2323r"""
2424Derivations from scikit-learn for Gaussian Processes.
2525
26+
2627Gaussian Process Model: Pairwise orientation angles
2728---------------------------------------------------
2829Squared Exponential covariance kernel
101102from sklearn .metrics .pairwise import cosine_similarity
102103from sklearn .utils ._param_validation import Interval , StrOptions
103104
104- BOUNDS_A : tuple [float , float ] = (0.1 , np .pi )
105- """The limits for the parameter *a*."""
105+ BOUNDS_A : tuple [float , float ] = (0.1 , 0.75 * np .pi )
106+ """The limits for the parameter *a* (angular distance) ."""
106107BOUNDS_LAMBDA : tuple [float , float ] = (1e-3 , 1000 )
107- """The limits for the parameter lambda ."""
108+ """The limits for the parameter λ (signal scaling factor) ."""
108109THETA_EPSILON : float = 1e-5
109110"""Minimum nonzero angle."""
110111LBFGS_CONFIGURABLE_OPTIONS = {"disp" , "maxiter" , "ftol" , "gtol" }
@@ -143,8 +144,7 @@ class EddyMotionGPR(GaussianProcessRegressor):
143144
144145 In principle, Scikit-Learn's implementation normalizes the training data
145146 as in [Andersson15]_ (see
146- `FSL's souce code <https://git.fmrib.ox.ac.uk/fsl/eddy/-/blob/\
147- 2480dda293d4cec83014454db3a193b87921f6b0/DiffusionGP.cpp#L218>`__).
147+ `FSL's souce code <https://git.fmrib.ox.ac.uk/fsl/eddy/-/blob/2480dda293d4cec83014454db3a193b87921f6b0/DiffusionGP.cpp#L218>`__).
148148 From their paper (p. 167, end of first column):
149149
150150 Typically one just substracts the mean (:math:`\bar{\mathbf{f}}`)
@@ -161,7 +161,7 @@ class EddyMotionGPR(GaussianProcessRegressor):
161161 I believe this is overlooked in [Andersson15]_, or they actually did not
162162 use analytical gradient-descent:
163163
164- _A note on optimisation_
164+ *A note on optimisation*
165165
166166 It is suggested, for example in Rasmussen and Williams (2006), that
167167 an optimisation method that uses derivative information should be
@@ -184,7 +184,7 @@ class EddyMotionGPR(GaussianProcessRegressor):
184184 "optimizer" : [StrOptions (SUPPORTED_OPTIMIZERS ), callable , None ],
185185 "n_restarts_optimizer" : [Interval (Integral , 0 , None , closed = "left" )],
186186 "copy_X_train" : ["boolean" ],
187- "zeromean_y " : ["boolean" ],
187+ "normalize_y " : ["boolean" ],
188188 "n_targets" : [Interval (Integral , 1 , None , closed = "left" ), None ],
189189 "random_state" : ["random_state" ],
190190 }
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