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Zhaoxu Liu / slandarer
Last activity 2024-6-9

How to set the AlphaData of a colorbar?

Many times when ploting, we not only need to set the color of the plot, but also its

transparency, Then how we set the alphaData of colorbar at the same time ?

It seems easy to do so :

data = rand(12,12); 
% Transparency range 0-1, .3-1 for better appearance here
AData = rescale(- data, .3, 1);
% Draw an imagesc with numerical control over colormap and transparency
imagesc(data, 'AlphaData',AData);
colormap(jet); 
ax = gca;
ax.DataAspectRatio = [1,1,1];
ax.TickDir = 'out';          
ax.Box = 'off';
% get colorbar object
CBarHdl = colorbar;
pause(1e-16)
% Modify the transparency of the colorbar
CData = CBarHdl.Face.Texture.CData;
ALim = [min(min(AData)), max(max(AData))];
CData(4,:) = uint8(255.*rescale(1:size(CData, 2), ALim(1), ALim(2)));
CBarHdl.Face.Texture.ColorType = 'TrueColorAlpha';
CBarHdl.Face.Texture.CData = CData;

But !!!!!!!!!!!!!!! We cannot preserve the changes when saving them as images ：

It seems that when saving plots, the `Texture` will be refresh, but the `Face` will not :

however, object Face only have 4 colors to change(The four corners of a quadrilateral), how

can we set more colors ??

`Face` is a quadrilateral object, and we can change the `VertexData` to draw more than one little quadrilaterals:

data = rand(12,12); 
% Transparency range 0-1, .3-1 for better appearance here
AData = rescale(- data, .3, 1);
%Draw an imagesc with numerical control over colormap and transparency
imagesc(data, 'AlphaData',AData);
colormap(jet); 
 
ax = gca;
ax.DataAspectRatio = [1,1,1];  
ax.TickDir = 'out';           
ax.Box = 'off';
% get colorbar object
CBarHdl = colorbar;
pause(1e-16)
% Modify the transparency of the colorbar
CData = CBarHdl.Face.Texture.CData;
ALim = [min(min(AData)), max(max(AData))];
CData(4,:) = uint8(255.*rescale(1:size(CData, 2), ALim(1), ALim(2)));
warning off
CBarHdl.Face.ColorType = 'TrueColorAlpha';
VertexData = CBarHdl.Face.VertexData;
tY = repmat((1:size(CData,2))./size(CData,2), [4,1]);
tY1 = tY(:).'; tY2 = tY  - tY(1,1); tY2(3:4,:) = 0; tY2 = tY2(:).';
tM1 = [tY1.*0 + 1; tY1; tY1.*0 + 1];
tM2 = [tY1.*0; tY2; tY1.*0];
CBarHdl.Face.VertexData = repmat(VertexData, [1,size(CData,2)]).*tM1 + tM2;
CBarHdl.Face.ColorData = reshape(repmat(CData, [4,1]), 4, []);

The higher the value, the more transparent it becomes

data = rand(12,12); 
AData = rescale(- data, .3, 1);
imagesc(data, 'AlphaData',AData);
colormap(jet); 
ax = gca;
ax.DataAspectRatio = [1,1,1];
ax.TickDir = 'out';          
ax.Box = 'off';
CBarHdl = colorbar;
pause(1e-16)
CData = CBarHdl.Face.Texture.CData;
ALim = [min(min(AData)), max(max(AData))];
CData(4,:) = uint8(255.*rescale(size(CData, 2):-1:1, ALim(1), ALim(2)));
warning off
CBarHdl.Face.ColorType = 'TrueColorAlpha';
VertexData = CBarHdl.Face.VertexData;
tY = repmat((1:size(CData,2))./size(CData,2), [4,1]);
tY1 = tY(:).'; tY2 = tY  - tY(1,1); tY2(3:4,:) = 0; tY2 = tY2(:).';
tM1 = [tY1.*0 + 1; tY1; tY1.*0 + 1];
tM2 = [tY1.*0; tY2; tY1.*0];
CBarHdl.Face.VertexData = repmat(VertexData, [1,size(CData,2)]).*tM1 + tM2;
CBarHdl.Face.ColorData = reshape(repmat(CData, [4,1]), 4, []);

More transparent in the middle

data = rand(12,12) - .5; 
AData = rescale(abs(data), .1, .9);
imagesc(data, 'AlphaData',AData);
colormap(jet); 
ax = gca;
ax.DataAspectRatio = [1,1,1];
ax.TickDir = 'out';          
ax.Box = 'off';
CBarHdl = colorbar;
pause(1e-16)
CData = CBarHdl.Face.Texture.CData;
ALim = [min(min(AData)), max(max(AData))];
CData(4,:) = uint8(255.*rescale(abs((1:size(CData, 2)) - (1 + size(CData, 2))/2), ALim(1), ALim(2)));
warning off
CBarHdl.Face.ColorType = 'TrueColorAlpha';
VertexData = CBarHdl.Face.VertexData;
tY = repmat((1:size(CData,2))./size(CData,2), [4,1]);
tY1 = tY(:).'; tY2 = tY  - tY(1,1); tY2(3:4,:) = 0; tY2 = tY2(:).';
tM1 = [tY1.*0 + 1; tY1; tY1.*0 + 1];
tM2 = [tY1.*0; tY2; tY1.*0];
CBarHdl.Face.VertexData = repmat(VertexData, [1,size(CData,2)]).*tM1 + tM2;
CBarHdl.Face.ColorData = reshape(repmat(CData, [4,1]), 4, []);

The code will work if the plot have AlphaData property

data = peaks(30);
AData = rescale(data, .2, 1);
surface(data, 'FaceAlpha','flat','AlphaData',AData);
colormap(jet(100)); 
ax = gca;
ax.DataAspectRatio = [1,1,1];
ax.TickDir = 'out';          
ax.Box = 'off';
view(3)
CBarHdl = colorbar;
pause(1e-16)
CData = CBarHdl.Face.Texture.CData;
ALim = [min(min(AData)), max(max(AData))];
CData(4,:) = uint8(255.*rescale(1:size(CData, 2), ALim(1), ALim(2)));
warning off
CBarHdl.Face.ColorType = 'TrueColorAlpha';
VertexData = CBarHdl.Face.VertexData;
tY = repmat((1:size(CData,2))./size(CData,2), [4,1]);
tY1 = tY(:).'; tY2 = tY  - tY(1,1); tY2(3:4,:) = 0; tY2 = tY2(:).';
tM1 = [tY1.*0 + 1; tY1; tY1.*0 + 1];
tM2 = [tY1.*0; tY2; tY1.*0];
CBarHdl.Face.VertexData = repmat(VertexData, [1,size(CData,2)]).*tM1 + tM2;
CBarHdl.Face.ColorData = reshape(repmat(CData, [4,1]), 4, []);

Athanasios Paraskevopoulos
Last activity 2024-6-9

Discovering an Excellent Resource on Ordinary Differential Equations

While searching the internet for some books on ordinary differential equations, I came across a link that I believe is very useful for all math students and not only. If you are interested in ODEs, it's worth taking the time to study it.

A First Look at Ordinary Differential Equations by Timothy S. Judson is an excellent resource for anyone looking to understand ODEs better. Here's a brief overview of the main topics covered:

Introduction to ODEs: Basic concepts, definitions, and initial differential equations.
Methods of Solution:

Separable equations
First-order linear equations
Exact equations
Transcendental functions

Applications of ODEs: Practical examples and applications in various scientific fields.
Systems of ODEs: Analysis and solutions of systems of differential equations.
Series and Numerical Methods: Use of series and numerical methods for solving ODEs.

This book provides a clear and comprehensive introduction to ODEs, making it suitable for students and new researchers in mathematics. If you're interested, you can explore the book in more detail here: A First Look at Ordinary Differential Equations.

Athanasios Paraskevopoulos
Last activity 2024-6-6

Numerical Simulation of the Discrete Klein-Gordon Equation: A Study on Damped, Driven Nonlinear Wave Systems with Spatially Extended Initial Conditions

The study of the dynamics of the discrete Klein - Gordon equation (DKG) with friction is given by the equation :

In the above equation, W describes the potential function:

to which every coupled unit

adheres. In Eq. (1), the variable $

$ is the unknown displacement of the oscillator occupying the n-th position of the lattice, and

is the discretization parameter. We denote by h the distance between the oscillators of the lattice. The chain (DKG) contains linear damping with a damping coefficient

, while

is the coefficient of the nonlinear cubic term.

For the DKG chain (1), we will consider the problem of initial-boundary values, with initial conditions

and Dirichlet boundary conditions at the boundary points

and

, that is,

Therefore, when necessary, we will use the short notation

for the one-dimensional discrete Laplacian

Now we want to investigate numerically the dynamics of the system (1)-(2)-(3). Our first aim is to conduct a numerical study of the property of Dynamic Stability of the system, which directly depends on the existence and linear stability of the branches of equilibrium points.

For the discussion of numerical results, it is also important to emphasize the role of the parameter

. By changing the time variable

, we rewrite Eq. (1) in the form

. We consider spatially extended initial conditions of the form:

where

is the distance of the grid and

is the amplitude of the initial condition

We also assume zero initial velocity:

the following graphs for

and

% Parameters
L = 200;  % Length of the system
K = 99;  % Number of spatial points
j = 2;  % Mode number
omega_d = 1;  % Characteristic frequency
beta = 1;  % Nonlinearity parameter
delta = 0.05;  % Damping coefficient
% Spatial grid
h = L / (K + 1);
n = linspace(-L/2, L/2, K+2);  % Spatial points
N = length(n);
omegaDScaled = h * omega_d;
deltaScaled = h * delta;
% Time parameters
dt = 1; % Time step
tmax = 3000; % Maximum time
tspan = 0:dt:tmax; % Time vector
% Values of amplitude 'a' to iterate over
a_values = [2, 1.95, 1.9, 1.85, 1.82];  % Modify this array as needed
% Differential equation solver function
function dYdt = odefun(~, Y, N, h, omegaDScaled, deltaScaled, beta)
    U = Y(1:N);
    Udot = Y(N+1:end);
    Uddot = zeros(size(U));
    % Laplacian (discrete second derivative)
    for k = 2:N-1
        Uddot(k) = (U(k+1) - 2 * U(k) + U(k-1)) ;
    end
    % System of equations
    dUdt = Udot;
    dUdotdt = Uddot - deltaScaled * Udot + omegaDScaled^2 * (U - beta * U.^3);
    % Pack derivatives
    dYdt = [dUdt; dUdotdt];
end
% Create a figure for subplots
figure;
% Initial plot
a_init = 2;  % Example initial amplitude for the initial condition plot
U0_init = a_init *  sin((j * pi * h * n) / L); % Initial displacement
U0_init(1) = 0; % Boundary condition at n = 0
U0_init(end) = 0; % Boundary condition at n = K+1
subplot(3, 2, 1);
plot(n, U0_init, 'r.-', 'LineWidth', 1.5, 'MarkerSize', 10); % Line and marker plot
xlabel('$x_n$', 'Interpreter', 'latex');
ylabel('$U_n$', 'Interpreter', 'latex');
title('$t=0$', 'Interpreter', 'latex');
set(gca, 'FontSize', 12, 'FontName', 'Times');
 xlim([-L/2 L/2]);
ylim([-3 3]);
grid on;
% Loop through each value of 'a' and generate the plot
for i = 1:length(a_values)
    a = a_values(i);
    % Initial conditions
    U0 = a * sin((j * pi * h * n) / L); % Initial displacement
    U0(1) = 0; % Boundary condition at n = 0
    U0(end) = 0; % Boundary condition at n = K+1
    Udot0 = zeros(size(U0)); % Initial velocity
    % Pack initial conditions
    Y0 = [U0, Udot0];
    % Solve ODE
    opts = odeset('RelTol', 1e-5, 'AbsTol', 1e-6);
    [t, Y] = ode45(@(t, Y) odefun(t, Y, N, h, omegaDScaled, deltaScaled, beta), tspan, Y0, opts);
    % Extract solutions
    U = Y(:, 1:N);
    Udot = Y(:, N+1:end);
    % Plot final displacement profile
    subplot(3, 2, i+1);
    plot(n, U(end,:), 'b.-', 'LineWidth', 1.5, 'MarkerSize', 10); % Line and marker plot
    xlabel('$x_n$', 'Interpreter', 'latex');
    ylabel('$U_n$', 'Interpreter', 'latex');
    title(['$t=3000$, $a=', num2str(a), '$'], 'Interpreter', 'latex');
    set(gca, 'FontSize', 12, 'FontName', 'Times');
      xlim([-L/2 L/2]);
ylim([-2 2]);
    grid on;
end
% Adjust layout
set(gcf, 'Position', [100, 100, 1200, 900]); % Adjust figure size as needed

Dynamics for the initial condition ,

, for

, for different amplitude values. By reducing the amplitude values, we observe the convergence to equilibrium points of different branches from

and the appearance of values

for which the solution converges to a non-linear equilibrium point

Parameters:

Detection of a stability threshold

: For

, the initial condition ,

, converges to a non-linear equilibrium point

Characteristics for

, with corresponding norm

where the dynamics appear in the first image of the third row, we observe convergence to a non-linear equilibrium point of branch

This has the same norm and the same energy as the previous case but the final state has a completely different profile. This result suggests secondary bifurcations have occurred in branch

By further reducing the amplitude, distinct values of

are discerned: 1.9, 1.85, 1.81 for which the initial condition

with norms

respectively, converges to a non-linear equilibrium point of branch

This equilibrium point has norm

and energy

. The behavior of this equilibrium is illustrated in the third row and in the first image of the third row of Figure 1, and also in the first image of the third row of Figure 2. For all the values between the aforementioned a, the initial condition

converges to geometrically different non-linear states of branch

as shown in the second image of the first row and the first image of the second row of Figure 2, for amplitudes

and

respectively.

Refference:

Dynamics of nonlinear lattices: asymptotic behavior and study of the existence and stability of tracked oscillations-Vetas Konstantinos (2018)

Chen Lin
Last activity 2024-6-13

Introducing a New Discussions Area for Cody Users!

Many MATLAB enthusiasts come Cody to sharpen their skills, face new challenges, and engage in friendly competition. We firmly believe that learning from peers is one of the most effective ways to grow.

With this in mind, the Cody team is thrilled to unveil a new feature aimed at enriching your learning journey: the Cody Discussion Channel. This space is designed for sharing expertise, acquiring new skills, and fostering connections within our community.

On the Cody homepage, you'll now notice a Discussions section, prominently displaying the four most recent posts. For those eager to contribute, we encourage you to familiarize yourself with our posting guidelines before creating a new post. This will help maintain a constructive and valuable exchange of ideas for everyone involved.

Together, let's create an environment where every member feels empowered to share, learn, and connect.

cody

Cody

goc3
Last activity 2024-6-7

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

Cody

Chen Lin
Last activity 2024-10-1，10:01

Welcome to the Cody Discussion Channel! Please Read Before Posting

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.

Content that belongs in the Cody Discussion Channel:

Tips & tricks: Discuss strategies for solving Cody problems that you've found effective.
Ideas or suggestions for improvement: Have thoughts on how to make Cody better? We'd love to hear them.
Issues: Encountering difficulties or bugs with Cody? Let us know so we can address them.
Requests for guidance: Stuck on a Cody problem? Ask for advice or hints, but make sure to show your efforts in attempting to solve the problem first.
General discussions: Anything else related to Cody that doesn't fit into the above categories.

Content that does not belong in the Cody Discussion Channel:

Comments on specific Cody problems: Examples include unclear problem descriptions or incorrect testing suites.
Comments on specific Cody solutions: For example, you find a solution creative or helpful.

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.

Gareth
Last activity 2024-5-30

Podcast highlighting a popular MATLAB community Toolbox.

Check out this episode about PIVLab: https://www.buzzsprout.com/2107763/15106425

Join the conversation with William Thielicke, the developer of PIVlab, as he shares insights into the world of particle image velocimetery (PIV) and its applications. Discover how PIV accurately measures fluid velocities, non invasively revolutionising research across the industries. Delve into the development journey of PI lab, including collaborations, key features and future advancements for aerodynamic studies, explore the advanced hardware setups camera technologies, and educational prospects offered by PIVlab, for enhanced fluid velocity measurements. If you are interested in the hardware he speaks of check out the company: Optolution.

Generative AI

Hans Scharler
Last activity 2024-5-30

Surprised that I was able to create a dice rolling simulation

One of the starter prompts is about rolling two six-sided dice and plot the results. As a hobby, I create my own board games. I was able to use the dice rolling prompt to show how a simple roll and move game would work. That was a great surprise!

playground

Adam Danz
Last activity 2024-5-30

How to leave feedback for documentation pages

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.

Oleksandr
Last activity 2024-5-28

Pricing and Licensing

Let's talk about probability theory in Matlab.

Conditions of the problem - how many more letters do I need to write to the sales department to get an answer?

To get closer to the problem, I need to buy a license under a contract. Maybe sometimes there are responsible employees sitting here who will give me an answer.

Thank you

How i use break in continues data in couple differential? it is possible? by cindyawati cindyawati

David
Last activity 2024-5-28

Week of May 27th - Must-See MATLAB Central Posts

Hello MATLAB Community!

We've had an exciting few weeks filled with insightful discussions, innovative tools, and engaging blog posts from our vibrant community. Here's a highlight of some noteworthy contributions that have sparked interest and inspired us all. Let's dive in!

Interesting Questions

Cindyawati explores the intriguing concept of interrupting continuous data in differential equations to study the effects of drug interventions in disease models. A thought-provoking question that bridges mathematics and medical research.

How to use LQR for setpoint tracking? by Pedro Carvalho

Pedro delves into the application of Linear Quadratic Regulator (LQR) for error dynamics and setpoint tracking, offering insights into control systems and their real-world implications.

Popular Discussions

Unveiling Creativity: An Interview with Zhaoxu Liu / slanderer by Chen Lin

Chen Lin shares an engaging interview with Zhaoxu Liu, shedding light on the creative processes behind some of the most innovative MATLAB contest entries of 2023. A must-read for anyone looking for inspiration!

Latest version of MATLAB-PLOT-CHEAT-SHEET by Zhaoxu Liu / slandarer

Zhaoxu Liu, also known as slanderer, updates the community with the latest version of the MATLAB Plot Cheat Sheet. This resource is invaluable for anyone looking to enhance their data visualization skills.

From File Exchange

Frequency estimation toolbox by Giorgio Matteo Vitetta

Giorgio introduces a toolbox for frequency estimation, making it simpler for users to import signals directly from the MATLAB workspace. A significant contribution for signal processing enthusiasts.

From the Blogs

A Sixty-Year Old Program for Predicting the Future by Cleve Moler

Cleve Moler revisits a classic program for predicting future trends based on census data, offering a fascinating glimpse into the evolution of computational forecasting.

Boost Your App Design Efficiency – Effortless Component Swapping & Labeling in App Designer by Adam Danz

With contributions from Dinesh Kavalakuntla, Adam presents an insightful guide on improving app design workflows in MATLAB App Designer, focusing on component swapping and labeling.

We're incredibly proud of the diverse and innovative contributions our community members make every day. Each post, discussion, and tool not only enriches our knowledge but also inspires others to explore and create. Let's continue to support and learn from each other as we advance in our MATLAB journey.

Happy Coding!

must-see

goc3
Last activity 2024-9-30，11:10

My favorite type of Cody problem is:

https://www.mathworks.com/help/predmaint/ref/lyapunovexponent.html

Jiahe Song
Last activity 2024-5-29

Report Ambiguity: Lyapunov Exponent

In the MATLAB description of the algorithm for Lyapunov exponents, I believe there is ambiguity and misuse.

The lambda(i) in the reference literature signifies the Lyapunov exponent of the entire phase space data after expanding by i time steps, but in the calculation formula provided in the MATLAB help documentation, Y_(i+K) represents the data point at the i-th point in the reconstructed data Y after K steps, and this calculation formula also does not match the calculation code given by MATLAB. I believe there should be some misguidance and misunderstanding here.

According to the symbol regulations in the algorithm description and the MATLAB code, I think the correct formula might be y(i) = 1/dt * 1/N * sum_j( log( ||Y_(j+i) - Y_(j*+i)|| ) )

Oge Marques
Last activity 2024-5-24

New book announcement: "Image Processing Recipes in MATLAB"

📚 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
Last activity 2024-5-23

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.

Jonny Pats
Last activity 2024-5-24

UX Night at MathWorks

Are you local to Boston?

Shape the Future of MATLAB: Join MathWorks' UX Night In-Person!

When: June 25th, 6 to 8 PM

Where: MathWorks Campus in Natick, MA

🌟 Calling All MATLAB Users! Here's your unique chance to influence the next wave of innovations in MATLAB and engineering software. MathWorks invites you to participate in our special after-hours usability studies. Dive deep into the latest MATLAB features, share your valuable feedback, and help us refine our solutions to better meet your needs.

🚀 This Opportunity Is Not to Be Missed:

Exclusive Hands-On Experience: Be among the first to explore new MATLAB features and capabilities.
Voice Your Expertise: Share your insights and suggestions directly with MathWorks developers.
Learn, Discover, and Grow: Expand your MATLAB knowledge and skills through firsthand experience with unreleased features.
Network Over Dinner: Enjoy a complimentary dinner with fellow MATLAB enthusiasts and the MathWorks team. It's a perfect opportunity to connect, share experiences, and network after work.
Earn Rewards: Participants will not only contribute to the advancement of MATLAB but will also be compensated for their time. Plus, enjoy special MathWorks swag as a token of our appreciation!

👉 Reserve Your Spot Now: Space is limited for these after-hours sessions. If you're passionate about MATLAB and eager to contribute to its development, we'd love to hear from you.

Chen Lin
Last activity 2024-5-22

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!