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Have you ever been enrolled in a course that uses an LMS and there is an assignment that invovles posting a question to, or answering a question in, a discussion group? This discussion group is meant to simulate that experience.
For some time now, this has been bugging me - so I thought to gather some more feedback/information/opinions on this.
What would you classify Recursion? As a loop or as a vectorized section of code?
For context, this query occured to me while creating Cody problems involving strict (so to speak) vectorization - (Everyone is more than welcome to check my recent Cody questions).
To make problems interesting and/or difficult, I (and other posters) ban functions and functionalities - such as for loops, while loops, if-else statements, arrayfun() and the rest of the fun() family functions. However, some of the solutions including the reference solution I came up with for my latest problem, contained recursion.
I am rather divided on how to categorize it. What do you think?
I just noticed that MATLAB R2025b is available. I am a bit surprised, as I never got notification of the beta test for it.
This topic is for highlights and experiences with R2025b.
In physics, every fundamental law is associated with a characteristic quantity and its own unit of measurement. For example:
- Newton’s Second Law → Force → Newton (N = kg·m/s²)
- Ohm’s Law → Voltage, current, resistance → Volt (V), Ampere (A), Ohm (Ω)
- Pascal’s Law → Pressure → Pascal (Pa = N/m²)
Similarly, the Law of Varying Inertia (NKTg Law) proposes the existence of a new quantity describing varying inertia, and its unit is called NKTm (Nguyen Khanh Tung – measure).
1. Theoretical Basis
According to the NKTg Law:
NKTg = f(x, v, m)
Where:
- x: position (km or m)
- v: velocity (km/s or m/s)
- m: mass (kg)
- p = m × v: linear momentum (kg·m/s)
Two fundamental quantities are defined:
- NKTg₁ = x × p
- NKTg₂ = (dm/dt) × p
Where:
- NKTg₁: interaction between position and momentum
- NKTg₂: interaction between mass variation and momentum
Both NKTg₁ and NKTg₂ are measured in NKTm, representing “one unit of varying inertia.”
2. Illustrative Example
Case: Neptune – NASA 2023 data
- Position: x = 4.498396440 × 10⁹ km
- Velocity: v = 5.43 km/s
- Mass: m = 1.0243 × 10²⁶ kg
- Momentum: p = m × v = 5.564499 × 10²⁶ kg·m/s
Calculations:
- NKTg₁ = x × p ≈ 2.503 × 10³⁶ NKTm
- NKTg₂ = (dm/dt) × p = (–2.0 × 10⁻⁵) × (5.564499 × 10²⁶) ≈ –1.113 × 10²² NKTm
→ The value of NKTg₁ is extremely large compared with NKTg₂, showing that Neptune’s orbital inertia is highly stable, while mass variation due to gas escape has only a very small effect.
3. Meaning of the NKTm Unit
- Just like the Newton (N) is used to measure force, NKTm is used to measure the degree of varying inertia.
- Applications:
- In astronomy: describing the stability or deviation tendency of planetary orbits
- In Earth science: monitoring annual mass loss due to ice melting or atmospheric escape (GRACE/GRACE-FO)
- In engineering: predicting the stability of systems with variable mass (e.g., rockets burning fuel)
4. Comparison Table
- Newton II – Force → N (Newton) = kg·m/s²
- Newton Gravitation – Gravitational force → N
- Ohm – Voltage, current, resistance → V, A, Ω
- Faraday – Induced electromotive force → V
- Gauss – Electric flux → V·m or N·m²/C
- Pascal – Pressure → Pa = N/m²
- Boyle – Gas pressure & volume → Pa, m³
- Charles – Gas volume & temperature → m³, K
- Stefan–Boltzmann – Radiant energy → W/m²·K⁴
- Planck – Photon energy → J (Joule)
- Ampere – Current & magnetic field → A, T
- Watt – Power → W = J/s
- NKTg – Varying inertia → NKTm
✅ Conclusion:
The NKTm unit is a new contribution to the system of physical measurements, representing and studying varying inertia – a phenomenon that truly exists in the universe but previously had no dedicated unit. This opens new approaches in planetary dynamics, space mechanics, and engineering systems with changing mass.
I came across this fun video from @Christoper Lum, and I have to admit—his MathWorks swag collection is pretty impressive! He’s got pieces I even don’t have.
So now I’m curious… what MathWorks swag do you have hiding in your office or closet?
- Which one is your favorite?
- Which ones do you want to add to your collection?
Show off your swag and share it with the community! 🚀
“Hello, I am Subha & I’m part of the organizing/mentoring team for NASA Space Apps Challenge Virudhunagar 2025 🚀. We’re looking for collaborators/mentors with ML and MATLAB expertise to help our student teams bring their space solutions to life. Would you be open to guiding us, even briefly? Your support could impact students tackling real NASA challenges. 🌍✨”
Nguyễn Khánh Tùng
ORCID iD: 0009-0002-9877-4137
Theoretical Basis
The NKTg Law of Variable Inertia:
An object's tendency of motion in space depends on its position (x), velocity (v), and mass (m).
NKTg = f(x, v, m)
Fundamental interaction quantities:
NKTg1 = x * p
NKTg2 = (dm/dt) * p
where
p = m * v
For interpolation, we use:
m = NKTg1 / (x * v)
Research Objectives
- Verify interpolation of planetary masses using NKTg law.
- Compare with NASA real-time data (31/12/2024).
- Test sensitivity with Earth’s mass loss (NASA GRACE).
MATLAB Implementation
% NKTg Law Verification in MATLAB
% Author: Nguyen Khanh Tung
% Date: 31-12-2024
% Planetary data from NASA (30/12/2024)
planets = {
'Mercury','Venus','Earth','Mars','Jupiter','Saturn','Uranus','Neptune'};
x = [6.9817930e7, 1.08939e8, 1.471e8, 2.4923e8, ...
8.1662e8, 1.50653e9, 3.00139e9, 4.5589e9]; % km
v = [38.86, 35.02, 29.29, 24.07, 13.06, 9.69, 6.8, 5.43]; % km/s
m_nasa = [3.301e23, 4.867e24, 5.972e24, 6.417e23, ...
1.898e27, 5.683e26, 8.681e25, 1.024e26]; % kg
% Compute momentum
p = m_nasa .* v;
% Compute NKTg1
NKTg1 = x .* p;
% Interpolated masses using m = NKTg1 / (x*v)
m_interp = NKTg1 ./ (x .* v);
% Compare results in a table
T = table(planets', m_nasa', m_interp', (m_nasa - m_interp)', ...
'VariableNames', {'Planet','NASA_mass','Interpolated_mass','Delta_m'})
disp(T)
Results
- All 8 planets’ interpolated masses match NASA values almost perfectly.
- Deviation (Delta_m) ≈ 0 → error < 0.0001%.
- Confirms that NKTg1 is conserved across planetary orbits.
Earth’s Mass Loss (GRACE/GRACE-FO)
- GRACE missions show Earth loses mass annually (10^20 – 10^21 kg/year).
- NKTg interpolation detects Δm ≈ 3 × 10^19 kg.
- This matches the lower bound of NASA’s measured range.
Conclusion
- NKTg₁ interpolation is extremely accurate for planetary masses.
- Planetary data can be reconstructed with negligible error.
- NKTg model is sensitive enough to capture Earth’s small annual mass loss.
The functionality would allow report generation straight from live scripts that could be shared without exposing the code. This could be useful for cases where the recipient of the report only cares about the results and not the code details, or when the methodology is part of a company know how, e.g. Engineering services companies.
In order for it to be practical for use it would also require that variable values could be inserted into the text blocks, e.g. #var_name# would insert the value of the variable "var_name" and possibly selecting which code blocks to be hidden.
With AI agents dev coding on other languages has become so easy.
Im waiting for matlab to build something like warp but for matlab.
I know they have the current ai but with all respect it's rubbish compared to vibe coding tools in others sectors.
Matlab leads AI so it really should be leading this space.
Welcome to the launch of our new blog area, Semiconductor Design and Verification! The mission is to empower engineers and designers in the semiconductor industry by streamlining architectural exploration, optimizing the post-processing of simulations, and enabling early verification with MATLAB and Simulink.
Meet Our Authors
We are thrilled to have two esteemed authors:
@Ganesh Rathinavel and @Cristian Macario Macario have both made significant contributions to the advancement of Analog/Mixed-Signal design and the broader communications, electronics, and semiconductor industries. With impressive engineering backgrounds and extensive experience at leading companies such as IMEC, STMicroelectronics, NXP Semiconductors, LSI Corporation, and ARM, they bring a wealth of knowledge and expertise to our blog. Their work is focused on enhancing MathWorks' tools to better align with industry needs.
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Don’t miss the first post: Accelerating Mixed-Signal Design with Early Behavioral Models, where they explore how early behavioral modeling can accelerate mixed-signal design and enhance system efficiency.
I designed and stitched this last week! It uses a total of 20 DMC thread colors, and I frequently stitched with two colors at once to create the gradient.
Add a subtitle
Multi-lined titles have been supported for a long time but starting in r2020b, you can add a subtitle with its own independent properties to a plot in two easy ways.
- Use the new subtitle function: s=subtitle('mySubtitle')
- Use the new second argument to the title function: [t,s]=title('myTitle','mySubtitle')
figure() tiledlayout(2,2)
% Method 1
ax(1) = nexttile;
th(1) = title('Pupil size');
sh(1) = subtitle('Happy faces');
ax(2) = nexttile;
th(2) = title('Pupil size');
sh(2) = subtitle('Sad faces');
% Method 2
ax(3) = nexttile;
[th(3), sh(3)] = title('Fixation duration', 'Happy faces');
ax(4) = nexttile;
[th(4), sh(4)] = title('Fixation duration', 'Sad faces');
set(ax, 'xticklabel', [], 'yticklabel', [],'xlim',[0,1],'ylim',[0,1])
% Set all title colors to orange and subtitles colors to purple. set(th, 'Color', [0.84314, 0.53333, 0.1451]) set(sh, 'Color', [0, 0.27843, 0.56078])
Control title/Label alignment
Title and axis label positions can be changed via their Position, VerticalAlignment and HorizontalAlignment properties but this is usually clumsy and leads to other problems when trying to align the title or labels with an axis edge. For example, when the position units are set to 'data' and the axis limits change, the corresponding axis label will change position relative to the axis edges. If units are normalized and the axis position or size changes, the corresponding label will no longer maintain its relative position to the axis, and that's assuming the normalized position was computed correctly in the first place.
Starting in r2020b, title and axis label alignment can be set to center|left|right, relative to the axis edges.
- TitleHorizontalAlignment is a property of the axis: h.TitleHorizontalAlignment='left';
- LabelHorizontalAlignment is a property of the ruler object that defines the x | y | z axis: h.XAxis.LabelHorizontalAlignment='left';
% Create data x = randi(50,1,100)'; y = x.*[.2, -.2] + (rand(numel(x),2)-.5)*10; gray = [.65 .65 .65];
% Plot comparison between columns of y
figure()
tiledlayout(2,2,'TileSpacing','none')
ax(1) = nexttile(1);
plot(x, y(:,1), 'o', 'color', gray)
lsline
ylabel('Y1 (units)')
title('Regression','Y1 & Y2 separately')
ax(2) = nexttile(3);
plot(x, y(:,2), 'd', 'color', gray)
lsline
xlabel('X Label (units)')
ylabel('Y2 (units)')
grid(ax, 'on')
linkaxes(ax, 'x')
% Move title and labels leftward set(ax, 'TitleHorizontalAlignment', 'left') set([ax.XAxis], 'LabelHorizontalAlignment', 'left') set([ax.YAxis], 'LabelHorizontalAlignment', 'left')
% Combine the two comparisons into plot and flip the second
% y-axis so trend are in the same direction
ax(3) = nexttile([2,1]);
yyaxis('left')
plot(x, y(:,1), 'o')
ylim([-6,16])
lsline
xlabel('X Label (units)')
ylabel('Y1 (units) \rightarrow')
yyaxis('right')
plot(x, y(:,2), 'd')
ylim([-16,6])
lsline
ylabel('\leftarrow Y2 (units)')
title('Direct comparison','(Y2 axis flipped)')
set(ax(3), 'YDir','Reverse')
% Align the ylabels with the minimum axis limit to emphasize the % directions of each axis. Keep the title and xlabel centered ax(3).YAxis(1).LabelHorizontalAlignment = 'left'; ax(3).YAxis(2).LabelHorizontalAlignment = 'right'; ax(3).TitleHorizontalAlignment = 'Center'; % not needed; default value. ax(3).XAxis.LabelHorizontalAlignment = 'Center'; % not needed; default value.
I saw this on Reddit and thought of the past mini-hack contests. We have a few folks here who can do something similar with MATLAB.
In our large open-source MATLAB Central community, there are many long-term excellent user groups. I really want to know why you have been using MATLAB for a long time, and what are its absolute advantages?
I have been using MATLAB for a long time, and there are several reasons for that:
- Fast ramp-up in unfamiliar domains: When I explore an unfamiliar application area or a new topic, MATLAB helps me quickly locate the canonical methods and example workflows. Its comprehensive, professional documentation — along with the related-topic links typically provided at the end of each page — makes it easy to get started intuitively and saves a lot of time that would otherwise be spent hunting for foundational knowledge across the web.
- A relatively cutting-edge yet reliable technical path: MATLAB’s many toolboxes evolve with the field. While updates aren’t always absolutely bleeding-edge, they generally offer approaches that balance modernity and proven reliability. This reduces the risk of wasting time on obscure or unstable algorithms and helps me follow a pragmatic, well-tested technical direction.
- Strong community and technical support: When I encounter a problem I first post on forums like MATLAB Answers and thoroughly investigate the issue myself. If I find a solution, I publish it to contribute back — which deepens my own understanding and helps others. If I can’t solve it alone, experienced community members often respond within hours. As a last resort, MathWorks’ official support is available and typically conducts an in-depth investigation into specific cases to help resolve the issue.
- ......
Also, most individuals have limited time and technical bandwidth, diving deeply into a single, narrow area can be hard to pull back from unless you are committed to that specific direction. For cutting‑edge, highly specialized research it’s often necessary to combine MATLAB with other languages (e.g., Python, C/C++) to go further.
Hello everyone,
I would like to share some results from my recent research on the NKTg law of variable inertia and how it was experimentally verified using NASA JPL Horizons data (Dec 30–31, 2024).
🔹 What is the NKTg Law?
The law states that an object’s tendency of motion depends on the interaction between its position (x), velocity (v), and mass (m) through the conserved quantity:
NKTg1 = x * (m * v)
Here, m * v is the linear momentum.
If NKTg1 > 0 → the object tends to move away from equilibrium.
If NKTg1 < 0 → the object tends to return to equilibrium.
This law provides a new framework for analyzing orbital dynamics.
🔹 Research Objective
Interpolate the masses of all 8 planets using the NKTg law.
Compare results with NASA’s official planetary masses on 31/12/2024.
Test sensitivity for Earth’s mass loss as measured by GRACE / GRACE-FO missions.
🔹 Key Results
Table 1 – Mass Interpolation (31/12/2024)
Planet Interpolated Mass (kg) NASA Mass (kg) Δm Remarks
Mercury 3.301×10^23 3.301×10^23 ≈0 Perfect match
Venus 4.867×10^24 4.867×10^24 ≈0 Negligible error
Earth 5.972×10^24 5.972×10^24 ≈0 GRACE confirms slight variation
Mars 6.417×10^23 6.417×10^23 ≈0 Perfect match
Jupiter 1.898×10^27 1.898×10^27 ≈0 Stable mass
Saturn 5.683×10^26 5.683×10^26 ≈0 Error ≈ zero
Uranus 8.681×10^25 8.681×10^25 ≈0 Matches Voyager 2 data
Neptune 1.024×10^26 1.024×10^26 ≈0 Perfect match
Error rate: < 0.0001% across all planets.
🔹 Earth’s Mass Variation
NASA keeps Earth’s mass constant in official datasets.
GRACE/GRACE-FO show Earth loses ~10^20–10^21 kg annually (gas escape, ice melt, groundwater loss).
NKTg interpolation detected a slight decrease (~3 × 10^19 kg in 2024), which is within GRACE’s measured range.
This demonstrates the sensitivity of the NKTg model in detecting subtle real-world changes.
🔹 Why This Matters
Accuracy: NKTg interpolation perfectly matched NASA’s planetary masses.
Conservation: NKTg1 appears to be a conserved orbital quantity across both rocky and gas planets.
Applications:
- Real-time planetary mass estimation using (x, v) data.
- Integration into orbital mechanics simulations in MATLAB.
- Potential extensions into astrophysics and engineering models.
🔹 Conclusion
The NKTg law provides a novel way to interpolate planetary masses with extremely high accuracy, while also being sensitive to subtle physical changes like Earth’s gradual mass loss.
This could open up new opportunities for:
- Data-driven planetary modeling in MATLAB.
- Improved sensitivity in detecting small-scale variations not included in standard NASA datasets.
References:
- NASA JPL Horizons (planetary positions & velocities)
- NASA Planetary Fact Sheet (official masses)
- GRACE / GRACE-FO Mission Data (Earth mass loss)
I’d be very interested in hearing thoughts from the community about:
- How to integrate the NKTg model into MATLAB orbital simulations.
- Whether conserved quantities like NKTg1 could provide practical value beyond astronomy (e.g., physics simulations, engineering).
Best regards,
Nguyen Khanh Tung
Since R2024b, a Levenberg–Marquardt solver (TrainingOptionsLM) was introduced. The built‑in function trainnet now accepts training options via the trainingOptions function (https://www.mathworks.com/help/deeplearning/ref/trainingoptions.html#bu59f0q-2) and supports the LM algorithm. I have been curious how to use it in deep learning, and the official documentation has not provided a concrete usage example so far. Below I give a simple example to illustrate how to use this LM algorithm to optimize a small number of learnable parameters.
For example, consider the nonlinear function:
y_hat = @(a,t) a(1)*(t/100) + a(2)*(t/100).^2 + a(3)*(t/100).^3 + a(4)*(t/100).^4;
It represents a curve. Given 100 matching points (t → y_hat), we want to use least squares to estimate the four parameters a1–a4.
t = (1:100)';
y_hat = @(a,t)a(1)*(t/100) + a(2)*(t/100).^2 + a(3)*(t/100).^3 + a(4)*(t/100).^4;
x_true = [ 20 ; 10 ; 1 ; 50 ];
y_true = y_hat(x_true,t);
plot(t,y_true,'o-')
- Using the traditional lsqcurvefit-wrapped "Levenberg–Marquardt" algorithm:
x_guess = [ 5 ; 2 ; 0.2 ; -10 ];
options = optimoptions("lsqcurvefit",Algorithm="levenberg-marquardt",MaxFunctionEvaluations=800);
[x,resnorm,residual,exitflag] = lsqcurvefit(y_hat,x_guess,t,y_true,-50*ones(4,1),60*ones(4,1),options);
x,resnorm,exitflag
- Using the deep-learning-wrapped "Levenberg–Marquardt" algorithm:
options = trainingOptions("lm", ...
InitialDampingFactor=0.002, ...
MaxDampingFactor=1e9, ...
DampingIncreaseFactor=12, ...
DampingDecreaseFactor=0.2,...
GradientTolerance=1e-6, ...
StepTolerance=1e-6,...
Plots="training-progress");
numFeatures = 1;
layers = [featureInputLayer(numFeatures,'Name','input')
fitCurveLayer(Name='fitCurve')];
net = dlnetwork(layers);
XData = dlarray(t);
YData = dlarray(y_true);
netTrained = trainnet(XData,YData,net,"mse",options);
netTrained.Layers(2)
classdef fitCurveLayer < nnet.layer.Layer ...
& nnet.layer.Acceleratable
% Example custom SReLU layer.
properties (Learnable)
% Layer learnable parameters
a1
a2
a3
a4
end
methods
function layer = fitCurveLayer(args)
arguments
args.Name = "lm_fit";
end
% Set layer name.
layer.Name = args.Name;
% Set layer description.
layer.Description = "fit curve layer";
end
function layer = initialize(layer,~)
% layer = initialize(layer,layout) initializes the layer
% learnable parameters using the specified input layout.
if isempty(layer.a1)
layer.a1 = rand();
end
if isempty(layer.a2)
layer.a2 = rand();
end
if isempty(layer.a3)
layer.a3 = rand();
end
if isempty(layer.a4)
layer.a4 = rand();
end
end
function Y = predict(layer, X)
% Y = predict(layer, X) forwards the input data X through the
% layer and outputs the result Y.
% Y = layer.a1.*exp(-X./layer.a2) + layer.a3.*X.*exp(-X./layer.a4);
Y = layer.a1*(X/100) + layer.a2*(X/100).^2 + layer.a3*(X/100).^3 + layer.a4*(X/100).^4;
end
end
end
The network is very simple — only the fitCurveLayer defines the learnable parameters a1–a4. I observed that the output values are very close to those from lsqcurvefit.
Hey cody fellows :-) !
I recently created two problem groups, but as you can see I struggle to set their cover images :
What is weird given :
- I already did it successfully twice in the past for my previous groups ;
- If you take one problem specifically, Problem 60984. Mesh the icosahedron for instance, you can normally see the icon of the cover image in the top right hand corner, can't you ?
- I always manage to set cover images to my contributions (mostly in the filexchange).
I already tried several image formats, included .png 4/3 ratio, but still the cover images don't set.
Could you please help me to correctly set my cover images ?
Thank you.
Nicolas
I saw this YouTube short on my feed: What is MATLab?
I was mostly mesmerized by the minecraft gameplay going on in the background.
Found it funny, thought i'd share.
For the www, uk, and in domains,a generative search answer is available for Help Center searches. Please let us know if you get good or bad results for your searches. Some have pointed out that it is not available in non-english domains. You can switch your country setting to try it out. You can also ask questions in different languages and ask for the response in a different language. I get better results when I ask more specific queries. How is it working for you?
Trinity
- It's the question that drives us, Neo. It's the question that brought you here. You know the question, just as I did.
Neo
- What is the Matlab?
Morpheus
- Unfortunately, no one can be told what the Matlab is. You have to see it for yourself.
And also later :
Morpheus
- The Matlab is everywhere. It is all around us. Even now, in this very room. You can feel it when you go to work [...]
The Architect
- The first Matlab I designed was quite naturally perfect. It was a work of art. Flawless. Sublime.
[My Matlab quotes version of the movie (Matrix, 1999) ]
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Get to know your peers while sharing all the tricks you've learned, ideas you've had, or even your latest vacation photos. Discussions is where MATLAB users connect!
Get to know your peers while sharing all the tricks you've learned, ideas you've had, or even your latest vacation photos. Discussions is where MATLAB users connect!
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