Code covered by the BSD License

# Speeding Up Optimization Problems with Parallel Computing

### Stuart Kozola (view profile)

Files from the webinar: Speeding up optimization problems with parallel computing

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

plotElectron.m
```function f = plotElectron(varargin)
% Plot electrons on conducting body after solution finishes.
% Copyright 2010 The MathWorks, Inc.

if nargin == 0
% return function handle to be used as a plotting function

f = @(x,itervals,flag) plotElectron(x,itervals,flag);

else
% plots with specified arguements

f = myElectronPlot(varargin{:});

end
end

function stop = myElectronPlot(x,itervals,flag, varargin)

if ~exist('flag','var')
myElectronPlot([],[],'init');
flag = 'done';
end

switch flag
case 'iter'
% Make updates to plot or guis as needed
case 'interrupt'
% Probably no action here. Check conditions to see
% whether optimization should quit.
case 'init'
tic
case 'done'
% Cleanup of plots, guis, or final plot
toc
E = length(x)/3;
% These two lines set up standard polar coordinates
R=0:.0025:1;
TH= 2*pi*(0:.0025:1);
% This line finds the maximum  radius value for each angle TH
Rmax = diag((abs(cos(TH)) + abs(sin(TH))) ./ (1 + abs(sin(TH).*cos(TH))));
% The equation to solve is
% z = -abs(x)  abs(y) (pyramid)
% x^2 + y^2 +(z+1)^2 = 1 (sphere centered at [0,0,-1])
% Solve for x and y, get the equation
% x^2 + y^2 = x + y  x*y
% Set x = R*cos(TH), y = R*sin(TH)
% R^2 = R(cos(TH) + sin(TH))  R^2*sin(TH)*cos(TH)
% R = (cos(TH) + sin(TH)) / (1 + sin(TH)*cos(TH)) modulo signs

% These two lines set up polar coordinates, then scale the maximum radius
% at each angle TH by the value of Rmax(TH)
% This is done in a vectorized, efficient calculation
X=R'*cos(TH) * Rmax;
Y=R'*sin(TH) * Rmax;

Z1 = - abs(X) - abs(Y); % pyramid
Z2 = -1 - real(sqrt(1 - X.^2 - Y.^2)); % sphere

surf(X,Y,Z1,'LineStyle','none'); % plot pyramid
hold on
surf(X,Y,Z2,'LineStyle','none'); % plot sphere

set(gcf,'Color','w') % white background
view(-44,18)
for i = 1:E
plot3(x(3*i-2),x(3*i-1),x(3*i),'r.','MarkerSize',25);
end
rotate3d
axis equal
drawnow
hold off
otherwise
% not used
end
stop = false;
end```