d = np.array([[0, 1, 2, 3, 1, 0], [2, 3, 4, 3, 2, 0]]) u = np.array([0, 1, 2, 3]) # 0 0 0 1 2 3 3 3 # Polygon 2 - ser lite skum ut d = np.array([[0, 1, 2, 3, 1, 0, -1, -2], [2, 3, 4, 3, 2, 0, -1, -2]]) u = np.array([0, 1, 2, 3, 4, 5]) # 0 0 0 1 2 3 3 3 s = Spline(d,u) s(d,u) s.plotSpline() x = 2 i = 3 N = s.basis(x,i) x = np.linspace(0, 10) plt.plot(x, np.sin(x), '--', linewidth=2) # funkar inte, d är för kort # Polygon 1 #d = np.array([[0, 1, 2, 3, 1, 0], [2, 3, 4, 3, 2, 0]]) #u = np.array([0, 1, 2, 3]) # 0 0 0 1 2 3 3 3
class TestSpline(unittest.TestCase):
def setUp(self):
"""
Creates a spline with uniform grid.
:return: --
""" ""
n = 10 # number of points
x = np.linspace(0, 2 * np.pi, n) #test with sine-curve
y = np.sin(x)
self.u = np.arange(len(x) - 2)
coord = np.array([x, y])
self.sp = Spline(coord, self.u, True) # define from interpolation
def tearDown(self):
pass
def test_normalized(self):
"""
Test that asserts sum(Ni(u)) = 1 for any u in [u_2, u_{K-2}]
:return: --
""" ""
t = self.u[0] + (self.u[-1] - self.u[0]) * np.random.rand(
1000) #randomized values over interval
np.append(t, self.u[-1]) #include final value
for i in range(t.shape[0]):
N = np.array(
[self.sp.basis(t[i], j) for j in range(self.u.shape[0] + 2)])
self.assertAlmostEqual(1., np.sum(N))
def test_byInterpolation(self):
"""
Test how well sine-function can be reproduced using spline interpolation.
:return: --
""" ""
spline_vec = self.sp.spline()
np.testing.assert_almost_equal(spline_vec[1, :],
np.sin(spline_vec[0, :]), 1)
def test_blossom(self):
"""
Test that spline calculation using basis interpolation and Blossom algorithm gives the same result,
s(u) = sum(d*N).
:return: --
""" ""
s_vec_blossom = self.sp.spline()
s_vec_intpol = self.sp.splineInterpol()
np.testing.assert_almost_equal(s_vec_blossom, s_vec_intpol)
def test_runtimes(self):
"""
Check runtimes of blossom algorithm vs basis interpolation.
:return: --
""" ""
tmin_intpol = 100
tmin_blossom = 100
for i in range(10):
start = timer()
s_vec_intpol = self.sp.splineInterpol()
end = timer()
if (end - start < tmin_intpol):
tmin_intpol = end - start
start = timer()
s_vec_blossom = self.sp.spline()
end = timer()
if (end - start < tmin_intpol):
tmin_blossom = end - start
print('Runtime basis interpolation: ', tmin_intpol)
print('Runtime blossom algorithm: ', tmin_blossom)
def test_uremark(self):
"""
Test that contribution from basis function N_0^2 that is multiplied with u[-1]-term is always zero.
:return: --
""" ""
t = self.u[0] + (self.u[-1] - self.u[0]) * np.random.rand(
100) # randomized values over interval
np.append(t, self.u[-1]) # include final value
N = self.sp.makeBasisFunc(0, 2) # create function N_0^2
Nvec = np.array([N(t[i]) for i in range(t.shape[0])])
self.assertAlmostEqual(0, np.linalg.norm(Nvec))
