Merge pull request #542 from ego-thales/develop

SRSF formula doc fix

skfda/misc/metrics/_fisher_rao.py

@@ -61,8 +61,8 @@ class FisherRaoDistance():
 
     .. math::
         d_{FR}(f_i, f_j) = \| q_i - q_j \|_2 =
-        \left ( \int_0^1 sgn(\dot{f_i}(t))\sqrt{|\dot{f_i}(t)|} -
-        sgn(\dot{f_j}(t))\sqrt{|\dot{f_j}(t)|} dt \right )^{\frac{1}{2}}
+        \left ( \int_0^1 sgn(f_i'(t))\sqrt{|f_i'(t)|} -
+        sgn(f_j'(t))\sqrt{|f_j'(t)|} dt \right )^{\frac{1}{2}}
 
     If the observations are distributions of random variables the distance will
     match with the usual Fisher-Rao distance in non-parametric form for
@@ -164,7 +164,7 @@ def fisher_rao_amplitude_distance(
     given by
 
     .. math::
-        \mathcal{R}(\gamma) = \|\sqrt{\dot{\gamma}}- 1 \|_{\mathbb{L}^2}^2
+        \mathcal{R}(\gamma) = \|\sqrt{\gamma'}- 1 \|_{\mathbb{L}^2}^2
 
     See the :footcite:`srivastava+klassen_2016_functionala` for a
     detailed explanation.
@@ -260,7 +260,7 @@ def fisher_rao_phase_distance(
 
     .. math::
         d_{P}(f_i, f_j) = d_{FR}(\gamma_{ij}, \gamma_{id}) =
-        arcos \left ( \int_0^1 \sqrt {\dot \gamma_{ij}(t)} dt \right )
+        arcos \left ( \int_0^1 \sqrt {\gamma_{ij}'(t)} dt \right )
 
     where :math:`\gamma_{id}` is the identity warping.
 
@@ -346,7 +346,7 @@ def _fisher_rao_warping_distance(
 
     .. math::
         d_{\Gamma}(\gamma_i, \gamma_j) = cos^{-1} \left ( \int_0^1
-        \sqrt{\dot \gamma_i(t)\dot \gamma_j(t)}dt \right )
+        \sqrt{\gamma_i'(t)\gamma_j'(t)}dt \right )
 
     See :footcite:`srivastava+klassen_2016_functionala` for a detailed
     explanation.

skfda/misc/operators/_srvf.py

@@ -24,7 +24,7 @@ class SRSF(
     function, the SRSF transform is defined as
 
     .. math::
-        SRSF(f(t)) = sgn(f(t)) \sqrt{|\dot f(t)|} = q(t)
+        SRSF(f(t)) = sgn(f'(t)) \sqrt{|f'(t)|} = q(t)
 
     This representation it is used to compute the extended non-parametric
     Fisher-Rao distance between functions, wich under the SRSF representation
@@ -137,7 +137,7 @@ def transform(self, X: FDataGrid, y: object = None) -> FDataGrid:
 
         .. math::
 
-            SRSF(f(t)) = sgn(f(t)) \sqrt{\dot f(t)|} = q(t)
+            SRSF(f(t)) = sgn(f'(t)) \sqrt{f'(t)|} = q(t)
 
         Args:
             X: Functions to be transformed.
@@ -166,7 +166,7 @@ def transform(self, X: FDataGrid, y: object = None) -> FDataGrid:
         # Evaluation with the corresponding interpolation
         data_matrix = g(output_points)[..., 0]
 
-        # SRSF(f) = sign(f) * sqrt|Df| (avoiding multiple allocation)
+        # SRSF(f) = sign(f') * sqrt|f'| (avoiding multiple allocation)
         sign_g = np.sign(data_matrix)
         data_matrix = np.abs(data_matrix, out=data_matrix)
         data_matrix = np.sqrt(data_matrix, out=data_matrix)

skfda/preprocessing/registration/_fisher_rao.py

@@ -42,13 +42,13 @@ class FisherRaoElasticRegistration(
 
     .. math::
         d_{\lambda}^2(f \circ \gamma, g) = \| SRSF(f \circ \gamma)
-        \sqrt{\dot{\gamma}} - SRSF(g)\|_{\mathbb{L}^2}^2 + \lambda
+        \sqrt{\gamma'} - SRSF(g)\|_{\mathbb{L}^2}^2 + \lambda
         \mathcal{R}(\gamma)
 
     In the implementation it is used as penalty term
 
     .. math::
-        \mathcal{R}(\gamma) = \|\sqrt{\dot{\gamma}}- 1 \|_{\mathbb{L}^2}^2
+        \mathcal{R}(\gamma) = \|\sqrt{\gamma'}- 1 \|_{\mathbb{L}^2}^2
 
     Wich restrict the amount of elasticity employed in the alignment.
 

skfda/preprocessing/registration/validation.py

@@ -464,12 +464,12 @@ class SobolevLeastSquares(RegistrationScorer[FData, FData]):
     [S11-5-2-3]_:
 
     .. math::
-        sls=1 - \frac{\sum_{i=1}^{N} \int\left(\dot{\tilde{f}}_{i}(t)-
-        \frac{1}{N} \sum_{j=1}^{N} \dot{\tilde{f}}_{j}\right)^{2} dt}
-        {\sum_{i=1}^{N} \int\left(\dot{f}_{i}(t)-\frac{1}{N} \sum_{j=1}^{N}
-        \dot{f}_{j}\right)^{2} dt}
+        sls=1 - \frac{\sum_{i=1}^{N} \int\left(\tilde{f}_i'(t)-
+        \frac{1}{N} \sum_{j=1}^{N} \tilde{f}_j'\right)^{2} dt}
+        {\sum_{i=1}^{N} \int\left(f_i'(t)-\frac{1}{N} \sum_{j=1}^{N}
+        f_j'\right)^{2} dt}
 
-    where :math:`\dot{f}_i` and :math:`\dot{\tilde{f}}_i` are the derivatives
+    where :math:`f_i'` and :math:`\tilde{f}_i'` are the derivatives
     of the original and the registered data respectively.
 
     This criterion measures the total cross-sectional variance of the