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