Doc consistency fixes

Author: Steven-Roberts

docs/conf.py

@@ -26,6 +26,7 @@
 primary_domain = 'mat'
 matlab_src_dir = '../toolbox'
 matlab_keep_package_prefix = False
+matlab_auto_link = 'basic'
 
 autodoc_default_options = {
     'member-order': 'bysource',

docs/references.bib

@@ -55,17 +55,16 @@ @Article{PR74
 }
 
 
-@Article{Rob67,
+@Article{Rob66,
     title={The Solution of a Set of Reaction Rate Equations},
     author={Robertson, H.H.},
     journal={Walsh, J., Ed., Numerical Analysis, An introduction},
-    year={1967},
+    year={1966},
     pages= {178--182},
-    publisher = "Academic Press",
-    address   = "Cambridge, Massachusetts",
+    volume={178182},
+    publisher = {Academic Press}
 }
 
-
 @article{SLH70,
     author = {Seinfeld, J. H. and Lapidus, Leon and Hwang, Myungkyu},
     title = {Review of Numerical Integration Techniques for Stiff Ordinary Differential Equations},

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

@@ -1,10 +1,10 @@
 classdef Canonical < otp.ascherlineardae.AscherLinearDAEProblem
-    % The problem defined by Uri Ascher in :cite:p:`Asc89` (sec. 2) which uses time span $t \in [0, 1]$ and intial 
+    % The problem defined by Uri Ascher in :cite:p:`Asc89` (sec. 2) which uses time span $t ∈ [0, 1]$ and intial 
     % condition $[y_0, z_0]^T = [1, β]^T$.
-    % 
+
     methods
         function obj = Canonical(varargin)
-            % Create the Canonical CUSP problem object.
+            % Create the Canonical Ascher Linear DAE problem object.
             %
             % Parameters
             % ----------
@@ -16,7 +16,6 @@
             params = otp.ascherlineardae.AscherLinearDAEParameters('Beta', 1, varargin{:});
             y0 = [1; params.Beta];
             tspan = [0.0; 1.0];
-            
             obj = obj@otp.ascherlineardae.AscherLinearDAEProblem(tspan, y0, params);
         end
     end

toolbox/+otp/+ascherlineardae/+presets/Petzold.m

@@ -1,15 +1,14 @@
 classdef Petzold < otp.ascherlineardae.AscherLinearDAEProblem
     % The Petzold DAE example :cite:p:`Pet86` as a special case of the Ascher linear DAE problem. This preset uses time
-    % span $t \in [0, 1]$ and $β = 0 $ with the initial condition $[y_0, z_0]^T = [1, 0]^T $.
-    % 
+    % span $t ∈ [0, 1]$ and $β = 0 $ with the initial condition $[y_0, z_0]^T = [1, 0]^T$.
+
     methods
-        function obj = Petzold
-            % Create the Petzold example of the Ascher linear DAE problem object.
+        function obj = Petzold()
+            % Create the Petzold Ascher Linear DAE problem object.
 
             params = otp.ascherlineardae.AscherLinearDAEParameters('Beta', 0);
             y0 = [1; params.Beta];
             tspan = [0.0; 1.0];
-            
             obj = obj@otp.ascherlineardae.AscherLinearDAEProblem(tspan, y0, params);
         end
     end

toolbox/+otp/+ascherlineardae/+presets/Stiff.m

@@ -1,15 +1,14 @@
 classdef Stiff < otp.ascherlineardae.AscherLinearDAEProblem
     % The Stiff example from :cite:p:`Asc89`. A variant of the Ascher linear DAE problem which uses time span 
-    % $t \in [0, 1]$ and $β = 100$ with the initial condition $[y_0, z_0]^T = [1, 100]^T$.
-    % 
+    % $t ∈ [0, 1]$ and $β = 100$ with the initial condition $[y_0, z_0]^T = [1, 100]^T$.
+
     methods
-        function obj = Stiff
-            % Create the stiff example of the Ascher linear DAE problem object.
+        function obj = Stiff()
+            % Create the stiff Ascher Linear DAE problem object.
 
             params = otp.ascherlineardae.AscherLinearDAEParameters('Beta', 100);
             y0 = [1; params.Beta];
             tspan = [0.0; 1.0];
-            
             obj = obj@otp.ascherlineardae.AscherLinearDAEProblem(tspan, y0, params);
         end
     end

toolbox/+otp/+ascherlineardae/AscherLinearDAEProblem.m

@@ -1,16 +1,16 @@
 classdef AscherLinearDAEProblem < otp.Problem
-    % A linear differential-algebraic problem with time-dependant mass matrix.
+    % A linear differential-algebraic problem with a time-dependant mass matrix.
     %
     % The Ascher linear DAE Problem :cite:p:`Asc89` is an index-1 differential-agebraic equation given by
     %
     % $$
     % \begin{bmatrix}
     % 1 & -t \\
     % 0 & 0
-    % \end{bmatrix} \begin{bmatrix} y'(t) \\ z'(t) \end{bmatrix} = \left[ \begin{array}{cc}
+    % \end{bmatrix} \begin{bmatrix} y'(t) \\ z'(t) \end{bmatrix} = \begin{bmatrix}
     % -1 & 1+t \\
     % β & -1-β t
-    % \end{array}\right] \begin{bmatrix} y(t) \\ z(t) \end{bmatrix} + \begin{bmatrix}
+    % \end{bmatrix} \begin{bmatrix} y(t) \\ z(t) \end{bmatrix} + \begin{bmatrix}
     % 0 \\
     % \sin(t)
     % \end{bmatrix}.
@@ -20,10 +20,11 @@
     %
     % $$
     % \begin{bmatrix} y(t)\\ z(t) \end{bmatrix} = \begin{bmatrix}
-    % t \sin(t) + (1 + β  t) e^{-t}\\
-    % β  e^{-t} + \sin(t)
+    % t \sin(t) + (1 + β t) e^{-t}\\
+    % β e^{-t} + \sin(t)
     % \end{bmatrix}.
     % $$
+    %
     % This DAE problem can be used to investigate the convergence of implcit time-stepping methods due to its stiffness
     % and time-dependant mass matrix.
     %

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

@@ -1,14 +1,14 @@
 classdef Canonical < otp.cusp.CUSPProblem
-    % The CUSP configuration from :cite:p:`HW96` (pp. 147-148) which uses time span $t \in [0, 1.1]$, $N = 32$ grid
-    % cells, and initial conditions
+    % The CUSP configuration from :cite:p:`HW96` (pp. 147-148) which uses time span $t ∈ [0, 1.1]$, $N = 32$ grid cells,
+    % and initial conditions
     %
     % $$
     % y_i(0) &= 0 ,\\
-    % a_i(0) &= -2 \cos\left( \frac{2 i \pi}{N} \right), \\
-    % b_i(0) &= 2 \sin\left( \frac{2 i \pi}{N} \right), \\
+    % a_i(0) &= -2 \cos\left( \frac{2 i π}{N} \right), \\
+    % b_i(0) &= 2 \sin\left( \frac{2 i π}{N} \right), \\
     % $$
     %
-    % for $i = 1, \dots, N$. The parameters are $ε = 10^{-4}$ and $σ = \frac{1}{144}$.
+    % for $i = 1, …, N$. The parameters are $ε = 10^{-4}$ and $σ = \frac{1}{144}$.
 
     methods
         function obj = Canonical(varargin)
@@ -22,11 +22,6 @@
             %    - ``N`` – The number of cells in the spatial discretization.
             %    - ``epsilon`` – Value of $ε$.
             %    - ``sigma`` – Value of $σ$.
-            %
-            % Returns
-            % -------
-            % obj : CUSPProblem
-            %    The constructed problem.
 
             p = inputParser;
             p.addParameter('N', 32);

toolbox/+otp/+cusp/CUSPProblem.m

@@ -10,7 +10,7 @@
     % $$
     %
     %
-    % where $v = u / (u + 0.1)$ and $u = (y - 0.7)(y - 1.3)$. The spatial domain $x \in [0, 1]$ has period boundary
+    % where $v = u / (u + 0.1)$ and $u = (y - 0.7)(y - 1.3)$. The spatial domain $x ∈ [0, 1]$ has period boundary
     % conditions. Discretization with second order finite difference on a grid with $N$ cells gives
     %
     % $$
@@ -19,7 +19,7 @@
     % b'_i &= (1 - a_i^2) b_i - a_i - 0.4 y_i + 0.035 v_i + σ N^2  (b_{i-1} - 2 b_i + b_{i+1}),
     % $$
     %
-    % where $i = 1, \dots, N$. Values at cell indices $i=0, N+1$ are specificied by the periodic boundary conditions.
+    % where $i = 1, …, N$. Values at cell indices $i=0, N+1$ are specificied by the periodic boundary conditions.
     %
     % Notes
     % -----
@@ -88,11 +88,7 @@
             %    The initial conditions.
             % parameters : CUSPParameters
             %    The parameters.
-            %
-            % Returns
-            % -------
-            % obj : CUSPProblem
-            %    The constructed problem.
+            
             obj@otp.Problem('CUSP', [], timeSpan, y0, parameters);
         end
     end

toolbox/+otp/+lorenz63/+presets/Canonical.m

@@ -1,6 +1,5 @@
 classdef Canonical < otp.lorenz63.Lorenz63Problem
-    % Original Lorenz '63 preset presented in :cite:p:`Lor63`
-    % which uses time span $t \in [0, 60]$, $σ = 10$, $ρ = 28$, 
+    % Original Lorenz '63 preset presented in :cite:p:`Lor63` which uses time span $t ∈ [0, 60]$, $σ = 10$, $ρ = 28$, 
     % $β = 8/3$, and intial conditions $y_0 = [0, 1, 0]^T$.
 
     methods
@@ -12,14 +11,13 @@
             % varargin
             %    A variable number of name-value pairs. The accepted names are
             %
-            %    - ``sigma`` – Value of $σ$.
-            %    - ``rho`` – Value of $ρ$.
-            %    - ``beta`` – Value of $β$.
+            %    - ``Sigma`` – Value of $σ$.
+            %    - ``Rho`` – Value of $ρ$.
+            %    - ``Beta`` – Value of $β$.
 
             y0    = [0; 1; 0];
             tspan = [0 60];
             params = otp.lorenz63.Lorenz63Parameters('Sigma', 10, 'Rho', 28, 'Beta', 8/3, varargin{:});
-            
             obj = obj@otp.lorenz63.Lorenz63Problem(tspan, y0, params);            
         end
     end

toolbox/+otp/+lorenz63/+presets/LimitCycle.m

@@ -1,19 +1,16 @@
 classdef LimitCycle < otp.lorenz63.Lorenz63Problem
-    % Lorenz '63 preset limit cycle, a non-chaotic preset, from :cite:p:`Str18` 
-    % which uses time span $t \in [0, 60]$, $σ = 10$, $ρ = 350$, 
-    % $β = 8/3$, and intial conditions $y_0 = [0, 1, 0]^T$.
+    % Lorenz '63 preset limit cycle, a non-chaotic preset, from :cite:p:`Str18` which uses time span $t ∈ [0, 60]$,
+    % $σ = 10$, $ρ = 350$, $β = 8/3$, and intial conditions $y_0 = [0, 1, 0]^T$.
 
     methods
         function obj = LimitCycle
             % Create the LimitCycle Lorenz '63 problem object.
 
             % We use Lorenz's initial conditions and timespan as Strogatz
             % does not specify those in his book.
-            
             y0    = [0; 1; 0];
             tspan = [0 60];
             params = otp.lorenz63.Lorenz63Parameters('Sigma', 10, 'Rho', 350, 'Beta', 8/3);
-            
             obj = obj@otp.lorenz63.Lorenz63Problem(tspan, y0, params);            
         end
     end