Matlab-Programs/harmonicOscillator.m

+
+
+
+
+
+
+F = @(t,y) [y(2); -y(1)];
+
+
+y0 = [0  1]';
+
+
+
+tspan= (0:1/36:1)*2*pi;
+
+[t,y] = ode45(F,tspan,y0)
+
+
+% plot phase-plane 
+
+plot(y(:,1),y(:,2), 'o-')
+axis square
+axis(1.2*[-1 1 -1 1])
\ No newline at end of file

Matlab-Programs/isosurfaceTest.m

+[x,y,z] = meshgrid(1:20,1:20,1:20);
+data = sqrt(x.^2 + y.^2 + z.^2);
+p = patch(isosurface(x,y,z,data,20));
+isonormals(x,y,z,data,p)
+[r,g,b] = meshgrid(20:-1:1,1:20,1:20);
+isocolors(x,y,z,r/20,g/20,b/20,p)
+p.FaceColor = 'interp';
+p.EdgeColor = 'none';
+view(150,30) 
+daspect([1 1 1])
+camlight 
+lighting gouraud
\ No newline at end of file

Matlab-Programs/license.txt

+Copyright (c) 2009, Adam Auton
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+    * Redistributions in binary form must reproduce the above copyright
+      notice, this list of conditions and the following disclaimer in
+      the documentation and/or other materials provided with the distribution
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.

Matlab-Programs/ode1.m

+
+
+
+
+function yout = ode1(F,t0,h,tfinal,y0)
+% ODE1 A simple ODE solver.
+%  yout = ode1(F,t0,h,tfinal,y0) uses Euler's 
+%  method with fixed step size h on the intervall
+%  t0 <=t <= tfinal
+%  to solve 
+%     dy/dt = F(t,y) 
+%  with y(t0) = y0
+
+    y = y0;
+    yout = y;
+    for t = t0 : h : tfinal-h
+       s = F(t,y);
+       y = y+ h*s;
+       yout = [yout, y];
+    end
+end
+

Matlab-Programs/ode2.m

+
+
+
+
+function yout = ode2(F,t0,h,tfinal,y0)
+% ODE1 A simple ODE solver.
+%  yout = ode1(F,t0,h,tfinal,y0) uses Euler's 
+%  method with fixed step size h on the intervall
+%  t0 <=t <= tfinal
+%  to solve 
+%     dy/dt = F(t,y) 
+%  with y(t0) = y0
+
+    y = y0;
+    yout = y;
+    
+    for t = t0 : h : tfinal-h
+       s1 = F(t,y);
+       s2 = F(t + h/2 , y+ (h/2)*s1);
+       y = y+ h*s2;
+       yout = [yout, y];
+    end
+end
+

Matlab-Programs/ode2t.m

+
+
+
+
+function yout = ode2t(F,t0,h,tfinal,y0)
+% ODE1 A simple ODE solver.
+%  yout = ode1(F,t0,h,tfinal,y0) uses Euler's 
+%  method with fixed step size h on the intervall
+%  t0 <=t <= tfinal
+%  to solve 
+%     dy/dt = F(t,y) 
+%  with y(t0) = y0
+
+    y = y0;
+    yout = y;
+    
+    for t = t0 : h : tfinal-h
+       s1 = F(t,y);
+       s2 = F(t + h , y+ h*s1);
+       y = y+ h*(s2+s1)/2;
+       yout = [yout, y];
+    end
+end
+

Matlab-Programs/redblue.m

+function c = redblue(m)
+%REDBLUE    Shades of red and blue color map
+%   REDBLUE(M), is an M-by-3 matrix that defines a colormap.
+%   The colors begin with bright blue, range through shades of
+%   blue to white, and then through shades of red to bright red.
+%   REDBLUE, by itself, is the same length as the current figure's
+%   colormap. If no figure exists, MATLAB creates one.
+%
+%   For example, to reset the colormap of the current figure:
+%
+%             colormap(redblue)
+%
+%   See also HSV, GRAY, HOT, BONE, COPPER, PINK, FLAG, 
+%   COLORMAP, RGBPLOT.
+
+%   Adam Auton, 9th October 2009
+
+if nargin < 1, m = size(get(gcf,'colormap'),1); end
+
+if (mod(m,2) == 0)
+    % From [0 0 1] to [1 1 1], then [1 1 1] to [1 0 0];
+    m1 = m*0.5;
+    r = (0:m1-1)'/max(m1-1,1);
+    g = r;
+    r = [r; ones(m1,1)];
+    g = [g; flipud(g)];
+    b = flipud(r);
+else
+    % From [0 0 1] to [1 1 1] to [1 0 0];
+    m1 = floor(m*0.5);
+    r = (0:m1-1)'/max(m1,1);
+    g = r;
+    r = [r; ones(m1+1,1)];
+    g = [g; 1; flipud(g)];
+    b = flipud(r);
+end
+
+c = [r g b]; 
+

Matlab-Programs/resources/addons_core.xml

+<?xml version="1.0" encoding="UTF-8"?>
+<addonCore>
+  <label>Red Blue Colormap</label>
+  <version>1.0.0.0</version>
+  <type>zip</type>
+  <identifier>e5698820-4a80-11e4-9553-005056977bd0</identifier>
+  <createdBy name="Adam Auton"/>
+  <image>resources/screenshot.png</image>
+</addonCore>

Matlab-Programs/resources/matlab_path_entries.xml

+<?xml version="1.0" encoding="UTF-8"?>
+<paths>
+  <path>.</path>
+</paths>

Matlab-Programs/resources/metadata.xml

+<?xml version="1.0" encoding="UTF-8"?>
+<addOn>
+  <identifier>e5698820-4a80-11e4-9553-005056977bd0</identifier>
+  <displayType>Function</displayType>
+  <translatedDisplayType>
+    <en_US>Function</en_US>
+    <ja_JP>関数</ja_JP>
+    <ko_KR>함수</ko_KR>
+    <zh_CN>函数</zh_CN>
+  </translatedDisplayType>
+  <name>Red Blue Colormap</name>
+  <author>Adam Auton</author>
+  <version>1.0.0.0</version>
+  <downloadUrl>https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/25536/versions/1/download/zip?src=addons_ml_desktop_install&amp;profile_id=14169257&amp;license=40758619&amp;release_family=R2020b</downloadUrl>
+  <licenseUrl>https://addons.mathworks.com/registry/v1/e5698820-4a80-11e4-9553-005056977bd0/1.0.0.0/-/license</licenseUrl>
+  <previewImageUrl>https://www.mathworks.com/responsive_image/160/120/0/0/0/cache/matlabcentral/mlc-downloads/downloads/submissions/25536/versions/1/screenshot.png</previewImageUrl>
+  <releaseNotesUrl>https://www.mathworks.com/add-ons/e5698820-4a80-11e4-9553-005056977bd0/d1034754-ea44-08f8-b658-22b590dfae7e/releaseNotes</releaseNotesUrl>
+  <installationFolder>Functions</installationFolder>
+</addOn>

Matlab-Programs/scriptTest.m

+clc
+clear all
+
+
+mu_1 = 1;
+rho_1 = 1;
+
+
+% HYPERBOLIC 
+b1 = @(a,b,t) (mu_1*rho_1/4).*(b./(t+(1-t).*b)).*(1-t.*(1+a));
+b2 = @(a,b,t) mu_1.*(rho_1/8).*(1-t.*(1+b.*a));
+
+h = @(a,b,t) b1(a,b,t).*b2(a,b,t);
+
+
+% fix alpha
+% a=1;
+
+
+% fix theta , value in (0,1)
+theta= 0.55;
+
+
+
+
+% ELLIPTIC 
+
+q1 = @(b,t) mu_1.*(b./(t+(1-t).*b)); %harmonic mean
+q2 = @(b,t) mu_1.*((1-t)+t.*b);    % mu_bar
+q3 = @(b,t) q1(b,t);
+
+b1 = @(a,b,t) (mu_1*rho_1/4).*(b./(t+(1-t).*b)).*(1-t.*(1+a));
+b2 = @(a,b,t) mu_1.*(rho_1/8).*(1-t.*(1+b.*a));
+
+a1 = @(a,b,t) (q2(b,t).*q1(b,t).*b1(a,b,t) - q3(b,t).*q2(b,t).*b2(a,b,t))./(q1(b,t).*q2(b,t)-q3(b,t).^2); 
+a2 = @(a,b,t) (q1(b,t).*q2(b,t).*b2(a,b,t) - q3(b,t).*q1(b,t).*b1(a,b,t))./(q1(b,t).*q2(b,t)-q3(b,t).^2); 
+
+e = @(a,b,t) a1(a,b,t).*a2(a,b,t);
+
+
+x = -20:0.2:20;
+y = 0:0.1:20;
+[X,Y] = meshgrid(x,y);
+T = theta*ones(size(X));
+
+
+V = e(X,Y,T);
+
+V2 = h(X,Y,T);
+
+% COLOR-Test
+% C = double((V>=0));
+% 
+% surf(X,Y,V,C, 'FaceAlpha',0.5,'EdgeColor','none') 
+% xlabel('alpha');
+% ylabel('beta');
+% axis([-20 20 0 20 -100 100])
+% % colorbar
+% hold on
+% 
+% C2 = double((V2>=0));
+% surf(X,Y,V2,C2,'FaceAlpha',0.5,'EdgeColor','none') 
+% xlabel('alpha');
+% ylabel('beta');
+% axis([-20 20 0 20 -100 100])
+% colorbar
+% mycolors = [1 0 0 ; 0 0 1];
+% colormap(mycolors);
+%  % view(90,0)
+
+
+
+% %plot values above zero 
+
+surf(X,Y,(V>=0).*V,'FaceAlpha',0.5,'EdgeColor','none','FaceColor','r') 
+xlabel('alpha');
+ylabel('beta');
+axis([-20 20 0 20 -100 100])
+colorbar
+hold on
+
+surf(X,Y,(V<0).*V,'FaceAlpha',0.5,'EdgeColor','none','FaceColor','b') 
+xlabel('alpha');
+ylabel('beta');
+axis([-20 20 0 20 -100 100])
+colorbar
+% view(90,0)
+
+hold on
+surf(X,Y,(V2>=0).*V2,'FaceAlpha',0.5,'EdgeColor','none','FaceColor','black') 
+xlabel('alpha');
+ylabel('beta');
+axis([-20 20 0 20 -100 100])
+colorbar
+hold on
+surf(X,Y,(V2<0).*V2,'FaceAlpha',0.5,'EdgeColor','none','FaceColor','g') 
+xlabel('alpha');
+ylabel('beta');
+axis([-20 20 0 20 -100 100])
+colorbar
\ No newline at end of file

Matlab-Programs/stVenant.m

+function [outputMatrix] = stVenant(inputMatrix,mu,lambda)
+
+
+
+%compute symmetric gradient
+symGrad = 0.5 * (inputMatrix'+ inputMatrix);
+
+
+
+
+outputMatrix = 2*mu*symGrad + lambda* trace(inputMatrix)*eye(size(inputMatrix));
+
+
+
+
+
+
+
+end
+

Matlab-Programs/trigExample.m

+
+
+
+
+
+
+F = @(t,y) sqrt(1-y^2);
+
+t0 = 0;
+h = pi/32;
+tfinal = pi/2;
+y0 = 0;
+
+ode2(F,t0,h,tfinal,y0);
\ No newline at end of file