fixes based on past conversations

Author: AndreyAPopov

toolbox/+otp/+lorenz96/+presets/Canonical.m

@@ -1,23 +1,21 @@
 classdef Canonical < otp.lorenz96.Lorenz96Problem
     % Original Lorenz '96 preset presented in :cite:p:`Lor96`
     % which uses time span $t \in [0, 720]$, $N = 40$, $F=8$, and initial
-    % conditions of $y_i = 8$ for all $i$ except for $y_20=8.008$. 
+    % conditions of $y_i = 8$ for all $i$ except for $y_{20}=8.008$. 
 
     methods
         function obj = Canonical(varargin)
             % Create a Canonial problem object.
             %
             % Parameters
             % ----------
-            % Size : numeric(1, 1)
-            %    The size of the problem as a positive integer.
-            % Forcing : numeric(N, 1)
-            %    The forcing as a vector of N constants.
+            % varargin
+            %    A variable number of name-value pairs. The accepted names are
+            %
+            %    - ``Size`` – The size of the problem as a positive integer.
+            %    - ``Forcing`` – The forcing as a scalar, vector of N constants, or as a
+            %    function.
             %
-            % Returns
-            % -------
-            % obj : Canonial
-            %    The constructed problem.
 
             p = inputParser;
             p.addParameter('Size', 40, @isscalar);

toolbox/+otp/+lorenz96/+presets/PopovSandu.m

@@ -1,29 +1,30 @@
 classdef PopovSandu < otp.lorenz96.Lorenz96Problem
     % A preset that has a cyclic forcing function that is different for
     % every variable. This preset was created for :cite:p:`PS19`.
-    % This preset uses time span $t \in [0, 720]$, $N = 40$, $F=8$, 
-    % four partitions, a forcing period of one time unit, and initial
-    % conditions of $y_i = 8$ for all $i$ except for $y_20=8.008$. 
+    % This preset uses time span $t \in [0, 720]$, $N = 40$, and initial
+    % conditions of $y_i = 8$ for all $i$ except for $y_{20}=8.008$. 
+    % The forcing, as a function of time is given by
+    %
+    % $$
+    % f(t) = 8 + 4\cos(2 \pi \omega (t+\text{mod}(i - 1, q)/q))
+    % $$
+    %
+    % where by default $q=4$ is the number of partitions, and $\omega = 1$
+    % is a forcing period of one time unit.
 
     methods
         function obj = PopovSandu(varargin)
             % Create a PopovSandu problem object.
             %
             % Parameters
             % ----------
-            % Size : numeric(1, 1)
-            %    The size of the problem as a positive integer.
-            % Partitions : numeric(1, 1)
-            %    The number of partitions into which to divide the
-            %    variables.
-            % ForcingPeriod : numeric(1, 1)
-            %    The period of the forcing function in radians per unit
-            %    time.
+            % varargin
+            %    A variable number of name-value pairs. The accepted names are
+            %
+            %    - ``Size`` – The size of the problem as a positive integer.
+            %    - ``Partitions`` – The number of partitions into which to divide the variables.
+            %    - ``ForcingPeriod`` – The period of the forcing function in radians per unit time.
             %
-            % Returns
-            % -------
-            % obj : PopovSandu
-            %    The constructed problem.
 
             p = inputParser;
 

toolbox/+otp/+lorenz96/Lorenz96Problem.m

@@ -1,22 +1,23 @@
 classdef Lorenz96Problem <  otp.Problem
-    % A chaotic system modeling the transfer of some quantity along some
-    % longitude.
-    %
-    %
+    % A chaotic system modeling nonlinear transfer of a dimensionless
+    % qauntity along a cyclic one dimensional domain.
+    % 
     % The $N$ variable dynamics :cite:p:`Lor96` are represented by the equation,
     %
     % $$
-    % y_i' = -y_{i-1}\left(y_{i-2} - y_{i+1}\right) - y_i + f(t),\quad i \in \mathbb{Z}_N,
+    % y_i' = -y_{i-1}\left(y_{i-2} - y_{i+1}\right) - y_i + f(t), \quad i = 1, \dots, N,
     % $$
-    %
-    % that exhibits chaotic behavior for certain values of the forcing function $f$.
+    % 
+    % where $y_0 = y_N$, $y_{-1} = y_{N - 1}$, and $y_{N + 1} = y_2$, exhibits 
+    % chaotic behavior for certain pairs of values of the dimension $N$ and
+    % forcing function $f$.
     %
     % Notes
     % -----
     % +---------------------+-----------------------------------------------------------+
     % | Type                | ODE                                                       |
     % +---------------------+-----------------------------------------------------------+
-    % | Number of Variables | $N$                                                       |
+    % | Number of Variables | $N$ for any postive integer four or greater               |
     % +---------------------+-----------------------------------------------------------+
     % | Stiff               | no                                                        |
     % +---------------------+-----------------------------------------------------------+
@@ -25,7 +26,7 @@
     % -------
     % >>> problem = otp.lorenz96.presets.Canonical('Forcing', @(t) 8 + 4*sin(t));
     % >>> sol = problem.solve();
-    % >>> problem.plotPhaseSpace(sol);
+    % >>> problem.movie(sol);
     %
     % See also
     % --------
@@ -43,15 +44,11 @@
             % ----------
             % timeSpan : numeric(1, 2)
             %    The start and final time.
-            % y0 : numeric(N, 1)
+            % y0 : numeric(:, 1)
             %    The initial conditions.
             % parameters : Lorenz96Parameters
             %    The parameters.
             %
-            % Returns
-            % -------
-            % obj : Lorenz96Problem
-            %    The constructed problem.
             obj@otp.Problem('Lorenz 96', [], timeSpan, y0, parameters);
         end
     end