source: anuga_core/source/anuga/fit_interpolate/fit.py @ 6252

Last change on this file since 6252 was 6252, checked in by ole, 14 years ago

Cleanup and comments in regard to ticket:314
File size: 26.1 KB
Line 
1"""Least squares fitting.
2
3   Implements a penalised least-squares fit.
4   putting point data onto the mesh.
5
6   The penalty term (or smoothing term) is controlled by the smoothing
7   parameter alpha.
8   With a value of alpha=0, the fit function will attempt
9   to interpolate as closely as possible in the least-squares sense.
10   With values alpha > 0, a certain amount of smoothing will be applied.
11   A positive alpha is essential in cases where there are too few
12   data points.
13   A negative alpha is not allowed.
14   A typical value of alpha is 1.0e-6
15
16
17   Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou
18   Geoscience Australia, 2004.
19
20   TO DO
21   * test geo_ref, geo_spatial
22
23   IDEAS
24   * (DSG-) Change the interface of fit, so a domain object can
25      be passed in. (I don't know if this is feasible). If could
26      save time/memory.
27"""
28import types
29
30from anuga.abstract_2d_finite_volumes.neighbour_mesh import Mesh
31from anuga.caching import cache           
32from anuga.geospatial_data.geospatial_data import Geospatial_data, \
33     ensure_absolute
34from anuga.fit_interpolate.general_fit_interpolate import FitInterpolate
35from anuga.utilities.sparse import Sparse, Sparse_CSR
36from anuga.utilities.polygon import inside_polygon, is_inside_polygon
37from anuga.fit_interpolate.search_functions import search_tree_of_vertices
38
39from anuga.utilities.cg_solve import conjugate_gradient
40from anuga.utilities.numerical_tools import ensure_numeric, gradient
41from anuga.config import default_smoothing_parameter as DEFAULT_ALPHA
42
43import exceptions
44class TooFewPointsError(exceptions.Exception): pass
45class VertsWithNoTrianglesError(exceptions.Exception): pass
46
47import Numeric as num
48
49
50class Fit(FitInterpolate):
51   
52    def __init__(self,
53                 vertex_coordinates=None,
54                 triangles=None,
55                 mesh=None,
56                 mesh_origin=None,
57                 alpha = None,
58                 verbose=False,
59                 max_vertices_per_cell=None):
60
61
62        """
63        Fit data at points to the vertices of a mesh.
64
65        Inputs:
66
67          vertex_coordinates: List of coordinate pairs [xi, eta] of
68              points constituting a mesh (or an m x 2 Numeric array or
69              a geospatial object)
70              Points may appear multiple times
71              (e.g. if vertices have discontinuities)
72
73          triangles: List of 3-tuples (or a Numeric array) of
74              integers representing indices of all vertices in the mesh.
75
76          mesh_origin: A geo_reference object or 3-tuples consisting of
77              UTM zone, easting and northing.
78              If specified vertex coordinates are assumed to be
79              relative to their respective origins.
80
81          max_vertices_per_cell: Number of vertices in a quad tree cell
82          at which the cell is split into 4.
83
84          Note: Don't supply a vertex coords as a geospatial object and
85              a mesh origin, since geospatial has its own mesh origin.
86
87
88        Usage,
89        To use this in a blocking way, call  build_fit_subset, with z info,
90        and then fit, with no point coord, z info.
91       
92        """
93        # Initialise variabels
94        if alpha is None:
95            self.alpha = DEFAULT_ALPHA
96        else:   
97            self.alpha = alpha
98           
99        FitInterpolate.__init__(self,
100                 vertex_coordinates,
101                 triangles,
102                 mesh,
103                 mesh_origin,
104                 verbose,
105                 max_vertices_per_cell)
106       
107        m = self.mesh.number_of_nodes # Nbr of basis functions (vertices)
108       
109        self.AtA = None
110        self.Atz = None
111
112        self.point_count = 0
113        if self.alpha <> 0:
114            if verbose: print 'Building smoothing matrix'
115            self._build_smoothing_matrix_D()
116           
117        bd_poly = self.mesh.get_boundary_polygon()   
118        self.mesh_boundary_polygon = ensure_numeric(bd_poly)
119           
120    def _build_coefficient_matrix_B(self,
121                                  verbose = False):
122        """
123        Build final coefficient matrix
124
125        Precon
126        If alpha is not zero, matrix D has been built
127        Matrix Ata has been built
128        """
129
130        if self.alpha <> 0:
131            #if verbose: print 'Building smoothing matrix'
132            #self._build_smoothing_matrix_D()
133            self.B = self.AtA + self.alpha*self.D
134        else:
135            self.B = self.AtA
136
137        # Convert self.B matrix to CSR format for faster matrix vector
138        self.B = Sparse_CSR(self.B)
139
140    def _build_smoothing_matrix_D(self):
141        """Build m x m smoothing matrix, where
142        m is the number of basis functions phi_k (one per vertex)
143
144        The smoothing matrix is defined as
145
146        D = D1 + D2
147
148        where
149
150        [D1]_{k,l} = \int_\Omega
151           \frac{\partial \phi_k}{\partial x}
152           \frac{\partial \phi_l}{\partial x}\,
153           dx dy
154
155        [D2]_{k,l} = \int_\Omega
156           \frac{\partial \phi_k}{\partial y}
157           \frac{\partial \phi_l}{\partial y}\,
158           dx dy
159
160
161        The derivatives \frac{\partial \phi_k}{\partial x},
162        \frac{\partial \phi_k}{\partial x} for a particular triangle
163        are obtained by computing the gradient a_k, b_k for basis function k
164        """
165       
166        # FIXME: algorithm might be optimised by computing local 9x9
167        # "element stiffness matrices:
168
169        m = self.mesh.number_of_nodes # Nbr of basis functions (1/vertex)
170
171        self.D = Sparse(m,m)
172
173        # For each triangle compute contributions to D = D1+D2
174        for i in range(len(self.mesh)):
175
176            # Get area
177            area = self.mesh.areas[i]
178
179            # Get global vertex indices
180            v0 = self.mesh.triangles[i,0]
181            v1 = self.mesh.triangles[i,1]
182            v2 = self.mesh.triangles[i,2]
183
184            # Get the three vertex_points
185            xi0 = self.mesh.get_vertex_coordinate(i, 0)
186            xi1 = self.mesh.get_vertex_coordinate(i, 1)
187            xi2 = self.mesh.get_vertex_coordinate(i, 2)
188
189            # Compute gradients for each vertex
190            a0, b0 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1],
191                              1, 0, 0)
192
193            a1, b1 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1],
194                              0, 1, 0)
195
196            a2, b2 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1],
197                              0, 0, 1)
198
199            # Compute diagonal contributions
200            self.D[v0,v0] += (a0*a0 + b0*b0)*area
201            self.D[v1,v1] += (a1*a1 + b1*b1)*area
202            self.D[v2,v2] += (a2*a2 + b2*b2)*area
203
204            # Compute contributions for basis functions sharing edges
205            e01 = (a0*a1 + b0*b1)*area
206            self.D[v0,v1] += e01
207            self.D[v1,v0] += e01
208
209            e12 = (a1*a2 + b1*b2)*area
210            self.D[v1,v2] += e12
211            self.D[v2,v1] += e12
212
213            e20 = (a2*a0 + b2*b0)*area
214            self.D[v2,v0] += e20
215            self.D[v0,v2] += e20
216
217    def get_D(self):
218        return self.D.todense()
219
220
221
222    def _build_matrix_AtA_Atz(self,
223                              point_coordinates,
224                              z,
225                              verbose = False):
226        """Build:
227        AtA  m x m  interpolation matrix, and,
228        Atz  m x a  interpolation matrix where,
229        m is the number of basis functions phi_k (one per vertex)
230        a is the number of data attributes
231
232        This algorithm uses a quad tree data structure for fast binning of
233        data points.
234
235        If Ata is None, the matrices AtA and Atz are created.
236
237        This function can be called again and again, with sub-sets of
238        the point coordinates.  Call fit to get the results.
239       
240        Preconditions
241        z and points are numeric
242        Point_coordindates and mesh vertices have the same origin.
243
244        The number of attributes of the data points does not change
245        """
246       
247        # Build n x m interpolation matrix
248        if self.AtA == None:
249            # AtA and Atz need to be initialised.
250            m = self.mesh.number_of_nodes
251            if len(z.shape) > 1:
252                att_num = z.shape[1]
253                self.Atz = num.zeros((m,att_num), num.Float)
254            else:
255                att_num = 1
256                self.Atz = num.zeros((m,), num.Float)
257            assert z.shape[0] == point_coordinates.shape[0] 
258
259            AtA = Sparse(m,m)
260            # The memory damage has been done by now.
261        else:
262             AtA = self.AtA #Did this for speed, did ~nothing
263        self.point_count += point_coordinates.shape[0]
264
265
266        inside_indices = inside_polygon(point_coordinates,
267                                        self.mesh_boundary_polygon,
268                                        closed=True,
269                                        verbose=False) # Suppress output
270       
271        n = len(inside_indices)
272
273        # Compute matrix elements for points inside the mesh
274        triangles = self.mesh.triangles # Shorthand
275        for d, i in enumerate(inside_indices):
276            # For each data_coordinate point
277            # if verbose and d%((n+10)/10)==0: print 'Doing %d of %d' %(d, n)
278            x = point_coordinates[i]
279           
280            element_found, sigma0, sigma1, sigma2, k = \
281                           search_tree_of_vertices(self.root, self.mesh, x)
282           
283            if element_found is True:
284                j0 = triangles[k,0] #Global vertex id for sigma0
285                j1 = triangles[k,1] #Global vertex id for sigma1
286                j2 = triangles[k,2] #Global vertex id for sigma2
287
288                sigmas = {j0:sigma0, j1:sigma1, j2:sigma2}
289                js     = [j0,j1,j2]
290
291                for j in js:
292                    self.Atz[j] +=  sigmas[j]*z[i]
293                    #print "self.Atz building", self.Atz
294                    #print "self.Atz[j]", self.Atz[j]
295                    #print " sigmas[j]", sigmas[j]
296                    #print "z[i]",z[i]
297                    #print "result", sigmas[j]*z[i]
298                   
299                    for k in js:
300                        AtA[j,k] += sigmas[j]*sigmas[k]
301            else:
302                flag = is_inside_polygon(x,
303                                         self.mesh_boundary_polygon,
304                                         closed=True,
305                                         verbose=False) # Suppress output
306                msg = 'Point (%f, %f) is not inside mesh boundary' % tuple(x)
307                assert flag is True, msg               
308               
309                # FIXME(Ole): This is the message referred to in ticket:314
310                minx = min(self.mesh_boundary_polygon[:,0])
311                maxx = max(self.mesh_boundary_polygon[:,0])               
312                miny = min(self.mesh_boundary_polygon[:,1])
313                maxy = max(self.mesh_boundary_polygon[:,1])
314                msg = 'Could not find triangle for point %s. ' % str(x) 
315                msg += 'Mesh boundary extent is (%.f, %.f), (%.f, %.f)'\
316                    % (minx, maxx, miny, maxy)
317                raise RuntimeError, msg
318               
319            self.AtA = AtA
320
321       
322    def fit(self, point_coordinates_or_filename=None, z=None,
323            verbose=False,
324            point_origin=None,
325            attribute_name=None,
326            max_read_lines=500):
327        """Fit a smooth surface to given 1d array of data points z.
328
329        The smooth surface is computed at each vertex in the underlying
330        mesh using the formula given in the module doc string.
331
332        Inputs:
333        point_coordinates: The co-ordinates of the data points.
334              List of coordinate pairs [x, y] of
335              data points or an nx2 Numeric array or a Geospatial_data object
336              or points file filename
337          z: Single 1d vector or array of data at the point_coordinates.
338         
339        """
340       
341        # Use blocking to load in the point info
342        if type(point_coordinates_or_filename) == types.StringType:
343            msg = "Don't set a point origin when reading from a file"
344            assert point_origin is None, msg
345            filename = point_coordinates_or_filename
346
347            G_data = Geospatial_data(filename,
348                                     max_read_lines=max_read_lines,
349                                     load_file_now=False,
350                                     verbose=verbose)
351
352            for i, geo_block in enumerate(G_data):
353                if verbose is True and 0 == i%200: 
354                    # The time this will take
355                    # is dependant on the # of Triangles
356                       
357                    print 'Processing Block %d' %i
358                    # FIXME (Ole): It would be good to say how many blocks
359                    # there are here. But this is no longer necessary
360                    # for pts files as they are reported in geospatial_data
361                    # I suggest deleting this verbose output and make
362                    # Geospatial_data more informative for txt files.
363                    #
364                    # I still think so (12/12/7, Ole).
365           
366
367                   
368                # Build the array
369
370                points = geo_block.get_data_points(absolute=True)
371                z = geo_block.get_attributes(attribute_name=attribute_name)
372                self.build_fit_subset(points, z, verbose=verbose)
373
374               
375            point_coordinates = None
376        else:
377            point_coordinates =  point_coordinates_or_filename
378           
379        if point_coordinates is None:
380            if verbose: print 'Warning: no data points in fit'
381            assert self.AtA <> None, 'no interpolation matrix'
382            assert self.Atz <> None
383           
384            # FIXME (DSG) - do  a message
385        else:
386            point_coordinates = ensure_absolute(point_coordinates,
387                                                geo_reference=point_origin)
388            # if isinstance(point_coordinates,Geospatial_data) and z is None:
389            # z will come from the geo-ref
390            self.build_fit_subset(point_coordinates, z, verbose)
391
392        # Check sanity
393        m = self.mesh.number_of_nodes # Nbr of basis functions (1/vertex)
394        n = self.point_count
395        if n<m and self.alpha == 0.0:
396            msg = 'ERROR (least_squares): Too few data points\n'
397            msg += 'There are only %d data points and alpha == 0. ' %n
398            msg += 'Need at least %d\n' %m
399            msg += 'Alternatively, set smoothing parameter alpha to a small '
400            msg += 'positive value,\ne.g. 1.0e-3.'
401            raise TooFewPointsError(msg)
402
403        self._build_coefficient_matrix_B(verbose)
404        loners = self.mesh.get_lone_vertices()
405        # FIXME  - make this as error message.
406        # test with
407        # Not_yet_test_smooth_att_to_mesh_with_excess_verts.
408        if len(loners)>0:
409            msg = 'WARNING: (least_squares): \nVertices with no triangles\n'
410            msg += 'All vertices should be part of a triangle.\n'
411            msg += 'In the future this will be inforced.\n'
412            msg += 'The following vertices are not part of a triangle;\n'
413            msg += str(loners)
414            print msg
415            #raise VertsWithNoTrianglesError(msg)
416       
417       
418        return conjugate_gradient(self.B, self.Atz, self.Atz,
419                                  imax=2*len(self.Atz) )
420
421       
422    def build_fit_subset(self, point_coordinates, z=None, attribute_name=None,
423                              verbose=False):
424        """Fit a smooth surface to given 1d array of data points z.
425
426        The smooth surface is computed at each vertex in the underlying
427        mesh using the formula given in the module doc string.
428
429        Inputs:
430        point_coordinates: The co-ordinates of the data points.
431              List of coordinate pairs [x, y] of
432              data points or an nx2 Numeric array or a Geospatial_data object
433        z: Single 1d vector or array of data at the point_coordinates.
434        attribute_name: Used to get the z values from the
435              geospatial object if no attribute_name is specified,
436              it's a bit of a lucky dip as to what attributes you get.
437              If there is only one attribute it will be that one.
438
439        """
440
441        # FIXME(DSG-DSG): Check that the vert and point coords
442        # have the same zone.
443        if isinstance(point_coordinates,Geospatial_data):
444            point_coordinates = point_coordinates.get_data_points( \
445                absolute = True)
446       
447        # Convert input to Numeric arrays
448        if z is not None:
449            z = ensure_numeric(z, num.Float)
450        else:
451            msg = 'z not specified'
452            assert isinstance(point_coordinates,Geospatial_data), msg
453            z = point_coordinates.get_attributes(attribute_name)
454
455        point_coordinates = ensure_numeric(point_coordinates, num.Float)
456        self._build_matrix_AtA_Atz(point_coordinates, z, verbose)
457
458
459############################################################################
460
461def fit_to_mesh(point_coordinates, # this can also be a points file name
462                vertex_coordinates=None,
463                triangles=None,
464                mesh=None,
465                point_attributes=None,
466                alpha=DEFAULT_ALPHA,
467                verbose=False,
468                acceptable_overshoot=1.01, 
469                # FIXME: Move to config - this value is assumed in caching test
470                # FIXME(Ole): Just realised that this was never implemented (29 Jan 2009). I suggest removing it altogether.
471                mesh_origin=None,
472                data_origin=None,
473                max_read_lines=None,
474                attribute_name=None,
475                use_cache=False):
476    """Wrapper around internal function _fit_to_mesh for use with caching.
477   
478    """
479   
480    args = (point_coordinates, )
481    kwargs = {'vertex_coordinates': vertex_coordinates,
482              'triangles': triangles,
483              'mesh': mesh,
484              'point_attributes': point_attributes,
485              'alpha': alpha,
486              'verbose': verbose,
487              'acceptable_overshoot': acceptable_overshoot,
488              'mesh_origin': mesh_origin,
489              'data_origin': data_origin,
490              'max_read_lines': max_read_lines,
491              'attribute_name': attribute_name
492              }
493
494    if use_cache is True:
495        if isinstance(point_coordinates, basestring):
496            # We assume that point_coordinates is the name of a .csv/.txt
497            # file which must be passed onto caching as a dependency
498            # (in case it has changed on disk)
499            dep = [point_coordinates]
500        else:
501            dep = None
502
503           
504        #from caching import myhash
505        #import copy
506        #print args
507        #print kwargs
508        #print 'hashing:'
509        #print 'args', myhash( (args, kwargs) )
510        #print 'again', myhash( copy.deepcopy( (args, kwargs)) )       
511       
512        #print 'mesh hash', myhash( kwargs['mesh'] )       
513       
514        #print '-------------------------'
515        #print 'vertices hash', myhash( kwargs['mesh'].nodes )
516        #print 'triangles hash', myhash( kwargs['mesh'].triangles )
517        #print '-------------------------'       
518       
519        #for key in mesh.__dict__:
520        #    print key, myhash(mesh.__dict__[key])
521       
522        #for key in mesh.quantities.keys():
523        #    print key, myhash(mesh.quantities[key])
524       
525        #import sys; sys.exit()
526           
527        return cache(_fit_to_mesh,
528                     args, kwargs,
529                     verbose=verbose,
530                     compression=False,
531                     dependencies=dep)
532    else:
533        return apply(_fit_to_mesh,
534                     args, kwargs)
535
536def _fit_to_mesh(point_coordinates, # this can also be a points file name
537                 vertex_coordinates=None,
538                 triangles=None,
539                 mesh=None,
540                 point_attributes=None,
541                 alpha=DEFAULT_ALPHA,
542                 verbose=False,
543                 acceptable_overshoot=1.01,
544                 mesh_origin=None,
545                 data_origin=None,
546                 max_read_lines=None,
547                 attribute_name=None):
548    """
549    Fit a smooth surface to a triangulation,
550    given data points with attributes.
551
552
553        Inputs:
554        vertex_coordinates: List of coordinate pairs [xi, eta] of
555              points constituting a mesh (or an m x 2 Numeric array or
556              a geospatial object)
557              Points may appear multiple times
558              (e.g. if vertices have discontinuities)
559
560          triangles: List of 3-tuples (or a Numeric array) of
561          integers representing indices of all vertices in the mesh.
562
563          point_coordinates: List of coordinate pairs [x, y] of data points
564          (or an nx2 Numeric array). This can also be a .csv/.txt/.pts
565          file name.
566
567          alpha: Smoothing parameter.
568
569          acceptable overshoot: NOT IMPLEMENTED
570          controls the allowed factor by which
571          fitted values
572          may exceed the value of input data. The lower limit is defined
573          as min(z) - acceptable_overshoot*delta z and upper limit
574          as max(z) + acceptable_overshoot*delta z
575         
576
577          mesh_origin: A geo_reference object or 3-tuples consisting of
578              UTM zone, easting and northing.
579              If specified vertex coordinates are assumed to be
580              relative to their respective origins.
581         
582
583          point_attributes: Vector or array of data at the
584                            point_coordinates.
585
586    """
587
588    if mesh is None:
589        # FIXME(DSG): Throw errors if triangles or vertex_coordinates
590        # are None
591           
592        #Convert input to Numeric arrays
593        triangles = ensure_numeric(triangles, num.Int)
594        vertex_coordinates = ensure_absolute(vertex_coordinates,
595                                             geo_reference = mesh_origin)
596
597        if verbose: print 'FitInterpolate: Building mesh'       
598        mesh = Mesh(vertex_coordinates, triangles)
599        mesh.check_integrity()
600   
601   
602    interp = Fit(mesh=mesh,
603                 verbose=verbose,
604                 alpha=alpha)
605
606    vertex_attributes = interp.fit(point_coordinates,
607                                   point_attributes,
608                                   point_origin=data_origin,
609                                   max_read_lines=max_read_lines,
610                                   attribute_name=attribute_name,
611                                   verbose=verbose)
612
613       
614    # Add the value checking stuff that's in least squares.
615    # Maybe this stuff should get pushed down into Fit.
616    # at least be a method of Fit.
617    # Or intigrate it into the fit method, saving teh max and min's
618    # as att's.
619   
620    return vertex_attributes
621
622
623#def _fit(*args, **kwargs):
624#    """Private function for use with caching. Reason is that classes
625#    may change their byte code between runs which is annoying.
626#    """
627#   
628#    return Fit(*args, **kwargs)
629
630
631def fit_to_mesh_file(mesh_file, point_file, mesh_output_file,
632                     alpha=DEFAULT_ALPHA, verbose= False,
633                     expand_search = False,
634                     precrop = False,
635                     display_errors = True):
636    """
637    Given a mesh file (tsh) and a point attribute file, fit
638    point attributes to the mesh and write a mesh file with the
639    results.
640
641    Note: the points file needs titles.  If you want anuga to use the tsh file,
642    make sure the title is elevation.
643
644    NOTE: Throws IOErrors, for a variety of file problems.
645   
646    """
647
648    from load_mesh.loadASCII import import_mesh_file, \
649         export_mesh_file, concatinate_attributelist
650
651
652    try:
653        mesh_dict = import_mesh_file(mesh_file)
654    except IOError,e:
655        if display_errors:
656            print "Could not load bad file. ", e
657        raise IOError  #Could not load bad mesh file.
658   
659    vertex_coordinates = mesh_dict['vertices']
660    triangles = mesh_dict['triangles']
661    if type(mesh_dict['vertex_attributes']) == num.ArrayType:
662        old_point_attributes = mesh_dict['vertex_attributes'].tolist()
663    else:
664        old_point_attributes = mesh_dict['vertex_attributes']
665
666    if type(mesh_dict['vertex_attribute_titles']) == num.ArrayType:
667        old_title_list = mesh_dict['vertex_attribute_titles'].tolist()
668    else:
669        old_title_list = mesh_dict['vertex_attribute_titles']
670
671    if verbose: print 'tsh file %s loaded' %mesh_file
672
673    # load in the points file
674    try:
675        geo = Geospatial_data(point_file, verbose=verbose)
676    except IOError,e:
677        if display_errors:
678            print "Could not load bad file. ", e
679        raise IOError  #Re-raise exception 
680
681    point_coordinates = geo.get_data_points(absolute=True)
682    title_list,point_attributes = concatinate_attributelist( \
683        geo.get_all_attributes())
684
685    if mesh_dict.has_key('geo_reference') and \
686           not mesh_dict['geo_reference'] is None:
687        mesh_origin = mesh_dict['geo_reference'].get_origin()
688    else:
689        mesh_origin = None
690
691    if verbose: print "points file loaded"
692    if verbose: print "fitting to mesh"
693    f = fit_to_mesh(point_coordinates,
694                    vertex_coordinates,
695                    triangles,
696                    None,
697                    point_attributes,
698                    alpha = alpha,
699                    verbose = verbose,
700                    data_origin = None,
701                    mesh_origin = mesh_origin)
702    if verbose: print "finished fitting to mesh"
703
704    # convert array to list of lists
705    new_point_attributes = f.tolist()
706    #FIXME have this overwrite attributes with the same title - DSG
707    #Put the newer attributes last
708    if old_title_list <> []:
709        old_title_list.extend(title_list)
710        #FIXME can this be done a faster way? - DSG
711        for i in range(len(old_point_attributes)):
712            old_point_attributes[i].extend(new_point_attributes[i])
713        mesh_dict['vertex_attributes'] = old_point_attributes
714        mesh_dict['vertex_attribute_titles'] = old_title_list
715    else:
716        mesh_dict['vertex_attributes'] = new_point_attributes
717        mesh_dict['vertex_attribute_titles'] = title_list
718
719    if verbose: print "exporting to file ", mesh_output_file
720
721    try:
722        export_mesh_file(mesh_output_file, mesh_dict)
723    except IOError,e:
724        if display_errors:
725            print "Could not write file. ", e
726        raise IOError
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