def tensor_from_eigs(evecs, evals, bvecs, bvals):
"""
Create a tensor from an eigen-vector/eigen-value combination, instead of
from the q-form
Parameters
"""
t_from_e = ozu.tensor_from_eigs(evals, evecs)
T = Tensor(t_from_e, bvecs, bvals)
return T
def tensor_from_eigs(evecs, evals, bvecs, bvals):
"""
Create a tensor from an eigen-vector/eigen-value combination, instead of
from the q-form
Parameters
"""
t_from_e = ozu.tensor_from_eigs(evals, evecs)
T = Tensor(t_from_e, bvecs, bvals)
return T
def test_decompose_tensor():
"""
Testing the decomposition and recomposition of tensors from eigen-vectors
and eigen-values
"""
# This is the self-diffusion tensor of water (according to Basser et
# al. 1994):
q1 = np.array([[1.7003, -0.041, 0.0027],
[-0.041, 1.6388, -0.0036],
[0.0027, -0.0036, 1.7007]])
evals1, evecs1 = ozu.decompose_tensor(q1)
q2 = ozu.tensor_from_eigs(evals1, evecs1)
npt.assert_almost_equal(q1, q2, decimal=2)
evals2, evecs2 = ozu.decompose_tensor(q2)
q3 = ozu.tensor_from_eigs(evals1, evecs2)
npt.assert_almost_equal(q2,q3, decimal=2)
# Let's see that we can do this many times:
for i in range(1000):
print i
A = np.random.rand(9).reshape(3,3)
# Make a symmetrical matrix (a 'tensor'):
T1 = np.dot(A, A.T)
evals, evecs = ozu.decompose_tensor(T1)
Q = ozu.tensor_from_eigs(evals, evecs)
evals_est, evecs_est = ozu.decompose_tensor(Q)
# The result is always going to be equal, up to a sign reversal of one
# of the vectors (why does this happen?):
npt.assert_almost_equal(np.abs(evecs_est), np.abs(evecs), decimal=3)
def test_decompose_tensor():
"""
Testing the decomposition and recomposition of tensors from eigen-vectors
and eigen-values
"""
# This is the self-diffusion tensor of water (according to Basser et
# al. 1994):
q1 = np.array([[1.7003, -0.041, 0.0027], [-0.041, 1.6388, -0.0036],
[0.0027, -0.0036, 1.7007]])
evals1, evecs1 = ozu.decompose_tensor(q1)
q2 = ozu.tensor_from_eigs(evals1, evecs1)
npt.assert_almost_equal(q1, q2, decimal=2)
evals2, evecs2 = ozu.decompose_tensor(q2)
q3 = ozu.tensor_from_eigs(evals1, evecs2)
npt.assert_almost_equal(q2, q3, decimal=2)
# Let's see that we can do this many times:
for i in range(1000):
print i
A = np.random.rand(9).reshape(3, 3)
# Make a symmetrical matrix (a 'tensor'):
T1 = np.dot(A, A.T)
evals, evecs = ozu.decompose_tensor(T1)
Q = ozu.tensor_from_eigs(evals, evecs)
evals_est, evecs_est = ozu.decompose_tensor(Q)
# The result is always going to be equal, up to a sign reversal of one
# of the vectors (why does this happen?):
npt.assert_almost_equal(np.abs(evecs_est), np.abs(evecs), decimal=3)
