moved the quadratic error calculation out of the baker method, and added a cubic version too
This commit is contained in:
Stephen Mardson McQuay
parent
700ccc8c25
commit
3efe335563
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@ -102,6 +102,88 @@ def qlinear_3D(X, R):
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qlin = sum([q_i * phi_i for q_i, phi_i in zip(R.q, phis)])
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return phis, qlin
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def get_error_quadratic(phi, R, S):
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear(s, R)
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(phi1, phi2, phi3) = cur_phi
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B.append(
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[
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phi1 * phi2,
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phi2 * phi3,
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phi3 * phi1,
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c) = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
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(a, b, c) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[1] * phi[2]\
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+ c * phi[2] * phi[0]
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return error_term, a, b, c
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def get_error_cubic(phi, R, S):
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear(s, R)
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(phi1, phi2, phi3) = cur_phi
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# basing this on eq 17
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B.append(
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[
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phi1 * phi2, # a
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phi1 * phi3, # b
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phi2 * phi1, # c
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phi2 * phi3, # d
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phi3 * phi1, # e
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phi3 * phi2, # f
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phi1 * phi2 * phi3, # g
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c, d, e, f, g) = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
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(a, b, c, d, e, f, g) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[0] * phi[2]\
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+ c * phi[1] * phi[0]\
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+ d * phi[1] * phi[2]\
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+ e * phi[2] * phi[0]\
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+ f * phi[2] * phi[1]\
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+ g * phi[0] * phi[1] * phi[2]\
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return error_term, a, b, c
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def run_baker(X, R, S, order=2):
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"""
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This is the main function to call to get an interpolation to X from the input meshes
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@ -135,38 +217,12 @@ def run_baker(X, R, S, order=2):
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}
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return answer
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B = [] # baker eq 9
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w = [] # baker eq 11
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for (s, q) in zip(S.points, S.q):
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cur_phi, cur_qlin = qlinear(s, R)
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(phi1, phi2, phi3) = cur_phi
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B.append(
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[
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phi1 * phi2,
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phi2 * phi3,
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phi3 * phi1,
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]
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)
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w.append(q - cur_qlin)
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B = np.array(B)
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w = np.array(w)
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A = np.dot(B.T, B)
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b = np.dot(B.T, w)
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# baker solve eq 10
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try:
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(a, b, c) = np.linalg.solve(A,b)
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except np.linalg.LinAlgError as e:
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print >> sys.stderr, "warning: run_baker: linear calculation went bad, resorting to np.linalg.pinv", e
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(a, b, c) = np.dot(np.linalg.pinv(A), b)
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error_term = a * phi[0] * phi[1]\
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+ b * phi[1] * phi[2]\
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+ c * phi[2] * phi[0]
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if order == 2:
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error_term, a, b, c = get_error_quadratic(phi, R, S)
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elif order == 3:
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error_term, a, b, c = get_error_cubic(phi, R, S)
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else:
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raise smberror('unacceptable order for baker method')
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q_final = qlin + error_term
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@ -0,0 +1,79 @@
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#!/usr/bin/python
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import unittest
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import math
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from baker import run_baker
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from grid.DD import grid
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from grid.simplex import contains
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def exact_func(X):
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x = X[0]
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y = X[0]
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return 1 - math.sin((x-0.5)**2 + (y-0.5)**2)
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class TestSequenceFunctions(unittest.TestCase):
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def setUp(self):
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self.points = [
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[ 0.25, 0.40], # 0
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[ 0.60, 0.80], # 1
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[ 0.65, 0.28], # 2
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[ 0.28, 0.65], # 3
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[ 1.00, 0.75], # 4
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[ 0.30, 0.95], # 5
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[ 0.80, 0.50], # 6
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[ 0.35, 0.15], # 7
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]
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self.q = [exact_func(p) for p in self.points]
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self.X = [0.25, 0.4001]
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self.X = [0.55, 0.45]
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self.g = grid(self.points, self.q)
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self.g.construct_connectivity()
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self.R = self.g.create_mesh(range(3))
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self.exact = exact_func(self.X)
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self.accuracy = 8
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def test_R_contains_X(self):
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self.assertTrue(contains(self.X, self.R.points))
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def test_RunBaker_1_extra_point(self, extra=1):
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S = self.g.create_mesh(range(3, 3 + extra))
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answer = run_baker(self.X, self.R, S, order=3)
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lin_err = abs(self.exact - answer['qlin'])
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final_err = abs(self.exact - answer['final'])
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self.assertTrue(lin_err >= final_err)
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def test_RunBaker_2_extra_point(self, extra=2):
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S = self.g.create_mesh(range(3, 3 + extra))
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answer = run_baker(self.X, self.R, S, order=3)
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lin_err = abs(self.exact - answer['qlin'])
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final_err = abs(self.exact - answer['final'])
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self.assertTrue(lin_err >= final_err)
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def test_RunBaker_3_extra_point(self, extra=3):
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S = self.g.create_mesh(range(3, 3 + extra))
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answer = run_baker(self.X, self.R, S, order=3)
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lin_err = abs(self.exact - answer['qlin'])
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final_err = abs(self.exact - answer['final'])
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self.assertTrue(lin_err >= final_err)
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def test_RunBaker_4_extra_point(self, extra=4):
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S = self.g.create_mesh(range(3, 3 + extra))
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answer = run_baker(self.X, self.R, S, order=3)
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lin_err = abs(self.exact - answer['qlin'])
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final_err = abs(self.exact - answer['final'])
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self.assertTrue(lin_err >= final_err)
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def test_RunBaker_5_extra_point(self, extra=5):
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S = self.g.create_mesh(range(3, 3 + extra))
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answer = run_baker(self.X, self.R, S, order=3)
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lin_err = abs(self.exact - answer['qlin'])
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final_err = abs(self.exact - answer['final'])
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self.assertTrue(lin_err >= final_err)
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if __name__ == '__main__':
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suite = unittest.TestLoader().loadTestsFromTestCase(TestSequenceFunctions)
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unittest.TextTestRunner(verbosity=3).run(suite)
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