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goc3
goc3
Last activity on 7 Jun 2024

Trick: Easy Digit Manipulation

There are a host of problems on Cody that require manipulation of the digits of a number. Examples include summing the digits of a number, separating the number into its powers, and adding very large numbers together.
If you haven't come across this trick yet, you might want to write it down (or save it electronically):
digits = num2str(4207) - '0'
That code results in the following:
digits =
4 2 0 7
Now, summing the digits of the number is easy:
sum(digits)
ans =
13
Hello and a warm welcome to everyone! We're excited to have you in the Cody Discussion Channel. To ensure the best possible experience for everyone, it's important to understand the types of content that are most suitable for this channel.
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  • Tips & tricks: Discuss strategies for solving Cody problems that you've found effective.
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  • Comments on specific Cody problems: Examples include unclear problem descriptions or incorrect testing suites.
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Please direct such comments to the Comments section on the problem or solution page itself.
We hope the Cody discussion channel becomes a vibrant space for sharing expertise, learning new skills, and connecting with others.
How to leave feedback on a doc page
Leaving feedback is a two-step process. At the bottom of most pages in the MATLAB documentation is a star rating.
Start by selecting a star that best answers the question. After selecting a star rating, an edit box appears where you can offer specific feedback.
When you press "Submit" you'll see the confirmation dialog below. You cannot go back and edit your content, although you can refresh the page to go through that process again.
Tips on leaving feedback
  • Be productive. The reader should clearly understand what action you'd like to see, what was unclear, what you think needs work, or what areas were really helpful.
  • Positive feedback is also helpful. By nature, feedback often focuses on suggestions for changes but it also helps to know what was clear and what worked well.
  • Point to specific areas of the page. This helps the reader to narrow the focus of the page to the area described by your feedback.
What happens to that feedback?
Before working at MathWorks I often left feedback on documentation pages but I never knew what happens after that. One day in 2021 I shared my speculation on the process:
> That feedback is received by MathWorks Gnomes which are never seen nor heard but visit the MathWorks documentation team at night while they are sleeping and whisper selected suggestions into their ears to manipulate their dreams. Occassionally this causes them to wake up with a Eureka moment that leads to changes in the documentation.
I'd like to let you in on the secret which is much less fanciful. Feedback left in the star rating and edit box are collected and periodically reviewed by the doc writers who look for trends on highly trafficked pages and finer grain feedback on less visited pages. Your feedback is important and often results in improvements.
📚 New Book Announcement: "Image Processing Recipes in MATLAB" 📚
I am delighted to share the release of my latest book, "Image Processing Recipes in MATLAB," co-authored by my dear friend and colleague Gustavo Benvenutti Borba.
This 'cookbook' contains 30 practical recipes for image processing, ranging from foundational techniques to recently published algorithms. It serves as a concise and readable reference for quickly and efficiently deploying image processing pipelines in MATLAB.
Gustavo and I are immensely grateful to the MathWorks Book Program for their support. We also want to thank Randi Slack and her fantastic team at CRC Press for their patience, expertise, and professionalism throughout the process.
___________
David
David
Last activity on 23 May 2024

Introduced in...

A colleague said that you can search the Help Center using the phrase 'Introduced in' followed by a release version. Such as, 'Introduced in R2022a'. Doing this yeilds search results specific for that release.
Seems pretty handy so I thought I'd share.
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!
A high school student called for help with this physics problem:
  • Car A moves with constant velocity v.
  • Car B starts to move when Car A passes through the point P.
  • Car B undergoes...
  • uniform acc. motion from P to Q.
  • uniform velocity motion from Q to R.
  • uniform acc. motion from R to S.
  • Car A and B pass through the point R simultaneously.
  • Car A and B arrive at the point S simultaneously.
Q1. When car A passes the point Q, which is moving faster?
Q2. Solve the time duration for car B to move from P to Q using L and v.
Q3. Magnitude of acc. of car B from P to Q, and from R to S: which is bigger?
Well, it can be solved with a series of tedious equations. But... how about this?
Code below:
%% get images and prepare stuffs
figure(WindowStyle="docked"),
ax1 = subplot(2,1,1);
hold on, box on
ax1.XTick = [];
ax1.YTick = [];
A = plot(0, 1, 'ro', MarkerSize=10, MarkerFaceColor='r');
B = plot(0, 0, 'bo', MarkerSize=10, MarkerFaceColor='b');
[carA, ~, alphaA] = imread('https://cdn.pixabay.com/photo/2013/07/12/11/58/car-145008_960_720.png');
[carB, ~, alphaB] = imread('https://cdn.pixabay.com/photo/2014/04/03/10/54/car-311712_960_720.png');
carA = imrotate(imresize(carA, 0.1), -90);
carB = imrotate(imresize(carB, 0.1), 180);
alphaA = imrotate(imresize(alphaA, 0.1), -90);
alphaB = imrotate(imresize(alphaB, 0.1), 180);
carA = imagesc(carA, AlphaData=alphaA, XData=[-0.1, 0.1], YData=[0.9, 1.1]);
carB = imagesc(carB, AlphaData=alphaB, XData=[-0.1, 0.1], YData=[-0.1, 0.1]);
txtA = text(0, 0.85, 'A', FontSize=12);
txtB = text(0, 0.17, 'B', FontSize=12);
yline(1, 'r--')
yline(0, 'b--')
xline(1, 'k--')
xline(2, 'k--')
text(1, -0.2, 'Q', FontSize=20, HorizontalAlignment='center')
text(2, -0.2, 'R', FontSize=20, HorizontalAlignment='center')
% legend('A', 'B') % this make the animation slow. why?
xlim([0, 3])
ylim([-.3, 1.3])
%% axes2: plots velocity graph
ax2 = subplot(2,1,2);
box on, hold on
xlabel('t'), ylabel('v')
vA = plot(0, 1, 'r.-');
vB = plot(0, 0, 'b.-');
xline(1, 'k--')
xline(2, 'k--')
xlim([0, 3])
ylim([-.3, 1.8])
p1 = patch([0, 0, 0, 0], [0, 1, 1, 0], [248, 209, 188]/255, ...
EdgeColor = 'none', ...
FaceAlpha = 0.3);
%% solution
v = 1; % car A moves with constant speed.
L = 1; % distances of P-Q, Q-R, R-S
% acc. of car B for three intervals
a(1) = 9*v^2/8/L;
a(2) = 0;
a(3) = -1;
t_BatQ = sqrt(2*L/a(1)); % time when car B arrives at Q
v_B2 = a(1) * t_BatQ; % speed of car B between Q-R
%% patches for velocity graph
p2 = patch([t_BatQ, t_BatQ, t_BatQ, t_BatQ], [1, 1, v_B2, v_B2], ...
[248, 209, 188]/255, ...
EdgeColor = 'none', ...
FaceAlpha = 0.3);
p3 = patch([2, 2, 2, 2], [1, v_B2, v_B2, 1], [194, 234, 179]/255, ...
EdgeColor = 'none', ...
FaceAlpha = 0.3);
%% animation
tt = linspace(0, 3, 2000);
for t = tt
A.XData = v * t;
vA.XData = [vA.XData, t];
vA.YData = [vA.YData, 1];
if t < t_BatQ
B.XData = 1/2 * a(1) * t^2;
vB.XData = [vB.XData, t];
vB.YData = [vB.YData, a(1) * t];
p1.XData = [0, t, t, 0];
p1.YData = [0, vB.YData(end), 1, 1];
elseif t >= t_BatQ && t < 2
B.XData = L + (t - t_BatQ) * v_B2;
vB.XData = [vB.XData, t];
vB.YData = [vB.YData, v_B2];
p2.XData = [t_BatQ, t, t, t_BatQ];
p2.YData = [1, 1, vB.YData(end), vB.YData(end)];
else
B.XData = 2*L + v_B2 * (t - 2) + 1/2 * a(3) * (t-2)^2;
vB.XData = [vB.XData, t];
vB.YData = [vB.YData, v_B2 + a(3) * (t - 2)];
p3.XData = [2, t, t, 2];
p3.YData = [1, 1, vB.YData(end), v_B2];
end
txtA.Position(1) = A.XData(end);
txtB.Position(1) = B.XData(end);
carA.XData = A.XData(end) + [-.1, .1];
carB.XData = B.XData(end) + [-.1, .1];
drawnow
end
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!
Updating some of my educational Livescripts to 2024a, really love the new "define a function anywhere" feature, and have a "new" idea for improving Livescripts -- support "hidden" code blocks similar to the Jupyter Notebooks functionality.
For example, I often create "complicated" plots with a bunch of ancillary items and I don't want this code exposed to the reader by default, as it might confuse the reader. For example, consider a Livescript that might read like this:
-----
Noting the similar structure of these two mappings, let's now write a function that simply maps from some domain to some other domain using change of variable.
function x = ChangeOfVariable( x, from_domain, to_domain )
x = x - from_domain(1);
x = x * ( ( to_domain(2) - to_domain(1) ) / ( from_domain(2) - from_domain(1) ) );
x = x + to_domain(1);
end
Let's see this function in action
% HIDE CELL
clear
close all
from_domain = [-1, 1];
to_domain = [2, 7];
from_values = [-1, -0.5, 0, 0.5, 1];
to_values = ChangeOfVariable( from_values, from_domain, to_domain )
to_values = 1×5
2.0000 3.2500 4.5000 5.7500 7.0000
We can plot the values of from_values and to_values, showing how they're connected to each other:
% HIDE CELL
figure
hold on
for n = 1 : 5
plot( [from_values(n) to_values(n)], [1 0], Color="k", LineWidth=1 )
end
ax = gca;
ax.YTick = [];
ax.XLim = [ min( [from_domain, to_domain] ) - 1, max( [from_domain, to_domain] ) + 1 ];
ax.YLim = [-0.5, 1.5];
ax.XGrid = "on";
scatter( from_values, ones( 5, 1 ), Marker="s", MarkerFaceColor="flat", MarkerEdgeColor="k", SizeData=120, LineWidth=1, SeriesIndex=1 )
text( mean( from_domain ), 1.25, "$\xi$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
scatter( to_values, zeros( 5, 1 ), Marker="o", MarkerFaceColor="flat", MarkerEdgeColor="k", SizeData=120, LineWidth=1, SeriesIndex=2 )
text( mean( to_domain ), -0.25, "$x$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
scaled_arrow( ax, [mean( [from_domain(1), to_domain(1) ] ) - 1, 0.5], ( 1 - 0 ) / ( from_domain(1) - to_domain(1) ), 1 )
scaled_arrow( ax, [mean( [from_domain(end), to_domain(end)] ) + 1, 0.5], ( 1 - 0 ) / ( from_domain(end) - to_domain(end) ), -1 )
text( mean( [from_domain(1), to_domain(1) ] ) - 1.5, 0.5, "$x(\xi)$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
text( mean( [from_domain(end), to_domain(end)] ) + 1.5, 0.5, "$\xi(x)$", Interpreter="latex", HorizontalAlignment="center", VerticalAlignment="middle" )
-----
Where scaled_arrow is some utility function I've defined elsewhere... See how a majority of the code is simply "drivel" to create the plot, clear and close? I'd like to be able to hide those cells so that it would look more like this:
-----
Noting the similar structure of these two mappings, let's now write a function that simply maps from some domain to some other domain using change of variable.
function x = ChangeOfVariable( x, from_domain, to_domain )
x = x - from_domain(1);
x = x * ( ( to_domain(2) - to_domain(1) ) / ( from_domain(2) - from_domain(1) ) );
x = x + to_domain(1);
end
Let's see this function in action
▶ Show code cell
from_domain = [-1, 1];
to_domain = [2, 7];
from_values = [-1, -0.5, 0, 0.5, 1];
to_values = ChangeOfVariable( from_values, from_domain, to_domain )
to_values = 1×5
2.0000 3.2500 4.5000 5.7500 7.0000
We can plot the values of from_values and to_values, showing how they're connected to each other:
▶ Show code cell
-----
Thoughts?
I recently had issues with code folding seeming to disappear and it turns out that I had unknowingly disabled the "show code folding margin" option by accident. Despite using MATLAB for several years, I had no idea this was an option, especially since there seemed to be no references to it in the code folding part of the "Preferences" menu.
It would be great if in the future, there was a warning that told you about this when you try enable/disable folding in the Preferences.
I am using 2023b by the way.
In the MATLAB editor, when clicking on a variable name, all the other instances of the variable name will be highlighted.
But this does not work for structure fields, which is a pity. Such feature would be quite often useful for me.
I show an illustration below, and compare it with Visual Studio Code that does it. ;-)
I am using MATLAB R2023a, sorry if it has been added to newer versions, but I didn't see it in the release notes.
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
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:
In short: support varying color in at least the plot, plot3, fplot, and fplot3 functions.
This has been a thing that's come up quite a few times, and includes questions/requests by users, workarounds by the community, and workarounds presented by MathWorks -- examples of each below. It's a feature that exists in Python's Matplotlib library and Sympy. Anyways, given that there are myriads of workarounds, it appears to be one of the most common requests for Matlab plots (Matlab's plotting is, IMO, one of the best features of the product), the request precedes the 21st century, and competitive tools provide the functionality, it would seem to me that this might be the next great feature for Matlab plotting.
I'm curious to get the rest of the community's thoughts... what's everyone else think about this?
---
User questions/requests
User-provided workarounds
MathWorks-provided workarounds
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!');
I would like to propose the creation of MATLAB EduHub, a dedicated channel within the MathWorks community where educators, students, and professionals can share and access a wealth of educational material that utilizes MATLAB. This platform would act as a central repository for articles, teaching notes, and interactive learning modules that integrate MATLAB into the teaching and learning of various scientific fields.
Key Features:
1. Resource Sharing: Users will be able to upload and share their own educational materials, such as articles, tutorials, code snippets, and datasets.
2. Categorization and Search: Materials can be categorized for easy searching by subject area, difficulty level, and MATLAB version..
3. Community Engagement: Features for comments, ratings, and discussions to encourage community interaction.
4. Support for Educators: Special sections for educators to share teaching materials and track engagement.
Benefits:
- Enhanced Educational Experience: The platform will enrich the learning experience through access to quality materials.
- Collaboration and Networking: It will promote collaboration and networking within the MATLAB community.
- Accessibility of Resources: It will make educational materials available to a wider audience.
By establishing MATLAB EduHub, I propose a space where knowledge and experience can be freely shared, enhancing the educational process and the MATLAB community as a whole.
Zhaoxu Liu / slandarer
Zhaoxu Liu / slandarer
Last activity on 15 Mar 2024

Happy Pi Day !!

Happy Pi Day!
3.14 π Day has arrived, and this post provides some very cool pi implementations and complete MATLAB code.
https://www.mathworks.com/matlabcentral/fileexchange/126210-happy-pi-day
Firstly, in order to obtain the first n decimal places of pi, we need to write the following code (to prevent inaccuracies, we need to take a few more tails and perform another operation of taking the first n decimal places when needed):
function Pi=getPi(n)
if nargin<1,n=3;end
Pi=char(vpa(sym(pi),n+10));
Pi=abs(Pi)-48;
Pi=Pi(3:n+2);
end
With this function to obtain the decimal places of pi, our visualization journey has begun~Step by step, from simple to complex~(Please try to use newer versions of MATLAB to run, at least R17b)
1 Pie chart
Just calculate the proportion of each digit to the first 1500 decimal places:
% 获取pi前1500位小数
Pi=getPi(1500);
% 统计各个数字出现次数
numNum=find([diff(sort(Pi)),1]);
numNum=[numNum(1),diff(numNum)];
% 配色列表
CM=[20,164,199;43,187,170;53,165,81;189,190,28;248,167,22;
232,74,27;244,57,99;240,118,177;168,109,195;78,125,187]./255;
% 绘图并修饰
pieHdl=pie(numNum);
set(gcf,'Color',[1,1,1],'Position',[200,100,620,620]);
for i=1:2:20
pieHdl(i).EdgeColor=[1,1,1];
pieHdl(i).LineWidth=1;
pieHdl(i).FaceColor=CM((i+1)/2,:);
end
for i=2:2:20
pieHdl(i).Color=CM(i/2,:);
pieHdl(i).FontWeight='bold';
pieHdl(i).FontSize=14;
end
% 绘制图例并修饰
lgdHdl=legend(num2cell('0123456789'));
lgdHdl.FontWeight='bold';
lgdHdl.FontSize=11;
lgdHdl.TextColor=[.5,.5,.5];
lgdHdl.Location='southoutside';
lgdHdl.Box='off';
lgdHdl.NumColumns=10;
lgdHdl.ItemTokenSize=[20,15];
title("VISUALIZING \pi 'Pi' Chart | 1500 digits",'FontSize',18,...
'FontName','Times New Roman','Color',[.5,.5,.5])
2 line chart
Calculate the change in the proportion of each number:
% 获取pi前1500位小数
Pi=getPi(1500);
% 计算比例变化
Ratio=cumsum(Pi==(0:9)',2);
Ratio=Ratio./sum(Ratio);
D=1:length(Ratio);
% 配色列表
CM=[20,164,199;43,187,170;53,165,81;189,190,28;248,167,22;
232,74,27;244,57,99;240,118,177;168,109,195;78,125,187]./255;
hold on
% 循环绘图
for i=1:10
plot(D(20:end),Ratio(i,20:end),'Color',[CM(i,:),.6],'LineWidth',1.8)
end
% 坐标区域修饰
ax=gca;box on;grid on
ax.YLim=[0,.2];
ax.YTick=0:.05:.2;
ax.XTick=0:200:1400;
ax.YTickLabel={'0%','5%','10%','15%','20%'};
ax.XMinorTick='on';
ax.YMinorTick='on';
ax.LineWidth=.8;
ax.GridLineStyle='-.';
ax.FontName='Cambria';
ax.FontSize=11;
ax.XLabel.String='Decimals';
ax.YLabel.String='Proportion';
ax.XLabel.FontSize=13;
ax.YLabel.FontSize=13;
% 绘制图例并修饰
lgdHdl=legend(num2cell('0123456789'));
lgdHdl.NumColumns=5;
lgdHdl.FontWeight='bold';
lgdHdl.FontSize=11;
lgdHdl.TextColor=[.5,.5,.5];
3 stacked area diagram
% 获取pi前500位小数
Pi=getPi(500);
% 计算比例变化
Ratio=cumsum(Pi==(0:9)',2);
Ratio=Ratio./sum(Ratio);
% 配色列表
CM=[231,98,84;239,138,71;247,170,88;255,208,111;255,230,183;
170,220,224;114,188,213;82,143,173;55,103,149;30,70,110]./255;
% 绘制堆叠面积图
hold on
areaHdl=area(Ratio');
for i=1:10
areaHdl(i).FaceColor=CM(i,:);
areaHdl(i).FaceAlpha=.9;
end
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,720,420]);
ax=gca;
ax.YLim=[0,1];
ax.XMinorTick='on';
ax.YMinorTick='on';
ax.LineWidth=.8;
ax.FontName='Cambria';
ax.FontSize=11;
ax.TickDir='out';
ax.XLabel.String='Decimals';
ax.YLabel.String='Proportion';
ax.XLabel.FontSize=13;
ax.YLabel.FontSize=13;
ax.Title.String='Area Chart of Proportion — 500 digits';
ax.Title.FontSize=14;
% 绘制图例并修饰
lgdHdl=legend(num2cell('0123456789'));
lgdHdl.NumColumns=5;
lgdHdl.FontSize=11;
lgdHdl.Location='southeast';
4 connected stacked bar chart
% 获取pi前100位小数
Pi=getPi(100);
% 计算比例变化
Ratio=cumsum(Pi==(0:9)',2);
Ratio=Ratio./sum(Ratio);
X=Ratio(:,10:10:80)';
barHdl=bar(X,'stacked','BarWidth',.2);
CM=[231,98,84;239,138,71;247,170,88;255,208,111;255,230,183;
170,220,224;114,188,213;82,143,173;55,103,149;30,70,110]./255;
for i=1:10
barHdl(i).FaceColor=CM(i,:);
end
% 以下是生成连接的部分
hold on;axis tight
yEndPoints=reshape([barHdl.YEndPoints]',length(barHdl(1).YData),[])';
zeros(1,length(barHdl(1).YData));
yEndPoints=[zeros(1,length(barHdl(1).YData));yEndPoints];
barWidth=barHdl(1).BarWidth;
for i=1:length(barHdl)
for j=1:length(barHdl(1).YData)-1
y1=min(yEndPoints(i,j),yEndPoints(i+1,j));
y2=max(yEndPoints(i,j),yEndPoints(i+1,j));
if y1*y2<0
ty=yEndPoints(find(yEndPoints(i+1,j)*yEndPoints(1:i,j)>=0,1,'last'),j);
y1=min(ty,yEndPoints(i+1,j));
y2=max(ty,yEndPoints(i+1,j));
end
y3=min(yEndPoints(i,j+1),yEndPoints(i+1,j+1));
y4=max(yEndPoints(i,j+1),yEndPoints(i+1,j+1));
if y3*y4<0
ty=yEndPoints(find(yEndPoints(i+1,j+1)*yEndPoints(1:i,j+1)>=0,1,'last'),j+1);
y3=min(ty,yEndPoints(i+1,j+1));
y4=max(ty,yEndPoints(i+1,j+1));
end
fill([j+.5.*barWidth,j+1-.5.*barWidth,j+1-.5.*barWidth,j+.5.*barWidth],...
[y1,y3,y4,y2],barHdl(i).FaceColor,'FaceAlpha',.4,'EdgeColor','none');
end
end
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,720,420]);
ax=gca;box off
ax.YLim=[0,1];
ax.XMinorTick='on';
ax.YMinorTick='on';
ax.LineWidth=.8;
ax.FontName='Cambria';
ax.FontSize=11;
ax.TickDir='out';
ax.XTickLabel={'10','20','30','40','50','60','70','80'};
ax.XLabel.String='Decimals';
ax.YLabel.String='Proportion';
ax.XLabel.FontSize=13;
ax.YLabel.FontSize=13;
ax.Title.String='Area Chart of Proportion — 10-80 digits';
ax.Title.FontSize=14;
% 绘制图例并修饰
lgdHdl=legend(barHdl,num2cell('0123456789'));
lgdHdl.NumColumns=5;
lgdHdl.FontSize=11;
lgdHdl.Location='southeast';
5 bichord chart
Need to use this tool:
https://www.mathworks.com/matlabcentral/fileexchange/121043-digraph-chord-chart
% 构建连接矩阵
dataMat=zeros(10,10);
Pi=getPi(1001);
for i=1:1000
dataMat(Pi(i)+1,Pi(i+1)+1)=dataMat(Pi(i)+1,Pi(i+1)+1)+1;
end
BCC=biChordChart(dataMat,'Arrow','on','Label',num2cell('0123456789'));
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)
set(gcf,'Position',[200,100,820,820]);
6 Gravity simulation diagram
Imagine each decimal as a small ball with a mass of
For example, if, the weight of ball 0 is 1, ball 9 is 1.2589, the initial velocity of the ball is 0, and it is attracted by other balls. Gravity follows the inverse square law, and if the balls are close enough, they will collide and their value will become
After adding, take the mod, add the velocity direction proportionally, and recalculate the weight.
Pi=[3,getPi(71)];K=.18;
% 基础配置
CM=[239,32,120;239,60,52;247,98,32;255,182,60;247,235,44;
142,199,57;55,180,70;0,170,239;40,56,146;147,37,139]./255;
T=linspace(0,2*pi,length(Pi)+1)';
T=T(1:end-1);
ct=linspace(0,2*pi,100);
cx=cos(ct).*.027;
cy=sin(ct).*.027;
% 初始数据
Pi=Pi(:);
N=Pi;
X=cos(T);Y=sin(T);
VX=T.*0;VY=T.*0;
PX=X;PY=Y;
% 未碰撞时初始质量
getM=@(x)(x+1).^K;
M=getM(N);
% 绘制初始圆圈
hold on
for i=1:length(N)
fill(cx+X(i),cy+Y(i),CM(N(i)+1,:),'EdgeColor','w','LineWidth',1)
end
for k=1:800
% 计算加速度
Rn2=1./squareform(pdist([X,Y])).^2;
Rn2(eye(length(X))==1)=0;
MRn2=Rn2.*(M');
AX=X'-X;AY=Y'-Y;
normXY=sqrt(AX.^2+AY.^2);
AX=AX./normXY;AX(eye(length(X))==1)=0;
AY=AY./normXY;AY(eye(length(X))==1)=0;
AX=sum(AX.*MRn2,2)./150000;
AY=sum(AY.*MRn2,2)./150000;
% 计算速度及新位置
VX=VX+AX;X=X+VX;PX=[PX,X];
VY=VY+AY;Y=Y+VY;PY=[PY,Y];
% 检测是否有碰撞
R=squareform(pdist([X,Y]));
R(triu(ones(length(X)))==1)=inf;
[row,col]=find(R<=0.04);
if length(X)==1
break;
end
if ~isempty(row)
% 碰撞的点合为一体
XC=(X(row)+X(col))./2;YC=(Y(row)+Y(col))./2;
VXC=(VX(row).*M(row)+VX(col).*M(col))./(M(row)+M(col));
VYC=(VY(row).*M(row)+VY(col).*M(col))./(M(row)+M(col));
PC=nan(length(row),size(PX,2));
NC=mod(N(row)+N(col),10);
% 删除碰撞点并绘图
uniNum=unique([row;col]);
X(uniNum)=[];VX(uniNum)=[];
Y(uniNum)=[];VY(uniNum)=[];
for i=1:length(uniNum)
plot(PX(uniNum(i),:),PY(uniNum(i),:),'LineWidth',2,'Color',CM(N(uniNum(i))+1,:))
end
PX(uniNum,:)=[];PY(uniNum,:)=[];N(uniNum,:)=[];
% 绘制圆形
for i=1:length(XC)
fill(cx+XC(i),cy+YC(i),CM(NC(i)+1,:),'EdgeColor','w','LineWidth',1)
end
% 补充合体点
X=[X;XC];Y=[Y;YC];VX=[VX;VXC];VY=[VY;VYC];
PX=[PX;PC];PY=[PY;PC];N=[N;NC];M=getM(N);
end
end
for i=1:size(PX,1)
plot(PX(i,:),PY(i,:),'LineWidth',2,'Color',CM(N(i)+1,:))
end
text(-1,1,{['Num=',num2str(length(Pi))];['K=',num2str(K)]},'FontSize',13,'FontName','Cambria')
% 图窗及坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.Position=[0,0,1,1];
ax.DataAspectRatio=[1,1,1];
ax.XLim=[-1.1,1.1];
ax.YLim=[-1.1,1.1];
ax.XTick=[];
ax.YTick=[];
ax.XColor='none';
ax.YColor='none';
7 forest chart
The method comes from
http://mkweb.bcgsc.ca/pi/piday2021
The digits of π are shown as a forest. Each tree in the forest represents the digits of π up to the next 9. The first 10 trees are "grown" from the digit sets 314159, 2653589, 79, 3238462643383279, 50288419, 7169, 39, 9, 3751058209, and 749.
BRANCHES
The first digit of a tree controls how many branches grow from the trunk of the tree. For example, the first tree's first digit is 3, so you see 3 branches growing from the trunk.
The next digit's branches grow from the end of a branch of the previous digit in left-to-right order. This process continues until all the tree's digits have been used up.
Each tree grows from a set of consecutive digits sampled from the digits of π up to the next 9. The first tree, shown here, grows from 314159. Each of the digits determine how many branches grow at each fork in the tree — the branches here are colored by their corresponding digit to illustrate this. Leaves encode the digits in a left-to-right order. The digit 9 spawns a flower on one of the branches of the previous digit. The branching exception is 0, which terminates the current branch — 0 branches grow!
LEAVES AND FLOWERS
The tree's digits themselves are drawn as circular leaves, color-coded by the digit.
The leaf exception is 9, which causes one of the branches of the previous digit to sprout a flower! The petals of the flower are colored by the digit before the 9 and the center is colored by the digit after the 9, which is on the next tree. This is how the forest propagates.
The colors of a flower are determined by the first digit of the next tree and the penultimate digit of the current tree. If the current tree only has one digit, then that digit is used. Leaves are placed at the tips of branches in a left-to-right order — you can "easily" read them off. Additionally, the leaves are distributed within the tree (without disturbing their left-to-right order) to spread them out as much as possible and avoid overlap. This order is deterministic.
The leaf placement exception are the branch set that sprouted the flower. These are not used to grow leaves — the flower needs space!
function PiTree(X,pos,D)
lw=2;
theta=pi/2+(rand(1)-.5).*pi./12;
% 树叶及花朵颜色
CM=[237,32,121;237,62,54;247,99,33;255,183,59;245,236,43;
141,196,63;57,178,74;0,171,238;40,56,145;146,39,139]./255;
hold on
if all(X(1:end-2)==0)
endSet=[pos,pos,theta];
else
kplot(pos(1)+[0,cos(theta)],pos(2)+[0,sin(theta)],lw./.6)
endSet=[pos,pos+[cos(theta),sin(theta)],theta];
% 计算层级
Layer=0;
for i=1:length(X)
Layer=[Layer,ones(1,X(i)).*i];
end
% 计算树枝
if D
for i=1:length(X)-2
if X(i)==0 % 若数值为0则不长树枝
newSet=endSet(1,:);
elseif X(i)==1 % 若数值为1则一长一短两个树枝
tTheta=endSet(1,5);
tTheta=linspace(tTheta+pi/8,tTheta-pi/8,2)'+(rand([2,1])-.5).*pi./8;
newSet=repmat(endSet(1,3:4),[X(i),1]);
newSet=[newSet.*[1;1],newSet+[cos(tTheta),sin(tTheta)].*.7^Layer(i).*[1;.1],tTheta];
else % 其他情况数值为几长几个树枝
tTheta=endSet(1,5);
tTheta=linspace(tTheta+pi/5,tTheta-pi/5,X(i))'+(rand([X(i),1])-.5).*pi./8;
newSet=repmat(endSet(1,3:4),[X(i),1]);
newSet=[newSet,newSet+[cos(tTheta),sin(tTheta)].*.7^Layer(i),tTheta];
end
% 绘制树枝
for j=1:size(newSet,1)
kplot(newSet(j,[1,3]),newSet(j,[2,4]),lw.*.6^Layer(i))
end
endSet=[endSet;newSet];
endSet(1,:)=[];
end
end
end
% 计算叶子和花朵位置
FLSet=endSet(:,3:4);
[~,FLInd]=sort(FLSet(:,1));
FLSet=FLSet(FLInd,:);
[~,tempInd]=sort(rand([1,size(FLSet,1)]));
tempInd=sort(tempInd(1:length(X)-2));
flowerInd=tempInd(randi([1,length(X)-2],[1,1]));
leafInd=tempInd(tempInd~=flowerInd);
% 绘制树叶
for i=1:length(leafInd)
scatter(FLSet(leafInd(i),1),FLSet(leafInd(i),2),70,'filled','CData',CM(X(i)+1,:))
end
% 绘制花朵
for i=1:5
% if ~D
% tC=CM(X(end)+1,:);
% else
% tC=CM(X(end-2)+1,:);
% end
scatter(FLSet(flowerInd,1)+cos(pi*2*i/5).*.18,FLSet(flowerInd,2)+sin(pi*2*i/5).*.18,60,...
'filled','CData',CM(X(end-2)+1,:),'MarkerEdgeColor',[1,1,1])
end
scatter(FLSet(flowerInd,1),FLSet(flowerInd,2),60,'filled','CData',CM(X(end)+1,:),'MarkerEdgeColor',[1,1,1])
drawnow;%axis tight
% =========================================================================
function kplot(XX,YY,LW,varargin)
LW=linspace(LW,LW*.6,10);%+rand(1,20).*LW./10;
XX=linspace(XX(1),XX(2),11)';
XX=[XX(1:end-1),XX(2:end)];
YY=linspace(YY(1),YY(2),11)';
YY=[YY(1:end-1),YY(2:end)];
for ii=1:10
plot(XX(ii,:),YY(ii,:),'LineWidth',LW(ii),'Color',[.1,.1,.1])
end
end
end
main part:
Pi=[3,getPi(800)];
pos9=[0,find(Pi==9)];
set(gcf,'Position',[200,50,900,900],'Color',[1,1,1]);
ax=gca;hold on
ax.Position=[0,0,1,1];
ax.DataAspectRatio=[1,1,1];
ax.XLim=[.5,36];
ax.XTick=[];
ax.YTick=[];
ax.XColor='none';
ax.YColor='none';
for j=1:8
for i=1:11
n=i+(j-1)*11;
if n<=85
tPi=Pi((pos9(n)+1):pos9(n+1)+1);
if length(tPi)>2
PiTree(tPi,[0+i*3,0-j*4],true);
else
PiTree([Pi(pos9(n)),tPi],[0+i*3,0-j*4],false);
end
end
end
end
8 random walk
n=1200;
% 获取pi前n位小数
Pi=getPi(n);
CM=[239,65,75;230,115,48;229,158,57;232,136,85;239,199,97;
144,180,116;78,166,136;81,140,136;90,118,142;43,121,159]./255;
hold on
endPoint=[0,0];
t=linspace(0,2*pi,100);
T=linspace(0,2*pi,11)+pi/2;
fill(endPoint(1)+cos(t).*.5,endPoint(2)+sin(t).*.5,CM(Pi(1)+1,:),'EdgeColor','none')
for i=1:n
theta=T(Pi(i)+1);
plot(endPoint(1)+[0,cos(theta)],endPoint(2)+[0,sin(theta)],'Color',[CM(Pi(i)+1,:),.8],'LineWidth',1.2);
endPoint=endPoint+[cos(theta),sin(theta)];
end
fill(endPoint(1)+cos(t).*.5,endPoint(2)+sin(t).*.5,CM(Pi(n)+1,:),'EdgeColor','none')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
ax.XLim=[-30,5];
ax.YLim=[-5,40];
% 绘制图例
endPoint=[1,35];
for i=1:10
theta=T(i);
plot(endPoint(1)+[0,cos(theta).*2],endPoint(2)+[0,sin(theta).*2],'Color',[CM(i,:),.8],'LineWidth',3);
text(endPoint(1)+cos(theta).*2.7,endPoint(2)+sin(theta).*2.7,num2str(i-1),'Color',[1,1,1].*.7,...
'FontSize',12,'FontWeight','bold','FontName','Cambria','HorizontalAlignment','center')
end
text(-15,35,'Random walk of \pi digits','Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','center','FontSize',25,'FontAngle','italic')
9 grid chart
Pi=[3,getPi(399)];
% 配色数据
CM=[248,65,69;246,152,36;249,198,81;67,170,139;87,118,146]./255;
% 绘制圆圈
hold on
t=linspace(0,2*pi,100);
x=cos(t).*.8.*.5;
y=sin(t).*.8.*.5;
for i=1:400
[col,row]=ind2sub([20,20],i);
if mod(Pi(i),2)==0
fill(x+col,y+row,CM(round((Pi(i)+1)/2),:),'LineWidth',1,'EdgeAlpha',.8)
else
fill(x+col,y+row,[0,0,0],'EdgeColor',CM(round((Pi(i)+1)/2),:),'LineWidth',1,'EdgeAlpha',.7)
end
end
text(10.5,-.4,'\pi on a grid — 400 digits','Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','center','FontSize',25,'FontAngle','italic')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.YDir='reverse';
ax.XLim=[.5,20.5];
ax.YLim=[-1,20.5];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
10 scale grid diagram
Let's still put the numbers in the form of circles, but the difference is that six numbers are grouped together, and the pure purple circle at the end is the six 9s that we are familiar with decimal places 762-767
Pi=[3,getPi(767)];
% 762-767
% 配色数据
CM=[239,32,120;239,60,52;247,98,32;255,182,60;247,235,44;
142,199,57;55,180,70;0,170,239;40,56,146;147,37,139]./255;
% 绘制圆圈
hold on
t=linspace(0,2*pi,100);
x=cos(t).*.9.*.5;
y=sin(t).*.9.*.5;
for i=1:6:length(Pi)
n=round((i-1)/6+1);
[col,row]=ind2sub([10,13],n);
tNum=Pi(i:i+5);
numNum=find([diff(sort(tNum)),1]);
numNum=[numNum(1),diff(numNum)];
cumNum=cumsum(numNum);
uniNum=unique(tNum);
for j=length(cumNum):-1:1
fill(x./6.*cumNum(j)+col,y./6.*cumNum(j)+row,CM(uniNum(j)+1,:),'EdgeColor','none')
end
end
% 绘制图例
for i=1:10
fill(x./4+5.5+(i-5.5)*.32,y./4+14.5,CM(i,:),'EdgeColor','none')
text(5.5+(i-5.5)*.32,14.9,num2str(i-1),'Color',[1,1,1],'FontSize',...
9,'FontName','Cambria','HorizontalAlignment','center')
end
text(5.5,-.2,'FEYNMAN POINT of \pi','Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','center','FontSize',25,'FontAngle','italic')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,600,820]);
ax=gca;
ax.YDir='reverse';
ax.Position=[0,0,1,1];
ax.XLim=[.3,10.7];
ax.YLim=[-1,15.5];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
11 text chart
First, write a code to generate an image of each letter:
function getLogo
if ~exist('image','dir')
mkdir('image\')
end
logoSet=['.',char(65:90)];
for i=1:27
figure();
ax=gca;
ax.XLim=[-1,1];
ax.YLim=[-1,1];
ax.XColor='none';
ax.YColor='none';
ax.DataAspectRatio=[1,1,1];
logo=logoSet(i);
hold on
text(0,0,logo,'HorizontalAlignment','center','FontSize',320,'FontName','Segoe UI Black')
exportgraphics(ax,['image\',logo,'.png'])
close
end
dotPic=imread('image\..png');
newDotPic=uint8(ones([400,size(dotPic,2),3]).*255);
newDotPic(end-size(dotPic,1)+1:end,:,1)=dotPic(:,:,1);
newDotPic(end-size(dotPic,1)+1:end,:,2)=dotPic(:,:,2);
newDotPic(end-size(dotPic,1)+1:end,:,3)=dotPic(:,:,3);
imwrite(newDotPic,'image\..png')
S=20;
for i=1:27
logo=logoSet(i);
tPic=imread(['image\',logo,'.png']);
sz=size(tPic,[1,2]);
sz=round(sz./sz(1).*400);
tPic=imresize(tPic,sz);
tBox=uint8(255.*ones(size(tPic,[1,2])+S));
tBox(S+1:S+size(tPic,1),S+1:S+size(tPic,2))=tPic(:,:,1);
imwrite(cat(3,tBox,tBox,tBox),['image\',logo,'.png'])
end
end
Pi=[3,-1,getPi(150)];
CM=[109,110,113;224,25,33;244,126,26;253,207,2;154,203,57;111,150,124;
121,192,235;6,109,183;190,168,209;151,118,181;233,93,163]./255;
ST={'.','ZERO','ONE','TWO','THREE','FOUR','FIVE','SIX','SEVEN','EIGHT','NINE'};
n=1;
hold on
% 循环绘制字母
for i=1:20%:10
STList='';
NMList=[];
PicListR=uint8(zeros(400,0));
PicListG=uint8(zeros(400,0));
PicListB=uint8(zeros(400,0));
% PicListA=uint8(zeros(400,0));
for j=1:6
STList=[STList,ST{Pi(n)+2}];
NMList=[NMList,ones(size(ST{Pi(n)+2})).*(Pi(n)+2)];
n=n+1;
if length(STList)>15&&length(STList)+length(ST{Pi(n)+2})>20
break;
end
end
for k=1:length(STList)
tPic=imread(['image\',STList(k),'.png']);
% PicListA=[PicListA,tPic(:,:,1)];
PicListR=[PicListR,(255-tPic(:,:,1)).*CM(NMList(k),1)];
PicListG=[PicListG,(255-tPic(:,:,2)).*CM(NMList(k),2)];
PicListB=[PicListB,(255-tPic(:,:,3)).*CM(NMList(k),3)];
end
PicList=cat(3,PicListR,PicListG,PicListB);
image([-1200,1200],[0,150]-(i-1)*150,flipud(PicList))
end
% 图窗及坐标区域修饰
set(gcf,'Position',[200,100,600,820]);
ax=gca;
ax.DataAspectRatio=[1,1,1];
ax.XLim=[-1300,1300];
ax.Position=[0,0,1,1];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.YLim=[-19*150-80,230];
12 spiral chart
Pi=getPi(600);
% 配色列表
CM=[78,121,167;242,142,43;225,87,89;118,183,178;89,161,79;
237,201,72;176,122,161;255,157,167;156,117,95;186,176,172]./255;
% 绘制圆圈
hold on
t=linspace(0,2*pi,100);
x=cos(t).*.8;
y=sin(t).*.8;
for i=1:600
X=i.*cos(i./10)./10;
Y=i.*sin(i./10)./10;
fill(X+x,Y+y,CM(Pi(i)+1,:),'EdgeColor','none','FaceAlpha',.9)
end
text(0,65,'The Circle of \pi','Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','center','FontSize',25,'FontAngle','italic')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.XLim=[-60,60];
ax.YLim=[-60,70];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
13 Archimedean spiral diagram
a=1;b=.227;
Pi=getPi(500);
% 配色列表
CM=[78,121,167;242,142,43;225,87,89;118,183,178;89,161,79;
237,201,72;176,122,161;255,157,167;156,117,95;186,176,172]./255;
% 绘制圆圈
hold on
T=0;R=1;
t=linspace(0,2*pi,100);
x=cos(t).*.7;
y=sin(t).*.7;
for i=1:500
X=R.*cos(T);Y=R.*sin(T);
fill(X+x,Y+y,CM(Pi(i)+1,:),'EdgeColor','none','FaceAlpha',.9)
T=T+1./R.*1.4;
R=a+b*T;
end
text(17.25,22,{'The Archimedes spiral of \pi';'—— 500 digits'},...
'Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','right','FontSize',25,'FontAngle','italic')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.XLim=[-19,18.5];
ax.YLim=[-20,25];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
14 proportional Archimedean spiral diagram
Pi=[3,getPi(1199)];
% 配色数据
CM=[239,32,120;239,60,52;247,98,32;255,182,60;247,235,44;
142,199,57;55,180,70;0,170,239;40,56,146;147,37,139]./255;
% CM=slanCM(184,10);
% 绘制圆圈
hold on
T=0;R=1;
t=linspace(0,2*pi,100);
x=cos(t).*.7;
y=sin(t).*.7;
for i=1:4:length(Pi)
X=R.*cos(T);Y=R.*sin(T);
tNum=Pi(i:i+3);
numNum=find([diff(sort(tNum)),1]);
numNum=[numNum(1),diff(numNum)];
cumNum=cumsum(numNum);
uniNum=unique(tNum);
for j=length(cumNum):-1:1
fill(x./4.*cumNum(j)+X,y./4.*cumNum(j)+Y,CM(uniNum(j)+1,:),'EdgeColor','none')
end
T=T+1./R.*1.4;
R=a+b*T;
end
text(14,16.5,{'The ratio of four numbers from \pi';'—— 1200 digits'},...
'Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','right','FontSize',23,'FontAngle','italic')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.XLim=[-15,15.5];
ax.YLim=[-15,19];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
15 graph
% 构建连接矩阵
corrMat=zeros(10,10);
Pi=getPi(401);
for i=1:400
corrMat(Pi(i)+1,Pi(i+1)+1)=corrMat(Pi(i)+1,Pi(i+1)+1)+1;
end
% 配色列表
colorList=[0.3725 0.2745 0.5647
0.1137 0.4118 0.5882
0.2196 0.6510 0.6471
0.0588 0.5216 0.3294
0.4510 0.6863 0.2824
0.9294 0.6784 0.0314
0.8824 0.4863 0.0196
0.8000 0.3137 0.2431
0.5804 0.2039 0.4314
0.4353 0.2510 0.4392];
t=linspace(0,2*pi,11);t=t(1:10)';
posXY=[cos(t),sin(t)];
maxWidth=max(corrMat(corrMat>0));
minWidth=min(corrMat(corrMat>0));
ttList=linspace(0,1,3)';
% 循环绘图
hold on
for i=1:size(corrMat,1)
for j=i+1:size(corrMat,2)
if corrMat(i,j)>0
tW=(corrMat(i,j)-minWidth)./(maxWidth-minWidth);
colorData=(1-ttList).*colorList(i,:)+ttList.*colorList(j,:);
CData(:,:,1)=colorData(:,1);
CData(:,:,2)=colorData(:,2);
CData(:,:,3)=colorData(:,3);
% 绘制连线
fill(linspace(posXY(i,1),posXY(j,1),3),...
linspace(posXY(i,2),posXY(j,2),3),[0,0,0],'LineWidth',tW.*12+1,...
'CData',CData,'EdgeColor','interp','EdgeAlpha',.7,'FaceAlpha',.7)
end
end
% 绘制圆点
scatter(posXY(i,1),posXY(i,2),200,'filled','LineWidth',1.2,...
'MarkerFaceColor',colorList(i,:),'MarkerEdgeColor',[.7,.7,.7]);
text(posXY(i,1).*1.13,posXY(i,2).*1.13,num2str(i-1),'Color',[1,1,1].*.7,...
'FontSize',30,'FontWeight','bold','FontName','Cambria','HorizontalAlignment','center')
end
text(0,1.3,'Numerical adjacency of \pi — 400 digits','Color',[1,1,1],'FontName','Cambria',...
'HorizontalAlignment','center','FontSize',25,'FontAngle','italic')
% 图窗和坐标区域修饰
set(gcf,'Position',[200,100,820,820]);
ax=gca;
ax.XLim=[-1.2,1.2];
ax.YLim=[-1.21,1.5];
ax.XTick=[];
ax.YTick=[];
ax.Color=[0,0,0];
ax.DataAspectRatio=[1,1,1];
16 circos chart
Need to use this tool:
https://www.mathworks.com/matlabcentral/fileexchange/118655-circos-plot
Class=getPi(1001)+1;
Data=diag(ones(1,1000),-1);
className={'0','1','2','3','4','5','6','7','8','9'};
colorOrder=[239,65,75;230,115,48;229,158,57;232,136,85;239,199,97;
144,180,116;78,166,136;81,140,136;90,118,142;43,121,159]./255;
CC=circosChart(Data,Class,'ClassName',className,'ColorOrder',colorOrder);
CC=CC.draw();
ax=gca;
ax.Color=[0,0,0];
CC.setClassLabel('Color',[1,1,1],'FontSize',25,'FontName','Cambria')
CC.setLine('LineWidth',.7)
YOU CAN GET ALL CODE HERE:
https://www.mathworks.com/matlabcentral/fileexchange/126210-happy-pi-day