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Steven-RobertsSteven-Roberts
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Make superclass for params (#118)
* Make superclass for params * Fix param capitalization * Add docs * Update Ascher Linear DAE * Update CUSP * Update L'96 * Update Oregonator * Update PR * Update Robertson * Typo fixes * Fix Greek letters
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‎docs/structure/index.rst‎

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@@ -8,4 +8,6 @@ TODO
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:maxdepth: 1
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:glob:
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*
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problem
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rhs
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parameters

‎docs/structure/parameters.rst‎

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Parameters
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================================================================================
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.. automodule:: +otp
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.. autoclass:: Parameters
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:members:

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

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%
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% - ``Beta`` – Value of $β$.
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p = inputParser;
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p.addParameter('beta', 1);
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p.parse(varargin{:});
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opts = p.Results;
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params = otp.ascherlineardae.AscherLinearDAEParameters;
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params.Beta = opts.beta;
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y0 = [1; params.Beta];
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params = otp.ascherlineardae.AscherLinearDAEParameters('Beta', 1, varargin{:});
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y0 = [1; params.Beta];
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tspan = [0.0; 1.0];
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obj = obj@otp.ascherlineardae.AscherLinearDAEProblem(tspan, y0, params);

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

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function obj = Petzold
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% Create the Petzold example of the Ascher linear DAE problem object.
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params = otp.ascherlineardae.AscherLinearDAEParameters;
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params.Beta = 0;
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y0 = [1; params.Beta];
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params = otp.ascherlineardae.AscherLinearDAEParameters('Beta', 0);
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y0 = [1; params.Beta];
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tspan = [0.0; 1.0];
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obj = obj@otp.ascherlineardae.AscherLinearDAEProblem(tspan, y0, params);

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

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methods
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function obj = Stiff
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% Create the stiff example of the Ascher linear DAE problem object.
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params = otp.ascherlineardae.AscherLinearDAEParameters;
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params.Beta = 100;
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y0 = [1; params.Beta];
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params = otp.ascherlineardae.AscherLinearDAEParameters('Beta', 100);
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y0 = [1; params.Beta];
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tspan = [0.0; 1.0];
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obj = obj@otp.ascherlineardae.AscherLinearDAEProblem(tspan, y0, params);

‎toolbox/+otp/+ascherlineardae/AscherLinearDAEParameters.m‎

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classdef AscherLinearDAEParameters
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classdef AscherLinearDAEParameters < otp.Parameters
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% Parameters for Ascher Linear DAE problem
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properties
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% A scalar parameter $β$ in the linear model. It affects the stifness of the problem.
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Beta %MATLAB ONLY: (1,1) {mustBeNumeric} = 1
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end
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methods
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function obj = AscherLinearDAEParameters(varargin)
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% Create a Ascher Linear DAE parameters object.
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%
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% Parameters
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% ----------
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% varargin
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% A variable number of name-value pairs. A name can be any property of this class, and the subsequent
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% value initializes that property.
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obj = obj@otp.Parameters(varargin{:});
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end
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end
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end

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

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% b_i(0) &= 2 \sin\left( \frac{2 i \pi}{N} \right), \\
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% $$
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%
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% for $i = 1, \dots, N$. The parameters are $\varepsilon = 10^{-4}$ and $\sigma = \frac{1}{144}$.
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% for $i = 1, \dots, N$. The parameters are $ε = 10^{-4}$ and $σ = \frac{1}{144}$.
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methods
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function obj = Canonical(varargin)
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% A variable number of name-value pairs. The accepted names are
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%
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% - ``N`` – The number of cells in the spatial discretization.
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% - ``epsilon`` – Value of $\varepsilon$.
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% - ``sigma`` – Value of $\sigma$.
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% - ``epsilon`` – Value of $ε$.
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% - ``sigma`` – Value of $σ$.
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%
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% Returns
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% -------
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p = inputParser;
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p.addParameter('N', 32);
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p.addParameter('epsilon', 1e-4);
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p.addParameter('sigma', 1/144);
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p.parse(varargin{:});
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opts = p.Results;
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n = p.Results.N;
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params = otp.cusp.CUSPParameters;
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params.Epsilon = opts.epsilon;
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params.Sigma = opts.sigma;
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ang = 2 * pi / opts.N * (1:opts.N).';
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y0 = zeros(opts.N, 1);
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a0 = -2*cos(ang);
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b0 = 2*sin(ang);
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ang = 2 * pi * (1:n).' / n;
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y0 = zeros(n, 1);
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a0 = -2 * cos(ang);
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b0 = 2 * sin(ang);
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u0 = [y0; a0; b0];
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tspan = [0; 1.1];
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unmatched = namedargs2cell(p.Unmatched);
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params = otp.cusp.CUSPParameters('Epsilon', 1e-4, 'Sigma', 1/144, unmatched{:});
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obj = obj@otp.cusp.CUSPProblem(tspan, u0, params);
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end

‎toolbox/+otp/+cusp/CUSPParameters.m‎

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classdef CUSPParameters
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classdef CUSPParameters < otp.Parameters
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% Parameters for the CUSP problem.
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properties
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% The stiffness parameter $\varepsilon$ for the "cusp catastrophe" model.
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% The stiffness parameter $ε$ for the "cusp catastrophe" model.
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Epsilon %MATLAB ONLY: (1,1) {mustBeNumeric}
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% The diffusion coefficient $\sigma$ for all three variables.
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% The diffusion coefficient $σ$ for all three variables.
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Sigma %MATLAB ONLY: (1,1) {mustBeNumeric}
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end
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methods
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function obj = CUSPParameters(varargin)
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% Create a CUSP parameters object.
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%
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% Parameters
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% ----------
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% varargin
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% A variable number of name-value pairs. A name can be any property of this class, and the subsequent
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% value initializes that property.
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obj = obj@otp.Parameters(varargin{:});
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end
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end
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end
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‎toolbox/+otp/+cusp/CUSPProblem.m‎

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% The CUSP problem :cite:p:`HW96` (pp. 147-148) is the PDE
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%
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% $$
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% \frac{\partial y}{\partial t} &= -\frac{1}{\varepsilon} (y^3 + a y + b)
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% + \sigma \frac{\partial^2 y}{\partial x^2}, \\
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% \frac{\partial a}{\partial t} &= b + 0.07 v + \sigma \frac{\partial^2 a}{\partial x^2}, \\
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% \frac{\partial b}{\partial t} &= (1 - a^2) b - a - 0.4 y + 0.035 v + \sigma \frac{\partial^2 b}{\partial x^2},
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% \frac{\partial y}{\partial t} &= -\frac{1}{ε} (y^3 + a y + b) + σ \frac{\partial^2 y}{\partial x^2}, \\
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% \frac{\partial a}{\partial t} &= b + 0.07 v + σ \frac{\partial^2 a}{\partial x^2}, \\
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% \frac{\partial b}{\partial t} &= (1 - a^2) b - a - 0.4 y + 0.035 v + σ \frac{\partial^2 b}{\partial x^2},
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% $$
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%
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%
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% where $v = u / (u + 0.1)$ and $u = (y - 0.7)(y - 1.3)$. The spatial domain $x \in [0, 1]$ has period boundary
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% conditions. Discretization with second order finite difference on a grid with $N$ cells gives
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%
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% $$
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% y'_i &= -\frac{1}{\varepsilon} (y_i^3 + a_i y_i + b_i) + \sigma N^2 (y_{i-1} - 2 y_i + y_{i+1}) \\
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% a'_i &= b_i + 0.07 v_i + \sigma N^2 (a_{i-1} - 2 a_i + a_{i+1}) \\
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% b'_i &= (1 - a_i^2) b_i - a_i - 0.4 y_i + 0.035 v_i + \sigma N^2 (b_{i-1} - 2 b_i + b_{i+1}),
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% y'_i &= -\frac{1}{ε} (y_i^3 + a_i y_i + b_i) + σ N^2 (y_{i-1} - 2 y_i + y_{i+1}) \\
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% a'_i &= b_i + 0.07 v_i + σ N^2 (a_{i-1} - 2 a_i + a_{i+1}) \\
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% b'_i &= (1 - a_i^2) b_i - a_i - 0.4 y_i + 0.035 v_i + σ N^2 (b_{i-1} - 2 b_i + b_{i+1}),
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% $$
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%
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% where $i = 1, \dots, N$. Values at cell indices $i=0, N+1$ are specificied by the periodic boundary conditions.
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%
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% Notes
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% -----
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% +---------------------+----------------------------------------------------------------------------+
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% | Type | PDE |
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% +---------------------+----------------------------------------------------------------------------+
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% | Number of Variables | arbitrary multiple of 3 |
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% +---------------------+----------------------------------------------------------------------------+
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% | Stiff | typically, depending on $\varepsilon$, $\sigma$, and number of grid points |
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% +---------------------+----------------------------------------------------------------------------+
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% +---------------------+-------------------------------------------------------------+
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% | Type | PDE |
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% +---------------------+-------------------------------------------------------------+
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% | Number of Variables | arbitrary multiple of 3 |
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% +---------------------+-------------------------------------------------------------+
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% | Stiff | typically, depending on $ε$, $σ$, and number of grid points |
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% +---------------------+-------------------------------------------------------------+
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%
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% Example
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% -------
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end
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properties (SetAccess = private)
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% Right-hand side containing the diffusion terms and the reaction terms multiplied by $\varepsilon^{-1}$.
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% Right-hand side containing the diffusion terms and the reaction terms multiplied by $ε^{-1}$.
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%
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% This partition of the RHS is used in :cite:p:`JM17`.
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%
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% RHSNonstiff
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RHSStiff
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% Right-hand side containing the reaction terms not scaled by $\varepsilon^{-1}$.
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% Right-hand side containing the reaction terms not scaled by $ε^{-1}$.
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%
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% This partition of the RHS is used in :cite:p:`JM17`.
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%

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

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% - ``sigma`` – Value of $σ$.
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% - ``rho`` – Value of $ρ$.
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% - ``beta`` – Value of $β$.
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%
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p = inputParser;
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p.addParameter('sigma', 10);
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p.addParameter('rho', 28);
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p.addParameter('beta', 8/3);
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p.parse(varargin{:});
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opts = p.Results;
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params = otp.lorenz63.Lorenz63Parameters;
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params.Sigma = opts.sigma;
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params.Rho = opts.rho;
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params.Beta = opts.beta;
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y0 = [0; 1; 0];
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tspan = [0 60];
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params = otp.lorenz63.Lorenz63Parameters('Sigma', 10, 'Rho', 28, 'Beta', 8/3, varargin{:});
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obj = obj@otp.lorenz63.Lorenz63Problem(tspan, y0, params);
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end

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