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</style></head><body><div class="content"><h2>Contents</h2><div><ul><li><a href="#2">Parameter Sweep of ODEs</a></li><li><a href="#3">Initialize Problem</a></li><li><a href="#4">Parameter Sweep</a></li><li><a href="#5">Visualize</a></li></ul></div><pre class="codeinput"><span class="keyword">function</span> [peakVals,mainComputationTime,nVals,aVals]=paramSweepParallel(nNum,aNum,hTopAxes)
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</pre><h2>Parameter Sweep of ODEs<a name="2"></a></h2><p>This is a parameter sweep study of a 2nd order ODE system.</p><p><img src="paramSweepParallel_eq65211.png" alt="$m\ddot{x} + b\dot{x} + kx = 0$"></p><p>We solve the ODE for a time span of 0 to 25 seconds, with initial conditions <img src="paramSweepParallel_eq62808.png" alt="$x(0) = 0$"> and <img src="paramSweepParallel_eq08342.png" alt="$\dot{x}(0) = 1$">. We sweep the parameters <img src="paramSweepParallel_eq28812.png" alt="$b$"> and <img src="paramSweepParallel_eq86607.png" alt="$k$"> and record the peak values of <img src="paramSweepParallel_eq43551.png" alt="$x$"> for each condition. At the end, we plot a surface of the results.</p><pre class="codeinput"><span class="comment">% SCd</span>
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<span class="keyword">if</span> ~nargin
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nNum = 5;
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aNum = 5;
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hTopAxes = gca;
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<span class="keyword">end</span>
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</pre><img vspace="5" hspace="5" src="paramSweepParallel_01.png" alt=""> <h2>Initialize Problem<a name="3"></a></h2><pre class="codeinput">nVals = round(linspace(10, 20, nNum)); <span class="comment">% number of segments</span>
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aVals = linspace(1, 200, aNum); <span class="comment">% cross sectional area</span>
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[nGrid, aGrid] = meshgrid(nVals, aVals);
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peakVals = nan(size(aGrid));
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</pre><h2>Parameter Sweep<a name="4"></a></h2><pre class="codeinput">t0 = tic;
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<span class="keyword">parfor</span> ii = 1:numel(aGrid)
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<span class="comment">% Solve ODE</span>
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Y=trussCantilever(nGrid(ii),aGrid(ii));
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<span class="comment">% Determine peak deflection in Y direction</span>
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peakVals(ii) = max(Y(:,2));
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<span class="keyword">end</span>
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mainComputationTime = toc(t0);
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</pre><pre class="codeoutput">Starting parallel pool (parpool) using the 'local' profile ... connected to 4 workers.
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</pre><h2>Visualize<a name="5"></a></h2><pre class="codeinput"><span class="keyword">if</span> ~isempty(hTopAxes)
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visualizeParamSweep(hTopAxes,nVals, aVals, peakVals);
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<span class="keyword">end</span>
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</pre><pre class="codeoutput">ans =
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1.0e-03 *
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0.0731 0.0342 0.0179 0.0195 0.0187
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0.2926 0.1737 0.1244 0.0790 0.0602
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0.2897 0.1861 0.1397 0.0948 0.0735
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0.2555 0.1783 0.1391 0.0956 0.0768
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0.2257 0.1634 0.1322 0.0952 0.0758
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</pre><img vspace="5" hspace="5" src="paramSweepParallel_02.png" alt=""> <p class="footer">Copyright 2009-2013 The MathWorks, Inc.<br><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB® R2013b</a><br></p></div><!--
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##### SOURCE BEGIN #####
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function [peakVals,mainComputationTime,nVals,aVals]=paramSweepParallel(nNum,aNum,hTopAxes)
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%% Parameter Sweep of ODEs
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% This is a parameter sweep study of a 2nd order ODE system.
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%
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% $m\ddot{x} + b\dot{x} + kx = 0$
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%
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% We solve the ODE for a time span of 0 to 25 seconds, with initial
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% conditions $x(0) = 0$ and $\dot{x}(0) = 1$. We sweep the parameters $b$
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% and $k$ and record the peak values of $x$ for each condition. At the end,
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% we plot a surface of the results.
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%
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% Copyright 2009-2013 The MathWorks, Inc.
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% SCd
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if ~nargin
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nNum = 5;
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aNum = 5;
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hTopAxes = gca;
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end
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%% Initialize Problem
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nVals = round(linspace(10, 20, nNum)); % number of segments
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aVals = linspace(1, 200, aNum); % cross sectional area
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[nGrid, aGrid] = meshgrid(nVals, aVals);
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peakVals = nan(size(aGrid));
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%% Parameter Sweep
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t0 = tic;
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parfor ii = 1:numel(aGrid)
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% Solve ODE
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Y=trussCantilever(nGrid(ii),aGrid(ii));
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% Determine peak deflection in Y direction
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peakVals(ii) = max(Y(:,2));
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end
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mainComputationTime = toc(t0);
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%% Visualize
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if ~isempty(hTopAxes)
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visualizeParamSweep(hTopAxes,nVals, aVals, peakVals);
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end
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##### SOURCE END #####
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