GUI, main file(plotVisualizer) and other functions

Author: dvoina13

180_r03.mat

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+function H2 = H2_norm(L, Q)
+
+% Inputs: L (Laplacian matrix), Q (projection matrix
+% onto n-1 dimensional space perpendicular to ones(n,1))
+
+Lbar = Q*L*Q';
+L0 = real(reduced_lyap(Lbar));
+H2 = sqrt(trace(L0));

180_r04.mat

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+function [V,S] = alphavol(X,R,fig)
+%ALPHAVOL Alpha shape of 2D or 3D point set.
+%   V = ALPHAVOL(X,R) gives the area or volume V of the basic alpha shape
+%   for a 2D or 3D point set. X is a coordinate matrix of size Nx2 or Nx3.
+%
+%   R is the probe radius with default value R = Inf. In the default case
+%   the basic alpha shape (or alpha hull) is the convex hull.
+%
+%   [V,S] = ALPHAVOL(X,R) outputs a structure S with fields:
+%    S.tri - Triangulation of the alpha shape (Mx3 or Mx4)
+%    S.vol - Area or volume of simplices in triangulation (Mx1)
+%    S.rcc - Circumradius of simplices in triangulation (Mx1)
+%    S.bnd - Boundary facets (Px2 or Px3)
+%
+%   ALPHAVOL(X,R,1) plots the alpha shape.
+%
+%   % 2D Example - C shape
+%   t = linspace(0.6,5.7,500)';
+%   X = 2*[cos(t),sin(t)] + rand(500,2);
+%   subplot(221), alphavol(X,inf,1);
+%   subplot(222), alphavol(X,1,1);
+%   subplot(223), alphavol(X,0.5,1);
+%   subplot(224), alphavol(X,0.2,1);
+%
+%   % 3D Example - Sphere
+%   [x,y,z] = sphere;
+%   [V,S] = alphavol([x(:),y(:),z(:)]);
+%   trisurf(S.bnd,x,y,z,'FaceColor','blue','FaceAlpha',1)
+%   axis equal
+%
+%   % 3D Example - Ring
+%   [x,y,z] = sphere;
+%   ii = abs(z) < 0.4;
+%   X = [x(ii),y(ii),z(ii)];
+%   X = [X; 0.8*X];
+%   subplot(211), alphavol(X,inf,1);
+%   subplot(212), alphavol(X,0.5,1);
+%
+%   See also DELAUNAY, TRIREP, TRISURF
+
+%   Author: Jonas Lundgren <[email protected]> 2010
+
+%   2010-09-27  First version of ALPHAVOL.
+%   2010-10-05  DelaunayTri replaced by DELAUNAYN. 3D plots added.
+%   2012-03-08  More output added. DELAUNAYN replaced by DELAUNAY.
+
+if nargin < 2 || isempty(R), R = inf; end
+if nargin < 3, fig = 0; end
+
+% Check coordinates
+dim = size(X,2);
+if dim < 2 || dim > 3
+    error('alphavol:dimension','X must have 2 or 3 columns.')
+end
+
+% Check probe radius
+if ~isscalar(R) || ~isreal(R) || isnan(R)
+    error('alphavol:radius','R must be a real number.')
+end
+
+% Unique points
+[X,imap] = unique(X,'rows');
+
+% Delaunay triangulation
+T = delaunay(X);
+
+% Remove zero volume tetrahedra since
+% these can be of arbitrary large circumradius
+if dim == 3
+    n = size(T,1);
+    vol = volumes(T,X);
+    epsvol = 1e-12*sum(vol)/n;
+    T = T(vol > epsvol,:);
+    holes = size(T,1) < n;
+end
+
+% Limit circumradius of simplices
+[~,rcc] = circumcenters(TriRep(T,X));
+T = T(rcc < R,:);
+rcc = rcc(rcc < R);
+
+% Volume/Area of alpha shape
+vol = volumes(T,X);
+V = sum(vol);
+
+% Return?
+if nargout < 2 && ~fig
+    return
+end
+
+% Turn off TriRep warning
+warning('off','MATLAB:TriRep:PtsNotInTriWarnId')
+
+% Alpha shape boundary
+if ~isempty(T)
+    % Facets referenced by only one simplex
+    B = freeBoundary(TriRep(T,X));
+    if dim == 3 && holes
+        % The removal of zero volume tetrahedra causes false boundary
+        % faces in the interior of the volume. Take care of these.
+        B = trueboundary(B,X);
+    end
+else
+    B = zeros(0,dim);
+end
+
+% Plot alpha shape
+if fig
+    figure(1)
+    if dim == 2
+        % Plot boundary edges and point set
+        x = X(:,1);
+        y = X(:,2);
+        plot(x(B)',y(B)','r','linewidth',2), hold on
+        plot(x,y,'k.'), hold off
+        str = 'Area';
+    elseif ~isempty(B)
+        % Plot boundary faces
+        trisurf(TriRep(B,X),'FaceColor','red','FaceAlpha',1/3);
+        str = 'Volume';
+    else
+        cla
+        str = 'Volume';
+    end
+    axis equal
+    str = sprintf('Radius = %g,   %s = %g', R, str, V);
+    title(str,'fontsize',12)
+end
+
+% Turn on TriRep warning
+warning('on','MATLAB:TriRep:PtsNotInTriWarnId')
+
+% Return structure
+if nargout == 2
+    S = struct('tri',imap(T),'vol',vol,'rcc',rcc,'bnd',imap(B));
+end
+
+
+%--------------------------------------------------------------------------
+function vol = volumes(T,X)
+%VOLUMES Volumes/areas of tetrahedra/triangles
+
+% Empty case
+if isempty(T)
+    vol = zeros(0,1);
+    return
+end
+
+% Local coordinates
+A = X(T(:,1),:);
+B = X(T(:,2),:) - A;
+C = X(T(:,3),:) - A;
+    
+if size(X,2) == 3
+    % 3D Volume
+    D = X(T(:,4),:) - A;
+    BxC = cross(B,C,2);
+    vol = dot(BxC,D,2);
+    vol = abs(vol)/6;
+else
+    % 2D Area
+    vol = B(:,1).*C(:,2) - B(:,2).*C(:,1);
+    vol = abs(vol)/2;
+end
+
+
+%--------------------------------------------------------------------------
+function B = trueboundary(B,X)
+%TRUEBOUNDARY True boundary faces
+%   Remove false boundary caused by the removal of zero volume
+%   tetrahedra. The input B is the output of TriRep/freeBoundary.
+
+% Surface triangulation
+facerep = TriRep(B,X);
+
+% Find edges attached to two coplanar faces
+E0 = edges(facerep);
+E1 = featureEdges(facerep, 1e-6);
+E2 = setdiff(E0,E1,'rows');
+
+% Nothing found
+if isempty(E2)
+    return
+end
+
+% Get face pairs attached to these edges
+% The edges connects faces into planar patches
+facelist = edgeAttachments(facerep,E2);
+pairs = cell2mat(facelist);
+
+% Compute planar patches (connected regions of faces)
+n = size(B,1);
+C = sparse(pairs(:,1),pairs(:,2),1,n,n);
+C = C + C' + speye(n);
+[~,p,r] = dmperm(C);
+
+% Count planar patches
+iface = diff(r);
+num = numel(iface);
+
+% List faces and vertices in patches
+facelist = cell(num,1);
+vertlist = cell(num,1);
+for k = 1:num
+
+    % Neglect singel face patches, they are true boundary
+    if iface(k) > 1
+        
+        % List of faces in patch k
+        facelist{k} = p(r(k):r(k+1)-1);
+        
+        % List of unique vertices in patch k
+        vk = B(facelist{k},:);
+        vk = sort(vk(:))';
+        ik = [true,diff(vk)>0];
+        vertlist{k} = vk(ik);
+        
+    end
+end
+
+% Sort patches by number of vertices
+ivert = cellfun(@numel,vertlist);
+[ivert,isort] = sort(ivert);
+facelist = facelist(isort);
+vertlist = vertlist(isort);
+
+% Group patches by number of vertices
+p = [0;find(diff(ivert));num] + 1;
+ipatch = diff(p);
+
+% Initiate true boundary list
+ibound = true(n,1);
+
+% Loop over groups
+for k = 1:numel(ipatch)
+
+    % Treat groups with at least two patches and four vertices
+    if ipatch(k) > 1 && ivert(p(k)) > 3
+
+        % Find double patches (identical vertex rows)
+        V = cell2mat(vertlist(p(k):p(k+1)-1));
+        [V,isort] = sortrows(V);
+        id = ~any(diff(V),2);
+        id = [id;0] | [0;id];
+        id(isort) = id;
+
+        % Deactivate faces in boundary list
+        for j = find(id')
+            ibound(facelist{j-1+p(k)}) = 0;
+        end
+        
+    end
+end
+
+% Remove false faces
+B = B(ibound,:);

180_r05.mat

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+function theta = anglerestrict(phi)
+%ANGLERESTRICT function to restrict an angle to a value between -PI and PI
+% ANGLERESTRICT(PHI) takes the angle PHI and computes the equivalent angle
+% between -PI and PI
+
+% George Young
+% August 2011
+
+theta = phi - 2*pi*ceil((phi-pi)/(2*pi));
+
+end

180_r_infty.mat

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+%**************************************************************************
+%
+%   This is a simple extension of the bar plot to include error bars.  It
+%   is called in exactly the same way as bar but with an extra input
+%   parameter "errors" passed first.
+%
+%   Parameters:
+%   errors - the errors to be plotted (extra dimension used if assymetric)
+%   varargin - parameters as passed to conventional bar plot
+%   See bar and errorbar documentation for more details.
+%
+%   Symmetric Example:
+%   y = randn(3,4);         % random y values (3 groups of 4 parameters) 
+%   errY = 0.1.*y;          % 10% error
+%   barwitherr(errY, y);    % Plot with errorbars
+%
+%   set(gca,'XTickLabel',{'Group A','Group B','Group C'})
+%   legend('Parameter 1','Parameter 2','Parameter 3','Parameter 4')
+%   ylabel('Y Value')
+%
+%
+%   Asymmetric Example:
+%   y = randn(3,4);         % random y values (3 groups of 4 parameters)
+%   errY = zeros(3,4,2);
+%   errY(:,:,1) = 0.1.*y;   % 10% lower error
+%   errY(:,:,2) = 0.2.*y;   % 20% upper error
+%   barwitherr(errY, y);    % Plot with errorbars
+%
+%   set(gca,'XTickLabel',{'Group A','Group B','Group C'})
+%   legend('Parameter 1','Parameter 2','Parameter 3','Parameter 4')
+%   ylabel('Y Value')
+%
+%
+%   Notes:
+%   Ideally used for group plots with non-overlapping bars because it
+%   will always plot in bar centre (so can look odd for over-lapping bars) 
+%   and for stacked plots the errorbars will be at the original y value is 
+%   not the stacked value so again odd appearance as is.
+%
+%   The data may not be in ascending order.  Only an issue if x-values are 
+%   passed to the fn in which case their order must be determined to 
+%   correctly position the errorbars.
+%
+%
+%   24/02/2011  Martina F. Callaghan    Created
+%   12/08/2011  Martina F. Callaghan    Updated for random x-values   
+%   24/10/2011  Martina F. Callaghan    Updated for asymmetric errors
+%   15/11/2011  Martina F. Callaghan    Fixed bug for assymetric errors &
+%                                       vector plots
+%
+%**************************************************************************
+
+function barwitherr(errors,varargin)
+
+% Check how the function has been called based on requirements for "bar"
+if nargin < 3
+    % This is the same as calling bar(y)
+    values = varargin{1};
+    xOrder = 1:size(values,1);
+else
+    % This means extra parameters have been specified
+    if isscalar(varargin{2}) || ischar(varargin{2})
+        % It is a width / property so the y values are still varargin{1}
+        values = varargin{1};
+        xOrder = 1:size(values,1);
+    else
+        % x-values have been specified so the y values are varargin{2}
+        % If x-values have been specified, they could be in a random order,
+        % get their indices in ascending order for use with the bar
+        % locations which will be in ascending order:
+        values = varargin{2};
+        [tmp xOrder] = sort(varargin{1});
+    end
+end
+
+% If an extra dimension is supplied for the errors then they are
+% assymetric split out into upper and lower:
+if ndims(errors) == ndims(values)+1
+    lowerErrors = errors(:,:,1);
+    upperErrors = errors(:,:,2);
+elseif isvector(values)~=isvector(errors)
+    lowerErrors = errors(:,1);
+    upperErrors = errors(:,2);
+else
+    lowerErrors = errors;
+    upperErrors = errors;
+end
+    
+% Check that the size of "errors" corresponsds to the size of the y-values.
+% Arbitrarily using lower errors as indicative.
+if any(size(values) ~= size(lowerErrors))
+    error('The values and errors have to be the same length')
+end
+
+[nRows nCols] = size(values);
+handles.bar = bar(varargin{:}); % standard implementation of bar fn
+hold on
+
+if nRows > 1
+    for col = 1:nCols
+        % Extract the x location data needed for the errorbar plots:
+        x = get(get(handles.bar(col),'children'),'xdata');
+        % Use the mean x values to call the standard errorbar fn; the
+        % errorbars will now be centred on each bar; these are in ascending
+        % order so use xOrder to ensure y values and errors are too:
+        errorbar(mean(x,1),values(xOrder,col),lowerErrors(xOrder,col), upperErrors(xOrder, col), '.k')
+    end
+else
+    x = get(get(handles.bar,'children'),'xdata');
+    errorbar(mean(x,1),values,errors,'.k')
+end
+
+hold off