def fa(self):
r"""
Fractional anisotropy (FA) calculated from cached eigenvalues.
Returns
---------
fa : array (V, 1)
Calculated FA. Note: range is 0 <= FA <= 1.
Notes
--------
FA is calculated with the following equation:
.. math::
FA = \sqrt{\frac{1}{2}\frac{(\lambda_1-\lambda_2)^2+(\lambda_1-
\lambda_3)^2+(\lambda_2-lambda_3)^2}{\lambda_1^2+
\lambda_2^2+\lambda_3^2} }
"""
evals, wrap = _makearray(self.model_params[..., :3])
ev1 = evals[..., 0]
ev2 = evals[..., 1]
ev3 = evals[..., 2]
fa = np.sqrt(0.5 * ((ev1 - ev2)**2 + (ev2 - ev3)**2 + (ev3 - ev1)**2)
/ (ev1*ev1 + ev2*ev2 + ev3*ev3))
fa = wrap(np.asarray(fa))
return _filled(fa)
def evecs(self):
"""
Returns the eigenvectors of teh tensor as an array
"""
evecs = _filled(self.model_params[..., 3:])
return evecs.reshape(self.shape + (3, 3))
def evals(self):
"""
Returns the eigenvalues of the tensor as an array
"""
return _filled(self.model_params[..., :3])
def evecs(self):
"""
Returns the eigenvectors of teh tensor as an array
"""
evecs = _filled(self.model_params[..., 3:])
return evecs.reshape(self.shape + (3, 3))
def _getD(self):
"""Calculates the 3x3 diffusion tensor for each voxel"""
params, wrap = _makearray(self.model_params)
evals = params[..., :3]
evecs = params[..., 3:]
evals_flat = evals.reshape((-1, 3))
evecs_flat = evecs.reshape((-1, 3, 3))
D_flat = np.empty(evecs_flat.shape)
for ii in xrange(len(D_flat)):
Q = evecs_flat[ii]
L = evals_flat[ii]
D_flat[ii] = np.dot(Q * L, Q.T)
D = _filled(wrap(D_flat))
D.shape = self.shape + (3, 3)
return D
def _getD(self):
"""Calculates the 3x3 diffusion tensor for each voxel"""
params, wrap = _makearray(self.model_params)
evals = params[..., :3]
evecs = params[..., 3:]
evals_flat = evals.reshape((-1, 3))
evecs_flat = evecs.reshape((-1, 3, 3))
D_flat = np.empty(evecs_flat.shape)
for ii in xrange(len(D_flat)):
Q = evecs_flat[ii]
L = evals_flat[ii]
D_flat[ii] = np.dot(Q * L, Q.T)
D = _filled(wrap(D_flat))
D.shape = self.shape + (3, 3)
return D
def fa(self, fill_value=0, nonans=True):
r"""
Fractional anisotropy (FA) calculated from cached eigenvalues.
Parameters
----------
fill_value : float
value of fa where self.mask == True.
nonans : Bool
When True, fa is 0 when all eigenvalues are 0, otherwise fa is nan
Returns
---------
fa : array (V, 1)
Calculated FA. Note: range is 0 <= FA <= 1.
Notes
--------
FA is calculated with the following equation:
.. math::
FA = \sqrt{\frac{1}{2}\frac{(\lambda_1-\lambda_2)^2+(\lambda_1-
\lambda_3)^2+(\lambda_2-lambda_3)^2}{\lambda_1^2+
\lambda_2^2+\lambda_3^2} }
"""
evals, wrap = _makearray(self.model_params[..., :3])
ev1 = evals[..., 0]
ev2 = evals[..., 1]
ev3 = evals[..., 2]
if nonans:
all_zero = (ev1 == 0) & (ev2 == 0) & (ev3 == 0)
else:
all_zero = 0.0
fa = np.sqrt(
0.5
* ((ev1 - ev2) ** 2 + (ev2 - ev3) ** 2 + (ev3 - ev1) ** 2)
/ (ev1 * ev1 + ev2 * ev2 + ev3 * ev3 + all_zero)
)
fa = wrap(np.asarray(fa))
return _filled(fa, fill_value)
def fa(self, fill_value=0, nonans=True):
r"""
Fractional anisotropy (FA) calculated from cached eigenvalues.
Parameters
----------
fill_value : float
value of fa where self.mask == True.
nonans : Bool
When True, fa is 0 when all eigenvalues are 0, otherwise fa is nan
Returns
---------
fa : array (V, 1)
Calculated FA. Note: range is 0 <= FA <= 1.
Notes
--------
FA is calculated with the following equation:
.. math::
FA = \sqrt{\frac{1}{2}\frac{(\lambda_1-\lambda_2)^2+(\lambda_1-
\lambda_3)^2+(\lambda_2-lambda_3)^2}{\lambda_1^2+
\lambda_2^2+\lambda_3^2} }
"""
evals, wrap = _makearray(self.model_params[..., :3])
ev1 = evals[..., 0]
ev2 = evals[..., 1]
ev3 = evals[..., 2]
if nonans:
all_zero = (ev1 == 0) & (ev2 == 0) & (ev3 == 0)
else:
all_zero = 0.
fa = np.sqrt(0.5 * ((ev1 - ev2)**2 + (ev2 - ev3)**2 + (ev3 - ev1)**2) /
(ev1 * ev1 + ev2 * ev2 + ev3 * ev3 + all_zero))
fa = wrap(np.asarray(fa))
return _filled(fa, fill_value)
def evals(self):
"""
Returns the eigenvalues of the tensor as an array
"""
return _filled(self.model_params[..., :3])
