Merge pull request #1726 from ShreyasFadnavis/ivim_mix

IVIM MIX Model (MicroLearn)

dipy/reconst/dti.py

@@ -52,7 +52,7 @@ def _roll_evals(evals, axis=-1):
 
 
 def fractional_anisotropy(evals, axis=-1):
-    """
+    r"""
     Fractional anisotropy (FA) of a diffusion tensor.
 
     Parameters
@@ -91,7 +91,7 @@ def fractional_anisotropy(evals, axis=-1):
 
 
 def geodesic_anisotropy(evals, axis=-1):
-    """
+    r"""
     Geodesic anisotropy (GA) of a diffusion tensor.
 
     Parameters
@@ -172,7 +172,7 @@ def geodesic_anisotropy(evals, axis=-1):
 
 
 def mean_diffusivity(evals, axis=-1):
-    """
+    r"""
     Mean Diffusivity (MD) of a diffusion tensor.
 
     Parameters
@@ -201,7 +201,7 @@ def mean_diffusivity(evals, axis=-1):
 
 
 def axial_diffusivity(evals, axis=-1):
-    """
+    r"""
     Axial Diffusivity (AD) of a diffusion tensor.
     Also called parallel diffusivity.
 
@@ -233,7 +233,7 @@ def axial_diffusivity(evals, axis=-1):
 
 
 def radial_diffusivity(evals, axis=-1):
-    """
+    r"""
     Radial Diffusivity (RD) of a diffusion tensor.
     Also called perpendicular diffusivity.
 
@@ -264,7 +264,7 @@ def radial_diffusivity(evals, axis=-1):
 
 
 def trace(evals, axis=-1):
-    """
+    r"""
     Trace of a diffusion tensor.
 
     Parameters
@@ -390,7 +390,7 @@ def isotropic(q_form):
 
 
 def deviatoric(q_form):
-    """
+    r"""
     Calculate the deviatoric (anisotropic) part of the tensor [1]_.
 
     Parameters
@@ -426,7 +426,7 @@ def deviatoric(q_form):
 
 
 def norm(q_form):
-    """
+    r"""
     Calculate the Frobenius norm of a tensor quadratic form
 
     Parameters
@@ -456,7 +456,7 @@ def norm(q_form):
 
 
 def mode(q_form):
-    """
+    r"""
     Mode (MO) of a diffusion tensor [1]_.
 
     Parameters
@@ -500,7 +500,7 @@ def mode(q_form):
 
 
 def linearity(evals, axis=-1):
-    """
+    r"""
     The linearity of the tensor [1]_
 
     Parameters
@@ -535,7 +535,7 @@ def linearity(evals, axis=-1):
 
 
 def planarity(evals, axis=-1):
-    """
+    r"""
     The planarity of the tensor [1]_
 
     Parameters
@@ -571,7 +571,7 @@ def planarity(evals, axis=-1):
 
 
 def sphericity(evals, axis=-1):
-    """
+    r"""
     The sphericity of the tensor [1]_
 
     Parameters
@@ -913,7 +913,7 @@ def mode(self):
 
     @auto_attr
     def md(self):
-        """
+        r"""
         Mean diffusivity (MD) calculated from cached eigenvalues.
 
         Returns
@@ -934,7 +934,7 @@ def md(self):
 
     @auto_attr
     def rd(self):
-        """
+        r"""
         Radial diffusivity (RD) calculated from cached eigenvalues.
 
         Returns
@@ -956,7 +956,7 @@ def rd(self):
 
     @auto_attr
     def ad(self):
-        """
+        r"""
         Axial diffusivity (AD) calculated from cached eigenvalues.
 
         Returns
@@ -978,7 +978,7 @@ def ad(self):
 
     @auto_attr
     def trace(self):
-        """
+        r"""
         Trace of the tensor calculated from cached eigenvalues.
 
         Returns
@@ -998,7 +998,7 @@ def trace(self):
 
     @auto_attr
     def planarity(self):
-        """
+        r"""
         Returns
         -------
         sphericity : array
@@ -1024,7 +1024,7 @@ def planarity(self):
 
     @auto_attr
     def linearity(self):
-        """
+        r"""
         Returns
         -------
         linearity : array
@@ -1050,7 +1050,7 @@ def linearity(self):
 
     @auto_attr
     def sphericity(self):
-        """
+        r"""
         Returns
         -------
         sphericity : array
@@ -1074,7 +1074,7 @@ def sphericity(self):
         return sphericity(self.evals)
 
     def odf(self, sphere):
-        """
+        r"""
         The diffusion orientation distribution function (dODF). This is an
         estimate of the diffusion distance in each direction
 
@@ -1105,7 +1105,9 @@ def odf(self, sphere):
 
         .. [Descoteaux2008] Descoteaux, M. (2008). PhD Thesis: High Angular
            Resolution Diffusion MRI: from Local Estimation to Segmentation and
-           Tractography. ftp://ftp-sop.inria.fr/athena/Publications/PhDs/descoteaux_thesis.pdf
+           Tractography.
+           ftp://ftp-sop.inria.fr/athena/Publications/PhDs/descoteaux_thesis.pdf
+
         """
         odf = np.zeros((self.evals.shape[:-1] + (sphere.vertices.shape[0],)))
         if len(self.evals.shape) > 1:
@@ -1313,7 +1315,7 @@ def wrapped_fit_tensor(design_matrix, data, return_S0_hat=False,
 
 @iter_fit_tensor()
 def wls_fit_tensor(design_matrix, data, return_S0_hat=False):
-    """
+    r"""
     Computes weighted least squares (WLS) fit to calculate self-diffusion
     tensor using a linear regression model [1]_.
 
@@ -1371,6 +1373,7 @@ def wls_fit_tensor(design_matrix, data, return_S0_hat=False):
     .. [1] Chung, SW., Lu, Y., Henry, R.G., 2006. Comparison of bootstrap
        approaches for estimation of uncertainties of DTI parameters.
        NeuroImage 33, 531-541.
+
     """
     tol = 1e-6
     data = np.asarray(data)
@@ -1391,7 +1394,7 @@ def wls_fit_tensor(design_matrix, data, return_S0_hat=False):
 
 @iter_fit_tensor()
 def ols_fit_tensor(design_matrix, data, return_S0_hat=False):
-    """
+    r"""
     Computes ordinary least squares (OLS) fit to calculate self-diffusion
     tensor using a linear regression model [1]_.
 
@@ -1470,7 +1473,7 @@ def _ols_fit_matrix(design_matrix):
 
 def _nlls_err_func(tensor, design_matrix, data, weighting=None,
                    sigma=None):
-    """
+    r"""
     Error function for the non-linear least-squares fit of the tensor.
 
     Parameters
@@ -1498,14 +1501,14 @@ def _nlls_err_func(tensor, design_matrix, data, weighting=None,
 
     Notes
     -----
-    The Geman-McClure M-estimator is described as follows [1]_ (page 1089): "The
-    scale factor C affects the shape of the GMM [Geman-McClure M-estimator]
-    weighting function and represents the expected spread of the residuals
-    (i.e., the SD of the residuals) due to Gaussian distributed noise. The
-    scale factor C can be estimated by many robust scale estimators. We used
-    the median absolute deviation (MAD) estimator because it is very robust to
-    outliers having a 50% breakdown point (6,7). The explicit formula for C
-    using the MAD estimator is:
+    The Geman-McClure M-estimator is described as follows [1]_ (page 1089):
+    "The scale factor C affects the shape of the GMM
+    [Geman-McClure M-estimator] weighting function and represents the expected
+    spread of the residuals (i.e., the SD of the residuals) due to Gaussian
+    distributed noise. The scale factor C can be estimated by many robust scale
+    estimators. We used the median absolute deviation (MAD) estimator because
+    it is very robust to outliers having a 50% breakdown point (6,7).
+    The explicit formula for C using the MAD estimator is:
 
     .. math ::