Contenuto principale

Results for


Let S be the closed surface composed of the hemisphere and the base Let be the electric field defined by . Find the electric flux through S. (Hint: Divide S into two parts and calculate ).
% Define the limits of integration for the hemisphere S1
theta_lim = [-pi/2, pi/2];
phi_lim = [0, pi/2];
% Perform the double integration over the spherical surface of the hemisphere S1
% Define the electric flux function for the hemisphere S1
flux_function_S1 = @(theta, phi) 2 * sin(phi);
electric_flux_S1 = integral2(flux_function_S1, theta_lim(1), theta_lim(2), phi_lim(1), phi_lim(2));
% For the base of the hemisphere S2, the electric flux is 0 since the electric
% field has no z-component at the base
electric_flux_S2 = 0;
% Calculate the total electric flux through the closed surface S
total_electric_flux = electric_flux_S1 + electric_flux_S2;
% Display the flux calculations
disp(['Electric flux through the hemisphere S1: ', num2str(electric_flux_S1)]);
disp(['Electric flux through the base of the hemisphere S2: ', num2str(electric_flux_S2)]);
disp(['Total electric flux through the closed surface S: ', num2str(total_electric_flux)]);
% Parameters for the plot
radius = 1; % Radius of the hemisphere
% Create a meshgrid for theta and phi for the plot
[theta, phi] = meshgrid(linspace(theta_lim(1), theta_lim(2), 20), linspace(phi_lim(1), phi_lim(2), 20));
% Calculate Cartesian coordinates for the points on the hemisphere
x = radius * sin(phi) .* cos(theta);
y = radius * sin(phi) .* sin(theta);
z = radius * cos(phi);
% Define the electric field components
Ex = 2 * x;
Ey = 2 * y;
Ez = 2 * z;
% Plot the hemisphere
figure;
surf(x, y, z, 'FaceAlpha', 0.5, 'EdgeColor', 'none');
hold on;
% Plot the electric field vectors
quiver3(x, y, z, Ex, Ey, Ez, 'r');
% Plot the base of the hemisphere
[x_base, y_base] = meshgrid(linspace(-radius, radius, 20), linspace(-radius, radius, 20));
z_base = zeros(size(x_base));
surf(x_base, y_base, z_base, 'FaceColor', 'cyan', 'FaceAlpha', 0.3);
% Additional plot settings
colormap('cool');
axis equal;
grid on;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Hemisphere and Electric Field');
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
isempty( [ ] )
10%
isempty( { } )
13%
isempty( '' ) % 2 single quotes
13%
isempty( "" ) % 2 double quotes
24%
c = categorical( [ ] ); isempty(c)
18%
s = struct("a", [ ] ); isempty(s.a)
22%
1324 voti
David
David
Last activity il 1 Apr 2024

Prompts Matter

I was in a meeting the other day and a coworker shared a smiley face they created using the AI Chat Playground. The image looked something like this:
And I suspect the prompt they used was something like this:
"Create a smiley face"
I imagine this output wasn't what my coworker had expected so he was left thinking that this was as good as it gets without manually editing the code, and that the AI Chat Playground couldn't do any better.
I thought I could get a better result using the Playground so I tried a more detailed prompt using a multi-step technique like this:
"Follow these instructions:
- Create code that plots a circle
- Create two smaller circles as eyes within the first circle
- Create an arc that looks like a smile in the lower part of the first circle"
The output of this prompt was better in my opinion.
These queries/prompts are examples of 'zero-shot' prompts, the expectation being a good result with just one query. As opposed to a back-and-forth chat session working towards a desired outcome.
I wonder how many attempts everyone tries before they decide they can't anything more from the AI/LLM. There are times I'll send dozens of chat queries if I feel like I'm getting close to my goal, while other times I'll try just one or two. One thing I always find useful is seeing how others interact with AI models, which is what inspired me to share this.
Does anyone have examples of techniques that work well? I find multi-step instructions often produces good results.
Toshiaki Takeuchi
Toshiaki Takeuchi
Last activity il 1 Apr 2024

Live Script Closed Beta

Looking for 10 candidates for a closed beta on new MATLAB live script features.
Do you use live scripts regularly in MATLAB? Do you collaborate with others using live scripts?
MathWorks is looking for 10 candidates for a closed beta on new features for live scripts. Help us develop exciting new features with your feedback.
Please apply via this web form. https://www.surveymonkey.com/r/TTComm
If you are selected, you will receive an email invitation to sign an NDA
I will post here when the quota is filled
The image was created with DALL-E 3.
Hello, brilliant minds of our engineering community!
We hope this message finds you in the midst of an exciting project or, perhaps, deep in the realms of a challenging problem, because we've got some groundbreaking news that might just make your day a whole lot more interesting.
🎉 Introducing PreAnswer AI - The Future of Community Support! 🎉
Have you ever found yourself pondering over a complex problem, wishing for an answer to magically appear before you even finish formulating the question? Well, wish no more! The MathWorks team, in collaboration with the most imaginative minds from the realms of science fiction, is thrilled to announce the launch of PreAnswer AI, an unprecedented feature set to revolutionize the way we interact within our MATLAB and Simulink community.
What is PreAnswer AI?
PreAnswer AI is our latest AI-driven initiative designed to answer your questions before you even ask them. Yes, you read that right! Through a combination of predictive analytics, machine learning, and a pinch of engineering wizardry, PreAnswer AI anticipates the challenges you're facing and provides you with solutions, insights, and code snippets in real-time.
How Does It Work?
  • Presentiment Algorithms: By simply logging into MATLAB Central, our AI begins to analyze your recent coding patterns, activity, and even the intensity of your keyboard strokes to understand your current state of mind.
  • Predictive Insights: Using a complex algorithm, affectionately dubbed "The Oracle", PreAnswer AI predicts the questions you're likely to ask and compiles comprehensive answers from our vast database of resources.
  • Efficiency and Speed: Imagine the time saved when the answers to your questions are already waiting for you. PreAnswer AI ensures you spend more time innovating and less time searching for solutions.
We are on the cusp of deploying PreAnswer AI in a beta phase and are eager for you to be among the first to experience its benefits. Your feedback will be invaluable as we refine this feature to better suit our community's needs.
---------------------------------------------------------------
Spoiler, it's April 1st if you hadn't noticed. While we might not (yet) have the technology to read minds or predict the future, we do have an incredible community filled with knowledgeable, supportive members ready to tackle any question you throw their way.
Let's continue to collaborate, innovate, and solve complex problems together, proving that while AI can do many things, the power of a united community of brilliant minds is truly unmatched.
Thank you for being such a fantastic part of our community. Here's to many more questions, answers, and shared laughs along the way.
Happy April Fools' Day!
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 il 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!');
Hans Scharler
Hans Scharler
Last activity il 29 Mar 2024

500k YouTube Subscribers!

More than 500,000 people have subscribed to the MATLAB channel. MathWorks would like to thank everyone who has taken the time to watch one of our videos, leave us a comment, or share our videos with others. Together we’re accelerating the pace of engineering and science.
https://www.youtube.com/@MATLAB
Hannah
Hannah
Last activity il 1 Apr 2024

Solar Eclipse

Although, I think I will only get to see a partial eclipse (April 8th!) from where I am at in the U.S. I will always have MATLAB to make my own solar eclipse. Just as good as the real thing.
Code (found on the @MATLAB instagram)
a=716;
v=255;
X=linspace(-10,10,a);
[~,r]=cart2pol(X,X');
colormap(gray.*[1 .78 .3]);
[t,g]=cart2pol(X+2.6,X'+1.4);
image(rescale(-1*(2*sin(t*10)+60*g.^.2),0,v))
hold on
h=exp(-(r-3)).*abs(ifft2(r.^-1.8.*cos(7*rand(a))));
h(r<3)=0;
image(v*ones(a),'AlphaData',rescale(h,0,1))
camva(3.8)
One of the privileges of working at MathWorks is that I get to hang out with some really amazing people. Steve Eddins, of ‘Steve on Image Processing’ fame is one of those people. He recently announced his retirement and before his final day, I got the chance to interview him. See what he had to say over at The MATLAB Blog The Steve Eddins Interview: 30 years of MathWorking
Before we begin, you will need to make sure you have 'sir_age_model.m' installed. Once you've downloaded this folder into your working directory, which can be located at your current folder. If you can see this file in your current folder, then it's safe to use it. If you choose to use MATLAB online or MATLAB Mobile, you may upload this to your MATLAB Drive.
This is the code for the SIR model stratified into 2 age groups (children and adults). For a detailed explanation of how to derive the force of infection by age group.
% Main script to run the SIR model simulation
% Initial state values
initial_state_values = [200000; 1; 0; 800000; 0; 0]; % [S1; I1; R1; S2; I2; R2]
% Parameters
parameters = [0.05; 7; 6; 1; 10; 1/5]; % [b; c_11; c_12; c_21; c_22; gamma]
% Time span for the simulation (3 months, with daily steps)
tspan = [0 90];
% Solve the ODE
[t, y] = ode45(@(t, y) sir_age_model(t, y, parameters), tspan, initial_state_values);
% Plotting the results
plot(t, y);
xlabel('Time (days)');
ylabel('Number of people');
legend('S1', 'I1', 'R1', 'S2', 'I2', 'R2');
title('SIR Model with Age Structure');
What was the cumulative incidence of infection during this epidemic? What proportion of those infections occurred in children?
In the SIR model, the cumulative incidence of infection is simply the decline in susceptibility.
% Assuming 'y' contains the simulation results from the ode45 function
% and 't' contains the time points
% Total cumulative incidence
total_cumulative_incidence = (y(1,1) - y(end,1)) + (y(1,4) - y(end,4));
fprintf('Total cumulative incidence: %f\n', total_cumulative_incidence);
% Cumulative incidence in children
cumulative_incidence_children = (y(1,1) - y(end,1));
% Proportion of infections in children
proportion_infections_children = cumulative_incidence_children / total_cumulative_incidence;
fprintf('Proportion of infections in children: %f\n', proportion_infections_children);
927,447 people became infected during this epidemic, 20.5% of which were children.
Which age group was most affected by the epidemic?
To answer this, we can calculate the proportion of children and adults that became infected.
% Assuming 'y' contains the simulation results from the ode45 function
% and 't' contains the time points
% Proportion of children that became infected
initial_children = 200000; % initial number of susceptible children
final_susceptible_children = y(end,1); % final number of susceptible children
proportion_infected_children = (initial_children - final_susceptible_children) / initial_children;
fprintf('Proportion of children that became infected: %f\n', proportion_infected_children);
% Proportion of adults that became infected
initial_adults = 800000; % initial number of susceptible adults
final_susceptible_adults = y(end,4); % final number of susceptible adults
proportion_infected_adults = (initial_adults - final_susceptible_adults) / initial_adults;
fprintf('Proportion of adults that became infected: %f\n', proportion_infected_adults);
Throughout this epidemic, 95% of all children and 92% of all adults were infected. Children were therefore slightly more affected in proportion to their population size, even though the majority of infections occurred in adults.
Are you going to be in the path of totality? How can you predict, track, and simulate the solar eclipse using MATLAB?
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.
Image Analyst
Image Analyst
Last activity il 17 Maggio 2024

Puzzle challenge - distance to horizon

In one line of MATLAB code, compute how far you can see at the seashore. In otherwords, how far away is the horizon from your eyes? You can assume you know your height and the diameter or radius of the earth.
Adam Danz
Adam Danz
Last activity il 22 Mar 2024

Look at this graph......

Me at the beginning of every meeting
https://youtu.be/sz2mmM-kN1I?si=tD-yaa-1qJy3LrkL
David
David
Last activity il 26 Mar 2024

Pi Day conspiracy

A bit late. Compliments to Chris for sharing.
Hey MATLAB Community! 🌟
March has been bustling with activity on MATLAB Central, bringing forth a treasure trove of insights, innovations, and fun. Whether you're delving into the intricacies of spline conversions or seeking inspiration from Pi Day celebrations, there's something for everyone.
Here’s a roundup of the top posts from the past few weeks that you won't want to miss:
Interesting questions
Steps to convert spline from B-form to pp-form (fn2fm) by @SA-W
Dive into the technicalities of converting spline forms with a focus on calculating coefficients. A must-read for anyone dealing with spline representations.
Unable to tune a pitch-damper autopilot gains with looptune by @Leonardo Molino
Explore the challenges and solutions in tuning autopilot gains within a non-linear model of a business jet aircraft.
Popular discussions
Happy Pi Day !! by @Zhaoxu Liu / slandarer
Celebrate Pi Day with cool MATLAB implementations and code. A delightful read filled with π-inspired creativity.
Integral Ghost by @Athanasios Paraskevopoulos
Get a glimpse of fun with MATLAB through an engaging visual shared by Athanasios. A light-hearted thread that showcases the fun side of mathematics.
From File Exchange
Precipitation-Variability-Analysis-MATLAB by @Kostas Leptokaropoulos
Unlock the secrets of global climate data with MATLAB. This thread offers tools and insights for analyzing precipitation variability.
Puddle Lab by @Nathaniel Barlow
Interact with a numerical puddle in real-time and explore the dynamics of disturbances. A fascinating exploration of fluid dynamics simulation.
From the Blogs
Celebrating Pi Day with cool visualizations by @Jiro Doke
Revisit Pi Day with Jiro's picks of the coolest π visualizations. A post that combines art, math, and the joy of exploration.
MATLAB extension for Visual Studio Code: Yes, it works with GitHub Copilot by @Mike Croucher
Discover the synergy between MATLAB and Visual Studio Code, enhanced by GitHub Copilot support. A game-changer for MATLAB developers.
These threads are just the tip of the iceberg. Each post is a gateway to new knowledge, ideas, and community connections. Dive in, explore, and don't forget to contribute your insights and questions. Together, we make MATLAB Central a vibrant hub of innovation and support.
Happy Coding!