_x: max_x = x |
---|
352 | if x < min_x: min_x = x |
---|
353 | y = point[1] |
---|
354 | if y > max_y: max_y = y |
---|
355 | if y < min_y: min_y = y |
---|
356 | |
---|
357 | #Create appropriate mesh |
---|
358 | vertex_coordinates, triangles, boundary =\ |
---|
359 | mesh_factory.rectangular(M, N, max_x-min_x, max_y-min_y, |
---|
360 | (min_x, min_y)) |
---|
361 | |
---|
362 | #Fit attributes to mesh |
---|
363 | vertex_attributes = fit_to_mesh(vertex_coordinates, |
---|
364 | triangles, |
---|
365 | points, |
---|
366 | elevation, alpha=alpha, verbose=verbose) |
---|
367 | |
---|
368 | |
---|
369 | |
---|
370 | return vertex_coordinates, triangles, boundary, vertex_attributes |
---|
371 | |
---|
372 | |
---|
373 | def _interpolation(*args, **kwargs): |
---|
374 | """Private function for use with caching. Reason is that classes |
---|
375 | may change their byte code between runs which is annoying. |
---|
376 | """ |
---|
377 | |
---|
378 | return Interpolation(*args, **kwargs) |
---|
379 | |
---|
380 | |
---|
381 | class Interpolation: |
---|
382 | |
---|
383 | def __init__(self, |
---|
384 | vertex_coordinates, |
---|
385 | triangles, |
---|
386 | point_coordinates = None, |
---|
387 | alpha = None, |
---|
388 | verbose = False, |
---|
389 | expand_search = True, |
---|
390 | interp_only = False, |
---|
391 | max_points_per_cell = 30, |
---|
392 | mesh_origin = None, |
---|
393 | data_origin = None, |
---|
394 | precrop = False): |
---|
395 | |
---|
396 | |
---|
397 | """ Build interpolation matrix mapping from |
---|
398 | function values at vertices to function values at data points |
---|
399 | |
---|
400 | Inputs: |
---|
401 | |
---|
402 | vertex_coordinates: List of coordinate pairs [xi, eta] of |
---|
403 | points constituting mesh (or a an m x 2 Numeric array) |
---|
404 | Points may appear multiple times |
---|
405 | (e.g. if vertices have discontinuities) |
---|
406 | |
---|
407 | triangles: List of 3-tuples (or a Numeric array) of |
---|
408 | integers representing indices of all vertices in the mesh. |
---|
409 | |
---|
410 | point_coordinates: List of coordinate pairs [x, y] of |
---|
411 | data points (or an nx2 Numeric array) |
---|
412 | If point_coordinates is absent, only smoothing matrix will |
---|
413 | be built |
---|
414 | |
---|
415 | alpha: Smoothing parameter |
---|
416 | |
---|
417 | data_origin and mesh_origin are 3-tuples consisting of |
---|
418 | UTM zone, easting and northing. If specified |
---|
419 | point coordinates and vertex coordinates are assumed to be |
---|
420 | relative to their respective origins. |
---|
421 | |
---|
422 | """ |
---|
423 | |
---|
424 | #Convert input to Numeric arrays |
---|
425 | triangles = ensure_numeric(triangles, Int) |
---|
426 | vertex_coordinates = ensure_numeric(vertex_coordinates, Float) |
---|
427 | |
---|
428 | #Build underlying mesh |
---|
429 | if verbose: print 'Building mesh' |
---|
430 | #self.mesh = General_mesh(vertex_coordinates, triangles, |
---|
431 | #FIXME: Trying the normal mesh while testing precrop, |
---|
432 | # The functionality of boundary_polygon is needed for that |
---|
433 | |
---|
434 | #FIXME - geo ref does not have to go into mesh. |
---|
435 | # Change the point co-ords to conform to the |
---|
436 | # mesh co-ords early in the code |
---|
437 | if mesh_origin is None: |
---|
438 | geo = None |
---|
439 | else: |
---|
440 | geo = Geo_reference(mesh_origin[0],mesh_origin[1],mesh_origin[2]) |
---|
441 | self.mesh = Mesh(vertex_coordinates, triangles, |
---|
442 | geo_reference = geo) |
---|
443 | |
---|
444 | if verbose: print 'Checking mesh integrity' |
---|
445 | self.mesh.check_integrity() |
---|
446 | |
---|
447 | if verbose: print 'Mesh integrity checked' |
---|
448 | |
---|
449 | self.data_origin = data_origin |
---|
450 | |
---|
451 | self.point_indices = None |
---|
452 | |
---|
453 | #Smoothing parameter |
---|
454 | if alpha is None: |
---|
455 | self.alpha = DEFAULT_ALPHA |
---|
456 | else: |
---|
457 | self.alpha = alpha |
---|
458 | |
---|
459 | |
---|
460 | if point_coordinates is not None: |
---|
461 | if verbose: print 'Building interpolation matrix' |
---|
462 | self.build_interpolation_matrix_A(point_coordinates, |
---|
463 | verbose = verbose, |
---|
464 | expand_search = expand_search, |
---|
465 | interp_only = interp_only, |
---|
466 | max_points_per_cell =\ |
---|
467 | max_points_per_cell, |
---|
468 | data_origin = data_origin, |
---|
469 | precrop = precrop) |
---|
470 | #Build coefficient matrices |
---|
471 | if interp_only == False: |
---|
472 | self.build_coefficient_matrix_B(point_coordinates, |
---|
473 | verbose = verbose, |
---|
474 | expand_search = expand_search, |
---|
475 | max_points_per_cell =\ |
---|
476 | max_points_per_cell, |
---|
477 | data_origin = data_origin, |
---|
478 | precrop = precrop) |
---|
479 | if verbose: print 'Finished interpolation' |
---|
480 | |
---|
481 | def set_point_coordinates(self, point_coordinates, |
---|
482 | data_origin = None, |
---|
483 | verbose = False, |
---|
484 | precrop = True): |
---|
485 | """ |
---|
486 | A public interface to setting the point co-ordinates. |
---|
487 | """ |
---|
488 | if point_coordinates is not None: |
---|
489 | if verbose: print 'Building interpolation matrix' |
---|
490 | self.build_interpolation_matrix_A(point_coordinates, |
---|
491 | verbose = verbose, |
---|
492 | data_origin = data_origin, |
---|
493 | precrop = precrop) |
---|
494 | self.build_coefficient_matrix_B(point_coordinates, data_origin) |
---|
495 | |
---|
496 | def build_coefficient_matrix_B(self, point_coordinates=None, |
---|
497 | verbose = False, expand_search = True, |
---|
498 | max_points_per_cell=30, |
---|
499 | data_origin = None, |
---|
500 | precrop = False): |
---|
501 | """Build final coefficient matrix""" |
---|
502 | |
---|
503 | |
---|
504 | if self.alpha <> 0: |
---|
505 | if verbose: print 'Building smoothing matrix' |
---|
506 | self.build_smoothing_matrix_D() |
---|
507 | |
---|
508 | if point_coordinates is not None: |
---|
509 | if self.alpha <> 0: |
---|
510 | self.B = self.AtA + self.alpha*self.D |
---|
511 | else: |
---|
512 | self.B = self.AtA |
---|
513 | |
---|
514 | #Convert self.B matrix to CSR format for faster matrix vector |
---|
515 | self.B = Sparse_CSR(self.B) |
---|
516 | |
---|
517 | def build_interpolation_matrix_A(self, point_coordinates, |
---|
518 | verbose = False, expand_search = True, |
---|
519 | max_points_per_cell=30, |
---|
520 | data_origin = None, |
---|
521 | precrop = False, |
---|
522 | interp_only = False): |
---|
523 | """Build n x m interpolation matrix, where |
---|
524 | n is the number of data points and |
---|
525 | m is the number of basis functions phi_k (one per vertex) |
---|
526 | |
---|
527 | This algorithm uses a quad tree data structure for fast binning of data points |
---|
528 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
---|
529 | If specified coordinates are assumed to be relative to this origin. |
---|
530 | |
---|
531 | This one will override any data_origin that may be specified in |
---|
532 | interpolation instance |
---|
533 | |
---|
534 | """ |
---|
535 | |
---|
536 | |
---|
537 | |
---|
538 | #FIXME (Ole): Check that this function is memeory efficient. |
---|
539 | #6 million datapoints and 300000 basis functions |
---|
540 | #causes out-of-memory situation |
---|
541 | #First thing to check is whether there is room for self.A and self.AtA |
---|
542 | # |
---|
543 | #Maybe we need some sort of blocking |
---|
544 | |
---|
545 | from pyvolution.quad import build_quadtree |
---|
546 | from utilities.polygon import inside_polygon |
---|
547 | |
---|
548 | |
---|
549 | if data_origin is None: |
---|
550 | data_origin = self.data_origin #Use the one from |
---|
551 | #interpolation instance |
---|
552 | |
---|
553 | #Convert input to Numeric arrays just in case. |
---|
554 | point_coordinates = ensure_numeric(point_coordinates, Float) |
---|
555 | |
---|
556 | #Keep track of discarded points (if any). |
---|
557 | #This is only registered if precrop is True |
---|
558 | self.cropped_points = False |
---|
559 | |
---|
560 | #Shift data points to same origin as mesh (if specified) |
---|
561 | |
---|
562 | #FIXME this will shift if there was no geo_ref. |
---|
563 | #But all this should be removed anyhow. |
---|
564 | #change coords before this point |
---|
565 | mesh_origin = self.mesh.geo_reference.get_origin() |
---|
566 | if point_coordinates is not None: |
---|
567 | if data_origin is not None: |
---|
568 | if mesh_origin is not None: |
---|
569 | |
---|
570 | #Transformation: |
---|
571 | # |
---|
572 | #Let x_0 be the reference point of the point coordinates |
---|
573 | #and xi_0 the reference point of the mesh. |
---|
574 | # |
---|
575 | #A point coordinate (x + x_0) is then made relative |
---|
576 | #to xi_0 by |
---|
577 | # |
---|
578 | # x_new = x + x_0 - xi_0 |
---|
579 | # |
---|
580 | #and similarly for eta |
---|
581 | |
---|
582 | x_offset = data_origin[1] - mesh_origin[1] |
---|
583 | y_offset = data_origin[2] - mesh_origin[2] |
---|
584 | else: #Shift back to a zero origin |
---|
585 | x_offset = data_origin[1] |
---|
586 | y_offset = data_origin[2] |
---|
587 | |
---|
588 | point_coordinates[:,0] += x_offset |
---|
589 | point_coordinates[:,1] += y_offset |
---|
590 | else: |
---|
591 | if mesh_origin is not None: |
---|
592 | #Use mesh origin for data points |
---|
593 | point_coordinates[:,0] -= mesh_origin[1] |
---|
594 | point_coordinates[:,1] -= mesh_origin[2] |
---|
595 | |
---|
596 | |
---|
597 | |
---|
598 | #Remove points falling outside mesh boundary |
---|
599 | #This reduced one example from 1356 seconds to 825 seconds |
---|
600 | |
---|
601 | |
---|
602 | if precrop is True: |
---|
603 | from Numeric import take |
---|
604 | |
---|
605 | if verbose: print 'Getting boundary polygon' |
---|
606 | P = self.mesh.get_boundary_polygon() |
---|
607 | |
---|
608 | if verbose: print 'Getting indices inside mesh boundary' |
---|
609 | indices = inside_polygon(point_coordinates, P, verbose = verbose) |
---|
610 | |
---|
611 | |
---|
612 | if len(indices) != point_coordinates.shape[0]: |
---|
613 | self.cropped_points = True |
---|
614 | if verbose: |
---|
615 | print 'Done - %d points outside mesh have been cropped.'\ |
---|
616 | %(point_coordinates.shape[0] - len(indices)) |
---|
617 | |
---|
618 | point_coordinates = take(point_coordinates, indices) |
---|
619 | self.point_indices = indices |
---|
620 | |
---|
621 | |
---|
622 | |
---|
623 | |
---|
624 | #Build n x m interpolation matrix |
---|
625 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
626 | n = point_coordinates.shape[0] #Nbr of data points |
---|
627 | |
---|
628 | if verbose: print 'Number of datapoints: %d' %n |
---|
629 | if verbose: print 'Number of basis functions: %d' %m |
---|
630 | |
---|
631 | #FIXME (Ole): We should use CSR here since mat-mat mult is now OK. |
---|
632 | #However, Sparse_CSR does not have the same methods as Sparse yet |
---|
633 | #The tests will reveal what needs to be done |
---|
634 | |
---|
635 | # |
---|
636 | #self.A = Sparse_CSR(Sparse(n,m)) |
---|
637 | #self.AtA = Sparse_CSR(Sparse(m,m)) |
---|
638 | self.A = Sparse(n,m) |
---|
639 | self.AtA = Sparse(m,m) |
---|
640 | |
---|
641 | #Build quad tree of vertices (FIXME: Is this the right spot for that?) |
---|
642 | root = build_quadtree(self.mesh, |
---|
643 | max_points_per_cell = max_points_per_cell) |
---|
644 | #root.show() |
---|
645 | self.expanded_quad_searches = [] |
---|
646 | #Compute matrix elements |
---|
647 | for i in range(n): |
---|
648 | #For each data_coordinate point |
---|
649 | |
---|
650 | if verbose and i%((n+10)/10)==0: print 'Doing %d of %d' %(i, n) |
---|
651 | x = point_coordinates[i] |
---|
652 | |
---|
653 | #Find vertices near x |
---|
654 | candidate_vertices = root.search(x[0], x[1]) |
---|
655 | is_more_elements = True |
---|
656 | |
---|
657 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
658 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
659 | first_expansion = True |
---|
660 | while not element_found and is_more_elements and expand_search: |
---|
661 | #if verbose: print 'Expanding search' |
---|
662 | if first_expansion == True: |
---|
663 | self.expanded_quad_searches.append(1) |
---|
664 | first_expansion = False |
---|
665 | else: |
---|
666 | end = len(self.expanded_quad_searches) - 1 |
---|
667 | assert end >= 0 |
---|
668 | self.expanded_quad_searches[end] += 1 |
---|
669 | candidate_vertices, branch = root.expand_search() |
---|
670 | if branch == []: |
---|
671 | # Searching all the verts from the root cell that haven't |
---|
672 | # been searched. This is the last try |
---|
673 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
674 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
675 | is_more_elements = False |
---|
676 | else: |
---|
677 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
678 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
679 | |
---|
680 | |
---|
681 | #Update interpolation matrix A if necessary |
---|
682 | if element_found is True: |
---|
683 | #Assign values to matrix A |
---|
684 | |
---|
685 | j0 = self.mesh.triangles[k,0] #Global vertex id for sigma0 |
---|
686 | j1 = self.mesh.triangles[k,1] #Global vertex id for sigma1 |
---|
687 | j2 = self.mesh.triangles[k,2] #Global vertex id for sigma2 |
---|
688 | |
---|
689 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
690 | js = [j0,j1,j2] |
---|
691 | |
---|
692 | for j in js: |
---|
693 | self.A[i,j] = sigmas[j] |
---|
694 | for k in js: |
---|
695 | if interp_only == False: |
---|
696 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
697 | else: |
---|
698 | pass |
---|
699 | #Ok if there is no triangle for datapoint |
---|
700 | #(as in brute force version) |
---|
701 | #raise 'Could not find triangle for point', x |
---|
702 | |
---|
703 | |
---|
704 | |
---|
705 | def search_triangles_of_vertices(self, candidate_vertices, x): |
---|
706 | #Find triangle containing x: |
---|
707 | element_found = False |
---|
708 | |
---|
709 | # This will be returned if element_found = False |
---|
710 | sigma2 = -10.0 |
---|
711 | sigma0 = -10.0 |
---|
712 | sigma1 = -10.0 |
---|
713 | k = -10.0 |
---|
714 | #print "*$* candidate_vertices", candidate_vertices |
---|
715 | #For all vertices in same cell as point x |
---|
716 | for v in candidate_vertices: |
---|
717 | #FIXME (DSG-DSG): this catches verts with no triangle. |
---|
718 | #Currently pmesh is producing these. |
---|
719 | #this should be stopped, |
---|
720 | if self.mesh.vertexlist[v] is None: |
---|
721 | continue |
---|
722 | #for each triangle id (k) which has v as a vertex |
---|
723 | for k, _ in self.mesh.vertexlist[v]: |
---|
724 | |
---|
725 | #Get the three vertex_points of candidate triangle |
---|
726 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
727 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
728 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
729 | |
---|
730 | #print "PDSG - k", k |
---|
731 | #print "PDSG - xi0", xi0 |
---|
732 | #print "PDSG - xi1", xi1 |
---|
733 | #print "PDSG - xi2", xi2 |
---|
734 | #print "PDSG element %i verts((%f, %f),(%f, %f),(%f, %f))"\ |
---|
735 | # % (k, xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1]) |
---|
736 | |
---|
737 | #Get the three normals |
---|
738 | n0 = self.mesh.get_normal(k, 0) |
---|
739 | n1 = self.mesh.get_normal(k, 1) |
---|
740 | n2 = self.mesh.get_normal(k, 2) |
---|
741 | |
---|
742 | |
---|
743 | #Compute interpolation |
---|
744 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
745 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
746 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
747 | |
---|
748 | #print "PDSG - sigma0", sigma0 |
---|
749 | #print "PDSG - sigma1", sigma1 |
---|
750 | #print "PDSG - sigma2", sigma2 |
---|
751 | |
---|
752 | #FIXME: Maybe move out to test or something |
---|
753 | epsilon = 1.0e-6 |
---|
754 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
755 | |
---|
756 | #Check that this triangle contains the data point |
---|
757 | |
---|
758 | #Sigmas can get negative within |
---|
759 | #machine precision on some machines (e.g nautilus) |
---|
760 | #Hence the small eps |
---|
761 | eps = 1.0e-15 |
---|
762 | if sigma0 >= -eps and sigma1 >= -eps and sigma2 >= -eps: |
---|
763 | element_found = True |
---|
764 | break |
---|
765 | |
---|
766 | if element_found is True: |
---|
767 | #Don't look for any other triangle |
---|
768 | break |
---|
769 | return element_found, sigma0, sigma1, sigma2, k |
---|
770 | |
---|
771 | |
---|
772 | |
---|
773 | def build_interpolation_matrix_A_brute(self, point_coordinates): |
---|
774 | """Build n x m interpolation matrix, where |
---|
775 | n is the number of data points and |
---|
776 | m is the number of basis functions phi_k (one per vertex) |
---|
777 | |
---|
778 | This is the brute force which is too slow for large problems, |
---|
779 | but could be used for testing |
---|
780 | """ |
---|
781 | |
---|
782 | |
---|
783 | #Convert input to Numeric arrays |
---|
784 | point_coordinates = ensure_numeric(point_coordinates, Float) |
---|
785 | |
---|
786 | #Build n x m interpolation matrix |
---|
787 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
788 | n = point_coordinates.shape[0] #Nbr of data points |
---|
789 | |
---|
790 | self.A = Sparse(n,m) |
---|
791 | self.AtA = Sparse(m,m) |
---|
792 | |
---|
793 | #Compute matrix elements |
---|
794 | for i in range(n): |
---|
795 | #For each data_coordinate point |
---|
796 | |
---|
797 | x = point_coordinates[i] |
---|
798 | element_found = False |
---|
799 | k = 0 |
---|
800 | while not element_found and k < len(self.mesh): |
---|
801 | #For each triangle (brute force) |
---|
802 | #FIXME: Real algorithm should only visit relevant triangles |
---|
803 | |
---|
804 | #Get the three vertex_points |
---|
805 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
806 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
807 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
808 | |
---|
809 | #Get the three normals |
---|
810 | n0 = self.mesh.get_normal(k, 0) |
---|
811 | n1 = self.mesh.get_normal(k, 1) |
---|
812 | n2 = self.mesh.get_normal(k, 2) |
---|
813 | |
---|
814 | #Compute interpolation |
---|
815 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
816 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
817 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
818 | |
---|
819 | #FIXME: Maybe move out to test or something |
---|
820 | epsilon = 1.0e-6 |
---|
821 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
822 | |
---|
823 | #Check that this triangle contains data point |
---|
824 | if sigma0 >= 0 and sigma1 >= 0 and sigma2 >= 0: |
---|
825 | element_found = True |
---|
826 | #Assign values to matrix A |
---|
827 | |
---|
828 | j0 = self.mesh.triangles[k,0] #Global vertex id |
---|
829 | #self.A[i, j0] = sigma0 |
---|
830 | |
---|
831 | j1 = self.mesh.triangles[k,1] #Global vertex id |
---|
832 | #self.A[i, j1] = sigma1 |
---|
833 | |
---|
834 | j2 = self.mesh.triangles[k,2] #Global vertex id |
---|
835 | #self.A[i, j2] = sigma2 |
---|
836 | |
---|
837 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
838 | js = [j0,j1,j2] |
---|
839 | |
---|
840 | for j in js: |
---|
841 | self.A[i,j] = sigmas[j] |
---|
842 | for k in js: |
---|
843 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
844 | k = k+1 |
---|
845 | |
---|
846 | |
---|
847 | |
---|
848 | def get_A(self): |
---|
849 | return self.A.todense() |
---|
850 | |
---|
851 | def get_B(self): |
---|
852 | return self.B.todense() |
---|
853 | |
---|
854 | def get_D(self): |
---|
855 | return self.D.todense() |
---|
856 | |
---|
857 | #FIXME: Remember to re-introduce the 1/n factor in the |
---|
858 | #interpolation term |
---|
859 | |
---|
860 | def build_smoothing_matrix_D(self): |
---|
861 | """Build m x m smoothing matrix, where |
---|
862 | m is the number of basis functions phi_k (one per vertex) |
---|
863 | |
---|
864 | The smoothing matrix is defined as |
---|
865 | |
---|
866 | D = D1 + D2 |
---|
867 | |
---|
868 | where |
---|
869 | |
---|
870 | [D1]_{k,l} = \int_\Omega |
---|
871 | \frac{\partial \phi_k}{\partial x} |
---|
872 | \frac{\partial \phi_l}{\partial x}\, |
---|
873 | dx dy |
---|
874 | |
---|
875 | [D2]_{k,l} = \int_\Omega |
---|
876 | \frac{\partial \phi_k}{\partial y} |
---|
877 | \frac{\partial \phi_l}{\partial y}\, |
---|
878 | dx dy |
---|
879 | |
---|
880 | |
---|
881 | The derivatives \frac{\partial \phi_k}{\partial x}, |
---|
882 | \frac{\partial \phi_k}{\partial x} for a particular triangle |
---|
883 | are obtained by computing the gradient a_k, b_k for basis function k |
---|
884 | """ |
---|
885 | |
---|
886 | #FIXME: algorithm might be optimised by computing local 9x9 |
---|
887 | #"element stiffness matrices: |
---|
888 | |
---|
889 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
890 | |
---|
891 | self.D = Sparse(m,m) |
---|
892 | |
---|
893 | #For each triangle compute contributions to D = D1+D2 |
---|
894 | for i in range(len(self.mesh)): |
---|
895 | |
---|
896 | #Get area |
---|
897 | area = self.mesh.areas[i] |
---|
898 | |
---|
899 | #Get global vertex indices |
---|
900 | v0 = self.mesh.triangles[i,0] |
---|
901 | v1 = self.mesh.triangles[i,1] |
---|
902 | v2 = self.mesh.triangles[i,2] |
---|
903 | |
---|
904 | #Get the three vertex_points |
---|
905 | xi0 = self.mesh.get_vertex_coordinate(i, 0) |
---|
906 | xi1 = self.mesh.get_vertex_coordinate(i, 1) |
---|
907 | xi2 = self.mesh.get_vertex_coordinate(i, 2) |
---|
908 | |
---|
909 | #Compute gradients for each vertex |
---|
910 | a0, b0 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
911 | 1, 0, 0) |
---|
912 | |
---|
913 | a1, b1 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
914 | 0, 1, 0) |
---|
915 | |
---|
916 | a2, b2 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
917 | 0, 0, 1) |
---|
918 | |
---|
919 | #Compute diagonal contributions |
---|
920 | self.D[v0,v0] += (a0*a0 + b0*b0)*area |
---|
921 | self.D[v1,v1] += (a1*a1 + b1*b1)*area |
---|
922 | self.D[v2,v2] += (a2*a2 + b2*b2)*area |
---|
923 | |
---|
924 | #Compute contributions for basis functions sharing edges |
---|
925 | e01 = (a0*a1 + b0*b1)*area |
---|
926 | self.D[v0,v1] += e01 |
---|
927 | self.D[v1,v0] += e01 |
---|
928 | |
---|
929 | e12 = (a1*a2 + b1*b2)*area |
---|
930 | self.D[v1,v2] += e12 |
---|
931 | self.D[v2,v1] += e12 |
---|
932 | |
---|
933 | e20 = (a2*a0 + b2*b0)*area |
---|
934 | self.D[v2,v0] += e20 |
---|
935 | self.D[v0,v2] += e20 |
---|
936 | |
---|
937 | |
---|
938 | def fit(self, z): |
---|
939 | """Fit a smooth surface to given 1d array of data points z. |
---|
940 | |
---|
941 | The smooth surface is computed at each vertex in the underlying |
---|
942 | mesh using the formula given in the module doc string. |
---|
943 | |
---|
944 | Pre Condition: |
---|
945 | self.A, self.AtA and self.B have been initialised |
---|
946 | |
---|
947 | Inputs: |
---|
948 | z: Single 1d vector or array of data at the point_coordinates. |
---|
949 | """ |
---|
950 | |
---|
951 | #Convert input to Numeric arrays |
---|
952 | z = ensure_numeric(z, Float) |
---|
953 | |
---|
954 | if len(z.shape) > 1 : |
---|
955 | raise VectorShapeError, 'Can only deal with 1d data vector' |
---|
956 | |
---|
957 | if self.point_indices is not None: |
---|
958 | #Remove values for any points that were outside mesh |
---|
959 | z = take(z, self.point_indices) |
---|
960 | |
---|
961 | #Compute right hand side based on data |
---|
962 | #FIXME (DSG-DsG): could Sparse_CSR be used here? Use this format |
---|
963 | # after a matrix is built, before calcs. |
---|
964 | Atz = self.A.trans_mult(z) |
---|
965 | |
---|
966 | |
---|
967 | #Check sanity |
---|
968 | n, m = self.A.shape |
---|
969 | if n<m and self.alpha == 0.0: |
---|
970 | msg = 'ERROR (least_squares): Too few data points\n' |
---|
971 | msg += 'There are only %d data points and alpha == 0. ' %n |
---|
972 | msg += 'Need at least %d\n' %m |
---|
973 | msg += 'Alternatively, set smoothing parameter alpha to a small ' |
---|
974 | msg += 'positive value,\ne.g. 1.0e-3.' |
---|
975 | raise Exception(msg) |
---|
976 | |
---|
977 | |
---|
978 | |
---|
979 | return conjugate_gradient(self.B, Atz, Atz, imax=2*len(Atz) ) |
---|
980 | #FIXME: Should we store the result here for later use? (ON) |
---|
981 | |
---|
982 | |
---|
983 | def fit_points(self, z, verbose=False): |
---|
984 | """Like fit, but more robust when each point has two or more attributes |
---|
985 | FIXME (Ole): The name fit_points doesn't carry any meaning |
---|
986 | for me. How about something like fit_multiple or fit_columns? |
---|
987 | """ |
---|
988 | |
---|
989 | try: |
---|
990 | if verbose: print 'Solving penalised least_squares problem' |
---|
991 | return self.fit(z) |
---|
992 | except VectorShapeError, e: |
---|
993 | # broadcasting is not supported. |
---|
994 | |
---|
995 | #Convert input to Numeric arrays |
---|
996 | z = ensure_numeric(z, Float) |
---|
997 | |
---|
998 | #Build n x m interpolation matrix |
---|
999 | m = self.mesh.coordinates.shape[0] #Number of vertices |
---|
1000 | n = z.shape[1] #Number of data points |
---|
1001 | |
---|
1002 | f = zeros((m,n), Float) #Resulting columns |
---|
1003 | |
---|
1004 | for i in range(z.shape[1]): |
---|
1005 | f[:,i] = self.fit(z[:,i]) |
---|
1006 | |
---|
1007 | return f |
---|
1008 | |
---|
1009 | |
---|
1010 | def interpolate(self, f): |
---|
1011 | """Evaluate smooth surface f at data points implied in self.A. |
---|
1012 | |
---|
1013 | The mesh values representing a smooth surface are |
---|
1014 | assumed to be specified in f. This argument could, |
---|
1015 | for example have been obtained from the method self.fit() |
---|
1016 | |
---|
1017 | Pre Condition: |
---|
1018 | self.A has been initialised |
---|
1019 | |
---|
1020 | Inputs: |
---|
1021 | f: Vector or array of data at the mesh vertices. |
---|
1022 | If f is an array, interpolation will be done for each column as |
---|
1023 | per underlying matrix-matrix multiplication |
---|
1024 | |
---|
1025 | Output: |
---|
1026 | Interpolated values at data points implied in self.A |
---|
1027 | |
---|
1028 | """ |
---|
1029 | |
---|
1030 | return self.A * f |
---|
1031 | |
---|
1032 | def cull_outsiders(self, f): |
---|
1033 | pass |
---|
1034 | |
---|
1035 | |
---|
1036 | |
---|
1037 | |
---|
1038 | class Interpolation_function: |
---|
1039 | """Interpolation_function - creates callable object f(t, id) or f(t,x,y) |
---|
1040 | which is interpolated from time series defined at vertices of |
---|
1041 | triangular mesh (such as those stored in sww files) |
---|
1042 | |
---|
1043 | Let m be the number of vertices, n the number of triangles |
---|
1044 | and p the number of timesteps. |
---|
1045 | |
---|
1046 | Mandatory input |
---|
1047 | time: px1 array of monotonously increasing times (Float) |
---|
1048 | quantities: Dictionary of arrays or 1 array (Float) |
---|
1049 | The arrays must either have dimensions pxm or mx1. |
---|
1050 | The resulting function will be time dependent in |
---|
1051 | the former case while it will be constant with |
---|
1052 | respect to time in the latter case. |
---|
1053 | |
---|
1054 | Optional input: |
---|
1055 | quantity_names: List of keys into the quantities dictionary |
---|
1056 | vertex_coordinates: mx2 array of coordinates (Float) |
---|
1057 | triangles: nx3 array of indices into vertex_coordinates (Int) |
---|
1058 | interpolation_points: Nx2 array of coordinates to be interpolated to |
---|
1059 | verbose: Level of reporting |
---|
1060 | |
---|
1061 | |
---|
1062 | The quantities returned by the callable object are specified by |
---|
1063 | the list quantities which must contain the names of the |
---|
1064 | quantities to be returned and also reflect the order, e.g. for |
---|
1065 | the shallow water wave equation, on would have |
---|
1066 | quantities = ['stage', 'xmomentum', 'ymomentum'] |
---|
1067 | |
---|
1068 | The parameter interpolation_points decides at which points interpolated |
---|
1069 | quantities are to be computed whenever object is called. |
---|
1070 | If None, return average value |
---|
1071 | """ |
---|
1072 | |
---|
1073 | |
---|
1074 | |
---|
1075 | def __init__(self, |
---|
1076 | time, |
---|
1077 | quantities, |
---|
1078 | quantity_names = None, |
---|
1079 | vertex_coordinates = None, |
---|
1080 | triangles = None, |
---|
1081 | interpolation_points = None, |
---|
1082 | verbose = False): |
---|
1083 | """Initialise object and build spatial interpolation if required |
---|
1084 | """ |
---|
1085 | |
---|
1086 | from Numeric import array, zeros, Float, alltrue, concatenate,\ |
---|
1087 | reshape, ArrayType |
---|
1088 | |
---|
1089 | |
---|
1090 | from config import time_format |
---|
1091 | import types |
---|
1092 | |
---|
1093 | |
---|
1094 | |
---|
1095 | #Check temporal info |
---|
1096 | time = ensure_numeric(time) |
---|
1097 | msg = 'Time must be a monotonuosly ' |
---|
1098 | msg += 'increasing sequence %s' %time |
---|
1099 | assert alltrue(time[1:] - time[:-1] >= 0 ), msg |
---|
1100 | |
---|
1101 | |
---|
1102 | #Check if quantities is a single array only |
---|
1103 | if type(quantities) != types.DictType: |
---|
1104 | quantities = ensure_numeric(quantities) |
---|
1105 | quantity_names = ['Attribute'] |
---|
1106 | |
---|
1107 | #Make it a dictionary |
---|
1108 | quantities = {quantity_names[0]: quantities} |
---|
1109 | |
---|
1110 | |
---|
1111 | #Use keys if no names are specified |
---|
1112 | if quantity_names is None: |
---|
1113 | quantity_names = quantities.keys() |
---|
1114 | |
---|
1115 | |
---|
1116 | #Check spatial info |
---|
1117 | if vertex_coordinates is None: |
---|
1118 | self.spatial = False |
---|
1119 | else: |
---|
1120 | vertex_coordinates = ensure_numeric(vertex_coordinates) |
---|
1121 | |
---|
1122 | assert triangles is not None, 'Triangles array must be specified' |
---|
1123 | triangles = ensure_numeric(triangles) |
---|
1124 | self.spatial = True |
---|
1125 | |
---|
1126 | |
---|
1127 | |
---|
1128 | #Save for use with statistics |
---|
1129 | self.quantity_names = quantity_names |
---|
1130 | self.quantities = quantities |
---|
1131 | self.vertex_coordinates = vertex_coordinates |
---|
1132 | self.interpolation_points = interpolation_points |
---|
1133 | self.T = time[:] # Time assumed to be relative to starttime |
---|
1134 | self.index = 0 # Initial time index |
---|
1135 | self.precomputed_values = {} |
---|
1136 | |
---|
1137 | |
---|
1138 | |
---|
1139 | #Precomputed spatial interpolation if requested |
---|
1140 | if interpolation_points is not None: |
---|
1141 | if self.spatial is False: |
---|
1142 | raise 'Triangles and vertex_coordinates must be specified' |
---|
1143 | |
---|
1144 | try: |
---|
1145 | self.interpolation_points = ensure_numeric(interpolation_points) |
---|
1146 | except: |
---|
1147 | msg = 'Interpolation points must be an N x 2 Numeric array '+\ |
---|
1148 | 'or a list of points\n' |
---|
1149 | msg += 'I got: %s.' %(str(self.interpolation_points)[:60] +\ |
---|
1150 | '...') |
---|
1151 | raise msg |
---|
1152 | |
---|
1153 | |
---|
1154 | m = len(self.interpolation_points) |
---|
1155 | p = len(self.T) |
---|
1156 | |
---|
1157 | for name in quantity_names: |
---|
1158 | self.precomputed_values[name] = zeros((p, m), Float) |
---|
1159 | |
---|
1160 | #Build interpolator |
---|
1161 | interpol = Interpolation(vertex_coordinates, |
---|
1162 | triangles, |
---|
1163 | point_coordinates = \ |
---|
1164 | self.interpolation_points, |
---|
1165 | alpha = 0, |
---|
1166 | precrop = False, |
---|
1167 | verbose = verbose) |
---|
1168 | |
---|
1169 | if verbose: print 'Interpolate' |
---|
1170 | for i, t in enumerate(self.T): |
---|
1171 | #Interpolate quantities at this timestep |
---|
1172 | if verbose and i%((p+10)/10)==0: |
---|
1173 | print ' time step %d of %d' %(i, p) |
---|
1174 | |
---|
1175 | for name in quantity_names: |
---|
1176 | if len(quantities[name].shape) == 2: |
---|
1177 | result = interpol.interpolate(quantities[name][i,:]) |
---|
1178 | else: |
---|
1179 | #Assume no time dependency |
---|
1180 | result = interpol.interpolate(quantities[name][:]) |
---|
1181 | |
---|
1182 | self.precomputed_values[name][i, :] = result |
---|
1183 | |
---|
1184 | |
---|
1185 | |
---|
1186 | #Report |
---|
1187 | if verbose: |
---|
1188 | print self.statistics() |
---|
1189 | #self.print_statistics() |
---|
1190 | |
---|
1191 | else: |
---|
1192 | #Store quantitites as is |
---|
1193 | for name in quantity_names: |
---|
1194 | self.precomputed_values[name] = quantities[name] |
---|
1195 | |
---|
1196 | |
---|
1197 | #else: |
---|
1198 | # #Return an average, making this a time series |
---|
1199 | # for name in quantity_names: |
---|
1200 | # self.values[name] = zeros(len(self.T), Float) |
---|
1201 | # |
---|
1202 | # if verbose: print 'Compute mean values' |
---|
1203 | # for i, t in enumerate(self.T): |
---|
1204 | # if verbose: print ' time step %d of %d' %(i, len(self.T)) |
---|
1205 | # for name in quantity_names: |
---|
1206 | # self.values[name][i] = mean(quantities[name][i,:]) |
---|
1207 | |
---|
1208 | |
---|
1209 | |
---|
1210 | |
---|
1211 | def __repr__(self): |
---|
1212 | #return 'Interpolation function (spatio-temporal)' |
---|
1213 | return self.statistics() |
---|
1214 | |
---|
1215 | |
---|
1216 | def __call__(self, t, point_id = None, x = None, y = None): |
---|
1217 | """Evaluate f(t), f(t, point_id) or f(t, x, y) |
---|
1218 | |
---|
1219 | Inputs: |
---|
1220 | t: time - Model time. Must lie within existing timesteps |
---|
1221 | point_id: index of one of the preprocessed points. |
---|
1222 | x, y: Overrides location, point_id ignored |
---|
1223 | |
---|
1224 | If spatial info is present and all of x,y,point_id |
---|
1225 | are None an exception is raised |
---|
1226 | |
---|
1227 | If no spatial info is present, point_id and x,y arguments are ignored |
---|
1228 | making f a function of time only. |
---|
1229 | |
---|
1230 | |
---|
1231 | FIXME: point_id could also be a slice |
---|
1232 | FIXME: What if x and y are vectors? |
---|
1233 | FIXME: What about f(x,y) without t? |
---|
1234 | """ |
---|
1235 | |
---|
1236 | from math import pi, cos, sin, sqrt |
---|
1237 | from Numeric import zeros, Float |
---|
1238 | from utilities.numerical_tools import mean |
---|
1239 | |
---|
1240 | if self.spatial is True: |
---|
1241 | if point_id is None: |
---|
1242 | if x is None or y is None: |
---|
1243 | msg = 'Either point_id or x and y must be specified' |
---|
1244 | raise Exception(msg) |
---|
1245 | else: |
---|
1246 | if self.interpolation_points is None: |
---|
1247 | msg = 'Interpolation_function must be instantiated ' +\ |
---|
1248 | 'with a list of interpolation points before parameter ' +\ |
---|
1249 | 'point_id can be used' |
---|
1250 | raise Exception(msg) |
---|
1251 | |
---|
1252 | |
---|
1253 | msg = 'Time interval [%s:%s]' %(self.T[0], self.T[1]) |
---|
1254 | msg += ' does not match model time: %s\n' %t |
---|
1255 | if t < self.T[0]: raise Exception(msg) |
---|
1256 | if t > self.T[-1]: raise Exception(msg) |
---|
1257 | |
---|
1258 | oldindex = self.index #Time index |
---|
1259 | |
---|
1260 | #Find current time slot |
---|
1261 | while t > self.T[self.index]: self.index += 1 |
---|
1262 | while t < self.T[self.index]: self.index -= 1 |
---|
1263 | |
---|
1264 | if t == self.T[self.index]: |
---|
1265 | #Protect against case where t == T[-1] (last time) |
---|
1266 | # - also works in general when t == T[i] |
---|
1267 | ratio = 0 |
---|
1268 | else: |
---|
1269 | #t is now between index and index+1 |
---|
1270 | ratio = (t - self.T[self.index])/\ |
---|
1271 | (self.T[self.index+1] - self.T[self.index]) |
---|
1272 | |
---|
1273 | #Compute interpolated values |
---|
1274 | q = zeros(len(self.quantity_names), Float) |
---|
1275 | |
---|
1276 | for i, name in enumerate(self.quantity_names): |
---|
1277 | Q = self.precomputed_values[name] |
---|
1278 | |
---|
1279 | if self.spatial is False: |
---|
1280 | #If there is no spatial info |
---|
1281 | assert len(Q.shape) == 1 |
---|
1282 | |
---|
1283 | Q0 = Q[self.index] |
---|
1284 | if ratio > 0: Q1 = Q[self.index+1] |
---|
1285 | |
---|
1286 | else: |
---|
1287 | if x is not None and y is not None: |
---|
1288 | #Interpolate to x, y |
---|
1289 | |
---|
1290 | raise 'x,y interpolation not yet implemented' |
---|
1291 | else: |
---|
1292 | #Use precomputed point |
---|
1293 | Q0 = Q[self.index, point_id] |
---|
1294 | if ratio > 0: Q1 = Q[self.index+1, point_id] |
---|
1295 | |
---|
1296 | #Linear temporal interpolation |
---|
1297 | if ratio > 0: |
---|
1298 | q[i] = Q0 + ratio*(Q1 - Q0) |
---|
1299 | else: |
---|
1300 | q[i] = Q0 |
---|
1301 | |
---|
1302 | |
---|
1303 | #Return vector of interpolated values |
---|
1304 | #if len(q) == 1: |
---|
1305 | # return q[0] |
---|
1306 | #else: |
---|
1307 | # return q |
---|
1308 | |
---|
1309 | |
---|
1310 | #Return vector of interpolated values |
---|
1311 | #FIXME: |
---|
1312 | if self.spatial is True: |
---|
1313 | return q |
---|
1314 | else: |
---|
1315 | #Replicate q according to x and y |
---|
1316 | #This is e.g used for Wind_stress |
---|
1317 | if x is None or y is None: |
---|
1318 | return q |
---|
1319 | else: |
---|
1320 | try: |
---|
1321 | N = len(x) |
---|
1322 | except: |
---|
1323 | return q |
---|
1324 | else: |
---|
1325 | from Numeric import ones, Float |
---|
1326 | #x is a vector - Create one constant column for each value |
---|
1327 | N = len(x) |
---|
1328 | assert len(y) == N, 'x and y must have same length' |
---|
1329 | res = [] |
---|
1330 | for col in q: |
---|
1331 | res.append(col*ones(N, Float)) |
---|
1332 | |
---|
1333 | return res |
---|
1334 | |
---|
1335 | |
---|
1336 | def statistics(self): |
---|
1337 | """Output statistics about interpolation_function |
---|
1338 | """ |
---|
1339 | |
---|
1340 | vertex_coordinates = self.vertex_coordinates |
---|
1341 | interpolation_points = self.interpolation_points |
---|
1342 | quantity_names = self.quantity_names |
---|
1343 | quantities = self.quantities |
---|
1344 | precomputed_values = self.precomputed_values |
---|
1345 | |
---|
1346 | x = vertex_coordinates[:,0] |
---|
1347 | y = vertex_coordinates[:,1] |
---|
1348 | |
---|
1349 | str = '------------------------------------------------\n' |
---|
1350 | str += 'Interpolation_function (spatio-temporal) statistics:\n' |
---|
1351 | str += ' Extent:\n' |
---|
1352 | str += ' x in [%f, %f], len(x) == %d\n'\ |
---|
1353 | %(min(x), max(x), len(x)) |
---|
1354 | str += ' y in [%f, %f], len(y) == %d\n'\ |
---|
1355 | %(min(y), max(y), len(y)) |
---|
1356 | str += ' t in [%f, %f], len(t) == %d\n'\ |
---|
1357 | %(min(self.T), max(self.T), len(self.T)) |
---|
1358 | str += ' Quantities:\n' |
---|
1359 | for name in quantity_names: |
---|
1360 | q = quantities[name][:].flat |
---|
1361 | str += ' %s in [%f, %f]\n' %(name, min(q), max(q)) |
---|
1362 | |
---|
1363 | if interpolation_points is not None: |
---|
1364 | str += ' Interpolation points (xi, eta):'\ |
---|
1365 | ' number of points == %d\n' %interpolation_points.shape[0] |
---|
1366 | str += ' xi in [%f, %f]\n' %(min(interpolation_points[:,0]), |
---|
1367 | max(interpolation_points[:,0])) |
---|
1368 | str += ' eta in [%f, %f]\n' %(min(interpolation_points[:,1]), |
---|
1369 | max(interpolation_points[:,1])) |
---|
1370 | str += ' Interpolated quantities (over all timesteps):\n' |
---|
1371 | |
---|
1372 | for name in quantity_names: |
---|
1373 | q = precomputed_values[name][:].flat |
---|
1374 | str += ' %s at interpolation points in [%f, %f]\n'\ |
---|
1375 | %(name, min(q), max(q)) |
---|
1376 | str += '------------------------------------------------\n' |
---|
1377 | |
---|
1378 | return str |
---|
1379 | |
---|
1380 | #FIXME: Delete |
---|
1381 | #print '------------------------------------------------' |
---|
1382 | #print 'Interpolation_function statistics:' |
---|
1383 | #print ' Extent:' |
---|
1384 | #print ' x in [%f, %f], len(x) == %d'\ |
---|
1385 | # %(min(x), max(x), len(x)) |
---|
1386 | #print ' y in [%f, %f], len(y) == %d'\ |
---|
1387 | # %(min(y), max(y), len(y)) |
---|
1388 | #print ' t in [%f, %f], len(t) == %d'\ |
---|
1389 | # %(min(self.T), max(self.T), len(self.T)) |
---|
1390 | #print ' Quantities:' |
---|
1391 | #for name in quantity_names: |
---|
1392 | # q = quantities[name][:].flat |
---|
1393 | # print ' %s in [%f, %f]' %(name, min(q), max(q)) |
---|
1394 | #print ' Interpolation points (xi, eta):'\ |
---|
1395 | # ' number of points == %d ' %interpolation_points.shape[0] |
---|
1396 | #print ' xi in [%f, %f]' %(min(interpolation_points[:,0]), |
---|
1397 | # max(interpolation_points[:,0])) |
---|
1398 | #print ' eta in [%f, %f]' %(min(interpolation_points[:,1]), |
---|
1399 | # max(interpolation_points[:,1])) |
---|
1400 | #print ' Interpolated quantities (over all timesteps):' |
---|
1401 | # |
---|
1402 | #for name in quantity_names: |
---|
1403 | # q = precomputed_values[name][:].flat |
---|
1404 | # print ' %s at interpolation points in [%f, %f]'\ |
---|
1405 | # %(name, min(q), max(q)) |
---|
1406 | #print '------------------------------------------------' |
---|
1407 | |
---|
1408 | |
---|
1409 | #------------------------------------------------------------- |
---|
1410 | if __name__ == "__main__": |
---|
1411 | """ |
---|
1412 | Load in a mesh and data points with attributes. |
---|
1413 | Fit the attributes to the mesh. |
---|
1414 | Save a new mesh file. |
---|
1415 | """ |
---|
1416 | import os, sys |
---|
1417 | usage = "usage: %s mesh_input.tsh point.xya mesh_output.tsh [expand|no_expand][vervose|non_verbose] [alpha] [display_errors|no_display_errors]"\ |
---|
1418 | %os.path.basename(sys.argv[0]) |
---|
1419 | |
---|
1420 | if len(sys.argv) < 4: |
---|
1421 | print usage |
---|
1422 | else: |
---|
1423 | mesh_file = sys.argv[1] |
---|
1424 | point_file = sys.argv[2] |
---|
1425 | mesh_output_file = sys.argv[3] |
---|
1426 | |
---|
1427 | expand_search = False |
---|
1428 | if len(sys.argv) > 4: |
---|
1429 | if sys.argv[4][0] == "e" or sys.argv[4][0] == "E": |
---|
1430 | expand_search = True |
---|
1431 | else: |
---|
1432 | expand_search = False |
---|
1433 | |
---|
1434 | verbose = False |
---|
1435 | if len(sys.argv) > 5: |
---|
1436 | if sys.argv[5][0] == "n" or sys.argv[5][0] == "N": |
---|
1437 | verbose = False |
---|
1438 | else: |
---|
1439 | verbose = True |
---|
1440 | |
---|
1441 | if len(sys.argv) > 6: |
---|
1442 | alpha = sys.argv[6] |
---|
1443 | else: |
---|
1444 | alpha = DEFAULT_ALPHA |
---|
1445 | |
---|
1446 | # This is used more for testing |
---|
1447 | if len(sys.argv) > 7: |
---|
1448 | if sys.argv[7][0] == "n" or sys.argv[5][0] == "N": |
---|
1449 | display_errors = False |
---|
1450 | else: |
---|
1451 | display_errors = True |
---|
1452 | |
---|
1453 | t0 = time.time() |
---|
1454 | try: |
---|
1455 | fit_to_mesh_file(mesh_file, |
---|
1456 | point_file, |
---|
1457 | mesh_output_file, |
---|
1458 | alpha, |
---|
1459 | verbose= verbose, |
---|
1460 | expand_search = expand_search, |
---|
1461 | display_errors = display_errors) |
---|
1462 | except IOError,e: |
---|
1463 | import sys; sys.exit(1) |
---|
1464 | |
---|
1465 | print 'That took %.2f seconds' %(time.time()-t0) |
---|
1466 | |
---|