eqn =
Results for
The int function in the Symbolic Toolbox has a hold/release functionality wherein the expression can be held to delay evaluation
syms x I
eqn = I == int(x,x,'Hold',true)
which allows one to show the integral, and then use release to show the result
release(eqn)
Maybe it would be nice to be able to hold/release any symbolic expression to delay the engine from doing evaluations/simplifications that it typically does. For example:
x*(x+1)/x, sin(sym(pi)/3)
If I'm trying to show a sequence of steps to develop a result, maybe I want to explicitly keep the x/x in the first case and then say "now the x in the numerator and denominator cancel and the result is ..." followed by the release command to get the final result.
Perhaps held expressions could even be nested to show a sequence of results upon subsequent releases.
Held expressions might be subject to other limitations, like maybe they can't be fplotted.
Seems like such a capability might not be useful for problem solving, but might be useful for exposition, instruction, etc.
I want to build a neural network that takes a matrix A as input and outputs a matrix B such that a constant C=f(A,B)is maximized as much as possible.(The function f()is a custom complex computation function involving random values,probability density,matrix norms,and a series of other calculations).
I tried to directly use 1/f(A,B)or-f(A,B)as the loss function,but I encountered an error stating:"The value to be differentiated is not tracked.It must be a tracked real number dlarray scalar.Use dlgradient to track variables in the function called by dlfeval."I suspect this is likely because f(A,B)is not differentiable.
However,I've also seen people say that no matter what function it is,the dlgradient function can differentiate it.
So,I'm not sure whether it's because the function f()is too complex to be used as a loss function to calculate gradients,or if there's an issue with my code.
If I can't directly use its reciprocal or negative as the loss function,how should I go about training this neural network?Currently,I only know how to implement:providing target values and using functions like mse or huber as loss functions.
We will be updating the MATLAB Answers infrastructure at 1PM EST today. We do not expect any disruption of service during this time. However, if you notice any issues, please be patient and try again later. Thank you for your understanding.
I am very excited to share my new book "Data-driven method for dynamic systems" available through SIAM publishing: https://epubs.siam.org/doi/10.1137/1.9781611978162
This book brings together modern computational tools to provide an accurate understanding of dynamic data. The techniques build on pencil-and-paper mathematical techniques that go back decades and sometimes even centuries. The result is an introduction to state-of-the-art methods that complement, rather than replace, traditional analysis of time-dependent systems. One can find methods in this book that are not found in other books, as well as methods developed exclusively for the book itself. I also provide an example-driven exploration that is (hopefully) appealing to graduate students and researchers who are new to the subject.
Each and every example for the book can be reproduced using the code at this repo: https://github.com/jbramburger/DataDrivenDynSyst
Hope you like it!
Christmas season is underway at my house:
(Sorry - the ornament is not available at the MathWorks Merch Shop -- I made it with a 3-D printer.)
Hello, MATLAB fans!
For years, many of you have expressed interest in getting your hands on some cool MathWorks merchandise. I'm thrilled to announce that the wait is over—the MathWorks Merch Shop is officially open!
In our shop, you'll find a variety of exciting items, including baseball caps, mugs, T-shirts, and YETI bottles.
Visit the shop today and explore all the fantastic merchandise we have to offer. Happy shopping!
We are thrilled to announce the grand prize winners of our MATLAB Shorts Mini Hack contest! This year, we invited the MATLAB Graphics and Charting team, the authors of the MATLAB functions used in every entry, to be our judges. After careful consideration, they have selected the top three winners:
Judge comments: Realism & detailed comments; wowed us with Manta Ray
2nd place – Jenny Bosten
Judge comments: Topical hacks : Auroras & Wind turbine; beautiful landscapes & nightscapes
3rd place - Vasilis Bellos
Judge comments: Nice algorithms & extra comments; can’t go wrong with Pumpkins
Judge comments: Impressive spring & cubes!
In addition, after validating the votes, we are pleased to announce the top 10 participants on the leaderboard:
Congratulations to all! Your creativity and skills have inspired many of us to explore and learn new skills, and make this contest a big success!
Dear MATLAB contest enthusiasts,
Welcome to the third installment of our interview series with top contest participants! This time we had the pleasure of talking to our all-time rock star – @Jenny Bosten. Every one of her entries is a masterpiece, demonstrating a deep understanding of the relationship between mathematics and aesthetics. Even Cleve Moler, the original author of MATLAB, is impressed and wrote in his blog: "Her code for Time Lapse of Lake View to the West shows she is also a wizard of coordinate systems and color maps."
you to read it to learn more about Jenny’s journey, her creative process, and her favorite entries.
Question: Who would you like to see featured in our next interview? Let us know your thoughts in the comments!
It would be nice to have a function to shade between two curves. This is a common question asked on Answers and there are some File Exchange entries on it but it's such a common thing to want to do I think there should be a built in function for it. I'm thinking of something like
plotsWithShading(x1, y1, 'r-', x2, y2, 'b-', 'ShadingColor', [.7, .5, .3], 'Opacity', 0.5);
So we can specify the coordinates of the two curves, and the shading color to be used, and its opacity, and it would shade the region between the two curves where the x ranges overlap. Other options should also be accepted, like line with, line style, markers or not, etc. Perhaps all those options could be put into a structure as fields, like
plotsWithShading(x1, y1, options1, x2, y2, options2, 'ShadingColor', [.7, .5, .3], 'Opacity', 0.5);
the shading options could also (optionally) be a structure. I know it can be done with a series of other functions like patch or fill, but it's kind of tricky and not obvious as we can see from the number of questions about how to do it.
Does anyone else think this would be a convenient function to add?
My favorite image processing book is The Image Processing Handbook by John Russ. It shows a wide variety of examples of algorithms from a wide variety of image sources and techniques. It's light on math so it's easy to read. You can find both hardcover and eBooks on Amazon.com Image Processing Handbook
There is also a Book by Steve Eddins, former leader of the image processing team at Mathworks. Has MATLAB code with it. Digital Image Processing Using MATLAB
You might also want to look at the free online book http://szeliski.org/Book/
Over the past 4 weeks, 250+ creative short movies have been crafted. We had a lot of fun and, more importantly, learned new skills from each other! Now it’s time to announce week 4 winners.
Nature:
3D:
Seamless loop:
Holiday:
Fractal:
Congratulations! Each of you won your choice of a T-shirt, a hat, or a coffee mug. We will contact you after the contest ends.
Weekly Special Prizes
Thank you for sharing your tips & tricks with the community. These great technical articles will benefit community users for many years. You won a limited-edition pair of MATLAB Shorts!
In week 5, let’s take a moment to sit back, explore all of the interesting entries, and cast your votes. Reflect what you have learned or which entries you like most. Share anything in our Discussions area! There is still time to win our limited-edition MATLAB Shorts.
In the past two years, large language models have brought us significant changes, leading to the emergence of programming tools such as GitHub Copilot, Tabnine, Kite, CodeGPT, Replit, Cursor, and many others. Most of these tools support code writing by providing auto-completion, prompts, and suggestions, and they can be easily integrated with various IDEs.
As far as I know, aside from the MATLAB-VSCode/MatGPT plugin, MATLAB lacks such AI assistant plugins for its native MATLAB-Desktop, although it can leverage other third-party plugins for intelligent programming assistance. There is hope for a native tool of this kind to be built-in.
What incredible short movies can be crafted with no more than 2000 characters of MATLAB code? Discover the creativity in our GALLERY from the MATLAB Shorts Mini Hack contest.
Vote on your favorite short movies by Nov.10th. We are giving out MATLAB T-shirts to 10 lucky voters!
Tips: the more you vote, the higher your chance to win.
Mark your calendar for November 13–14 and get ready for two days of learning, inspiration, and connections!
We are thrilled to announce that MathWork’s incredible María Elena Gavilán Alfonso was selected as a keynote speaker at this year’s MATLAB Expo.
Her session, "From Embedded to Empowered: The Rise of Software-Defined Products," promises to be a game-changer! With her expertise and insights, María is set to inspire and elevate our understanding of the evolving world of software-defined products.
I know we have all been in that all-too-common situation of needing to inefficiently identify prime numbers using only a regular expression... and now Matt Parker from Standup Maths helpfully released a YouTube video entitled "How on Earth does ^.?$|^(..+?)\1+$ produce primes?" in which he explains a simple regular expression (aka Halloween incantation) which matches composite numbers:
Here is my first attempt using MATLAB and Matt Parker's example values:
fnh = @(n) isempty(regexp(repelem('*',n),'^.?$|^(..+?)\1+$','emptymatch'));
fnh(13)
fnh(15)
fnh(101)
fnh(1000)
Feel free to try/modify the incantation yourself. Happy Halloween!
We are thrilled to see the incredible short movies created during Week 3. The bar has been set exceptionally high! This week, we invited our Community Advisory Board (CAB) members to select winners. Here are their picks:
Mini Hack Winners - Week 3
Game:
Holidays:
Fractals:
Realism:
Great Remixes:
Seamless loop:
Fun:
Weekly Special Prizes
Thank you for sharing your tips & tricks with the community. You won a limited-edition MATLAB Shorts.
We still have plenty of MATLAB Shorts available, so be sure to create your posts before the contest ends. Don't miss out on the opportunity to showcase your creativity!
clc
clear
close all
% Load the dataset from a CSV file with headers
data = readtable('C:\Users\PMLS\Downloads\output_file.csv');
% Convert the table to a numeric array
dataArray = table2array(data);
% Normalize inputs and outputs using mapminmax
X = mapminmax(dataArray(:, 1:4)', 0, 1); % Normalize input features to [0, 1]
Y = mapminmax(dataArray(:, 5)', 0, 1); % Normalize target variable to [0, 1]
% Set display format to long for better precision
format long;
%rng(0); % Set random seed for reproducibility
% Create a simpler network with one hidden layer of 20 neurons
%net = feedforwardnet([40,70]);
net = feedforwardnet([70,40]);
% Change activation functions
net.layers{1}.transferFcn = 'poslin'; % ReLU
net.layers{2}.transferFcn = 'logsig'; % logsig
% Set the training function to Resilient Backpropagation
net.trainFcn = 'trainrp';
% Enable data division for validation and testing
net.divideFcn = 'divideblock';
net.divideParam.trainRatio = 0.8; % 70% training data
%net.divideParam.valRatio = 0.15; % 15% validation data
net.divideParam.testRatio = 0.2; % 15% testing data
% Custom training parameters
net.trainParam.epochs = 8000;
net.trainParam.goal = 0.0001;
net.trainParam.min_grad = 1e-6;
net.trainParam.max_fail = 2000;
net.trainParam.lr = 0.001; % Learning rate
net.trainParam.momentum = 0.9; % Momentum
%net.trainParam.batchSize = 10; % Example batch size
% Add regularization
net.performParam.regularization = 0.01; % Example L2 regularization
%Train the neural network
[net, tr] = train(net, X, Y);
% Predict and save results
predicted_ranges = net(X);
outputTable = array2table([X' Y' predicted_ranges'], ...
'VariableNames', {'w1', 'w2', 'w3', 'wpl', 'Actual_Range', 'Predicted_Range'});
writetable(outputTable, 'predicted_ranges_with_trainrp.xlsx');
% Calculate performance metrics
Y = Y'; % Transpose to match predicted output dimensions
predicted_ranges = predicted_ranges';
MAE = mean(abs(Y - predicted_ranges)); % Mean Absolute Error
MSE = mean((Y - predicted_ranges).^2); % Mean Squared Error
RMSE = sqrt(MSE); % Root Mean Square Error
R_squared = 1 - sum((Y - predicted_ranges).^2) / sum((Y - mean(Y)).^2); % R-squared
% Display the results in the command window
disp('Performance Metrics:');
disp(['Mean Absolute Error (MAE): ', num2str(MAE)]);
disp(['Mean Squared Error (MSE): ', num2str(MSE)]);
disp(['Root Mean Square Error (RMSE): ', num2str(RMSE)]);
disp(['R-squared (R^2): ', num2str(R_squared)]);
% Plot performance
plotperform(tr);
view(net);
% Plot the actual and predicted values as lines
figure;
plot(Y, 'b-', 'LineWidth', 1.5); % Plot actual values as a blue line
hold on;
plot(predicted_ranges, 'r--', 'LineWidth', 1.5); % Plot predicted values as a red dashed line
xlabel('Sample');
ylabel('Normalized Range');
legend('Actual Range', 'Predicted Range');
title('Comparison of Actual and Predicted Ranges');
grid on;
