[1160] | 1 | """Least squares smooting and interpolation. |
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| 2 | |
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| 3 | Implements a penalised least-squares fit and associated interpolations. |
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| 4 | |
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| 5 | The penalty term (or smoothing term) is controlled by the smoothing |
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| 6 | parameter alpha. |
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| 7 | With a value of alpha=0, the fit function will attempt |
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| 8 | to interpolate as closely as possible in the least-squares sense. |
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| 9 | With values alpha > 0, a certain amount of smoothing will be applied. |
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| 10 | A positive alpha is essential in cases where there are too few |
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| 11 | data points. |
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| 12 | A negative alpha is not allowed. |
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| 13 | A typical value of alpha is 1.0e-6 |
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| 14 | |
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| 15 | |
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| 16 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 17 | Geoscience Australia, 2004. |
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| 18 | """ |
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| 19 | |
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| 20 | import exceptions |
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| 21 | class ShapeError(exceptions.Exception): pass |
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| 22 | |
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| 23 | #from general_mesh import General_mesh |
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| 24 | from Numeric import zeros, array, Float, Int, dot, transpose, concatenate, ArrayType |
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| 25 | from mesh import Mesh |
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| 26 | |
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| 27 | from Numeric import zeros, take, array, Float, Int, dot, transpose, concatenate, ArrayType |
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| 28 | from sparse import Sparse, Sparse_CSR |
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| 29 | from cg_solve import conjugate_gradient, VectorShapeError |
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[1178] | 30 | |
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| 31 | from coordinate_transforms.geo_reference import Geo_reference |
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| 32 | |
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[1160] | 33 | import time |
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| 34 | |
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[1178] | 35 | |
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[1160] | 36 | try: |
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| 37 | from util import gradient |
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| 38 | except ImportError, e: |
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| 39 | #FIXME reduce the dependency of modules in pyvolution |
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| 40 | # Have util in a dir, working like load_mesh, and get rid of this |
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| 41 | def gradient(x0, y0, x1, y1, x2, y2, q0, q1, q2): |
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| 42 | """ |
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| 43 | """ |
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| 44 | |
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| 45 | det = (y2-y0)*(x1-x0) - (y1-y0)*(x2-x0) |
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| 46 | a = (y2-y0)*(q1-q0) - (y1-y0)*(q2-q0) |
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| 47 | a /= det |
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| 48 | |
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| 49 | b = (x1-x0)*(q2-q0) - (x2-x0)*(q1-q0) |
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| 50 | b /= det |
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| 51 | |
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| 52 | return a, b |
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| 53 | |
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| 54 | |
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| 55 | DEFAULT_ALPHA = 0.001 |
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| 56 | |
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| 57 | def fit_to_mesh_file(mesh_file, point_file, mesh_output_file, |
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| 58 | alpha=DEFAULT_ALPHA, verbose= False, |
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| 59 | expand_search = False, |
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| 60 | data_origin = None, |
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| 61 | mesh_origin = None, |
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[1814] | 62 | precrop = False, |
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| 63 | display_errors = True): |
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[1160] | 64 | """ |
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| 65 | Given a mesh file (tsh) and a point attribute file (xya), fit |
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| 66 | point attributes to the mesh and write a mesh file with the |
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| 67 | results. |
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| 68 | |
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| 69 | |
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| 70 | If data_origin is not None it is assumed to be |
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| 71 | a 3-tuple with geo referenced |
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| 72 | UTM coordinates (zone, easting, northing) |
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| 73 | |
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| 74 | mesh_origin is the same but refers to the input tsh file. |
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| 75 | FIXME: When the tsh format contains it own origin, these parameters can go. |
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| 76 | FIXME: And both origins should be obtained from the specified files. |
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| 77 | """ |
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| 78 | |
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[1423] | 79 | from load_mesh.loadASCII import import_mesh_file, \ |
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[1379] | 80 | import_points_file, export_mesh_file, \ |
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[1160] | 81 | concatinate_attributelist |
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| 82 | |
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[1869] | 83 | |
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[1814] | 84 | try: |
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| 85 | mesh_dict = import_mesh_file(mesh_file) |
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| 86 | except IOError,e: |
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| 87 | if display_errors: |
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| 88 | print "Could not load bad file. ", e |
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[1869] | 89 | raise IOError #Re-raise exception |
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| 90 | |
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[1160] | 91 | vertex_coordinates = mesh_dict['vertices'] |
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| 92 | triangles = mesh_dict['triangles'] |
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| 93 | if type(mesh_dict['vertex_attributes']) == ArrayType: |
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| 94 | old_point_attributes = mesh_dict['vertex_attributes'].tolist() |
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| 95 | else: |
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| 96 | old_point_attributes = mesh_dict['vertex_attributes'] |
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| 97 | |
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| 98 | if type(mesh_dict['vertex_attribute_titles']) == ArrayType: |
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| 99 | old_title_list = mesh_dict['vertex_attribute_titles'].tolist() |
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| 100 | else: |
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| 101 | old_title_list = mesh_dict['vertex_attribute_titles'] |
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| 102 | |
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| 103 | if verbose: print 'tsh file %s loaded' %mesh_file |
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| 104 | |
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| 105 | # load in the .pts file |
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| 106 | try: |
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[1814] | 107 | point_dict = import_points_file(point_file, verbose=verbose) |
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| 108 | except IOError,e: |
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| 109 | if display_errors: |
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| 110 | print "Could not load bad file. ", e |
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[1882] | 111 | raise IOError #Re-raise exception |
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[1160] | 112 | |
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| 113 | point_coordinates = point_dict['pointlist'] |
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| 114 | title_list,point_attributes = concatinate_attributelist(point_dict['attributelist']) |
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| 115 | |
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| 116 | if point_dict.has_key('geo_reference') and not point_dict['geo_reference'] is None: |
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| 117 | data_origin = point_dict['geo_reference'].get_origin() |
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| 118 | else: |
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| 119 | data_origin = (56, 0, 0) #FIXME(DSG-DSG) |
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| 120 | |
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| 121 | if mesh_dict.has_key('geo_reference') and not mesh_dict['geo_reference'] is None: |
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| 122 | mesh_origin = mesh_dict['geo_reference'].get_origin() |
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| 123 | else: |
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| 124 | mesh_origin = (56, 0, 0) #FIXME(DSG-DSG) |
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| 125 | |
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| 126 | if verbose: print "points file loaded" |
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| 127 | if verbose:print "fitting to mesh" |
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| 128 | f = fit_to_mesh(vertex_coordinates, |
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| 129 | triangles, |
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| 130 | point_coordinates, |
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| 131 | point_attributes, |
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| 132 | alpha = alpha, |
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| 133 | verbose = verbose, |
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| 134 | expand_search = expand_search, |
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| 135 | data_origin = data_origin, |
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| 136 | mesh_origin = mesh_origin, |
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| 137 | precrop = precrop) |
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| 138 | if verbose: print "finished fitting to mesh" |
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| 139 | |
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| 140 | # convert array to list of lists |
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| 141 | new_point_attributes = f.tolist() |
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| 142 | #FIXME have this overwrite attributes with the same title - DSG |
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| 143 | #Put the newer attributes last |
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| 144 | if old_title_list <> []: |
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| 145 | old_title_list.extend(title_list) |
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| 146 | #FIXME can this be done a faster way? - DSG |
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| 147 | for i in range(len(old_point_attributes)): |
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| 148 | old_point_attributes[i].extend(new_point_attributes[i]) |
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| 149 | mesh_dict['vertex_attributes'] = old_point_attributes |
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| 150 | mesh_dict['vertex_attribute_titles'] = old_title_list |
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| 151 | else: |
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| 152 | mesh_dict['vertex_attributes'] = new_point_attributes |
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| 153 | mesh_dict['vertex_attribute_titles'] = title_list |
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| 154 | |
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| 155 | #FIXME (Ole): Remember to output mesh_origin as well |
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| 156 | if verbose: print "exporting to file ",mesh_output_file |
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| 157 | |
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[1814] | 158 | try: |
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| 159 | export_mesh_file(mesh_output_file, mesh_dict) |
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| 160 | except IOError,e: |
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| 161 | if display_errors: |
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| 162 | print "Could not write file. ", e |
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[1871] | 163 | raise IOError |
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[1160] | 164 | |
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| 165 | def fit_to_mesh(vertex_coordinates, |
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| 166 | triangles, |
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| 167 | point_coordinates, |
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| 168 | point_attributes, |
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| 169 | alpha = DEFAULT_ALPHA, |
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| 170 | verbose = False, |
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| 171 | expand_search = False, |
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| 172 | data_origin = None, |
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| 173 | mesh_origin = None, |
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| 174 | precrop = False): |
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| 175 | """ |
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| 176 | Fit a smooth surface to a triangulation, |
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| 177 | given data points with attributes. |
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| 178 | |
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| 179 | |
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| 180 | Inputs: |
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| 181 | |
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| 182 | vertex_coordinates: List of coordinate pairs [xi, eta] of points |
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| 183 | constituting mesh (or a an m x 2 Numeric array) |
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| 184 | |
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| 185 | triangles: List of 3-tuples (or a Numeric array) of |
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| 186 | integers representing indices of all vertices in the mesh. |
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| 187 | |
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| 188 | point_coordinates: List of coordinate pairs [x, y] of data points |
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| 189 | (or an nx2 Numeric array) |
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| 190 | |
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| 191 | alpha: Smoothing parameter. |
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| 192 | |
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| 193 | point_attributes: Vector or array of data at the point_coordinates. |
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| 194 | |
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| 195 | data_origin and mesh_origin are 3-tuples consisting of |
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| 196 | UTM zone, easting and northing. If specified |
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| 197 | point coordinates and vertex coordinates are assumed to be |
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| 198 | relative to their respective origins. |
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| 199 | |
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| 200 | """ |
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| 201 | interp = Interpolation(vertex_coordinates, |
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| 202 | triangles, |
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| 203 | point_coordinates, |
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| 204 | alpha = alpha, |
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| 205 | verbose = verbose, |
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| 206 | expand_search = expand_search, |
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| 207 | data_origin = data_origin, |
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| 208 | mesh_origin = mesh_origin, |
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| 209 | precrop = precrop) |
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| 210 | |
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| 211 | vertex_attributes = interp.fit_points(point_attributes, verbose = verbose) |
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| 212 | return vertex_attributes |
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| 213 | |
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| 214 | |
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| 215 | |
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| 216 | def pts2rectangular(pts_name, M, N, alpha = DEFAULT_ALPHA, |
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| 217 | verbose = False, reduction = 1, format = 'netcdf'): |
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| 218 | """Fits attributes from pts file to MxN rectangular mesh |
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| 219 | |
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| 220 | Read pts file and create rectangular mesh of resolution MxN such that |
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| 221 | it covers all points specified in pts file. |
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| 222 | |
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| 223 | FIXME: This may be a temporary function until we decide on |
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| 224 | netcdf formats etc |
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| 225 | |
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| 226 | FIXME: Uses elevation hardwired |
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| 227 | """ |
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| 228 | |
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| 229 | import util, mesh_factory |
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| 230 | |
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| 231 | if verbose: print 'Read pts' |
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| 232 | points, attributes = util.read_xya(pts_name, format) |
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| 233 | |
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| 234 | #Reduce number of points a bit |
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| 235 | points = points[::reduction] |
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| 236 | elevation = attributes['elevation'] #Must be elevation |
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| 237 | elevation = elevation[::reduction] |
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| 238 | |
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| 239 | if verbose: print 'Got %d data points' %len(points) |
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| 240 | |
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| 241 | if verbose: print 'Create mesh' |
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| 242 | #Find extent |
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| 243 | max_x = min_x = points[0][0] |
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| 244 | max_y = min_y = points[0][1] |
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| 245 | for point in points[1:]: |
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| 246 | x = point[0] |
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| 247 | if x > max_x: max_x = x |
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| 248 | if x < min_x: min_x = x |
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| 249 | y = point[1] |
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| 250 | if y > max_y: max_y = y |
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| 251 | if y < min_y: min_y = y |
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| 252 | |
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| 253 | #Create appropriate mesh |
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| 254 | vertex_coordinates, triangles, boundary =\ |
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| 255 | mesh_factory.rectangular(M, N, max_x-min_x, max_y-min_y, |
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| 256 | (min_x, min_y)) |
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| 257 | |
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| 258 | #Fit attributes to mesh |
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| 259 | vertex_attributes = fit_to_mesh(vertex_coordinates, |
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| 260 | triangles, |
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| 261 | points, |
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| 262 | elevation, alpha=alpha, verbose=verbose) |
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| 263 | |
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| 264 | |
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| 265 | |
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| 266 | return vertex_coordinates, triangles, boundary, vertex_attributes |
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| 267 | |
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| 268 | |
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| 269 | |
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| 270 | class Interpolation: |
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| 271 | |
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| 272 | def __init__(self, |
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| 273 | vertex_coordinates, |
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| 274 | triangles, |
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| 275 | point_coordinates = None, |
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[1787] | 276 | alpha = None, |
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[1160] | 277 | verbose = False, |
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| 278 | expand_search = True, |
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| 279 | max_points_per_cell = 30, |
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| 280 | mesh_origin = None, |
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| 281 | data_origin = None, |
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| 282 | precrop = False): |
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| 283 | |
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| 284 | |
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| 285 | """ Build interpolation matrix mapping from |
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| 286 | function values at vertices to function values at data points |
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| 287 | |
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| 288 | Inputs: |
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| 289 | |
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| 290 | vertex_coordinates: List of coordinate pairs [xi, eta] of |
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| 291 | points constituting mesh (or a an m x 2 Numeric array) |
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[1632] | 292 | Points may appear multiple times |
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| 293 | (e.g. if vertices have discontinuities) |
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[1160] | 294 | |
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| 295 | triangles: List of 3-tuples (or a Numeric array) of |
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| 296 | integers representing indices of all vertices in the mesh. |
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| 297 | |
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| 298 | point_coordinates: List of coordinate pairs [x, y] of |
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| 299 | data points (or an nx2 Numeric array) |
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| 300 | If point_coordinates is absent, only smoothing matrix will |
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| 301 | be built |
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| 302 | |
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| 303 | alpha: Smoothing parameter |
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| 304 | |
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| 305 | data_origin and mesh_origin are 3-tuples consisting of |
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| 306 | UTM zone, easting and northing. If specified |
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| 307 | point coordinates and vertex coordinates are assumed to be |
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| 308 | relative to their respective origins. |
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| 309 | |
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| 310 | """ |
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| 311 | from util import ensure_numeric |
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| 312 | |
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| 313 | #Convert input to Numeric arrays |
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| 314 | triangles = ensure_numeric(triangles, Int) |
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| 315 | vertex_coordinates = ensure_numeric(vertex_coordinates, Float) |
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| 316 | |
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| 317 | #Build underlying mesh |
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| 318 | if verbose: print 'Building mesh' |
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| 319 | #self.mesh = General_mesh(vertex_coordinates, triangles, |
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| 320 | #FIXME: Trying the normal mesh while testing precrop, |
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| 321 | # The functionality of boundary_polygon is needed for that |
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[1178] | 322 | |
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| 323 | #FIXME - geo ref does not have to go into mesh. |
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| 324 | # Change the point co-ords to conform to the |
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| 325 | # mesh co-ords early in the code |
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| 326 | if mesh_origin == None: |
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| 327 | geo = None |
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| 328 | else: |
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| 329 | geo = Geo_reference(mesh_origin[0],mesh_origin[1],mesh_origin[2]) |
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[1160] | 330 | self.mesh = Mesh(vertex_coordinates, triangles, |
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[1178] | 331 | geo_reference = geo) |
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[1711] | 332 | |
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[1741] | 333 | self.mesh.check_integrity() |
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[1711] | 334 | |
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[1160] | 335 | self.data_origin = data_origin |
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| 336 | |
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| 337 | self.point_indices = None |
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| 338 | |
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| 339 | #Smoothing parameter |
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[1787] | 340 | if alpha is None: |
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| 341 | self.alpha = DEFAULT_ALPHA |
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| 342 | else: |
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| 343 | self.alpha = alpha |
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[1160] | 344 | |
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| 345 | #Build coefficient matrices |
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| 346 | self.build_coefficient_matrix_B(point_coordinates, |
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| 347 | verbose = verbose, |
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| 348 | expand_search = expand_search, |
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| 349 | max_points_per_cell =\ |
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| 350 | max_points_per_cell, |
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| 351 | data_origin = data_origin, |
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| 352 | precrop = precrop) |
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| 353 | |
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| 354 | |
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| 355 | def set_point_coordinates(self, point_coordinates, |
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| 356 | data_origin = None): |
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| 357 | """ |
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| 358 | A public interface to setting the point co-ordinates. |
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| 359 | """ |
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| 360 | self.build_coefficient_matrix_B(point_coordinates, data_origin) |
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| 361 | |
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| 362 | def build_coefficient_matrix_B(self, point_coordinates=None, |
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| 363 | verbose = False, expand_search = True, |
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| 364 | max_points_per_cell=30, |
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| 365 | data_origin = None, |
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| 366 | precrop = False): |
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| 367 | """Build final coefficient matrix""" |
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| 368 | |
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| 369 | |
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| 370 | if self.alpha <> 0: |
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| 371 | if verbose: print 'Building smoothing matrix' |
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| 372 | self.build_smoothing_matrix_D() |
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| 373 | |
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| 374 | if point_coordinates is not None: |
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| 375 | |
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| 376 | if verbose: print 'Building interpolation matrix' |
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| 377 | self.build_interpolation_matrix_A(point_coordinates, |
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| 378 | verbose = verbose, |
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| 379 | expand_search = expand_search, |
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| 380 | max_points_per_cell =\ |
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| 381 | max_points_per_cell, |
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| 382 | data_origin = data_origin, |
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| 383 | precrop = precrop) |
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| 384 | |
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| 385 | if self.alpha <> 0: |
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| 386 | self.B = self.AtA + self.alpha*self.D |
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| 387 | else: |
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| 388 | self.B = self.AtA |
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| 389 | |
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| 390 | #Convert self.B matrix to CSR format for faster matrix vector |
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| 391 | self.B = Sparse_CSR(self.B) |
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| 392 | |
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| 393 | def build_interpolation_matrix_A(self, point_coordinates, |
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| 394 | verbose = False, expand_search = True, |
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| 395 | max_points_per_cell=30, |
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| 396 | data_origin = None, |
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| 397 | precrop = False): |
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| 398 | """Build n x m interpolation matrix, where |
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| 399 | n is the number of data points and |
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| 400 | m is the number of basis functions phi_k (one per vertex) |
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| 401 | |
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| 402 | This algorithm uses a quad tree data structure for fast binning of data points |
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| 403 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
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| 404 | If specified coordinates are assumed to be relative to this origin. |
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| 405 | |
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| 406 | This one will override any data_origin that may be specified in |
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| 407 | interpolation instance |
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| 408 | |
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| 409 | """ |
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| 410 | |
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[1653] | 411 | |
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| 412 | #FIXME (Ole): Check that this function is memeory efficient. |
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| 413 | #6 million datapoints and 300000 basis functions |
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| 414 | #causes out-of-memory situation |
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| 415 | #First thing to check is whether there is room for self.A and self.AtA |
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| 416 | # |
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| 417 | #Maybe we need some sort of blocking |
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| 418 | |
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[1160] | 419 | from quad import build_quadtree |
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| 420 | from util import ensure_numeric |
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| 421 | |
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| 422 | if data_origin is None: |
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| 423 | data_origin = self.data_origin #Use the one from |
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| 424 | #interpolation instance |
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| 425 | |
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| 426 | #Convert input to Numeric arrays just in case. |
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| 427 | point_coordinates = ensure_numeric(point_coordinates, Float) |
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| 428 | |
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[1670] | 429 | #Keep track of discarded points (if any). |
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| 430 | #This is only registered if precrop is True |
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| 431 | self.cropped_points = False |
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[1160] | 432 | |
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| 433 | #Shift data points to same origin as mesh (if specified) |
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[1178] | 434 | |
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| 435 | #FIXME this will shift if there was no geo_ref. |
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[1627] | 436 | #But all this should be removed anyhow. |
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[1178] | 437 | #change coords before this point |
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| 438 | mesh_origin = self.mesh.geo_reference.get_origin() |
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[1160] | 439 | if point_coordinates is not None: |
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| 440 | if data_origin is not None: |
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| 441 | if mesh_origin is not None: |
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| 442 | |
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| 443 | #Transformation: |
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| 444 | # |
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| 445 | #Let x_0 be the reference point of the point coordinates |
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| 446 | #and xi_0 the reference point of the mesh. |
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| 447 | # |
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| 448 | #A point coordinate (x + x_0) is then made relative |
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| 449 | #to xi_0 by |
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| 450 | # |
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| 451 | # x_new = x + x_0 - xi_0 |
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| 452 | # |
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| 453 | #and similarly for eta |
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| 454 | |
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| 455 | x_offset = data_origin[1] - mesh_origin[1] |
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| 456 | y_offset = data_origin[2] - mesh_origin[2] |
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| 457 | else: #Shift back to a zero origin |
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| 458 | x_offset = data_origin[1] |
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| 459 | y_offset = data_origin[2] |
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| 460 | |
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| 461 | point_coordinates[:,0] += x_offset |
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| 462 | point_coordinates[:,1] += y_offset |
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| 463 | else: |
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| 464 | if mesh_origin is not None: |
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| 465 | #Use mesh origin for data points |
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| 466 | point_coordinates[:,0] -= mesh_origin[1] |
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| 467 | point_coordinates[:,1] -= mesh_origin[2] |
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| 468 | |
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| 469 | |
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| 470 | |
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| 471 | #Remove points falling outside mesh boundary |
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| 472 | #This reduced one example from 1356 seconds to 825 seconds |
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| 473 | if precrop is True: |
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| 474 | from Numeric import take |
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| 475 | from util import inside_polygon |
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| 476 | |
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| 477 | if verbose: print 'Getting boundary polygon' |
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| 478 | P = self.mesh.get_boundary_polygon() |
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| 479 | |
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| 480 | if verbose: print 'Getting indices inside mesh boundary' |
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| 481 | indices = inside_polygon(point_coordinates, P, verbose = verbose) |
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| 482 | |
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[1670] | 483 | |
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| 484 | if len(indices) != point_coordinates.shape[0]: |
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| 485 | self.cropped_points = True |
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| 486 | if verbose: |
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| 487 | print 'Done - %d points outside mesh have been cropped.'\ |
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[1160] | 488 | %(point_coordinates.shape[0] - len(indices)) |
---|
[1670] | 489 | |
---|
[1160] | 490 | point_coordinates = take(point_coordinates, indices) |
---|
| 491 | self.point_indices = indices |
---|
| 492 | |
---|
| 493 | |
---|
| 494 | |
---|
| 495 | |
---|
| 496 | #Build n x m interpolation matrix |
---|
| 497 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
| 498 | n = point_coordinates.shape[0] #Nbr of data points |
---|
| 499 | |
---|
| 500 | if verbose: print 'Number of datapoints: %d' %n |
---|
| 501 | if verbose: print 'Number of basis functions: %d' %m |
---|
| 502 | |
---|
| 503 | #FIXME (Ole): We should use CSR here since mat-mat mult is now OK. |
---|
| 504 | #However, Sparse_CSR does not have the same methods as Sparse yet |
---|
| 505 | #The tests will reveal what needs to be done |
---|
[1846] | 506 | #self.A = Sparse_CSR(Sparse(n,m)) |
---|
| 507 | #self.AtA = Sparse_CSR(Sparse(m,m)) |
---|
[1160] | 508 | self.A = Sparse(n,m) |
---|
| 509 | self.AtA = Sparse(m,m) |
---|
| 510 | |
---|
| 511 | #Build quad tree of vertices (FIXME: Is this the right spot for that?) |
---|
| 512 | root = build_quadtree(self.mesh, |
---|
| 513 | max_points_per_cell = max_points_per_cell) |
---|
| 514 | |
---|
| 515 | #Compute matrix elements |
---|
| 516 | for i in range(n): |
---|
| 517 | #For each data_coordinate point |
---|
| 518 | |
---|
| 519 | if verbose and i%((n+10)/10)==0: print 'Doing %d of %d' %(i, n) |
---|
| 520 | x = point_coordinates[i] |
---|
| 521 | |
---|
| 522 | #Find vertices near x |
---|
| 523 | candidate_vertices = root.search(x[0], x[1]) |
---|
| 524 | is_more_elements = True |
---|
| 525 | |
---|
| 526 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 527 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
| 528 | while not element_found and is_more_elements and expand_search: |
---|
| 529 | #if verbose: print 'Expanding search' |
---|
| 530 | candidate_vertices, branch = root.expand_search() |
---|
| 531 | if branch == []: |
---|
| 532 | # Searching all the verts from the root cell that haven't |
---|
| 533 | # been searched. This is the last try |
---|
| 534 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 535 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
| 536 | is_more_elements = False |
---|
| 537 | else: |
---|
| 538 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 539 | self.search_triangles_of_vertices(candidate_vertices, x) |
---|
| 540 | |
---|
| 541 | |
---|
| 542 | #Update interpolation matrix A if necessary |
---|
| 543 | if element_found is True: |
---|
| 544 | #Assign values to matrix A |
---|
| 545 | |
---|
| 546 | j0 = self.mesh.triangles[k,0] #Global vertex id for sigma0 |
---|
| 547 | j1 = self.mesh.triangles[k,1] #Global vertex id for sigma1 |
---|
| 548 | j2 = self.mesh.triangles[k,2] #Global vertex id for sigma2 |
---|
| 549 | |
---|
| 550 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
| 551 | js = [j0,j1,j2] |
---|
| 552 | |
---|
| 553 | for j in js: |
---|
| 554 | self.A[i,j] = sigmas[j] |
---|
| 555 | for k in js: |
---|
| 556 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
| 557 | else: |
---|
| 558 | pass |
---|
| 559 | #Ok if there is no triangle for datapoint |
---|
| 560 | #(as in brute force version) |
---|
| 561 | #raise 'Could not find triangle for point', x |
---|
| 562 | |
---|
| 563 | |
---|
| 564 | |
---|
| 565 | def search_triangles_of_vertices(self, candidate_vertices, x): |
---|
| 566 | #Find triangle containing x: |
---|
| 567 | element_found = False |
---|
| 568 | |
---|
| 569 | # This will be returned if element_found = False |
---|
| 570 | sigma2 = -10.0 |
---|
| 571 | sigma0 = -10.0 |
---|
| 572 | sigma1 = -10.0 |
---|
| 573 | k = -10.0 |
---|
| 574 | |
---|
| 575 | #For all vertices in same cell as point x |
---|
| 576 | for v in candidate_vertices: |
---|
| 577 | |
---|
| 578 | #for each triangle id (k) which has v as a vertex |
---|
| 579 | for k, _ in self.mesh.vertexlist[v]: |
---|
| 580 | |
---|
| 581 | #Get the three vertex_points of candidate triangle |
---|
| 582 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
| 583 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
| 584 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
| 585 | |
---|
| 586 | #print "PDSG - k", k |
---|
| 587 | #print "PDSG - xi0", xi0 |
---|
| 588 | #print "PDSG - xi1", xi1 |
---|
| 589 | #print "PDSG - xi2", xi2 |
---|
| 590 | #print "PDSG element %i verts((%f, %f),(%f, %f),(%f, %f))"\ |
---|
| 591 | # % (k, xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1]) |
---|
| 592 | |
---|
| 593 | #Get the three normals |
---|
| 594 | n0 = self.mesh.get_normal(k, 0) |
---|
| 595 | n1 = self.mesh.get_normal(k, 1) |
---|
| 596 | n2 = self.mesh.get_normal(k, 2) |
---|
| 597 | |
---|
| 598 | |
---|
| 599 | #Compute interpolation |
---|
| 600 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
| 601 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
| 602 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
| 603 | |
---|
| 604 | #print "PDSG - sigma0", sigma0 |
---|
| 605 | #print "PDSG - sigma1", sigma1 |
---|
| 606 | #print "PDSG - sigma2", sigma2 |
---|
| 607 | |
---|
| 608 | #FIXME: Maybe move out to test or something |
---|
| 609 | epsilon = 1.0e-6 |
---|
| 610 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
| 611 | |
---|
| 612 | #Check that this triangle contains the data point |
---|
| 613 | |
---|
| 614 | #Sigmas can get negative within |
---|
| 615 | #machine precision on some machines (e.g nautilus) |
---|
| 616 | #Hence the small eps |
---|
| 617 | eps = 1.0e-15 |
---|
| 618 | if sigma0 >= -eps and sigma1 >= -eps and sigma2 >= -eps: |
---|
| 619 | element_found = True |
---|
| 620 | break |
---|
| 621 | |
---|
| 622 | if element_found is True: |
---|
| 623 | #Don't look for any other triangle |
---|
| 624 | break |
---|
| 625 | return element_found, sigma0, sigma1, sigma2, k |
---|
| 626 | |
---|
| 627 | |
---|
| 628 | |
---|
| 629 | def build_interpolation_matrix_A_brute(self, point_coordinates): |
---|
| 630 | """Build n x m interpolation matrix, where |
---|
| 631 | n is the number of data points and |
---|
| 632 | m is the number of basis functions phi_k (one per vertex) |
---|
| 633 | |
---|
| 634 | This is the brute force which is too slow for large problems, |
---|
| 635 | but could be used for testing |
---|
| 636 | """ |
---|
| 637 | |
---|
| 638 | from util import ensure_numeric |
---|
| 639 | |
---|
| 640 | #Convert input to Numeric arrays |
---|
| 641 | point_coordinates = ensure_numeric(point_coordinates, Float) |
---|
| 642 | |
---|
| 643 | #Build n x m interpolation matrix |
---|
| 644 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
| 645 | n = point_coordinates.shape[0] #Nbr of data points |
---|
| 646 | |
---|
| 647 | self.A = Sparse(n,m) |
---|
| 648 | self.AtA = Sparse(m,m) |
---|
| 649 | |
---|
| 650 | #Compute matrix elements |
---|
| 651 | for i in range(n): |
---|
| 652 | #For each data_coordinate point |
---|
| 653 | |
---|
| 654 | x = point_coordinates[i] |
---|
| 655 | element_found = False |
---|
| 656 | k = 0 |
---|
| 657 | while not element_found and k < len(self.mesh): |
---|
| 658 | #For each triangle (brute force) |
---|
| 659 | #FIXME: Real algorithm should only visit relevant triangles |
---|
| 660 | |
---|
| 661 | #Get the three vertex_points |
---|
| 662 | xi0 = self.mesh.get_vertex_coordinate(k, 0) |
---|
| 663 | xi1 = self.mesh.get_vertex_coordinate(k, 1) |
---|
| 664 | xi2 = self.mesh.get_vertex_coordinate(k, 2) |
---|
| 665 | |
---|
| 666 | #Get the three normals |
---|
| 667 | n0 = self.mesh.get_normal(k, 0) |
---|
| 668 | n1 = self.mesh.get_normal(k, 1) |
---|
| 669 | n2 = self.mesh.get_normal(k, 2) |
---|
| 670 | |
---|
| 671 | #Compute interpolation |
---|
| 672 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
---|
| 673 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
---|
| 674 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
---|
| 675 | |
---|
| 676 | #FIXME: Maybe move out to test or something |
---|
| 677 | epsilon = 1.0e-6 |
---|
| 678 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
---|
| 679 | |
---|
| 680 | #Check that this triangle contains data point |
---|
| 681 | if sigma0 >= 0 and sigma1 >= 0 and sigma2 >= 0: |
---|
| 682 | element_found = True |
---|
| 683 | #Assign values to matrix A |
---|
| 684 | |
---|
| 685 | j0 = self.mesh.triangles[k,0] #Global vertex id |
---|
| 686 | #self.A[i, j0] = sigma0 |
---|
| 687 | |
---|
| 688 | j1 = self.mesh.triangles[k,1] #Global vertex id |
---|
| 689 | #self.A[i, j1] = sigma1 |
---|
| 690 | |
---|
| 691 | j2 = self.mesh.triangles[k,2] #Global vertex id |
---|
| 692 | #self.A[i, j2] = sigma2 |
---|
| 693 | |
---|
| 694 | sigmas = {j0:sigma0, j1:sigma1, j2:sigma2} |
---|
| 695 | js = [j0,j1,j2] |
---|
| 696 | |
---|
| 697 | for j in js: |
---|
| 698 | self.A[i,j] = sigmas[j] |
---|
| 699 | for k in js: |
---|
| 700 | self.AtA[j,k] += sigmas[j]*sigmas[k] |
---|
| 701 | k = k+1 |
---|
| 702 | |
---|
| 703 | |
---|
| 704 | |
---|
| 705 | def get_A(self): |
---|
| 706 | return self.A.todense() |
---|
| 707 | |
---|
| 708 | def get_B(self): |
---|
| 709 | return self.B.todense() |
---|
| 710 | |
---|
| 711 | def get_D(self): |
---|
| 712 | return self.D.todense() |
---|
| 713 | |
---|
| 714 | #FIXME: Remember to re-introduce the 1/n factor in the |
---|
| 715 | #interpolation term |
---|
| 716 | |
---|
| 717 | def build_smoothing_matrix_D(self): |
---|
| 718 | """Build m x m smoothing matrix, where |
---|
| 719 | m is the number of basis functions phi_k (one per vertex) |
---|
| 720 | |
---|
| 721 | The smoothing matrix is defined as |
---|
| 722 | |
---|
| 723 | D = D1 + D2 |
---|
| 724 | |
---|
| 725 | where |
---|
| 726 | |
---|
| 727 | [D1]_{k,l} = \int_\Omega |
---|
| 728 | \frac{\partial \phi_k}{\partial x} |
---|
| 729 | \frac{\partial \phi_l}{\partial x}\, |
---|
| 730 | dx dy |
---|
| 731 | |
---|
| 732 | [D2]_{k,l} = \int_\Omega |
---|
| 733 | \frac{\partial \phi_k}{\partial y} |
---|
| 734 | \frac{\partial \phi_l}{\partial y}\, |
---|
| 735 | dx dy |
---|
| 736 | |
---|
| 737 | |
---|
| 738 | The derivatives \frac{\partial \phi_k}{\partial x}, |
---|
| 739 | \frac{\partial \phi_k}{\partial x} for a particular triangle |
---|
| 740 | are obtained by computing the gradient a_k, b_k for basis function k |
---|
| 741 | """ |
---|
| 742 | |
---|
| 743 | #FIXME: algorithm might be optimised by computing local 9x9 |
---|
| 744 | #"element stiffness matrices: |
---|
| 745 | |
---|
| 746 | m = self.mesh.coordinates.shape[0] #Nbr of basis functions (1/vertex) |
---|
| 747 | |
---|
| 748 | self.D = Sparse(m,m) |
---|
| 749 | |
---|
| 750 | #For each triangle compute contributions to D = D1+D2 |
---|
| 751 | for i in range(len(self.mesh)): |
---|
| 752 | |
---|
| 753 | #Get area |
---|
| 754 | area = self.mesh.areas[i] |
---|
| 755 | |
---|
| 756 | #Get global vertex indices |
---|
| 757 | v0 = self.mesh.triangles[i,0] |
---|
| 758 | v1 = self.mesh.triangles[i,1] |
---|
| 759 | v2 = self.mesh.triangles[i,2] |
---|
| 760 | |
---|
| 761 | #Get the three vertex_points |
---|
| 762 | xi0 = self.mesh.get_vertex_coordinate(i, 0) |
---|
| 763 | xi1 = self.mesh.get_vertex_coordinate(i, 1) |
---|
| 764 | xi2 = self.mesh.get_vertex_coordinate(i, 2) |
---|
| 765 | |
---|
| 766 | #Compute gradients for each vertex |
---|
| 767 | a0, b0 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
| 768 | 1, 0, 0) |
---|
| 769 | |
---|
| 770 | a1, b1 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
| 771 | 0, 1, 0) |
---|
| 772 | |
---|
| 773 | a2, b2 = gradient(xi0[0], xi0[1], xi1[0], xi1[1], xi2[0], xi2[1], |
---|
| 774 | 0, 0, 1) |
---|
| 775 | |
---|
| 776 | #Compute diagonal contributions |
---|
| 777 | self.D[v0,v0] += (a0*a0 + b0*b0)*area |
---|
| 778 | self.D[v1,v1] += (a1*a1 + b1*b1)*area |
---|
| 779 | self.D[v2,v2] += (a2*a2 + b2*b2)*area |
---|
| 780 | |
---|
| 781 | #Compute contributions for basis functions sharing edges |
---|
| 782 | e01 = (a0*a1 + b0*b1)*area |
---|
| 783 | self.D[v0,v1] += e01 |
---|
| 784 | self.D[v1,v0] += e01 |
---|
| 785 | |
---|
| 786 | e12 = (a1*a2 + b1*b2)*area |
---|
| 787 | self.D[v1,v2] += e12 |
---|
| 788 | self.D[v2,v1] += e12 |
---|
| 789 | |
---|
| 790 | e20 = (a2*a0 + b2*b0)*area |
---|
| 791 | self.D[v2,v0] += e20 |
---|
| 792 | self.D[v0,v2] += e20 |
---|
| 793 | |
---|
| 794 | |
---|
| 795 | def fit(self, z): |
---|
| 796 | """Fit a smooth surface to given 1d array of data points z. |
---|
| 797 | |
---|
| 798 | The smooth surface is computed at each vertex in the underlying |
---|
| 799 | mesh using the formula given in the module doc string. |
---|
| 800 | |
---|
| 801 | Pre Condition: |
---|
[1653] | 802 | self.A, self.AtA and self.B have been initialised |
---|
[1160] | 803 | |
---|
| 804 | Inputs: |
---|
| 805 | z: Single 1d vector or array of data at the point_coordinates. |
---|
| 806 | """ |
---|
| 807 | |
---|
| 808 | #Convert input to Numeric arrays |
---|
| 809 | from util import ensure_numeric |
---|
| 810 | z = ensure_numeric(z, Float) |
---|
| 811 | |
---|
| 812 | if len(z.shape) > 1 : |
---|
| 813 | raise VectorShapeError, 'Can only deal with 1d data vector' |
---|
| 814 | |
---|
| 815 | if self.point_indices is not None: |
---|
| 816 | #Remove values for any points that were outside mesh |
---|
| 817 | z = take(z, self.point_indices) |
---|
| 818 | |
---|
| 819 | #Compute right hand side based on data |
---|
| 820 | Atz = self.A.trans_mult(z) |
---|
| 821 | |
---|
| 822 | |
---|
| 823 | #Check sanity |
---|
| 824 | n, m = self.A.shape |
---|
| 825 | if n<m and self.alpha == 0.0: |
---|
| 826 | msg = 'ERROR (least_squares): Too few data points\n' |
---|
| 827 | msg += 'There are only %d data points and alpha == 0. ' %n |
---|
| 828 | msg += 'Need at least %d\n' %m |
---|
| 829 | msg += 'Alternatively, set smoothing parameter alpha to a small ' |
---|
| 830 | msg += 'positive value,\ne.g. 1.0e-3.' |
---|
| 831 | raise msg |
---|
| 832 | |
---|
| 833 | |
---|
| 834 | |
---|
[1653] | 835 | return conjugate_gradient(self.B, Atz, Atz, imax=2*len(Atz) ) |
---|
[1160] | 836 | #FIXME: Should we store the result here for later use? (ON) |
---|
| 837 | |
---|
| 838 | |
---|
| 839 | def fit_points(self, z, verbose=False): |
---|
| 840 | """Like fit, but more robust when each point has two or more attributes |
---|
| 841 | FIXME (Ole): The name fit_points doesn't carry any meaning |
---|
| 842 | for me. How about something like fit_multiple or fit_columns? |
---|
| 843 | """ |
---|
| 844 | |
---|
| 845 | try: |
---|
| 846 | if verbose: print 'Solving penalised least_squares problem' |
---|
| 847 | return self.fit(z) |
---|
| 848 | except VectorShapeError, e: |
---|
| 849 | # broadcasting is not supported. |
---|
| 850 | |
---|
| 851 | #Convert input to Numeric arrays |
---|
| 852 | from util import ensure_numeric |
---|
| 853 | z = ensure_numeric(z, Float) |
---|
| 854 | |
---|
| 855 | #Build n x m interpolation matrix |
---|
| 856 | m = self.mesh.coordinates.shape[0] #Number of vertices |
---|
| 857 | n = z.shape[1] #Number of data points |
---|
| 858 | |
---|
| 859 | f = zeros((m,n), Float) #Resulting columns |
---|
| 860 | |
---|
| 861 | for i in range(z.shape[1]): |
---|
| 862 | f[:,i] = self.fit(z[:,i]) |
---|
| 863 | |
---|
| 864 | return f |
---|
| 865 | |
---|
| 866 | |
---|
| 867 | def interpolate(self, f): |
---|
| 868 | """Evaluate smooth surface f at data points implied in self.A. |
---|
| 869 | |
---|
| 870 | The mesh values representing a smooth surface are |
---|
| 871 | assumed to be specified in f. This argument could, |
---|
| 872 | for example have been obtained from the method self.fit() |
---|
| 873 | |
---|
| 874 | Pre Condition: |
---|
| 875 | self.A has been initialised |
---|
| 876 | |
---|
| 877 | Inputs: |
---|
| 878 | f: Vector or array of data at the mesh vertices. |
---|
| 879 | If f is an array, interpolation will be done for each column as |
---|
| 880 | per underlying matrix-matrix multiplication |
---|
| 881 | |
---|
| 882 | Output: |
---|
| 883 | Interpolated values at data points implied in self.A |
---|
| 884 | |
---|
| 885 | """ |
---|
| 886 | |
---|
| 887 | return self.A * f |
---|
| 888 | |
---|
| 889 | def cull_outsiders(self, f): |
---|
| 890 | pass |
---|
| 891 | |
---|
| 892 | |
---|
[1670] | 893 | |
---|
| 894 | |
---|
| 895 | class Interpolation_function: |
---|
| 896 | """Interpolation_function - creates callable object f(t, id) or f(t,x,y) |
---|
| 897 | which is interpolated from time series defined at vertices of |
---|
| 898 | triangular mesh (such as those stored in sww files) |
---|
| 899 | |
---|
| 900 | Let m be the number of vertices, n the number of triangles |
---|
| 901 | and p the number of timesteps. |
---|
| 902 | |
---|
| 903 | Mandatory input |
---|
| 904 | time: px1 array of monotonously increasing times (Float) |
---|
| 905 | quantities: Dictionary of pxm arrays or 1 pxm array (Float) |
---|
| 906 | |
---|
| 907 | Optional input: |
---|
[1681] | 908 | quantity_names: List of keys into the quantities dictionary |
---|
[1670] | 909 | vertex_coordinates: mx2 array of coordinates (Float) |
---|
| 910 | triangles: nx3 array of indices into vertex_coordinates (Int) |
---|
| 911 | interpolation_points: array of coordinates to be interpolated to |
---|
| 912 | verbose: Level of reporting |
---|
| 913 | |
---|
| 914 | |
---|
| 915 | The quantities returned by the callable object are specified by |
---|
| 916 | the list quantities which must contain the names of the |
---|
| 917 | quantities to be returned and also reflect the order, e.g. for |
---|
| 918 | the shallow water wave equation, on would have |
---|
| 919 | quantities = ['stage', 'xmomentum', 'ymomentum'] |
---|
| 920 | |
---|
| 921 | The parameter interpolation_points decides at which points interpolated |
---|
| 922 | quantities are to be computed whenever object is called. |
---|
| 923 | If None, return average value |
---|
| 924 | """ |
---|
| 925 | |
---|
| 926 | |
---|
| 927 | |
---|
| 928 | def __init__(self, |
---|
| 929 | time, |
---|
| 930 | quantities, |
---|
| 931 | quantity_names = None, |
---|
| 932 | vertex_coordinates = None, |
---|
| 933 | triangles = None, |
---|
| 934 | interpolation_points = None, |
---|
| 935 | verbose = False): |
---|
| 936 | """Initialise object and build spatial interpolation if required |
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| 937 | """ |
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| 938 | |
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| 939 | from Numeric import array, zeros, Float, alltrue, concatenate,\ |
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| 940 | reshape, ArrayType |
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| 941 | |
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[1884] | 942 | |
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[1670] | 943 | from util import mean, ensure_numeric |
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| 944 | from config import time_format |
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| 945 | import types |
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| 946 | |
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| 947 | |
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| 948 | |
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| 949 | #Check temporal info |
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| 950 | time = ensure_numeric(time) |
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| 951 | msg = 'Time must be a monotonuosly ' |
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| 952 | msg += 'increasing sequence %s' %time |
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| 953 | assert alltrue(time[1:] - time[:-1] > 0 ), msg |
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| 954 | |
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| 955 | |
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| 956 | #Check if quantities is a single array only |
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| 957 | if type(quantities) != types.DictType: |
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| 958 | quantities = ensure_numeric(quantities) |
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| 959 | quantity_names = ['Attribute'] |
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| 960 | |
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| 961 | #Make it a dictionary |
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| 962 | quantities = {quantity_names[0]: quantities} |
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| 963 | |
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| 964 | |
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| 965 | #Use keys if no names are specified |
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[1820] | 966 | if quantity_names is None: |
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| 967 | quantity_names = quantities.keys() |
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[1670] | 968 | |
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| 969 | |
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| 970 | #Check spatial info |
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| 971 | if vertex_coordinates is None: |
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| 972 | self.spatial = False |
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| 973 | else: |
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| 974 | vertex_coordinates = ensure_numeric(vertex_coordinates) |
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| 975 | |
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| 976 | assert triangles is not None, 'Triangles array must be specified' |
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| 977 | triangles = ensure_numeric(triangles) |
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| 978 | self.spatial = True |
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| 979 | |
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[1820] | 980 | |
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[1670] | 981 | |
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[1820] | 982 | #Save for use with statistics |
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| 983 | self.quantity_names = quantity_names |
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| 984 | self.quantities = quantities |
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| 985 | self.vertex_coordinates = vertex_coordinates |
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[1819] | 986 | self.interpolation_points = interpolation_points |
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[1670] | 987 | self.T = time[:] #Time assumed to be relative to starttime |
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| 988 | self.index = 0 #Initial time index |
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| 989 | self.precomputed_values = {} |
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| 990 | |
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| 991 | |
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| 992 | |
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| 993 | #Precomputed spatial interpolation if requested |
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| 994 | if interpolation_points is not None: |
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| 995 | if self.spatial is False: |
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| 996 | raise 'Triangles and vertex_coordinates must be specified' |
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| 997 | |
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| 998 | |
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| 999 | try: |
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[1820] | 1000 | self.interpolation_points =\ |
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| 1001 | ensure_numeric(self.interpolation_points) |
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[1670] | 1002 | except: |
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| 1003 | msg = 'Interpolation points must be an N x 2 Numeric array '+\ |
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| 1004 | 'or a list of points\n' |
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[1820] | 1005 | msg += 'I got: %s.' %( str(self.interpolation_points)[:60] + '...') |
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[1670] | 1006 | raise msg |
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| 1007 | |
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| 1008 | |
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| 1009 | for name in quantity_names: |
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| 1010 | self.precomputed_values[name] =\ |
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| 1011 | zeros((len(self.T), |
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[1820] | 1012 | len(self.interpolation_points)), |
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[1670] | 1013 | Float) |
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| 1014 | |
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| 1015 | #Build interpolator |
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| 1016 | interpol = Interpolation(vertex_coordinates, |
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| 1017 | triangles, |
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[1820] | 1018 | point_coordinates = self.interpolation_points, |
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[1670] | 1019 | alpha = 0, |
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| 1020 | precrop = False, |
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| 1021 | verbose = verbose) |
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| 1022 | |
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| 1023 | if verbose: print 'Interpolate' |
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[1828] | 1024 | n = len(self.T) |
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[1670] | 1025 | for i, t in enumerate(self.T): |
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| 1026 | #Interpolate quantities at this timestep |
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[1828] | 1027 | if verbose and i%((n+10)/10)==0: |
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| 1028 | print ' time step %d of %d' %(i, n) |
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| 1029 | |
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[1670] | 1030 | for name in quantity_names: |
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| 1031 | self.precomputed_values[name][i, :] =\ |
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| 1032 | interpol.interpolate(quantities[name][i,:]) |
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| 1033 | |
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| 1034 | #Report |
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| 1035 | if verbose: |
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[1820] | 1036 | print self.statistics() |
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| 1037 | #self.print_statistics() |
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[1670] | 1038 | |
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| 1039 | else: |
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| 1040 | #Store quantitites as is |
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| 1041 | for name in quantity_names: |
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| 1042 | self.precomputed_values[name] = quantities[name] |
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| 1043 | |
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| 1044 | |
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| 1045 | #else: |
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| 1046 | # #Return an average, making this a time series |
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| 1047 | # for name in quantity_names: |
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| 1048 | # self.values[name] = zeros(len(self.T), Float) |
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| 1049 | # |
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| 1050 | # if verbose: print 'Compute mean values' |
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| 1051 | # for i, t in enumerate(self.T): |
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| 1052 | # if verbose: print ' time step %d of %d' %(i, len(self.T)) |
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| 1053 | # for name in quantity_names: |
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| 1054 | # self.values[name][i] = mean(quantities[name][i,:]) |
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| 1055 | |
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| 1056 | |
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| 1057 | |
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| 1058 | |
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| 1059 | def __repr__(self): |
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[1820] | 1060 | #return 'Interpolation function (spation-temporal)' |
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| 1061 | return self.statistics() |
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| 1062 | |
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[1670] | 1063 | |
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| 1064 | def __call__(self, t, point_id = None, x = None, y = None): |
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| 1065 | """Evaluate f(t), f(t, point_id) or f(t, x, y) |
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| 1066 | |
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| 1067 | Inputs: |
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| 1068 | t: time - Model time. Must lie within existing timesteps |
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| 1069 | point_id: index of one of the preprocessed points. |
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| 1070 | x, y: Overrides location, point_id ignored |
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| 1071 | |
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| 1072 | If spatial info is present and all of x,y,point_id |
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| 1073 | are None an exception is raised |
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| 1074 | |
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| 1075 | If no spatial info is present, point_id and x,y arguments are ignored |
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| 1076 | making f a function of time only. |
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| 1077 | |
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| 1078 | |
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| 1079 | FIXME: point_id could also be a slice |
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| 1080 | FIXME: What if x and y are vectors? |
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| 1081 | FIXME: What about f(x,y) without t? |
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| 1082 | """ |
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| 1083 | |
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| 1084 | from math import pi, cos, sin, sqrt |
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| 1085 | from Numeric import zeros, Float |
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| 1086 | from util import mean |
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| 1087 | |
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| 1088 | if self.spatial is True: |
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| 1089 | if point_id is None: |
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| 1090 | if x is None or y is None: |
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| 1091 | msg = 'Either point_id or x and y must be specified' |
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| 1092 | raise msg |
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| 1093 | else: |
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| 1094 | if self.interpolation_points is None: |
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| 1095 | msg = 'Interpolation_function must be instantiated ' +\ |
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| 1096 | 'with a list of interpolation points before parameter ' +\ |
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| 1097 | 'point_id can be used' |
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| 1098 | raise msg |
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| 1099 | |
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| 1100 | |
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| 1101 | msg = 'Time interval [%s:%s]' %(self.T[0], self.T[1]) |
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| 1102 | msg += ' does not match model time: %s\n' %t |
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| 1103 | if t < self.T[0]: raise msg |
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| 1104 | if t > self.T[-1]: raise msg |
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| 1105 | |
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| 1106 | oldindex = self.index #Time index |
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| 1107 | |
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| 1108 | #Find current time slot |
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| 1109 | while t > self.T[self.index]: self.index += 1 |
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| 1110 | while t < self.T[self.index]: self.index -= 1 |
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| 1111 | |
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| 1112 | if t == self.T[self.index]: |
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| 1113 | #Protect against case where t == T[-1] (last time) |
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| 1114 | # - also works in general when t == T[i] |
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| 1115 | ratio = 0 |
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| 1116 | else: |
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| 1117 | #t is now between index and index+1 |
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| 1118 | ratio = (t - self.T[self.index])/\ |
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| 1119 | (self.T[self.index+1] - self.T[self.index]) |
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| 1120 | |
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| 1121 | #Compute interpolated values |
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| 1122 | q = zeros(len(self.quantity_names), Float) |
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| 1123 | |
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| 1124 | for i, name in enumerate(self.quantity_names): |
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| 1125 | Q = self.precomputed_values[name] |
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| 1126 | |
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| 1127 | if self.spatial is False: |
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| 1128 | #If there is no spatial info |
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| 1129 | assert len(Q.shape) == 1 |
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| 1130 | |
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| 1131 | Q0 = Q[self.index] |
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| 1132 | if ratio > 0: Q1 = Q[self.index+1] |
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| 1133 | |
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| 1134 | else: |
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| 1135 | if x is not None and y is not None: |
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| 1136 | #Interpolate to x, y |
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| 1137 | |
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| 1138 | raise 'x,y interpolation not yet implemented' |
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| 1139 | else: |
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| 1140 | #Use precomputed point |
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| 1141 | Q0 = Q[self.index, point_id] |
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| 1142 | if ratio > 0: Q1 = Q[self.index+1, point_id] |
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| 1143 | |
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| 1144 | #Linear temporal interpolation |
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| 1145 | if ratio > 0: |
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| 1146 | q[i] = Q0 + ratio*(Q1 - Q0) |
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| 1147 | else: |
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| 1148 | q[i] = Q0 |
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| 1149 | |
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| 1150 | |
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| 1151 | #Return vector of interpolated values |
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[1671] | 1152 | #if len(q) == 1: |
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| 1153 | # return q[0] |
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| 1154 | #else: |
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| 1155 | # return q |
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| 1156 | |
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| 1157 | |
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| 1158 | #Return vector of interpolated values |
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| 1159 | #FIXME: |
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| 1160 | if self.spatial is True: |
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| 1161 | return q |
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[1670] | 1162 | else: |
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[1671] | 1163 | #Replicate q according to x and y |
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| 1164 | #This is e.g used for Wind_stress |
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| 1165 | if x == None or y == None: |
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| 1166 | return q |
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| 1167 | else: |
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| 1168 | try: |
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| 1169 | N = len(x) |
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| 1170 | except: |
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| 1171 | return q |
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| 1172 | else: |
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| 1173 | from Numeric import ones, Float |
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| 1174 | #x is a vector - Create one constant column for each value |
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| 1175 | N = len(x) |
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| 1176 | assert len(y) == N, 'x and y must have same length' |
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| 1177 | res = [] |
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| 1178 | for col in q: |
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| 1179 | res.append(col*ones(N, Float)) |
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| 1180 | |
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| 1181 | return res |
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[1670] | 1182 | |
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| 1183 | |
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[1820] | 1184 | def statistics(self): |
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| 1185 | """Output statistics about interpolation_function |
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| 1186 | """ |
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| 1187 | |
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| 1188 | vertex_coordinates = self.vertex_coordinates |
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| 1189 | interpolation_points = self.interpolation_points |
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| 1190 | quantity_names = self.quantity_names |
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| 1191 | quantities = self.quantities |
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| 1192 | precomputed_values = self.precomputed_values |
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| 1193 | |
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| 1194 | x = vertex_coordinates[:,0] |
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| 1195 | y = vertex_coordinates[:,1] |
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[1670] | 1196 | |
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[1820] | 1197 | str = '------------------------------------------------\n' |
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| 1198 | str += 'Interpolation_function (spation-temporal) statistics:\n' |
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| 1199 | str += ' Extent:\n' |
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| 1200 | str += ' x in [%f, %f], len(x) == %d\n'\ |
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| 1201 | %(min(x), max(x), len(x)) |
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| 1202 | str += ' y in [%f, %f], len(y) == %d\n'\ |
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| 1203 | %(min(y), max(y), len(y)) |
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| 1204 | str += ' t in [%f, %f], len(t) == %d\n'\ |
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| 1205 | %(min(self.T), max(self.T), len(self.T)) |
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| 1206 | str += ' Quantities:\n' |
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| 1207 | for name in quantity_names: |
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| 1208 | q = quantities[name][:].flat |
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| 1209 | str += ' %s in [%f, %f]\n' %(name, min(q), max(q)) |
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[1822] | 1210 | |
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| 1211 | if interpolation_points is not None: |
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| 1212 | str += ' Interpolation points (xi, eta):'\ |
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| 1213 | ' number of points == %d\n' %interpolation_points.shape[0] |
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| 1214 | str += ' xi in [%f, %f]\n' %(min(interpolation_points[:,0]), |
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| 1215 | max(interpolation_points[:,0])) |
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| 1216 | str += ' eta in [%f, %f]\n' %(min(interpolation_points[:,1]), |
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| 1217 | max(interpolation_points[:,1])) |
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| 1218 | str += ' Interpolated quantities (over all timesteps):\n' |
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[1820] | 1219 | |
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[1822] | 1220 | for name in quantity_names: |
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| 1221 | q = precomputed_values[name][:].flat |
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| 1222 | str += ' %s at interpolation points in [%f, %f]\n'\ |
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| 1223 | %(name, min(q), max(q)) |
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[1820] | 1224 | str += '------------------------------------------------\n' |
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[1670] | 1225 | |
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[1820] | 1226 | return str |
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| 1227 | |
---|
| 1228 | #FIXME: Delete |
---|
| 1229 | #print '------------------------------------------------' |
---|
| 1230 | #print 'Interpolation_function statistics:' |
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| 1231 | #print ' Extent:' |
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| 1232 | #print ' x in [%f, %f], len(x) == %d'\ |
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| 1233 | # %(min(x), max(x), len(x)) |
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| 1234 | #print ' y in [%f, %f], len(y) == %d'\ |
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| 1235 | # %(min(y), max(y), len(y)) |
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| 1236 | #print ' t in [%f, %f], len(t) == %d'\ |
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| 1237 | # %(min(self.T), max(self.T), len(self.T)) |
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| 1238 | #print ' Quantities:' |
---|
| 1239 | #for name in quantity_names: |
---|
| 1240 | # q = quantities[name][:].flat |
---|
| 1241 | # print ' %s in [%f, %f]' %(name, min(q), max(q)) |
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| 1242 | #print ' Interpolation points (xi, eta):'\ |
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| 1243 | # ' number of points == %d ' %interpolation_points.shape[0] |
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| 1244 | #print ' xi in [%f, %f]' %(min(interpolation_points[:,0]), |
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| 1245 | # max(interpolation_points[:,0])) |
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| 1246 | #print ' eta in [%f, %f]' %(min(interpolation_points[:,1]), |
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| 1247 | # max(interpolation_points[:,1])) |
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| 1248 | #print ' Interpolated quantities (over all timesteps):' |
---|
| 1249 | # |
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| 1250 | #for name in quantity_names: |
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| 1251 | # q = precomputed_values[name][:].flat |
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| 1252 | # print ' %s at interpolation points in [%f, %f]'\ |
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| 1253 | # %(name, min(q), max(q)) |
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| 1254 | #print '------------------------------------------------' |
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| 1255 | |
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| 1256 | |
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[1160] | 1257 | #------------------------------------------------------------- |
---|
| 1258 | if __name__ == "__main__": |
---|
| 1259 | """ |
---|
| 1260 | Load in a mesh and data points with attributes. |
---|
| 1261 | Fit the attributes to the mesh. |
---|
| 1262 | Save a new mesh file. |
---|
| 1263 | """ |
---|
| 1264 | import os, sys |
---|
| 1265 | usage = "usage: %s mesh_input.tsh point.xya mesh_output.tsh [expand|no_expand][vervose|non_verbose] [alpha]"\ |
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| 1266 | %os.path.basename(sys.argv[0]) |
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| 1267 | |
---|
| 1268 | if len(sys.argv) < 4: |
---|
| 1269 | print usage |
---|
| 1270 | else: |
---|
| 1271 | mesh_file = sys.argv[1] |
---|
| 1272 | point_file = sys.argv[2] |
---|
| 1273 | mesh_output_file = sys.argv[3] |
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| 1274 | |
---|
| 1275 | expand_search = False |
---|
| 1276 | if len(sys.argv) > 4: |
---|
| 1277 | if sys.argv[4][0] == "e" or sys.argv[4][0] == "E": |
---|
| 1278 | expand_search = True |
---|
| 1279 | else: |
---|
| 1280 | expand_search = False |
---|
| 1281 | |
---|
| 1282 | verbose = False |
---|
| 1283 | if len(sys.argv) > 5: |
---|
| 1284 | if sys.argv[5][0] == "n" or sys.argv[5][0] == "N": |
---|
| 1285 | verbose = False |
---|
| 1286 | else: |
---|
| 1287 | verbose = True |
---|
| 1288 | |
---|
| 1289 | if len(sys.argv) > 6: |
---|
| 1290 | alpha = sys.argv[6] |
---|
| 1291 | else: |
---|
| 1292 | alpha = DEFAULT_ALPHA |
---|
| 1293 | |
---|
| 1294 | t0 = time.time() |
---|
| 1295 | fit_to_mesh_file(mesh_file, |
---|
| 1296 | point_file, |
---|
| 1297 | mesh_output_file, |
---|
| 1298 | alpha, |
---|
| 1299 | verbose= verbose, |
---|
| 1300 | expand_search = expand_search) |
---|
| 1301 | |
---|
| 1302 | print 'That took %.2f seconds' %(time.time()-t0) |
---|
| 1303 | |
---|