def test_streamline_tensors():
# Small streamline
streamline = [[1, 2, 3], [4, 5, 3], [5, 6, 3]]
# Non-default eigenvalues:
evals = [0.0012, 0.0006, 0.0004]
streamline_tensors = life.streamline_tensors(streamline, evals=evals)
npt.assert_array_almost_equal(streamline_tensors[0],
np.array([[0.0009, 0.0003, 0.],
[0.0003, 0.0009, 0.],
[0., 0., 0.0004]]))
# Get the eigenvalues/eigenvectors:
eigvals, eigvecs = la.eig(streamline_tensors[0])
eigvecs = eigvecs[np.argsort(eigvals)[::-1]]
eigvals = eigvals[np.argsort(eigvals)[::-1]]
npt.assert_array_almost_equal(eigvals,
np.array([0.0012, 0.0006, 0.0004]))
npt.assert_array_almost_equal(eigvecs[0],
np.array([0.70710678, -0.70710678, 0.]))
# Another small streamline
streamline = [[1, 0, 0], [2, 0, 0], [3, 0, 0]]
streamline_tensors = life.streamline_tensors(streamline, evals=evals)
for t in streamline_tensors:
eigvals, eigvecs = la.eig(t)
eigvecs = eigvecs[np.argsort(eigvals)[::-1]]
# This one has no rotations - all tensors are simply the canonical:
npt.assert_almost_equal(np.rad2deg(np.arccos(
np.dot(eigvecs[0], [1, 0, 0]))), 0)
npt.assert_almost_equal(np.rad2deg(np.arccos(
np.dot(eigvecs[1], [0, 1, 0]))), 0)
npt.assert_almost_equal(np.rad2deg(np.arccos(
np.dot(eigvecs[2], [0, 0, 1]))), 0)
def test_streamline_tensors():
# Small streamline
streamline = [[1, 2, 3], [4, 5, 3], [5, 6, 3]]
# Non-default eigenvalues:
evals = [0.0012, 0.0006, 0.0004]
streamline_tensors = life.streamline_tensors(streamline, evals=evals)
npt.assert_array_almost_equal(
streamline_tensors[0],
np.array([[0.0009, 0.0003, 0.], [0.0003, 0.0009, 0.], [0., 0.,
0.0004]]))
# Get the eigenvalues/eigenvectors:
eigvals, eigvecs = la.eig(streamline_tensors[0])
eigvecs = eigvecs[np.argsort(eigvals)[::-1]]
eigvals = eigvals[np.argsort(eigvals)[::-1]]
npt.assert_array_almost_equal(eigvals, np.array([0.0012, 0.0006, 0.0004]))
npt.assert_array_almost_equal(eigvecs[0],
np.array([0.70710678, -0.70710678, 0.]))
# Another small streamline
streamline = [[1, 0, 0], [2, 0, 0], [3, 0, 0]]
streamline_tensors = life.streamline_tensors(streamline, evals=evals)
for t in streamline_tensors:
eigvals, eigvecs = la.eig(t)
eigvecs = eigvecs[np.argsort(eigvals)[::-1]]
eigvals = eigvals[np.argsort(eigvals)[::-1]]
# This one has no rotations - all tensors are simply the canonical:
npt.assert_almost_equal(
np.rad2deg(np.arccos(np.dot(eigvecs[0], [1, 0, 0]))), 0)
npt.assert_almost_equal(
np.rad2deg(np.arccos(np.dot(eigvecs[1], [0, 1, 0]))), 0)
npt.assert_almost_equal(
np.rad2deg(np.arccos(np.dot(eigvecs[2], [0, 0, 1]))), 0)
def test_streamline_tensors():
# Small streamline
streamline = [[1, 2, 3], [4, 5, 3], [5, 6, 3]]
# Non-default eigenvalues:
evals = [0.0012, 0.0006, 0.0004]
streamline_tensors = life.streamline_tensors(streamline, evals=evals)
# Get the resulting eigenvalues:
eigvals = la.eigvals(streamline_tensors[0])
# la.eigvals returns things in a strange order, so reorder them:
idx = np.argsort(eigvals)[::-1]
# The eigenvalues are the same:
npt.assert_array_almost_equal(eigvals[idx], evals)
eigvecs = la.eig(streamline_tensors[0])[1][idx]
# The rotation on the first vector is 45 degrees:
npt.assert_almost_equal(np.rad2deg(np.arccos(np.dot(eigvecs[0], [1, 0, 0]))),
45)
# The rotation on the first vector is 135 degrees:
npt.assert_almost_equal(np.rad2deg(np.arccos(np.dot(eigvecs[1], [0, 1, 0]))),
135)
# The rotation on the last vector is 0 degrees (the same coordinate in all
# three z components):
npt.assert_almost_equal(np.rad2deg(np.arccos(np.dot(eigvecs[2], [0, 0, 1]))),
0)
# Another small streamline
streamline = [[1, 0, 0], [2, 0, 0], [3, 0, 0]]
streamline_tensors = life.streamline_tensors(streamline, evals=evals)
for t in streamline_tensors:
eigvals = la.eigvals(t)
idx = np.argsort(eigvals)[::-1]
# The eigenvalues are the same:
npt.assert_array_almost_equal(eigvals[idx], evals)
# This one has no rotations - all tensors are simply the canonical:
eigvecs = la.eig(streamline_tensors[0])[1][idx]
npt.assert_almost_equal(np.rad2deg(np.arccos(
np.dot(eigvecs[0], [1, 0, 0]))), 0)
npt.assert_almost_equal(np.rad2deg(np.arccos(
np.dot(eigvecs[1], [0, 1, 0]))), 0)
npt.assert_almost_equal(np.rad2deg(np.arccos(
np.dot(eigvecs[2], [0, 0, 1]))), 0)