source: anuga_core/source/anuga/fit_interpolate/fit.py @ 6493

Last change on this file since 6493 was 6493, checked in by duncan, 15 years ago

bug fix, ticket#314

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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        # Use blocking to load in the point info
341        if type(point_coordinates_or_filename) == types.StringType:
342            msg = "Don't set a point origin when reading from a file"
343            assert point_origin is None, msg
344            filename = point_coordinates_or_filename
345            G_data = Geospatial_data(filename,
346                                     max_read_lines=max_read_lines,
347                                     load_file_now=False,
348                                     verbose=verbose)
349
350            for i, geo_block in enumerate(G_data):
351                if verbose is True and 0 == i%200: 
352                    # The time this will take
353                    # is dependant on the # of Triangles
354                       
355                    print 'Processing Block %d' %i
356                    # FIXME (Ole): It would be good to say how many blocks
357                    # there are here. But this is no longer necessary
358                    # for pts files as they are reported in geospatial_data
359                    # I suggest deleting this verbose output and make
360                    # Geospatial_data more informative for txt files.
361                    #
362                    # I still think so (12/12/7, Ole).
363           
364
365                   
366                # Build the array
367
368                points = geo_block.get_data_points(absolute=True)
369                z = geo_block.get_attributes(attribute_name=attribute_name)
370                self.build_fit_subset(points, z, verbose=verbose)
371
372                # FIXME(Ole): I thought this test would make sense here
373                # See test_fitting_example_that_crashed_2 in test_shallow_water_domain.py
374                # Committed 11 March 2009
375                #msg = 'Matrix AtA was not built'
376                #assert self.AtA is not None, msg
377               
378                #print 'Matrix was built OK'
379
380               
381            point_coordinates = None
382        else:
383            point_coordinates =  point_coordinates_or_filename
384           
385        if point_coordinates is None:
386            if verbose: print 'Warning: no data points in fit'
387            msg = 'No interpolation matrix.'
388            assert self.AtA is not None, msg
389            assert self.Atz is not None
390           
391            # FIXME (DSG) - do  a message
392        else:
393            point_coordinates = ensure_absolute(point_coordinates,
394                                                geo_reference=point_origin)
395            # if isinstance(point_coordinates,Geospatial_data) and z is None:
396            # z will come from the geo-ref
397            self.build_fit_subset(point_coordinates, z, verbose)
398
399        # Check sanity
400        m = self.mesh.number_of_nodes # Nbr of basis functions (1/vertex)
401        n = self.point_count
402        if n<m and self.alpha == 0.0:
403            msg = 'ERROR (least_squares): Too few data points\n'
404            msg += 'There are only %d data points and alpha == 0. ' %n
405            msg += 'Need at least %d\n' %m
406            msg += 'Alternatively, set smoothing parameter alpha to a small '
407            msg += 'positive value,\ne.g. 1.0e-3.'
408            raise TooFewPointsError(msg)
409
410        self._build_coefficient_matrix_B(verbose)
411        loners = self.mesh.get_lone_vertices()
412        # FIXME  - make this as error message.
413        # test with
414        # Not_yet_test_smooth_att_to_mesh_with_excess_verts.
415        if len(loners)>0:
416            msg = 'WARNING: (least_squares): \nVertices with no triangles\n'
417            msg += 'All vertices should be part of a triangle.\n'
418            msg += 'In the future this will be inforced.\n'
419            msg += 'The following vertices are not part of a triangle;\n'
420            msg += str(loners)
421            print msg
422            #raise VertsWithNoTrianglesError(msg)
423       
424       
425        return conjugate_gradient(self.B, self.Atz, self.Atz,
426                                  imax=2*len(self.Atz) )
427
428       
429    def build_fit_subset(self, point_coordinates, z=None, attribute_name=None,
430                              verbose=False):
431        """Fit a smooth surface to given 1d array of data points z.
432
433        The smooth surface is computed at each vertex in the underlying
434        mesh using the formula given in the module doc string.
435
436        Inputs:
437        point_coordinates: The co-ordinates of the data points.
438              List of coordinate pairs [x, y] of
439              data points or an nx2 Numeric array or a Geospatial_data object
440        z: Single 1d vector or array of data at the point_coordinates.
441        attribute_name: Used to get the z values from the
442              geospatial object if no attribute_name is specified,
443              it's a bit of a lucky dip as to what attributes you get.
444              If there is only one attribute it will be that one.
445
446        """
447
448        # FIXME(DSG-DSG): Check that the vert and point coords
449        # have the same zone.
450        if isinstance(point_coordinates,Geospatial_data):
451            point_coordinates = point_coordinates.get_data_points( \
452                absolute = True)
453       
454        # Convert input to Numeric arrays
455        if z is not None:
456            z = ensure_numeric(z, num.Float)
457        else:
458            msg = 'z not specified'
459            assert isinstance(point_coordinates,Geospatial_data), msg
460            z = point_coordinates.get_attributes(attribute_name)
461
462        point_coordinates = ensure_numeric(point_coordinates, num.Float)
463        self._build_matrix_AtA_Atz(point_coordinates, z, verbose)
464       
465
466############################################################################
467
468def fit_to_mesh(point_coordinates, # this can also be a points file name
469                vertex_coordinates=None,
470                triangles=None,
471                mesh=None,
472                point_attributes=None,
473                alpha=DEFAULT_ALPHA,
474                verbose=False,
475                acceptable_overshoot=1.01, 
476                # FIXME: Move to config - this value is assumed in caching test
477                # FIXME(Ole): Just realised that this was never implemented (29 Jan 2009). I suggest removing it altogether.
478                mesh_origin=None,
479                data_origin=None,
480                max_read_lines=None,
481                attribute_name=None,
482                use_cache=False):
483    """Wrapper around internal function _fit_to_mesh for use with caching.
484   
485    """
486   
487    args = (point_coordinates, )
488    kwargs = {'vertex_coordinates': vertex_coordinates,
489              'triangles': triangles,
490              'mesh': mesh,
491              'point_attributes': point_attributes,
492              'alpha': alpha,
493              'verbose': verbose,
494              'acceptable_overshoot': acceptable_overshoot,
495              'mesh_origin': mesh_origin,
496              'data_origin': data_origin,
497              'max_read_lines': max_read_lines,
498              'attribute_name': attribute_name
499              }
500
501    if use_cache is True:
502        if isinstance(point_coordinates, basestring):
503            # We assume that point_coordinates is the name of a .csv/.txt
504            # file which must be passed onto caching as a dependency
505            # (in case it has changed on disk)
506            dep = [point_coordinates]
507        else:
508            dep = None
509
510           
511        #from caching import myhash
512        #import copy
513        #print args
514        #print kwargs
515        #print 'hashing:'
516        #print 'args', myhash( (args, kwargs) )
517        #print 'again', myhash( copy.deepcopy( (args, kwargs)) )       
518       
519        #print 'mesh hash', myhash( kwargs['mesh'] )       
520       
521        #print '-------------------------'
522        #print 'vertices hash', myhash( kwargs['mesh'].nodes )
523        #print 'triangles hash', myhash( kwargs['mesh'].triangles )
524        #print '-------------------------'       
525       
526        #for key in mesh.__dict__:
527        #    print key, myhash(mesh.__dict__[key])
528       
529        #for key in mesh.quantities.keys():
530        #    print key, myhash(mesh.quantities[key])
531       
532        #import sys; sys.exit()
533           
534        return cache(_fit_to_mesh,
535                     args, kwargs,
536                     verbose=verbose,
537                     compression=False,
538                     dependencies=dep)
539    else:
540        return apply(_fit_to_mesh,
541                     args, kwargs)
542
543def _fit_to_mesh(point_coordinates, # this can also be a points file name
544                 vertex_coordinates=None,
545                 triangles=None,
546                 mesh=None,
547                 point_attributes=None,
548                 alpha=DEFAULT_ALPHA,
549                 verbose=False,
550                 acceptable_overshoot=1.01,
551                 mesh_origin=None,
552                 data_origin=None,
553                 max_read_lines=None,
554                 attribute_name=None):
555    """
556    Fit a smooth surface to a triangulation,
557    given data points with attributes.
558
559
560        Inputs:
561        vertex_coordinates: List of coordinate pairs [xi, eta] of
562              points constituting a mesh (or an m x 2 Numeric array or
563              a geospatial object)
564              Points may appear multiple times
565              (e.g. if vertices have discontinuities)
566
567          triangles: List of 3-tuples (or a Numeric array) of
568          integers representing indices of all vertices in the mesh.
569
570          point_coordinates: List of coordinate pairs [x, y] of data points
571          (or an nx2 Numeric array). This can also be a .csv/.txt/.pts
572          file name.
573
574          alpha: Smoothing parameter.
575
576          acceptable overshoot: NOT IMPLEMENTED
577          controls the allowed factor by which
578          fitted values
579          may exceed the value of input data. The lower limit is defined
580          as min(z) - acceptable_overshoot*delta z and upper limit
581          as max(z) + acceptable_overshoot*delta z
582         
583
584          mesh_origin: A geo_reference object or 3-tuples consisting of
585              UTM zone, easting and northing.
586              If specified vertex coordinates are assumed to be
587              relative to their respective origins.
588         
589
590          point_attributes: Vector or array of data at the
591                            point_coordinates.
592
593    """
594
595    if mesh is None:
596        # FIXME(DSG): Throw errors if triangles or vertex_coordinates
597        # are None
598           
599        #Convert input to Numeric arrays
600        triangles = ensure_numeric(triangles, num.Int)
601        vertex_coordinates = ensure_absolute(vertex_coordinates,
602                                             geo_reference = mesh_origin)
603
604        if verbose: print 'FitInterpolate: Building mesh'       
605        mesh = Mesh(vertex_coordinates, triangles)
606        mesh.check_integrity()
607   
608   
609    interp = Fit(mesh=mesh,
610                 verbose=verbose,
611                 alpha=alpha)
612
613    vertex_attributes = interp.fit(point_coordinates,
614                                   point_attributes,
615                                   point_origin=data_origin,
616                                   max_read_lines=max_read_lines,
617                                   attribute_name=attribute_name,
618                                   verbose=verbose)
619
620       
621    # Add the value checking stuff that's in least squares.
622    # Maybe this stuff should get pushed down into Fit.
623    # at least be a method of Fit.
624    # Or intigrate it into the fit method, saving teh max and min's
625    # as att's.
626   
627    return vertex_attributes
628
629
630#def _fit(*args, **kwargs):
631#    """Private function for use with caching. Reason is that classes
632#    may change their byte code between runs which is annoying.
633#    """
634#   
635#    return Fit(*args, **kwargs)
636
637
638def fit_to_mesh_file(mesh_file, point_file, mesh_output_file,
639                     alpha=DEFAULT_ALPHA, verbose= False,
640                     expand_search = False,
641                     precrop = False,
642                     display_errors = True):
643    """
644    Given a mesh file (tsh) and a point attribute file, fit
645    point attributes to the mesh and write a mesh file with the
646    results.
647
648    Note: the points file needs titles.  If you want anuga to use the tsh file,
649    make sure the title is elevation.
650
651    NOTE: Throws IOErrors, for a variety of file problems.
652   
653    """
654
655    from load_mesh.loadASCII import import_mesh_file, \
656         export_mesh_file, concatinate_attributelist
657
658
659    try:
660        mesh_dict = import_mesh_file(mesh_file)
661    except IOError,e:
662        if display_errors:
663            print "Could not load bad file. ", e
664        raise IOError  #Could not load bad mesh file.
665   
666    vertex_coordinates = mesh_dict['vertices']
667    triangles = mesh_dict['triangles']
668    if type(mesh_dict['vertex_attributes']) == num.ArrayType:
669        old_point_attributes = mesh_dict['vertex_attributes'].tolist()
670    else:
671        old_point_attributes = mesh_dict['vertex_attributes']
672
673    if type(mesh_dict['vertex_attribute_titles']) == num.ArrayType:
674        old_title_list = mesh_dict['vertex_attribute_titles'].tolist()
675    else:
676        old_title_list = mesh_dict['vertex_attribute_titles']
677
678    if verbose: print 'tsh file %s loaded' %mesh_file
679
680    # load in the points file
681    try:
682        geo = Geospatial_data(point_file, verbose=verbose)
683    except IOError,e:
684        if display_errors:
685            print "Could not load bad file. ", e
686        raise IOError  #Re-raise exception 
687
688    point_coordinates = geo.get_data_points(absolute=True)
689    title_list,point_attributes = concatinate_attributelist( \
690        geo.get_all_attributes())
691
692    if mesh_dict.has_key('geo_reference') and \
693           not mesh_dict['geo_reference'] is None:
694        mesh_origin = mesh_dict['geo_reference'].get_origin()
695    else:
696        mesh_origin = None
697
698    if verbose: print "points file loaded"
699    if verbose: print "fitting to mesh"
700    f = fit_to_mesh(point_coordinates,
701                    vertex_coordinates,
702                    triangles,
703                    None,
704                    point_attributes,
705                    alpha = alpha,
706                    verbose = verbose,
707                    data_origin = None,
708                    mesh_origin = mesh_origin)
709    if verbose: print "finished fitting to mesh"
710
711    # convert array to list of lists
712    new_point_attributes = f.tolist()
713    #FIXME have this overwrite attributes with the same title - DSG
714    #Put the newer attributes last
715    if old_title_list <> []:
716        old_title_list.extend(title_list)
717        #FIXME can this be done a faster way? - DSG
718        for i in range(len(old_point_attributes)):
719            old_point_attributes[i].extend(new_point_attributes[i])
720        mesh_dict['vertex_attributes'] = old_point_attributes
721        mesh_dict['vertex_attribute_titles'] = old_title_list
722    else:
723        mesh_dict['vertex_attributes'] = new_point_attributes
724        mesh_dict['vertex_attribute_titles'] = title_list
725
726    if verbose: print "exporting to file ", mesh_output_file
727
728    try:
729        export_mesh_file(mesh_output_file, mesh_dict)
730    except IOError,e:
731        if display_errors:
732            print "Could not write file. ", e
733        raise IOError
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