111 lines
3.4 KiB
Python
111 lines
3.4 KiB
Python
#!/usr/bin/env python
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import unittest
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from interp import baker
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from interp.grid import grid
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import numpy as np
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from interp.grid import contains
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def exact_func(point):
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x = point[0]
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y = point[1]
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return 0.5 + x * x + y
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def calculate_error_term(self, a, b, c, d, e, f):
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B = np.array([
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self.p1[a] * self.p1[b], self.p1[c] * self.p1[d], self.p1[e] * self.p1[f],
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self.p2[a] * self.p2[b], self.p2[c] * self.p2[d], self.p2[e] * self.p2[f],
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self.p3[a] * self.p3[b], self.p3[c] * self.p3[d], self.p3[e] * self.p3[f],
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self.p4[a] * self.p4[b], self.p4[c] * self.p4[d], self.p4[e] * self.p4[f],
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])
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B.shape = (4, 3)
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A = np.dot(B.T, B)
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rhs = np.dot(B.T, self.w)
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abc = np.linalg.solve(A, rhs)
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err = \
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abc[0] * self.phis[a] * self.phis[b] + \
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abc[1] * self.phis[c] * self.phis[d] + \
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abc[2] * self.phis[e] * self.phis[f]
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return err
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class Test(unittest.TestCase):
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def setUp(self):
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self.verts = [
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[2, 3], # 0
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[7, 4], # 1
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[4, 8], # 2
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[0, 7], # 3, 1
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[5, 0], # 4, 2
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[0, 5], # 5, 3
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[8, 9], # 6, 4
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]
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self.q = [exact_func(v) for v in self.verts]
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self.g = grid()
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self.g.verts = self.verts
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self.g.q = self.q
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self.R, self.R_q = (self.verts[:3], self.q[:3])
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self.S, self.S_q = (self.verts[3:], self.q[3:])
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self.p1, self.ql1 = baker.qlinear(self.verts[3], self.R, self.q)
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self.p2, self.ql2 = baker.qlinear(self.verts[4], self.R, self.q)
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self.p3, self.ql3 = baker.qlinear(self.verts[5], self.R, self.q)
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self.p4, self.ql4 = baker.qlinear(self.verts[6], self.R, self.q)
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self.q1 = exact_func(self.verts[3])
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self.q2 = exact_func(self.verts[4])
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self.q3 = exact_func(self.verts[5])
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self.q4 = exact_func(self.verts[6])
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self.w = np.array([
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self.q1 - self.ql1,
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self.q2 - self.ql2,
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self.q3 - self.ql3,
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self.q4 - self.ql4,
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])
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self.X = [4, 5]
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self.phis, self.qlin = baker.qlinear(self.X, self.R, self.q)
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self.exact = exact_func(self.X)
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self.answer = baker.interpolate(self.X, self.R,
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self.R_q, self.S, self.S_q)
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def test_R_contains_X(self):
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self.assertTrue(contains(self.X, self.R))
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def test_1(self):
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a, b, c, d, e, f = (0, 1, 1, 2, 2, 0)
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err = calculate_error_term(self, a, b, c, d, e, f)
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self.assertAlmostEqual(err, self.answer.error)
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def test_swap_first_elements(self):
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a, b, c, d, e, f = (1, 0, 1, 2, 2, 0)
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err = calculate_error_term(self, a, b, c, d, e, f)
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self.assertAlmostEqual(err, self.answer.error)
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def test_swap_two_pairs(self):
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a, b, c, d, e, f = (1, 2, 0, 1, 2, 0)
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err = calculate_error_term(self, a, b, c, d, e, f)
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self.assertAlmostEqual(err, self.answer.error)
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def test_swap_all_pairs(self):
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a, b, c, d, e, f = (0, 2, 0, 1, 2, 1)
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err = calculate_error_term(self, a, b, c, d, e, f)
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self.assertAlmostEqual(err, self.answer.error)
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if __name__ == '__main__':
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suite = unittest.TestLoader().loadTestsFromTestCase(Test)
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unittest.TextTestRunner(verbosity=3).run(suite)
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