Sirt documentation improvements

Wrappers/Python/cil/optimisation/algorithms/SIRT.py

@@ -37,10 +37,10 @@ class SIRT(Algorithm):
 
     The SIRT algorithm is
 
-    .. math:: x^{k+1} =  \mathrm{proj}_{C}( x^{k} + \omega * D ( A^{T} ( M * (b - Ax^{k}) ) ) ),
+    .. math:: x^{k+1} =  \mathrm{proj}_{C}( x^{k} + \omega  D ( A^{T} ( M  (b - Ax^{k}) ) ) ),
 
     where,
-    :math:`M = \frac{1}{A*\mathbb{1}}`,
+    :math:`M = \frac{1}{A\mathbb{1}}`,
     :math:`D = \frac{1}{A^{T}\mathbb{1}}`,
     :math:`\mathbb{1}` is a :code:`DataContainer` of ones,
     :math:`\mathrm{prox}_{C}` is the projection over a set :math:`C`,
@@ -77,21 +77,22 @@ class SIRT(Algorithm):
 
     The preconditioning arrays (weights) :code:`M` and :code:`D` used in SIRT are defined as
 
-    .. math:: M = \frac{1}{A*\mathbb{1}} = \frac{1}{\sum_{j}a_{i,j}}
+    .. math:: M = \frac{1}{A\mathbb{1}} = \frac{1}{\sum_{j}a_{i,j}}
 
-    .. math:: D = \frac{1}{A*\mathbb{1}} = \frac{1}{\sum_{i}a_{i,j}}
+    .. math:: D = \frac{1}{A^T\mathbb{1}} = \frac{1}{\sum_{i}a_{i,j}}
 
 
     Examples
     --------
-    .. math:: \underset{x}{\mathrm{argmin}} \frac{1}{2}\| x - d\|^{2}
+    .. math:: \underset{x}{\mathrm{argmin}} \frac{1}{2}\| Ax - d\|^{2}
 
     >>> sirt = SIRT(initial = ig.allocate(0), operator = A, data = d, max_iteration = 5)
 
     """
 
 
     def __init__(self, initial=None, operator=None, data=None, lower=None, upper=None, constraint=None, **kwargs):
+        """Constructor of SIRT algorithm"""
 
         super(SIRT, self).__init__(**kwargs)
 
@@ -140,6 +141,7 @@ def set_up(self, initial, operator, data, lower=None, upper=None, constraint=Non
 
     @property
     def relaxation_parameter(self):
+        """Get the relaxation parameter :math:`\omega`"""
         return self._relaxation_parameter
 
     @property
@@ -164,6 +166,7 @@ def set_relaxation_parameter(self, value=1.0):
 
 
     def _set_up_weights(self):
+        """Set up the preconditioning arrays M and D"""
         self.M = 1./self.operator.direct(self.operator.domain_geometry().allocate(value=1.0))
         self._Dscaled = 1./self.operator.adjoint(self.operator.range_geometry().allocate(value=1.0))
 
@@ -198,7 +201,7 @@ def update(self):
 
         r""" Performs a single iteration of the SIRT algorithm
 
-        .. math:: x^{k+1} =  \mathrm{proj}_{C}( x^{k} + \omega * D ( A^{T} ( M * (b - Ax) ) ) )
+        .. math:: x^{k+1} =  \mathrm{proj}_{C}( x^{k} + \omega  D ( A^{T} ( M (b - Ax) ) ) )
 
         """