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Chen Lin
Chen Lin
Last activity on 22 May 2024

Celebrating Spring: MATLAB Tulip

Bringing the beauty of MathWorks Natick's tulips to life through code!
Get the code from @Eric Ludlam.
Remix challenge: create and share with us your new breeds of MATLAB tulips!
Are you a Simulink user eager to learn how to create apps with App Designer? Or an App Designer enthusiast looking to dive into Simulink?
Don't miss today's article on the Graphics and App Building Blog by @Robert Philbrick! Discover how to build Simulink Apps with App Designer, streamlining control of your simulations!
Build Simulink Apps with App Designer
From Alpha Vantage's website: API Documentation | Alpha Vantage
Try using the built-in Matlab function webread(URL)... for example:
% copy a URL from the examples on the site
URL = 'https://www.alphavantage.co/query?function=TIME_SERIES_DAILY&symbol=IBM&apikey=demo'
% or use the pattern to create one
tickers = [{'IBM'} {'SPY'} {'DJI'} {'QQQ'}]; i = 1;
URL = ...
['https://www.alphavantage.co/query?function=TIME_SERIES_DAILY_ADJUSTED&outputsize=full&symbol=', ...
+ tickers{i}, ...
+ '&apikey=***Put Your API Key here***'];
X = webread(URL);
You can access any of the data available on the site as per the Alpha Vantage documentation using these two lines of code but with different designations for the requested data as per the documentation.
It's fun!
Daniele Lupo
Daniele Lupo
Last activity on 12 May 2024

Which toolboxes for crypto trading?

Hi to all.
I'm trying to learn a bit about trading with cryptovalues. At the moment I'm using Freqtrade (in dry-run mode of course) for automatic trading. The tool is written in python and it allows to create custom strategies in python classes and then run them.
I've written some strategy just to learn how to do, but now I'd like to create some interesting algorithm. I've a matlab license, and I'd like to know what are suggested tollboxes for following work:
  • Create a criptocurrency strategy algorythm (for buying and selling some crypto like BTC, ETH etc).
  • Backtesting the strategy with historical data (I've a bunch of json files with different timeframes, downloaded with freqtrade from binance).
  • Optimize the strategy given some parameters (they can be numeric, like ROI, some kind of enumeration, like "selltype" and so on).
  • Convert the strategy algorithm in python, so I can use it with Freqtrade without worrying of manually copying formulas and parameters that's error prone.
  • I'd like to write both classic algorithm and some deep neural one, that try to find best strategy with little neural network (they should run on my pc with 32gb of ram and a 3080RTX if it can be gpu accelerated).
What do you suggest?
Dear MATLAB contest enthusiasts,
I believe many of you have been captivated by the innovative entries from Zhaoxu Liu / slanderer, in the 2023 MATLAB Flipbook Mini Hack contest.
Ever wondered about the person behind these creative entries? What drives a MATLAB user to such levels of skill? And what inspired his participation in the contest? We were just as curious as you are!
We were delighted to catch up with him and learn more about his use of MATLAB. The interview has recently been published in MathWorks Blogs. For an in-depth look into his insights and experiences, be sure to read our latest blog post: Community Q&A – Zhaoxu Liu.
But the conversation doesn't end here! Who would you like to see featured in our next interview? Drop their name in the comments section below and let us know who we should reach out to next!
The study of the dynamics of the discrete Klein - Gordon equation (DKG) with friction is given by the equation :
above equation, W describes the potential function :
The objective of this simulation is to model the dynamics of a segment of DNA under thermal fluctuations with fixed boundaries using a modified discrete Klein-Gordon equation. The model incorporates elasticity, nonlinearity, and damping to provide insights into the mechanical behavior of DNA under various conditions.
% Parameters
numBases = 200; % Number of base pairs, representing a segment of DNA
kappa = 0.1; % Elasticity constant
omegaD = 0.2; % Frequency term
beta = 0.05; % Nonlinearity coefficient
delta = 0.01; % Damping coefficient
  • Position: Random initial perturbations between 0.01 and 0.02 to simulate the thermal fluctuations at the start.
  • Velocity: All bases start from rest, assuming no initial movement except for the thermal perturbations.
% Random initial perturbations to simulate thermal fluctuations
initialPositions = 0.01 + (0.02-0.01).*rand(numBases,1);
initialVelocities = zeros(numBases,1); % Assuming initial rest state
The simulation uses fixed ends to model the DNA segment being anchored at both ends, which is typical in experimental setups for studying DNA mechanics. The equations of motion for each base are derived from a modified discrete Klein-Gordon equation with the inclusion of damping:
% Define the differential equations
dt = 0.05; % Time step
tmax = 50; % Maximum time
tspan = 0:dt:tmax; % Time vector
x = zeros(numBases, length(tspan)); % Displacement matrix
x(:,1) = initialPositions; % Initial positions
% Velocity-Verlet algorithm for numerical integration
for i = 2:length(tspan)
% Compute acceleration for internal bases
acceleration = zeros(numBases,1);
for n = 2:numBases-1
acceleration(n) = kappa * (x(n+1, i-1) - 2 * x(n, i-1) + x(n-1, i-1)) ...
- delta * initialVelocities(n) - omegaD^2 * (x(n, i-1) - beta * x(n, i-1)^3);
end
% positions for internal bases
x(2:numBases-1, i) = x(2:numBases-1, i-1) + dt * initialVelocities(2:numBases-1) ...
+ 0.5 * dt^2 * acceleration(2:numBases-1);
% velocities using new accelerations
newAcceleration = zeros(numBases,1);
for n = 2:numBases-1
newAcceleration(n) = kappa * (x(n+1, i) - 2 * x(n, i) + x(n-1, i)) ...
- delta * initialVelocities(n) - omegaD^2 * (x(n, i) - beta * x(n, i)^3);
end
initialVelocities(2:numBases-1) = initialVelocities(2:numBases-1) + 0.5 * dt * (acceleration(2:numBases-1) + newAcceleration(2:numBases-1));
end
% Visualization of displacement over time for each base pair
figure;
hold on;
for n = 2:numBases-1
plot(tspan, x(n, :));
end
xlabel('Time');
ylabel('Displacement');
legend(arrayfun(@(n) ['Base ' num2str(n)], 2:numBases-1, 'UniformOutput', false));
title('Displacement of DNA Bases Over Time');
hold off;
The results are visualized using a plot that shows the displacements of each base over time . Key observations from the simulation include :
  • Wave Propagation: The initial perturbations lead to wave-like dynamics along the segment, with visible propagation and reflection at the boundaries.
  • Damping Effects: The inclusion of damping leads to a gradual reduction in the amplitude of the oscillations, indicating energy dissipation over time.
  • Nonlinear Behavior: The nonlinear term influences the response, potentially stabilizing the system against large displacements or leading to complex dynamic patterns.
% 3D plot for displacement
figure;
[X, T] = meshgrid(1:numBases, tspan);
surf(X', T', x);
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D View of DNA Base Displacements');
colormap('jet');
shading interp;
colorbar; % Adds a color bar to indicate displacement magnitude
% Snapshot visualization at a specific time
snapshotTime = 40; % Desired time for the snapshot
[~, snapshotIndex] = min(abs(tspan - snapshotTime)); % Find closest index
snapshotSolution = x(:, snapshotIndex); % Extract displacement at the snapshot time
% Plotting the snapshot
figure;
stem(1:numBases, snapshotSolution, 'filled'); % Discrete plot using stem
title(sprintf('DNA Model Displacement at t = %d seconds', snapshotTime));
xlabel('Base Pair Index');
ylabel('Displacement');
% Time vector for detailed sampling
tDetailed = 0:0.5:50; % Detailed time steps
% Initialize an empty array to hold the data
data = [];
% Generate the data for 3D plotting
for i = 1:numBases
% Interpolate to get detailed solution data for each base pair
detailedSolution = interp1(tspan, x(i, :), tDetailed);
% Concatenate the current base pair's data to the main data array
data = [data; repmat(i, length(tDetailed), 1), tDetailed', detailedSolution'];
end
% 3D Plot
figure;
scatter3(data(:,1), data(:,2), data(:,3), 10, data(:,3), 'filled');
xlabel('Base Pair');
ylabel('Time');
zlabel('Displacement');
title('3D Plot of DNA Base Pair Displacements Over Time');
colorbar; % Adds a color bar to indicate displacement magnitude
Temporary print statements are often helpful during debugging but it's easy to forget to remove the statements or sometimes you may not have writing privileges for the file. This tip uses conditional breakpoints to add print statements without ever editing the file!
What are conditional breakpoints?
Conditional breakpoints allow you to write a conditional statement that is executed when the selected line is hit and if the condition returns true, MATLAB pauses at that line. Otherwise, it continues.
The Hack: use ~fprintf() as the condition
fprintf prints information to the command window and returns the size of the message in bytes. The message size will always be greater than 0 which will always evaluate as true when converted to logical. Therefore, by negating an fprintf statement within a conditional breakpoint, the fprintf command will execute, print to the command window, and evalute as false which means the execution will continue uninterupted!
How to set a conditional break point
1. Right click the line number where you want the condition to be evaluated and select "Set Conditional Breakpoint"
2. Enter a valid MATLAB expression that returns a logical scalar value in the editor dialog.
Handy one-liners
Check if a line is reached: Don't forget the negation (~) and the line break (\n)!
~fprintf('Entered callback function\n')
Display the call stack from the break point line: one of my favorites!
~fprintf('%s\n',formattedDisplayText(struct2table(dbstack)))
Inspect variable values: For scalar values,
~fprintf('v = %.5f\n', v)
Use formattedDisplayText to convert more complex data to a string
~fprintf('%s\n', formattedDisplayText(v)).
Make sense of frequent hits: In some situations such as responses to listeners or interactive callbacks, a line can be executed 100s of times per second. Incorporate a timestamp to differentiate messages during rapid execution.
~fprintf('WindowButtonDownFcn - %s\n', datetime('now'))
Closing
This tip not only keeps your code clean but also offers a dynamic way to monitor code execution and variable states without permanent modifications. Interested in digging deeper? @Steve Eddins takes this tip to the next level with his Code Trace for MATLAB tool available on the File Exchange (read more).
Summary animation
To reproduce the events in this animation:
% buttonDownFcnDemo.m
fig = figure();
tcl = tiledlayout(4,4,'TileSpacing','compact');
for i = 1:16
ax = nexttile(tcl);
title(ax,"#"+string(i))
ax.ButtonDownFcn = @axesButtonDownFcn;
xlim(ax,[-1 1])
ylim(ax,[-1,1])
hold(ax,'on')
end
function axesButtonDownFcn(obj,event)
colors = lines(16);
plot(obj,event.IntersectionPoint(1),event.IntersectionPoint(2),...
'ko','MarkerFaceColor',colors(obj.Layout.Tile,:))
end
As far as I know, the MATLAB Community (including Matlab Central and Mathworks' official GitHub repository) has always been a vibrant and diverse professional and amateur community of MATLAB users from various fields globally. Being a part of it myself, especially in recent years, I have not only benefited continuously from the community but also tried to give back by helping other users in need.
I am a senior MATLAB user from Shenzhen, China, and I have a deep passion for MATLAB, applying it in various scenarios. Due to the less than ideal job market in my current social environment, I am hoping to find a position for remote support work within the Matlab Community. I wonder if this is realistic. For instance, Mathworks has been open-sourcing many repositories in recent years, especially in the field of deep learning with typical applications across industries. I am eager to use the latest MATLAB features to implement state-of-the-art algorithms. Additionally, I occasionally contribute through GitHub issues and pull requests.
In conclusion, I am looking forward to the opportunity to formally join the Matlab Community in a remote support role, dedicating more energy to giving back to the community and making the world a better place! (If a Mathworks employer can contact me, all the better~)
I created an ellipse visualizer in #MATLAB using App Designer! To read more about it, and how it ties to the recent total solar eclipse, check out my latest blog post:
https://www.davidyding.com/navPages/Ellipse
Github Repo of the app (you can open it on MATLAB Online!):
https://github.com/dvfire123/EllipseVisualizer/tree/main
The beautiful and elegant chord diagrams were all created using MATLAB?
Indeed, they were all generated using the chord diagram plotting toolkit that I developed myself:
You can download these toolkits from the provided links.
The reason for writing this article is that many people have started using the chord diagram plotting toolkit that I developed. However, some users are unsure about customizing certain styles. As the developer, I have a good understanding of the implementation principles of the toolkit and can apply it flexibly. This has sparked the idea of challenging myself to create various styles of chord diagrams. Currently, the existing code is quite lengthy. In the future, I may integrate some of this code into the toolkit, enabling users to achieve the effects of many lines of code with just a few lines.
Without further ado, let's see the extent to which this MATLAB toolkit can currently perform.
demo 1
rng(2)
dataMat = randi([0,5], [11,5]);
dataMat(1:6,1) = 0;
dataMat([11,7],1) = [45,25];
dataMat([1,4,5,7],2) = [20,20,30,30];
dataMat(:,3) = 0;
dataMat(6,3) = 45;
dataMat(1:5,4) = 0;
dataMat([6,7],4) = [25,25];
dataMat([5,6,9],5) = [25,25,25];
colName = {'Fly', 'Beetle', 'Leaf', 'Soil', 'Waxberry'};
rowName = {'Bartomella', 'Bradyrhizobium', 'Dysgomonas', 'Enterococcus',...
'Lactococcus', 'norank', 'others', 'Pseudomonas', 'uncultured',...
'Vibrionimonas', 'Wolbachia'};
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
CC = chordChart(dataMat, 'rowName',rowName, 'colName',colName, 'Sep',1/80);
CC = CC.draw();
% 修改上方方块颜色(Modify the color of the blocks above)
CListT = [0.7765 0.8118 0.5216; 0.4431 0.4706 0.3843; 0.5804 0.2275 0.4549;
0.4471 0.4039 0.6745; 0.0157 0 0 ];
for i = 1:size(dataMat, 2)
CC.setSquareT_N(i, 'FaceColor',CListT(i,:))
end
% 修改下方方块颜色(Modify the color of the blocks below)
CListF = [0.5843 0.6863 0.7843; 0.1098 0.1647 0.3255; 0.0902 0.1608 0.5373;
0.6314 0.7961 0.2118; 0.0392 0.2078 0.1059; 0.0157 0 0 ;
0.8549 0.9294 0.8745; 0.3882 0.3255 0.4078; 0.5020 0.7216 0.3843;
0.0902 0.1843 0.1804; 0.8196 0.2314 0.0706];
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'FaceColor',CListF(i,:))
end
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListT(j,:), 'FaceAlpha',.5)
end
end
CC.tickState('on')
CC.labelRotate('on')
CC.setFont('FontSize',17, 'FontName','Cambria')
% CC.labelRotate('off')
% textHdl = findobj(gca,'Tag','ChordLabel');
% for i = 1:length(textHdl)
% if textHdl(i).Position(2) < 0
% if abs(textHdl(i).Position(1)) > .7
% textHdl(i).Rotation = textHdl(i).Rotation + 45;
% textHdl(i).HorizontalAlignment = 'right';
% if textHdl(i).Rotation > 90
% textHdl(i).Rotation = textHdl(i).Rotation + 180;
% textHdl(i).HorizontalAlignment = 'left';
% end
% else
% textHdl(i).Rotation = textHdl(i).Rotation + 10;
% textHdl(i).HorizontalAlignment = 'right';
% end
% end
% end
demo 2
rng(3)
dataMat = randi([1,15], [7,22]);
dataMat(dataMat < 11) = 0;
dataMat(1, sum(dataMat, 1) == 0) = 15;
colName = {'A2M', 'FGA', 'FGB', 'FGG', 'F11', 'KLKB1', 'SERPINE1', 'VWF',...
'THBD', 'TFPI', 'PLAT', 'SERPINA5', 'SERPIND1', 'F2', 'PLG', 'F12',...
'SERPINC1', 'SERPINA1', 'PROS1', 'SERPINF2', 'F13A1', 'PROC'};
rowName = {'Lung', 'Spleen', 'Liver', 'Heart',...
'Renal cortex', 'Renal medulla', 'Thyroid'};
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
CC = chordChart(dataMat, 'rowName',rowName, 'colName',colName, 'Sep',1/80, 'LRadius',1.21);
CC = CC.draw();
CC.labelRotate('on')
% 单独设置每一个弦末端方块(Set individual end blocks for each chord)
% Use obj.setEachSquareF_Prop
% or obj.setEachSquareT_Prop
% F means from (blocks below)
% T means to (blocks above)
CListT = [173,70,65; 79,135,136]./255;
% Upregulated:1 | Downregulated:2
Regulated = rand([7, 22]);
Regulated = (Regulated < .8) + 1;
for i = 1:size(Regulated, 1)
for j = 1:size(Regulated, 2)
CC.setEachSquareT_Prop(i, j, 'FaceColor', CListT(Regulated(i,j),:))
end
end
% 绘制图例(Draw legend)
H1 = fill([0,1,0] + 100, [1,0,1] + 100, CListT(1,:), 'EdgeColor','none');
H2 = fill([0,1,0] + 100, [1,0,1] + 100, CListT(2,:), 'EdgeColor','none');
lgdHdl = legend([H1,H2], {'Upregulated','Downregulated'}, 'AutoUpdate','off', 'Location','best');
lgdHdl.ItemTokenSize = [12,12];
lgdHdl.Box = 'off';
lgdHdl.FontSize = 13;
% 修改下方方块颜色(Modify the color of the blocks below)
CListF = [128,108,171; 222,208,161; 180,196,229; 209,150,146; 175,201,166;
134,156,118; 175,175,173]./255;
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'FaceColor',CListF(i,:))
end
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListF(i,:), 'FaceAlpha',.45)
end
end
demo 3
dataMat = rand([15,15]);
dataMat(dataMat > .15) = 0;
CList = [ 75,146,241; 252,180, 65; 224, 64, 10; 5,100,146; 191,191,191;
26, 59,105; 255,227,130; 18,156,221; 202,107, 75; 0, 92,219;
243,210,136; 80, 99,129; 241,185,168; 224,131, 10; 120,147,190]./255;
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList);
BCC = BCC.draw();
% 添加刻度
BCC.tickState('on')
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria', 'FontSize',17, 'Color',[0,0,.8])
demo 4
rng(5)
dataMat = randi([1,20], [5,5]);
dataMat(1,1) = 110;
dataMat(2,2) = 40;
dataMat(3,3) = 50;
dataMat(5,5) = 50;
CList1 = [164,190,158; 216,213,153; 177,192,208; 238,238,227; 249,217,153]./255;
CList2 = [247,204,138; 128,187,185; 245,135,124; 140,199,197; 252,223,164]./255;
CList = CList2;
NameList={'CHORD','CHART','MADE','BY','SLANDARER'};
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList, 'Sep',1/30, 'Label',NameList, 'LRadius',1.33);
BCC = BCC.draw();
% 添加刻度
BCC.tickState('on')
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.7, 'EdgeColor',CList(i,:)./1.1)
end
end
end
% 修改方块颜色(Modify the color of the blocks)
for i = 1:size(dataMat, 1)
BCC.setSquareN(i, 'EdgeColor',CList(i,:)./1.7)
end
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria', 'FontSize',17)
BCC.tickLabelState('on')
BCC.setTickFont('FontName','Cambria', 'FontSize',9)
demo 5
dataMat=randi([1,20], [14,3]);
dataMat(11:14,1) = 0;
dataMat(6:10,2) = 0;
dataMat(1:5,3) = 0;
colName = compose('C%d', 1:3);
rowName = [compose('A%d', 1:7), compose('B%d', 7:-1:1)];
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
CC = chordChart(dataMat, 'rowName',rowName, 'colName',colName, 'Sep',1/80);
CC = CC.draw();
% 修改上方方块颜色(Modify the color of the blocks above)
for i = 1:size(dataMat, 2)
CC.setSquareT_N(i, 'FaceColor',[190,190,190]./255)
end
% 修改下方方块颜色(Modify the color of the blocks below)
CListF=[255,244,138; 253,220,117; 254,179, 78; 253,190, 61;
252, 78, 41; 228, 26, 26; 178, 0, 36; 4, 84,119;
1,113,137; 21,150,155; 67,176,173; 68,173,158;
123,204,163; 184,229,162]./255;
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'FaceColor',CListF(i,:))
end
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListF(i,:), 'FaceAlpha',.5)
end
end
CC.tickState('on')
CC.tickLabelState('on')
demo 6
rng(2)
dataMat = randi([0,40], [20,4]);
dataMat(rand([20,4]) < .2) = 0;
dataMat(1,3) = 500;
dataMat(20,1:4) = [140; 150; 80; 90];
colName = compose('T%d', 1:4);
rowName = compose('SL%d', 1:20);
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
CC = chordChart(dataMat, 'rowName',rowName, 'colName',colName, 'Sep',1/80, 'LRadius',1.23);
CC = CC.draw();
% 修改上方方块颜色(Modify the color of the blocks above)
CListT = [0.62,0.49,0.27; 0.28,0.57,0.76
0.25,0.53,0.30; 0.86,0.48,0.34];
for i = 1:size(dataMat, 2)
CC.setSquareT_N(i, 'FaceColor',CListT(i,:))
end
% 修改下方方块颜色(Modify the color of the blocks below)
CListF = [0.94,0.84,0.60; 0.16,0.50,0.67; 0.92,0.62,0.49;
0.48,0.44,0.60; 0.48,0.44,0.60; 0.71,0.79,0.73;
0.96,0.98,0.98; 0.51,0.82,0.95; 0.98,0.70,0.82;
0.97,0.85,0.84; 0.55,0.64,0.62; 0.94,0.93,0.60;
0.98,0.90,0.85; 0.72,0.84,0.81; 0.85,0.45,0.49;
0.76,0.76,0.84; 0.59,0.64,0.62; 0.62,0.14,0.15;
0.75,0.75,0.75; 1.00,1.00,1.00];
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'FaceColor',CListF(i,:))
end
CC.setSquareF_N(size(dataMat, 1), 'EdgeColor','k', 'LineWidth',1)
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListT(j,:), 'FaceAlpha',.46)
end
end
CC.tickState('on')
CC.labelRotate('on')
CC.setFont('FontSize',17, 'FontName','Cambria')
demo 7
dataMat = randi([10,10000], [10,10]);
dataMat(6:10,:) = 0;
dataMat(:,1:5) = 0;
NameList = {'BOC', 'ICBC', 'ABC', 'BOCM', 'CCB', ...
'yama', 'nikoto', 'saki', 'koto', 'kawa'};
CList = [0.63,0.75,0.88
0.67,0.84,0.75
0.85,0.78,0.88
1.00,0.92,0.93
0.92,0.63,0.64
0.57,0.67,0.75
1.00,0.65,0.44
0.72,0.73,0.40
0.65,0.57,0.58
0.92,0.94,0.96];
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList, 'Label',NameList);
BCC = BCC.draw();
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.85, 'EdgeColor',CList(i,:)./1.5, 'LineWidth',.8)
end
end
end
for i = 1:size(dataMat, 1)
BCC.setSquareN(i, 'EdgeColor',CList(i,:)./1.5, 'LineWidth',1)
end
% 添加刻度、修改字体
BCC.tickState('on')
BCC.setFont('FontName','Cambria', 'FontSize',17)
demo 8
dataMat = rand([11,4]);
dataMat = round(10.*dataMat.*((11:-1:1).'+1))./10;
colName = {'A','B','C','D'};
rowName = {'Acidobacteriota', 'Actinobacteriota', 'Proteobacteria', ...
'Chloroflexi', 'Bacteroidota', 'Firmicutes', 'Gemmatimonadota', ...
'Verrucomicrobiota', 'Patescibacteria', 'Planctomyetota', 'Others'};
figure('Units','normalized', 'Position',[.02,.05,.8,.85])
CC = chordChart(dataMat, 'colName',colName, 'Sep',1/80, 'SSqRatio',30/100);% -30/100
CC = CC.draw();
% 修改上方方块颜色(Modify the color of the blocks above)
CListT = [0.93,0.60,0.62
0.55,0.80,0.99
0.95,0.82,0.18
1.00,0.81,0.91];
for i = 1:size(dataMat, 2)
CC.setSquareT_N(i, 'FaceColor',CListT(i,:))
end
% 修改下方方块颜色(Modify the color of the blocks below)
CListF = [0.75,0.73,0.86
0.56,0.83,0.78
0.00,0.60,0.20
1.00,0.49,0.02
0.78,0.77,0.95
0.59,0.24,0.36
0.98,0.51,0.45
0.96,0.55,0.75
0.47,0.71,0.84
0.65,0.35,0.16
0.40,0.00,0.64];
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'FaceColor',CListF(i,:))
end
% 修改弦颜色(Modify chord color)
CListC = [0.55,0.83,0.76
0.75,0.73,0.86
0.00,0.60,0.19
1.00,0.51,0.04];
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListC(j,:), 'FaceAlpha',.4)
end
end
% 单独设置每一个弦末端方块(Set individual end blocks for each chord)
% Use obj.setEachSquareF_Prop
% or obj.setEachSquareT_Prop
% F means from (blocks below)
% T means to (blocks above)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setEachSquareT_Prop(i,j, 'FaceColor', CListF(i,:))
end
end
% 添加刻度
CC.tickState('on')
% 修改字体，字号及颜色
CC.setFont('FontName','Cambria', 'FontSize',17)
% 隐藏下方标签
textHdl = findobj(gca, 'Tag','ChordLabel');
for i = 1:length(textHdl)
if textHdl(i).Position(2) < 0
set(textHdl(i), 'Visible','off')
end
end
% 绘制图例(Draw legend)
scatterHdl = scatter(10.*ones(size(dataMat,1)),10.*ones(size(dataMat,1)), ...
55, 'filled');
for i = 1:length(scatterHdl)
scatterHdl(i).CData = CListF(i,:);
end
lgdHdl = legend(scatterHdl, rowName, 'Location','best', 'FontSize',16, 'FontName','Cambria', 'Box','off');
set(lgdHdl, 'Position',[.7482,.3577,.1658,.3254])
demo 9
dataMat = randi([0,10], [5,5]);
CList1 = [0.70,0.59,0.67
0.62,0.70,0.62
0.81,0.75,0.62
0.80,0.62,0.56
0.62,0.65,0.65];
CList2 = [0.02,0.02,0.02
0.59,0.26,0.33
0.38,0.49,0.38
0.03,0.05,0.03
0.29,0.28,0.32];
CList = CList2;
NameList={'CHORD','CHART','MADE','BY','SLANDARER'};
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList, 'Sep',1/30, 'Label',NameList, 'LRadius',1.33);
BCC = BCC.draw();
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
BCC.setChordMN(i,j, 'FaceAlpha',.5)
end
end
% 修改方块颜色(Modify the color of the blocks)
for i = 1:size(dataMat, 1)
BCC.setSquareN(i, 'EdgeColor',[0,0,0], 'LineWidth',5)
end
% 添加刻度
BCC.tickState('on')
% 修改字体，字号及颜色
BCC.setFont('FontSize',17, 'FontWeight','bold')
BCC.tickLabelState('on')
BCC.setTickFont('FontSize',9)
demo 10
rng(2)
dataMat = rand([14,5]) > .3;
colName = {'phosphorylation', 'vasculature development', 'blood vessel development', ...
'cell adhesion', 'plasma membrane'};
rowName = {'THY1', 'FGF2', 'MAP2K1', 'CDH2', 'HBEGF', 'CXCR4', 'ECSCR',...
'ACVRL1', 'RECK', 'PNPLA6', 'CDH5', 'AMOT', 'EFNB2', 'CAV1'};
figure('Units','normalized', 'Position',[.02,.05,.9,.85])
CC = chordChart(dataMat, 'colName',colName, 'rowName',rowName, 'Sep',1/80, 'LRadius',1.2);
CC = CC.draw();
% 修改上方方块颜色(Modify the color of the blocks above)
CListT1 = [0.5686 0.1961 0.2275
0.2275 0.2863 0.3765
0.8431 0.7882 0.4118
0.4275 0.4510 0.2706
0.3333 0.2706 0.2510];
CListT2 = [0.4941 0.5490 0.4118
0.9059 0.6510 0.3333
0.8980 0.6157 0.4980
0.8902 0.5137 0.4667
0.4275 0.2824 0.2784];
CListT3 = [0.4745 0.5843 0.7569
0.4824 0.5490 0.5843
0.6549 0.7216 0.6510
0.9412 0.9216 0.9059
0.9804 0.7608 0.6863];
CListT = CListT3;
for i = 1:size(dataMat, 2)
CC.setSquareT_N(i, 'FaceColor',CListT(i,:), 'EdgeColor',[0,0,0])
end
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListT(j,:), 'FaceAlpha',.9, 'EdgeColor',[0,0,0])
end
end
% 修改下方方块颜色(Modify the color of the blocks below)
logFC = sort(rand(1,14))*6 - 3;
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'CData',logFC(i), 'FaceColor','flat', 'EdgeColor',[0,0,0])
end
CMap = [ 0 0 1.0000; 0.0645 0.0645 1.0000; 0.1290 0.1290 1.0000; 0.1935 0.1935 1.0000
0.2581 0.2581 1.0000; 0.3226 0.3226 1.0000; 0.3871 0.3871 1.0000; 0.4516 0.4516 1.0000
0.5161 0.5161 1.0000; 0.5806 0.5806 1.0000; 0.6452 0.6452 1.0000; 0.7097 0.7097 1.0000
0.7742 0.7742 1.0000; 0.8387 0.8387 1.0000; 0.9032 0.9032 1.0000; 0.9677 0.9677 1.0000
1.0000 0.9677 0.9677; 1.0000 0.9032 0.9032; 1.0000 0.8387 0.8387; 1.0000 0.7742 0.7742
1.0000 0.7097 0.7097; 1.0000 0.6452 0.6452; 1.0000 0.5806 0.5806; 1.0000 0.5161 0.5161
1.0000 0.4516 0.4516; 1.0000 0.3871 0.3871; 1.0000 0.3226 0.3226; 1.0000 0.2581 0.2581
1.0000 0.1935 0.1935; 1.0000 0.1290 0.1290; 1.0000 0.0645 0.0645; 1.0000 0 0];
colormap(CMap);
try clim([-3,3]),catch,end
try caxis([-3,3]),catch,end
CBHdl = colorbar();
CBHdl.Position = [0.74,0.25,0.02,0.2];
% =========================================================================
% 交换XY轴(Swap XY axis)
patchHdl = findobj(gca, 'Type','patch');
for i = 1:length(patchHdl)
tX = patchHdl(i).XData;
tY = patchHdl(i).YData;
patchHdl(i).XData = tY;
patchHdl(i).YData = - tX;
end
txtHdl = findobj(gca, 'Type','text');
for i = 1:length(txtHdl)
txtHdl(i).Position([1,2]) = [1,-1].*txtHdl(i).Position([2,1]);
if txtHdl(i).Position(1) < 0
txtHdl(i).HorizontalAlignment = 'right';
else
txtHdl(i).HorizontalAlignment = 'left';
end
end
lineHdl = findobj(gca, 'Type','line');
for i = 1:length(lineHdl)
tX = lineHdl(i).XData;
tY = lineHdl(i).YData;
lineHdl(i).XData = tY;
lineHdl(i).YData = - tX;
end
% =========================================================================
txtHdl = findobj(gca, 'Type','text');
for i = 1:length(txtHdl)
if txtHdl(i).Position(1) > 0
txtHdl(i).Visible = 'off';
end
end
text(1.25,-.15, 'LogFC', 'FontSize',16)
text(1.25,1, 'Terms', 'FontSize',16)
patchHdl = [];
for i = 1:size(dataMat, 2)
patchHdl(i) = fill([10,11,12],[10,13,13], CListT(i,:), 'EdgeColor',[0,0,0]);
end
lgdHdl = legend(patchHdl, colName, 'Location','best', 'FontSize',14, 'FontName','Cambria', 'Box','off');
lgdHdl.Position = [.735,.53,.167,.27];
lgdHdl.ItemTokenSize = [18,8];
demo 11
rng(2)
dataMat = rand([12,12]);
dataMat(dataMat < .85) = 0;
dataMat(7,:) = 1.*(rand(1,12)+.1);
dataMat(11,:) = .6.*(rand(1,12)+.1);
dataMat(12,:) = [2.*(rand(1,10)+.1), 0, 0];
CList = [repmat([49,49,49],[10,1]); 235,28,34; 19,146,241]./255;
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','off', 'CData',CList);
BCC = BCC.draw();
% 添加刻度
BCC.tickState('on')
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria', 'FontSize',17)
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.78, 'EdgeColor',[0,0,0])
end
end
end
% 修改方块颜色(Modify the color of the blocks)
for i = 1:size(dataMat, 1)
BCC.setSquareN(i, 'EdgeColor',[0,0,0], 'LineWidth',2)
end
demo 12
dataMat = rand([9,9]);
dataMat(dataMat > .7) = 0;
dataMat(eye(9) == 1) = (rand([1,9])+.2).*3;
CList = [0.85,0.23,0.24
0.96,0.39,0.18
0.98,0.63,0.22
0.99,0.80,0.26
0.70,0.76,0.21
0.24,0.74,0.71
0.27,0.65,0.84
0.09,0.37,0.80
0.64,0.40,0.84];
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList);
BCC = BCC.draw();
% 添加刻度、刻度标签
BCC.tickState('on')
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria', 'FontSize',17)
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.7)
end
end
end
demo 13
rng(2)
dataMat = randi([1,40], [7,4]);
dataMat(rand([7,4]) < .1) = 0;
colName = compose('MATLAB%d', 1:4);
rowName = compose('SL%d', 1:7);
figure('Units','normalized', 'Position',[.02,.05,.7,.85])
CC = chordChart(dataMat, 'rowName',rowName, 'colName',colName, 'Sep',1/80, 'LRadius',1.32);
CC = CC.draw();
% 修改上方方块颜色(Modify the color of the blocks above)
CListT = [0.49,0.64,0.53
0.75,0.39,0.35
0.80,0.74,0.42
0.40,0.55,0.66];
for i = 1:size(dataMat, 2)
CC.setSquareT_N(i, 'FaceColor',CListT(i,:))
end
% 修改下方方块颜色(Modify the color of the blocks below)
CListF = [0.91,0.91,0.97
0.62,0.95,0.66
0.91,0.61,0.20
0.54,0.45,0.82
0.99,0.76,0.81
0.91,0.85,0.83
0.53,0.42,0.43];
for i = 1:size(dataMat, 1)
CC.setSquareF_N(i, 'FaceColor',CListF(i,:))
end
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
CC.setChordMN(i,j, 'FaceColor',CListT(j,:), 'FaceAlpha',.46)
end
end
CC.tickState('on')
CC.tickLabelState('on')
CC.setFont('FontSize',17, 'FontName','Cambria')
CC.setTickFont('FontSize',8, 'FontName','Cambria')
% 绘制图例(Draw legend)
scatterHdl = scatter(10.*ones(size(dataMat,1)),10.*ones(size(dataMat,1)), ...
55, 'filled');
for i = 1:length(scatterHdl)
scatterHdl(i).CData = CListF(i,:);
end
lgdHdl = legend(scatterHdl, rowName, 'Location','best', 'FontSize',16, 'FontName','Cambria', 'Box','off');
set(lgdHdl, 'Position',[.77,.38,.1658,.27])
demo 14
rng(6)
dataMat = randi([1,20], [8,8]);
dataMat(dataMat > 5) = 0;
dataMat(1,:) = randi([1,15], [1,8]);
dataMat(1,8) = 40;
dataMat(8,8) = 60;
dataMat = dataMat./sum(sum(dataMat));
CList = [0.33,0.53,0.86
0.94,0.50,0.42
0.92,0.58,0.30
0.59,0.47,0.45
0.37,0.76,0.82
0.82,0.68,0.29
0.75,0.62,0.87
0.43,0.69,0.57];
NameList={'CHORD', 'CHART', 'AND', 'BICHORD',...
'CHART', 'MADE', 'BY', 'SLANDARER'};
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList, 'Sep',1/12, 'Label',NameList, 'LRadius',1.33);
BCC = BCC.draw();
% 添加刻度
BCC.tickState('on')
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.7, 'EdgeColor',CList(i,:)./1.1)
end
end
end
% 修改方块颜色(Modify the color of the blocks)
for i = 1:size(dataMat, 1)
BCC.setSquareN(i, 'EdgeColor',CList(i,:)./1.7)
end
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria', 'FontSize',17)
BCC.tickLabelState('on')
BCC.setTickFont('FontName','Cambria', 'FontSize',9)
% 调整数值字符串格式
% Adjust numeric string format
BCC.setTickLabelFormat(@(x)[num2str(round(x*100)),'%'])
demo 15
CList = [0.81,0.72,0.83
0.69,0.82,0.89
0.17,0.44,0.64
0.70,0.85,0.55
0.03,0.57,0.13
0.97,0.67,0.64
0.84,0.09,0.12
1.00,0.80,0.46
0.98,0.52,0.01
];
figure('Units','normalized', 'Position',[.02,.05,.53,.85], 'Color',[1,1,1])
% =========================================================================
ax1 = axes('Parent',gcf, 'Position',[0,1/2,1/2,1/2]);
dataMat = rand([9,9]);
dataMat(dataMat > .4) = 0;
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList);
BCC = BCC.draw();
BCC.tickState('on')
BCC.setFont('Visible','off')
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.6)
end
end
end
text(-1.2,1.2, 'a', 'FontName','Times New Roman', 'FontSize',35)
% =========================================================================
ax2 = axes('Parent',gcf, 'Position',[1/2,1/2,1/2,1/2]);
dataMat = rand([9,9]);
dataMat(dataMat > .4) = 0;
dataMat = dataMat.*(1:9);
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList);
BCC = BCC.draw();
BCC.tickState('on')
BCC.setFont('Visible','off')
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.6)
end
end
end
text(-1.2,1.2, 'b', 'FontName','Times New Roman', 'FontSize',35)
% =========================================================================
ax3 = axes('Parent',gcf, 'Position',[0,0,1/2,1/2]);
dataMat = rand([9,9]);
dataMat(dataMat > .4) = 0;
dataMat = dataMat.*(1:9).';
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList);
BCC = BCC.draw();
BCC.tickState('on')
BCC.setFont('Visible','off')
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceAlpha',.6)
end
end
end
text(-1.2,1.2, 'c', 'FontName','Times New Roman', 'FontSize',35)
% =========================================================================
ax4 = axes('Parent',gcf, 'Position',[1/2,0,1/2,1/2]);
ax4.XColor = 'none'; ax4.YColor = 'none';
ax4.XLim = [-1,1]; ax4.YLim = [-1,1];
hold on
NameList = {'Food supply', 'Biodiversity', 'Water quality regulation', ...
'Air quality regulation', 'Erosion control', 'Carbon storage', ...
'Water retention', 'Recreation', 'Soil quality regulation'};
patchHdl = [];
for i = 1:size(dataMat, 2)
patchHdl(i) = fill([10,11,12],[10,13,13], CList(i,:), 'EdgeColor',[0,0,0]);
end
lgdHdl = legend(patchHdl, NameList, 'Location','best', 'FontSize',14, 'FontName','Cambria', 'Box','off');
lgdHdl.Position = [.625,.11,.255,.27];
lgdHdl.ItemTokenSize = [18,8];
demo 16
dataMat = rand([15,15]);
dataMat(dataMat > .2) = 0;
CList = [ 75,146,241; 252,180, 65; 224, 64, 10; 5,100,146; 191,191,191;
26, 59,105; 255,227,130; 18,156,221; 202,107, 75; 0, 92,219;
243,210,136; 80, 99,129; 241,185,168; 224,131, 10; 120,147,190]./255;
CListC = [54,69,92]./255;
CList = CList.*.6 + CListC.*.4;
figure('Units','normalized', 'Position',[.02,.05,.6,.85])
BCC = biChordChart(dataMat, 'Arrow','on', 'CData',CList);
BCC = BCC.draw();
% 添加刻度
BCC.tickState('on')
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria', 'FontSize',17, 'Color',[0,0,0])
% 修改弦颜色(Modify chord color)
for i = 1:size(dataMat, 1)
for j = 1:size(dataMat, 2)
if dataMat(i,j) > 0
BCC.setChordMN(i,j, 'FaceColor',CListC ,'FaceAlpha',.07)
end
end
end
[~, N] = max(sum(dataMat > 0, 2));
for j = 1:size(dataMat, 2)
BCC.setChordMN(N,j, 'FaceColor',CList(N,:) ,'FaceAlpha',.6)
end
You need to download following tools:
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Let S be the closed surface composed of the hemisphere and the base Let be the electric field defined by . Find the electric flux through S. (Hint: Divide S into two parts and calculate ).
% Define the limits of integration for the hemisphere S1
theta_lim = [-pi/2, pi/2];
phi_lim = [0, pi/2];
% Perform the double integration over the spherical surface of the hemisphere S1
% Define the electric flux function for the hemisphere S1
flux_function_S1 = @(theta, phi) 2 * sin(phi);
electric_flux_S1 = integral2(flux_function_S1, theta_lim(1), theta_lim(2), phi_lim(1), phi_lim(2));
% For the base of the hemisphere S2, the electric flux is 0 since the electric
% field has no z-component at the base
electric_flux_S2 = 0;
% Calculate the total electric flux through the closed surface S
total_electric_flux = electric_flux_S1 + electric_flux_S2;
% Display the flux calculations
disp(['Electric flux through the hemisphere S1: ', num2str(electric_flux_S1)]);
disp(['Electric flux through the base of the hemisphere S2: ', num2str(electric_flux_S2)]);
disp(['Total electric flux through the closed surface S: ', num2str(total_electric_flux)]);
% Parameters for the plot
radius = 1; % Radius of the hemisphere
% Create a meshgrid for theta and phi for the plot
[theta, phi] = meshgrid(linspace(theta_lim(1), theta_lim(2), 20), linspace(phi_lim(1), phi_lim(2), 20));
% Calculate Cartesian coordinates for the points on the hemisphere
x = radius * sin(phi) .* cos(theta);
y = radius * sin(phi) .* sin(theta);
z = radius * cos(phi);
% Define the electric field components
Ex = 2 * x;
Ey = 2 * y;
Ez = 2 * z;
% Plot the hemisphere
figure;
surf(x, y, z, 'FaceAlpha', 0.5, 'EdgeColor', 'none');
hold on;
% Plot the electric field vectors
quiver3(x, y, z, Ex, Ey, Ez, 'r');
% Plot the base of the hemisphere
[x_base, y_base] = meshgrid(linspace(-radius, radius, 20), linspace(-radius, radius, 20));
z_base = zeros(size(x_base));
surf(x_base, y_base, z_base, 'FaceColor', 'cyan', 'FaceAlpha', 0.3);
% Additional plot settings
colormap('cool');
axis equal;
grid on;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Hemisphere and Electric Field');
The line integral , where C is the boundary of the square oriented counterclockwise, can be evaluated in two ways:
Using the definition of the line integral:
% Initialize the integral sum
integral_sum = 0;
% Segment C1: x = -1, y goes from -1 to 1
y = linspace(-1, 1);
x = -1 * ones(size(y));
dy = diff(y);
integral_sum = integral_sum + sum(-x(1:end-1) .* dy);
% Segment C2: y = 1, x goes from -1 to 1
x = linspace(-1, 1);
y = ones(size(x));
dx = diff(x);
integral_sum = integral_sum + sum(y(1:end-1).^2 .* dx);
% Segment C3: x = 1, y goes from 1 to -1
y = linspace(1, -1);
x = ones(size(y));
dy = diff(y);
integral_sum = integral_sum + sum(-x(1:end-1) .* dy);
% Segment C4: y = -1, x goes from 1 to -1
x = linspace(1, -1);
y = -1 * ones(size(x));
dx = diff(x);
integral_sum = integral_sum + sum(y(1:end-1).^2 .* dx);
disp(['Direct Method Integral: ', num2str(integral_sum)]);
Plotting the square path
% Define the square's vertices
vertices = [-1 -1; -1 1; 1 1; 1 -1; -1 -1];
% Plot the square
figure;
plot(vertices(:,1), vertices(:,2), '-o');
title('Square Path for Line Integral');
xlabel('x');
ylabel('y');
grid on;
axis equal;
% Add arrows to indicate the path direction (counterclockwise)
hold on;
for i = 1:size(vertices,1)-1
% Calculate direction
dx = vertices(i+1,1) - vertices(i,1);
dy = vertices(i+1,2) - vertices(i,2);
% Reduce the length of the arrow for better visibility
scale = 0.2;
dx = scale * dx;
dy = scale * dy;
% Calculate the start point of the arrow
startx = vertices(i,1) + (1 - scale) * dx;
starty = vertices(i,2) + (1 - scale) * dy;
% Plot the arrow
quiver(startx, starty, dx, dy, 'MaxHeadSize', 0.5, 'Color', 'r', 'AutoScale', 'off');
end
hold off;
Apply Green's Theorem for the line integral
% Define the partial derivatives of P and Q
f = @(x, y) -1 - 2*y; % derivative of -x with respect to x is -1, and derivative of y^2 with respect to y is 2y
% Compute the double integral over the square [-1,1]x[-1,1]
integral_value = integral2(f, -1, 1, 1, -1);
disp(['Green''s Theorem Integral: ', num2str(integral_value)]);
Plotting the vector field related to Green’s theorem
% Define the grid for the vector field
[x, y] = meshgrid(linspace(-2, 2, 20), linspace(-2 ,2, 20));
% Define the vector field components
P = y.^2; % y^2 component
Q = -x; % -x component
% Plot the vector field
figure;
quiver(x, y, P, Q, 'b');
hold on; % Hold on to plot the square on the same figure
% Define the square's vertices
vertices = [-1 -1; -1 1; 1 1; 1 -1; -1 -1];
% Plot the square path
plot(vertices(:,1), vertices(:,2), '-o', 'Color', 'k'); % 'k' for black color
title('Vector Field (P = y^2, Q = -x) with Square Path');
xlabel('x');
ylabel('y');
axis equal;
% Add arrows to indicate the path direction (counterclockwise)
for i = 1:size(vertices,1)-1
% Calculate direction
dx = vertices(i+1,1) - vertices(i,1);
dy = vertices(i+1,2) - vertices(i,2);
% Reduce the length of the arrow for better visibility
scale = 0.2;
dx = scale * dx;
dy = scale * dy;
% Calculate the start point of the arrow
startx = vertices(i,1) + (1 - scale) * dx;
starty = vertices(i,2) + (1 - scale) * dy;
% Plot the arrow
quiver(startx, starty, dx, dy, 'MaxHeadSize', 0.5, 'Color', 'r', 'AutoScale', 'off');
end
hold off;
To solve a surface integral for example the over the sphere easily in MATLAB, you can leverage the symbolic toolbox for a direct and clear solution. Here is a tip to simplify the process:
  1. Use Symbolic Variables and Functions: Define your variables symbolically, including the parameters of your spherical coordinates θ and ϕ and the radius r . This allows MATLAB to handle the expressions symbolically, making it easier to manipulate and integrate them.
  2. Express in Spherical Coordinates Directly: Since you already know the sphere's equation and the relationship in spherical coordinates, define x, y, and z in terms of r , θ and ϕ directly.
  3. Perform Symbolic Integration: Use MATLAB's `int` function to integrate symbolically. Since the sphere and the function are symmetric, you can exploit these symmetries to simplify the calculation.
Here’s how you can apply this tip in MATLAB code:
% Include the symbolic math toolbox
syms theta phi
% Define the limits for theta and phi
theta_limits = [0, pi];
phi_limits = [0, 2*pi];
% Define the integrand function symbolically
integrand = 16 * sin(theta)^3 * cos(phi)^2;
% Perform the symbolic integral for the surface integral
surface_integral = int(int(integrand, theta, theta_limits(1), theta_limits(2)), phi, phi_limits(1), phi_limits(2));
% Display the result of the surface integral symbolically
disp(['The surface integral of x^2 over the sphere is ', char(surface_integral)]);
% Number of points for plotting
num_points = 100;
% Define theta and phi for the sphere's surface
[theta_mesh, phi_mesh] = meshgrid(linspace(double(theta_limits(1)), double(theta_limits(2)), num_points), ...
linspace(double(phi_limits(1)), double(phi_limits(2)), num_points));
% Spherical to Cartesian conversion for plotting
r = 2; % radius of the sphere
x = r * sin(theta_mesh) .* cos(phi_mesh);
y = r * sin(theta_mesh) .* sin(phi_mesh);
z = r * cos(theta_mesh);
% Plot the sphere
figure;
surf(x, y, z, 'FaceColor', 'interp', 'EdgeColor', 'none');
colormap('jet'); % Color scheme
shading interp; % Smooth shading
camlight headlight; % Add headlight-type lighting
lighting gouraud; % Use Gouraud shading for smooth color transitions
title('Sphere: x^2 + y^2 + z^2 = 4');
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
colorbar; % Add color bar to indicate height values
axis square; % Maintain aspect ratio to be square
view([-30, 20]); % Set a nice viewing angle
Hans Scharler
Hans Scharler
Last activity on 19 Apr 2024

Starter MATLAB Script

I am often talking to new MATLAB users. I have put together one script. If you know how this script works, why, and what each line means, you will be well on your way on your MATLAB learning journey.
% Clear existing variables and close figures
clear;
close all;
% Print to the Command Window
disp('Hello, welcome to MATLAB!');
% Create a simple vector and matrix
vector = [1, 2, 3, 4, 5];
matrix = [1, 2, 3; 4, 5, 6; 7, 8, 9];
% Display the created vector and matrix
disp('Created vector:');
disp(vector);
disp('Created matrix:');
disp(matrix);
% Perform element-wise multiplication
result = vector .* 2;
% Display the result of the operation
disp('Result of element-wise multiplication of the vector by 2:');
disp(result);
% Create plot
x = 0:0.1:2*pi; % Generate values from 0 to 2*pi
y = sin(x); % Calculate the sine of these values
% Plotting
figure; % Create a new figure window
plot(x, y); % Plot x vs. y
title('Simple Plot of sin(x)'); % Give the plot a title
xlabel('x'); % Label the x-axis
ylabel('sin(x)'); % Label the y-axis
grid on; % Turn on the grid
disp('This is the end of the script. Explore MATLAB further to learn more!');
Hannah
Hannah
Last activity on 1 Apr 2024

Solar Eclipse

Although, I think I will only get to see a partial eclipse (April 8th!) from where I am at in the U.S. I will always have MATLAB to make my own solar eclipse. Just as good as the real thing.
Code (found on the @MATLAB instagram)
a=716;
v=255;
X=linspace(-10,10,a);
[~,r]=cart2pol(X,X');
colormap(gray.*[1 .78 .3]);
[t,g]=cart2pol(X+2.6,X'+1.4);
image(rescale(-1*(2*sin(t*10)+60*g.^.2),0,v))
hold on
h=exp(-(r-3)).*abs(ifft2(r.^-1.8.*cos(7*rand(a))));
h(r<3)=0;
image(v*ones(a),'AlphaData',rescale(h,0,1))
camva(3.8)
One of the privileges of working at MathWorks is that I get to hang out with some really amazing people. Steve Eddins, of ‘Steve on Image Processing’ fame is one of those people. He recently announced his retirement and before his final day, I got the chance to interview him. See what he had to say over at The MATLAB Blog The Steve Eddins Interview: 30 years of MathWorking
Before we begin, you will need to make sure you have 'sir_age_model.m' installed. Once you've downloaded this folder into your working directory, which can be located at your current folder. If you can see this file in your current folder, then it's safe to use it. If you choose to use MATLAB online or MATLAB Mobile, you may upload this to your MATLAB Drive.
This is the code for the SIR model stratified into 2 age groups (children and adults). For a detailed explanation of how to derive the force of infection by age group.
% Main script to run the SIR model simulation
% Initial state values
initial_state_values = [200000; 1; 0; 800000; 0; 0]; % [S1; I1; R1; S2; I2; R2]
% Parameters
parameters = [0.05; 7; 6; 1; 10; 1/5]; % [b; c_11; c_12; c_21; c_22; gamma]
% Time span for the simulation (3 months, with daily steps)
tspan = [0 90];
% Solve the ODE
[t, y] = ode45(@(t, y) sir_age_model(t, y, parameters), tspan, initial_state_values);
% Plotting the results
plot(t, y);
xlabel('Time (days)');
ylabel('Number of people');
legend('S1', 'I1', 'R1', 'S2', 'I2', 'R2');
title('SIR Model with Age Structure');
What was the cumulative incidence of infection during this epidemic? What proportion of those infections occurred in children?
In the SIR model, the cumulative incidence of infection is simply the decline in susceptibility.
% Assuming 'y' contains the simulation results from the ode45 function
% and 't' contains the time points
% Total cumulative incidence
total_cumulative_incidence = (y(1,1) - y(end,1)) + (y(1,4) - y(end,4));
fprintf('Total cumulative incidence: %f\n', total_cumulative_incidence);
% Cumulative incidence in children
cumulative_incidence_children = (y(1,1) - y(end,1));
% Proportion of infections in children
proportion_infections_children = cumulative_incidence_children / total_cumulative_incidence;
fprintf('Proportion of infections in children: %f\n', proportion_infections_children);
927,447 people became infected during this epidemic, 20.5% of which were children.
Which age group was most affected by the epidemic?
To answer this, we can calculate the proportion of children and adults that became infected.
% Assuming 'y' contains the simulation results from the ode45 function
% and 't' contains the time points
% Proportion of children that became infected
initial_children = 200000; % initial number of susceptible children
final_susceptible_children = y(end,1); % final number of susceptible children
proportion_infected_children = (initial_children - final_susceptible_children) / initial_children;
fprintf('Proportion of children that became infected: %f\n', proportion_infected_children);
% Proportion of adults that became infected
initial_adults = 800000; % initial number of susceptible adults
final_susceptible_adults = y(end,4); % final number of susceptible adults
proportion_infected_adults = (initial_adults - final_susceptible_adults) / initial_adults;
fprintf('Proportion of adults that became infected: %f\n', proportion_infected_adults);
Throughout this epidemic, 95% of all children and 92% of all adults were infected. Children were therefore slightly more affected in proportion to their population size, even though the majority of infections occurred in adults.