| 1 | #!/usr/bin/env python |
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| 2 | |
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| 3 | #TEST |
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| 4 | import sys |
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| 5 | import unittest |
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| 6 | from math import sqrt |
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| 7 | |
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| 8 | |
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| 9 | from interpolate import * |
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| 10 | from Numeric import allclose, array, transpose |
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| 11 | |
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| 12 | from coordinate_transforms.geo_reference import Geo_reference |
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| 13 | |
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| 14 | def distance(x, y): |
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| 15 | return sqrt( sum( (array(x)-array(y))**2 )) |
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| 16 | |
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| 17 | def linear_function(point): |
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| 18 | point = array(point) |
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| 19 | return point[:,0]+point[:,1] |
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| 20 | |
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| 21 | |
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| 22 | class Test_Interpolate(unittest.TestCase): |
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| 23 | |
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| 24 | def setUp(self): |
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| 25 | pass |
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| 26 | |
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| 27 | def tearDown(self): |
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| 28 | pass |
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| 29 | |
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| 30 | def test_datapoint_at_centroid(self): |
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| 31 | a = [0.0, 0.0] |
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| 32 | b = [0.0, 2.0] |
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| 33 | c = [2.0,0.0] |
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| 34 | points = [a, b, c] |
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| 35 | vertices = [ [1,0,2] ] #bac |
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| 36 | |
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| 37 | data = [ [2.0/3, 2.0/3] ] #Use centroid as one data point |
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| 38 | |
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| 39 | interp = Interpolate(points, vertices) |
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| 40 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 41 | [[1./3, 1./3, 1./3]]) |
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| 42 | |
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| 43 | |
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| 44 | def test_quad_tree(self): |
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| 45 | p0 = [-10.0, -10.0] |
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| 46 | p1 = [20.0, -10.0] |
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| 47 | p2 = [-10.0, 20.0] |
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| 48 | p3 = [10.0, 50.0] |
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| 49 | p4 = [30.0, 30.0] |
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| 50 | p5 = [50.0, 10.0] |
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| 51 | p6 = [40.0, 60.0] |
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| 52 | p7 = [60.0, 40.0] |
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| 53 | p8 = [-66.0, 20.0] |
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| 54 | p9 = [10.0, -66.0] |
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| 55 | |
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| 56 | points = [p0, p1, p2, p3, p4, p5, p6, p7, p8, p9] |
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| 57 | triangles = [ [0, 1, 2], |
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| 58 | [3, 2, 4], |
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| 59 | [4, 2, 1], |
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| 60 | [4, 1, 5], |
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| 61 | [3, 4, 6], |
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| 62 | [6, 4, 7], |
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| 63 | [7, 4, 5], |
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| 64 | [8, 0, 2], |
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| 65 | [0, 9, 1]] |
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| 66 | |
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| 67 | data = [ [4,4] ] |
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| 68 | interp = Interpolate(points, triangles, |
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| 69 | max_vertices_per_cell = 4) |
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| 70 | #print "PDSG - interp.get_A()", interp.get_A() |
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| 71 | answer = [ [ 0.06666667, 0.46666667, 0.46666667, 0., |
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| 72 | 0., 0. , 0., 0., 0., 0.]] |
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| 73 | |
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| 74 | |
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| 75 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 76 | answer) |
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| 77 | #interp.set_point_coordinates([[-30, -30]]) #point outside of mesh |
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| 78 | #print "PDSG - interp.get_A()", interp.get_A() |
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| 79 | data = [[-30, -30]] |
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| 80 | answer = [ [ 0.0, 0.0, 0.0, 0., |
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| 81 | 0., 0. , 0., 0., 0., 0.]] |
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| 82 | |
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| 83 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 84 | answer) |
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| 85 | |
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| 86 | |
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| 87 | #point outside of quad tree root cell |
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| 88 | #interp.set_point_coordinates([[-70, -70]]) |
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| 89 | #print "PDSG - interp.get_A()", interp.get_A() |
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| 90 | data = [[-70, -70]] |
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| 91 | answer = [ [ 0.0, 0.0, 0.0, 0., |
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| 92 | 0., 0. , 0., 0., 0., 0.]] |
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| 93 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 94 | answer) |
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| 95 | |
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| 96 | def test_datapoints_at_vertices(self): |
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| 97 | """Test that data points coinciding with vertices yield a diagonal matrix |
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| 98 | """ |
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| 99 | |
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| 100 | a = [0.0, 0.0] |
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| 101 | b = [0.0, 2.0] |
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| 102 | c = [2.0,0.0] |
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| 103 | points = [a, b, c] |
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| 104 | vertices = [ [1,0,2] ] #bac |
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| 105 | |
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| 106 | data = points #Use data at vertices |
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| 107 | |
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| 108 | interp = Interpolate(points, vertices) |
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| 109 | answer = [[1., 0., 0.], |
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| 110 | [0., 1., 0.], |
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| 111 | [0., 0., 1.]] |
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| 112 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 113 | answer) |
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| 114 | |
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| 115 | |
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| 116 | def test_datapoints_on_edge_midpoints(self): |
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| 117 | """Try datapoints midway on edges - |
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| 118 | each point should affect two matrix entries equally |
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| 119 | """ |
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| 120 | |
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| 121 | a = [0.0, 0.0] |
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| 122 | b = [0.0, 2.0] |
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| 123 | c = [2.0,0.0] |
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| 124 | points = [a, b, c] |
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| 125 | vertices = [ [1,0,2] ] #bac |
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| 126 | |
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| 127 | data = [ [0., 1.], [1., 0.], [1., 1.] ] |
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| 128 | answer = [[0.5, 0.5, 0.0], #Affects vertex 1 and 0 |
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| 129 | [0.5, 0.0, 0.5], #Affects vertex 0 and 2 |
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| 130 | [0.0, 0.5, 0.5]] |
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| 131 | interp = Interpolate(points, vertices, data) |
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| 132 | |
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| 133 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 134 | answer) |
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| 135 | |
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| 136 | def test_datapoints_on_edges(self): |
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| 137 | """Try datapoints on edges - |
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| 138 | each point should affect two matrix entries in proportion |
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| 139 | """ |
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| 140 | |
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| 141 | a = [0.0, 0.0] |
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| 142 | b = [0.0, 2.0] |
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| 143 | c = [2.0,0.0] |
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| 144 | points = [a, b, c] |
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| 145 | vertices = [ [1,0,2] ] #bac |
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| 146 | |
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| 147 | data = [ [0., 1.5], [1.5, 0.], [1.5, 0.5] ] |
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| 148 | answer = [[0.25, 0.75, 0.0], #Affects vertex 1 and 0 |
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| 149 | [0.25, 0.0, 0.75], #Affects vertex 0 and 2 |
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| 150 | [0.0, 0.25, 0.75]] |
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| 151 | |
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| 152 | interp = Interpolate(points, vertices, data) |
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| 153 | |
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| 154 | assert allclose(interp._build_interpolation_matrix_A(data).todense(), |
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| 155 | answer) |
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| 156 | |
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| 157 | |
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| 158 | def test_arbitrary_datapoints(self): |
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| 159 | """Try arbitrary datapoints |
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| 160 | """ |
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| 161 | |
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| 162 | from Numeric import sum |
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| 163 | |
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| 164 | a = [0.0, 0.0] |
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| 165 | b = [0.0, 2.0] |
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| 166 | c = [2.0,0.0] |
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| 167 | points = [a, b, c] |
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| 168 | vertices = [ [1,0,2] ] #bac |
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| 169 | |
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| 170 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44] ] |
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| 171 | |
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| 172 | interp = Interpolate(points, vertices, data) |
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| 173 | #print "interp.get_A()", interp.get_A() |
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| 174 | results = interp._build_interpolation_matrix_A(data).todense() |
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| 175 | assert allclose(sum(results, axis=1), 1.0) |
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| 176 | |
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| 177 | #FIXME - have to change this test to check default info |
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| 178 | def NO_test_arbitrary_datapoints_some_outside(self): |
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| 179 | """Try arbitrary datapoints one outside the triangle. |
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| 180 | That one should be ignored |
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| 181 | """ |
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| 182 | |
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| 183 | from Numeric import sum |
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| 184 | |
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| 185 | a = [0.0, 0.0] |
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| 186 | b = [0.0, 2.0] |
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| 187 | c = [2.0,0.0] |
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| 188 | points = [a, b, c] |
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| 189 | vertices = [ [1,0,2] ] #bac |
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| 190 | |
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| 191 | data = [ [0.2, 1.5], [0.123, 1.768], [1.43, 0.44], [5.0, 7.0]] |
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| 192 | |
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| 193 | |
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| 194 | interp = Interpolate(points, vertices, data, precrop = True) |
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| 195 | |
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| 196 | results = interp._build_interpolation_matrix_A(data).todense() |
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| 197 | assert allclose(sum(results, axis=1), 1.0) |
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| 198 | |
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| 199 | interp = Interpolate(points, vertices, data, precrop = False) |
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| 200 | results = interp._build_interpolation_matrix_A(data).todense() |
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| 201 | assert allclose(sum(results, axis=1), [1,1,1,0]) |
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| 202 | |
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| 203 | |
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| 204 | |
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| 205 | # this causes a memory error in scipy.sparse |
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| 206 | def test_more_triangles(self): |
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| 207 | |
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| 208 | a = [-1.0, 0.0] |
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| 209 | b = [3.0, 4.0] |
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| 210 | c = [4.0,1.0] |
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| 211 | d = [-3.0, 2.0] #3 |
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| 212 | e = [-1.0,-2.0] |
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| 213 | f = [1.0, -2.0] #5 |
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| 214 | |
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| 215 | points = [a, b, c, d,e,f] |
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| 216 | triangles = [[0,1,3],[1,0,2],[0,4,5], [0,5,2]] #abd bac aef afc |
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| 217 | |
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| 218 | #Data points |
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| 219 | data = [ [-3., 2.0], [-2, 1], [0.0, 1], [0, 3], [2, 3], [-1.0/3,-4./3] ] |
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| 220 | interp = Interpolate(points, triangles) |
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| 221 | |
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| 222 | answer = [[0.0, 0.0, 0.0, 1.0, 0.0, 0.0], #Affects point d |
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| 223 | [0.5, 0.0, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
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| 224 | [0.75, 0.25, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
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| 225 | [0.0, 0.5, 0.0, 0.5, 0.0, 0.0], #Affects points a and d |
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| 226 | [0.25, 0.75, 0.0, 0.0, 0.0, 0.0], #Affects points a and b |
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| 227 | [1./3, 0.0, 0.0, 0.0, 1./3, 1./3]] #Affects points a, e and f |
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| 228 | |
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| 229 | |
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| 230 | A = interp._build_interpolation_matrix_A(data).todense() |
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| 231 | for i in range(A.shape[0]): |
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| 232 | for j in range(A.shape[1]): |
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| 233 | if not allclose(A[i,j], answer[i][j]): |
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| 234 | print i,j,':',A[i,j], answer[i][j] |
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| 235 | |
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| 236 | |
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| 237 | #results = interp._build_interpolation_matrix_A(data).todense() |
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| 238 | |
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| 239 | assert allclose(A, answer) |
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| 240 | |
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| 241 | |
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| 242 | def test_interpolate_attributes_to_points(self): |
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| 243 | v0 = [0.0, 0.0] |
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| 244 | v1 = [0.0, 5.0] |
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| 245 | v2 = [5.0, 0.0] |
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| 246 | |
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| 247 | vertices = [v0, v1, v2] |
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| 248 | triangles = [ [1,0,2] ] #bac |
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| 249 | |
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| 250 | d0 = [1.0, 1.0] |
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| 251 | d1 = [1.0, 2.0] |
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| 252 | d2 = [3.0, 1.0] |
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| 253 | point_coords = [ d0, d1, d2] |
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| 254 | |
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| 255 | interp = Interpolate(vertices, triangles, point_coords) |
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| 256 | f = linear_function(vertices) |
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| 257 | z = interp.interpolate(f, point_coords) |
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| 258 | answer = linear_function(point_coords) |
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| 259 | |
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| 260 | |
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| 261 | assert allclose(z, answer) |
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| 262 | |
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| 263 | |
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| 264 | |
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| 265 | def test_interpolate_attributes_to_pointsII(self): |
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| 266 | a = [-1.0, 0.0] |
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| 267 | b = [3.0, 4.0] |
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| 268 | c = [4.0, 1.0] |
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| 269 | d = [-3.0, 2.0] #3 |
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| 270 | e = [-1.0, -2.0] |
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| 271 | f = [1.0, -2.0] #5 |
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| 272 | |
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| 273 | vertices = [a, b, c, d,e,f] |
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| 274 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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| 275 | |
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| 276 | |
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| 277 | point_coords = [[-2.0, 2.0], |
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| 278 | [-1.0, 1.0], |
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| 279 | [0.0, 2.0], |
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| 280 | [1.0, 1.0], |
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| 281 | [2.0, 1.0], |
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| 282 | [0.0, 0.0], |
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| 283 | [1.0, 0.0], |
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| 284 | [0.0, -1.0], |
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| 285 | [-0.2, -0.5], |
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| 286 | [-0.9, -1.5], |
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| 287 | [0.5, -1.9], |
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| 288 | [3.0, 1.0]] |
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| 289 | |
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| 290 | interp = Interpolate(vertices, triangles) |
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| 291 | f = linear_function(vertices) |
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| 292 | z = interp.interpolate(f, point_coords) |
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| 293 | answer = linear_function(point_coords) |
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| 294 | #print "z",z |
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| 295 | #print "answer",answer |
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| 296 | assert allclose(z, answer) |
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| 297 | |
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| 298 | def test_interpolate_attributes_to_pointsIII(self): |
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| 299 | """Test linear interpolation of known values at vertices to |
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| 300 | new points inside a triangle |
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| 301 | """ |
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| 302 | a = [0.0, 0.0] |
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| 303 | b = [0.0, 5.0] |
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| 304 | c = [5.0, 0.0] |
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| 305 | d = [5.0, 5.0] |
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| 306 | |
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| 307 | vertices = [a, b, c, d] |
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| 308 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
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| 309 | |
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| 310 | #Points within triangle 1 |
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| 311 | d0 = [1.0, 1.0] |
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| 312 | d1 = [1.0, 2.0] |
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| 313 | d2 = [3.0, 1.0] |
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| 314 | |
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| 315 | #Point within triangle 2 |
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| 316 | d3 = [4.0, 3.0] |
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| 317 | |
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| 318 | #Points on common edge |
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| 319 | d4 = [2.5, 2.5] |
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| 320 | d5 = [4.0, 1.0] |
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| 321 | |
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| 322 | #Point on common vertex |
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| 323 | d6 = [0., 5.] |
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| 324 | |
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| 325 | point_coords = [d0, d1, d2, d3, d4, d5, d6] |
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| 326 | |
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| 327 | interp = Interpolate(vertices, triangles) |
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| 328 | |
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| 329 | #Known values at vertices |
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| 330 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
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| 331 | f = [ [0., 0., 0., -5.], # (0,0) |
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| 332 | [5., 10., 5., -10.], # (0,5) |
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| 333 | [5., 5., 10.0, 0.], # (5,0) |
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| 334 | [10., 15., 15., -5.]] # (5,5) |
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| 335 | |
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| 336 | z = interp.interpolate(f, point_coords) |
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| 337 | answer = [ [2., 3., 3., -5.], # (1,1) |
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| 338 | [3., 5., 4., -6.], # (1,2) |
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| 339 | [4., 5., 7., -3.], # (3,1) |
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| 340 | [7., 10., 11., -4.], # (4,3) |
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| 341 | [5., 7.5, 7.5, -5.], # (2.5, 2.5) |
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| 342 | [5., 6., 9., -2.], # (4,1) |
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| 343 | [5., 10., 5., -10.]] # (0,5) |
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| 344 | |
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| 345 | #print "***********" |
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| 346 | #print "z",z |
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| 347 | #print "answer",answer |
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| 348 | #print "***********" |
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| 349 | |
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| 350 | #Should an error message be returned if points are outside |
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| 351 | # of the mesh? Not currently. |
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| 352 | |
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| 353 | assert allclose(z, answer) |
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| 354 | |
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| 355 | |
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| 356 | def test_interpolate_point_outside_of_mesh(self): |
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| 357 | """Test linear interpolation of known values at vertices to |
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| 358 | new points inside a triangle |
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| 359 | """ |
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| 360 | a = [0.0, 0.0] |
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| 361 | b = [0.0, 5.0] |
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| 362 | c = [5.0, 0.0] |
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| 363 | d = [5.0, 5.0] |
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| 364 | |
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| 365 | vertices = [a, b, c, d] |
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| 366 | triangles = [ [1,0,2], [2,3,1] ] #bac, cdb |
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| 367 | |
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| 368 | #Far away point |
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| 369 | d7 = [-1., -1.] |
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| 370 | |
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| 371 | point_coords = [ d7] |
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| 372 | interp = Interpolate(vertices, triangles) |
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| 373 | |
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| 374 | #Known values at vertices |
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| 375 | #Functions are x+y, x+2y, 2x+y, x-y-5 |
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| 376 | f = [ [0., 0., 0., -5.], # (0,0) |
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| 377 | [5., 10., 5., -10.], # (0,5) |
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| 378 | [5., 5., 10.0, 0.], # (5,0) |
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| 379 | [10., 15., 15., -5.]] # (5,5) |
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| 380 | |
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| 381 | z = interp.interpolate(f, point_coords) |
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| 382 | answer = [ [0., 0., 0., 0.]] # (-1,-1) |
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| 383 | |
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| 384 | #print "***********" |
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| 385 | #print "z",z |
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| 386 | #print "answer",answer |
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| 387 | #print "***********" |
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| 388 | |
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| 389 | #Should an error message be returned if points are outside |
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| 390 | # of the mesh? Not currently. |
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| 391 | |
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| 392 | assert allclose(z, answer) |
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| 393 | |
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| 394 | def test_interpolate_attributes_to_pointsIV(self): |
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| 395 | a = [-1.0, 0.0] |
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| 396 | b = [3.0, 4.0] |
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| 397 | c = [4.0, 1.0] |
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| 398 | d = [-3.0, 2.0] #3 |
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| 399 | e = [-1.0, -2.0] |
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| 400 | f = [1.0, -2.0] #5 |
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| 401 | |
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| 402 | vertices = [a, b, c, d,e,f] |
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| 403 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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| 404 | |
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| 405 | |
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| 406 | point_coords = [[-2.0, 2.0], |
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| 407 | [-1.0, 1.0], |
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| 408 | [0.0, 2.0], |
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| 409 | [1.0, 1.0], |
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| 410 | [2.0, 1.0], |
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| 411 | [0.0, 0.0], |
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| 412 | [1.0, 0.0], |
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| 413 | [0.0, -1.0], |
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| 414 | [-0.2, -0.5], |
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| 415 | [-0.9, -1.5], |
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| 416 | [0.5, -1.9], |
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| 417 | [3.0, 1.0]] |
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| 418 | |
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| 419 | interp = Interpolate(vertices, triangles) |
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| 420 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
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| 421 | f = transpose(f) |
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| 422 | #print "f",f |
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| 423 | z = interp.interpolate(f, point_coords) |
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| 424 | answer = [linear_function(point_coords), |
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| 425 | 2*linear_function(point_coords) ] |
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| 426 | answer = transpose(answer) |
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| 427 | #print "z",z |
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| 428 | #print "answer",answer |
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| 429 | assert allclose(z, answer) |
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| 430 | |
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| 431 | |
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| 432 | def test_interpolate_blocking(self): |
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| 433 | a = [-1.0, 0.0] |
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| 434 | b = [3.0, 4.0] |
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| 435 | c = [4.0, 1.0] |
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| 436 | d = [-3.0, 2.0] #3 |
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| 437 | e = [-1.0, -2.0] |
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| 438 | f = [1.0, -2.0] #5 |
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| 439 | |
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| 440 | vertices = [a, b, c, d,e,f] |
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| 441 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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| 442 | |
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| 443 | |
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| 444 | point_coords = [[-2.0, 2.0], |
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| 445 | [-1.0, 1.0], |
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| 446 | [0.0, 2.0], |
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| 447 | [1.0, 1.0], |
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| 448 | [2.0, 1.0], |
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| 449 | [0.0, 0.0], |
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| 450 | [1.0, 0.0], |
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| 451 | [0.0, -1.0], |
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| 452 | [-0.2, -0.5], |
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| 453 | [-0.9, -1.5], |
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| 454 | [0.5, -1.9], |
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| 455 | [3.0, 1.0]] |
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| 456 | |
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| 457 | interp = Interpolate(vertices, triangles) |
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| 458 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
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| 459 | f = transpose(f) |
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| 460 | #print "f",f |
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| 461 | for blocking_max in range(len(point_coords)+2): |
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| 462 | #if True: |
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| 463 | # blocking_max = 5 |
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| 464 | z = interp.interpolate(f, point_coords, |
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| 465 | start_blocking_len=blocking_max) |
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| 466 | answer = [linear_function(point_coords), |
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| 467 | 2*linear_function(point_coords) ] |
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| 468 | answer = transpose(answer) |
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| 469 | #print "z",z |
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| 470 | #print "answer",answer |
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| 471 | assert allclose(z, answer) |
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| 472 | |
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| 473 | def test_interpolate_reuse(self): |
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| 474 | a = [-1.0, 0.0] |
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| 475 | b = [3.0, 4.0] |
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| 476 | c = [4.0, 1.0] |
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| 477 | d = [-3.0, 2.0] #3 |
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| 478 | e = [-1.0, -2.0] |
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| 479 | f = [1.0, -2.0] #5 |
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| 480 | |
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| 481 | vertices = [a, b, c, d,e,f] |
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| 482 | triangles = [[0,1,3], [1,0,2], [0,4,5], [0,5,2]] #abd bac aef afc |
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| 483 | |
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| 484 | |
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| 485 | point_coords = [[-2.0, 2.0], |
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| 486 | [-1.0, 1.0], |
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| 487 | [0.0, 2.0], |
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| 488 | [1.0, 1.0], |
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| 489 | [2.0, 1.0], |
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| 490 | [0.0, 0.0], |
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| 491 | [1.0, 0.0], |
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| 492 | [0.0, -1.0], |
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| 493 | [-0.2, -0.5], |
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| 494 | [-0.9, -1.5], |
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| 495 | [0.5, -1.9], |
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| 496 | [3.0, 1.0]] |
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| 497 | |
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| 498 | interp = Interpolate(vertices, triangles) |
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| 499 | f = array([linear_function(vertices),2*linear_function(vertices) ]) |
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| 500 | f = transpose(f) |
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| 501 | z = interp.interpolate(f, point_coords, |
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| 502 | start_blocking_len=20) |
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| 503 | answer = [linear_function(point_coords), |
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| 504 | 2*linear_function(point_coords) ] |
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| 505 | answer = transpose(answer) |
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| 506 | #print "z",z |
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| 507 | #print "answer",answer |
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| 508 | assert allclose(z, answer) |
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| 509 | assert allclose(interp._A_can_be_reused, True) |
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| 510 | |
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| 511 | z = interp.interpolate(f) |
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| 512 | assert allclose(z, answer) |
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| 513 | |
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| 514 | # This causes blocking to occur. |
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| 515 | z = interp.interpolate(f, start_blocking_len=10) |
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| 516 | assert allclose(z, answer) |
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| 517 | assert allclose(interp._A_can_be_reused, False) |
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| 518 | |
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| 519 | #A is recalculated |
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| 520 | z = interp.interpolate(f) |
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| 521 | assert allclose(z, answer) |
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| 522 | assert allclose(interp._A_can_be_reused, True) |
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| 523 | |
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| 524 | interp = Interpolate(vertices, triangles) |
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| 525 | #Must raise an exception, no points specified |
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| 526 | try: |
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| 527 | z = interp.interpolate(f) |
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| 528 | except: |
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| 529 | pass |
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| 530 | |
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| 531 | |
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| 532 | #------------------------------------------------------------- |
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| 533 | if __name__ == "__main__": |
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| 534 | suite = unittest.makeSuite(Test_Interpolate,'test') |
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| 535 | runner = unittest.TextTestRunner(verbosity=1) |
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| 536 | runner.run(suite) |
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| 537 | |
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| 538 | |
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| 539 | |
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| 540 | |
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| 541 | |
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