結果:
What is a rough number? What can they be used for? Today I'll take you down a journey into the land of prime numbers (in MATLAB). But remember that a journey is not always about your destination, but about what you learn along the way. And so, while this will be all about primes, and specifically large primes, before we get there we need some background. That will start with rough numbers.
Rough numbers are what I would describe as wannabe primes. Almost primes, and even sometimes prime, but often not prime. They could've been prime, but may not quite make it to the top. (If you are thinking of Marlon Brando here, telling us he "could've been a contender", you are on the right track.)
Mathematically, we could call a number k-rough if it is evenly divisible by no prime smaller than k. (Some authors will use the term k-rough to denote a number where the smallest prime factor is GREATER than k. The difference here is a minor one, and inconsequential for my purposes.) And there are also smooth numbers, numerical antagonists to the rough ones, those numbers with only small prime factors. They are not relevant to the topic today, even though smooth numbers are terribly valuable tools in mathematics. Please forward my apologies to the smooth numbers.
Have you seen rough numbers in use before? Probably so, at least if you ever learned about the sieve of Eratosthenes for prime numbers, though probably the concept of roughness was never explicitly discussed at the time. The sieve is simple. Suppose you wanted a list of all primes less than 100? (Without using the primes function itself.)
% simple sieve of Eratosthenes
Nmax = 100;
N = true(1,Nmax); % A boolean vector which when done, will indicate primes
N(1) = false; % 1 is not a prime by definition
nextP = find(N,1,'first'); % the first prime is 2
while nextP <= sqrt(Nmax)
% flag multiples of nextP as not prime
N(nextP*nextP:nextP:end) = false;
% find the first element after nextP that remains true
nextP = nextP + find(N(nextP+1:end),1,'first');
end
primeList = find(N)
Indeed, that is the set of all 25 primes not exceeding 100. If you think about how the sieve worked, it first found 2 is prime. Then it discarded all integer multiples of 2. The first element after 2 that remains as true is 3. 3 is of course the second prime. At each pass through the loop, the true elements that remain correspond to numbers which are becoming more and more rough. By the time we have eliminated all multiples of 2, 3, 5, and finally 7, everything else that remains below 100 must be prime! The next prime on the list we would find is 11, but we have already removed all multiples of 11 that do not exceed 100, since 11^2=121. For example, 77 is 11*7, but we already removed it, because 77 is a multiple of 7.
Such a simple sieve to find primes is great for small primes. However is not remotely useful in terms of finding primes with many thousands or even millions of decimal digits. And that is where I want to go, eventually. So how might we use roughness in a useful way? You can think of roughness as a way to increase the relative density of primes. That is, all primes are rough numbers. In fact, they are maximally rough. But not all rough numbers are primes. We might think of roughness as a necessary, but not sufficient condition to be prime.
How many primes lie in the interval [1e6,2e6]?
numel(primes(2e6)) - numel(primes(1e6))
There are 70435 primes greater than 1e6, but less than 2e6. Given there are 1 million natural numbers in that set, roughly 7% of those numbers were prime. Next, how many 100-rough numbers lie in that same interval?
N = (1e6:2e6)';
roughInd = all(mod(N,primes(100)) > 0,2);
sum(roughInd)
That is, there are 120571 100-rough numbers in that interval, but all those 70435 primes form a subset of the 100-rough numbers. What does this tell us? Of the 1 million numbers in that interval, approximately 12% of them were 100-rough, but 58% of the rough set were prime.
The point being, if we can efficiently identify a number as being rough, then we can substantially increase the chance it is also prime. Roughness in this sense is a prime densifier. (Is that even a word? It is now.) If we can reduce the number of times we need to perform an explicit isprime test, that will gain greatly because a direct test for primality is often quite costly in CPU time, at least on really large numbers.
In my next post, I'll show some ways we can employ rough numbers to look for some large primes.
When will the Mathlab issue about licence be resolved
I've been trying this problem a lot of time and i don't understand why my solution doesnt't work.
In 4 tests i get the error Assertion failed but when i run the code myself i get the diag and antidiag correctly.
function [diag_elements, antidg_elements] = your_fcn_name(x)
[m, n] = size(x);
% Inicializar los vectores de la diagonal y la anti-diagonal
diag_elements = zeros(1, min(m, n));
antidg_elements = zeros(1, min(m, n));
% Extraer los elementos de la diagonal
for i = 1:min(m, n)
diag_elements(i) = x(i, i);
end
% Extraer los elementos de la anti-diagonal
for i = 1:min(m, n)
antidg_elements(i) = x(m-i+1, i);
end
end
Creating data visualizations
79%
Interpreting data visualizations
21%
28 票
Have you ever wanted to search for a community member but didn't know where to start? Or perhaps you knew where to search but couldn't find enough information from the results? You're not alone. Many community users have shared this frustration with us. That's why the community team is excited to introduce the new ‘People’ page to address this need.
What Does the ‘People’ Page Offer?
- Comprehensive User Search: Search for users across different applications seamlessly.
- Detailed User Information: View a list of community members along with additional details such as their join date, rankings, and total contributions.
- Sorting Options: Use the ‘sort by’ filter located below the search bar to organize the list according to your preferences.
- Easy Navigation: Access the Answers, File Exchange, and Cody Leaderboard by clicking the ‘Leaderboards’ button in the upper right corner.
In summary, the ‘People’ page provides a gateway to search for individuals and gain deeper insights into the community.
How Can You Access It?
Navigate to the global menu, click on the ‘More’ link, and you’ll find the ‘People’ option.
Now you know where to go if you want to search for a user. We encourage you to give it a try and share your feedback with us.
Los invito a conocer el libro "Sistemas dinámicos en contexto: Modelación matemática, simulación, estimación y control con MATLAB", el cual ya está disponible en formato digital.
El libro integra diversos temas de los sistemas dinámicos desde un punto de vista práctico utilizando programas de MATLAB y simulaciones en Simulink y utilizando métodos numéricos (ver enlace). Existe mucho material en el blog del libro con posibilidades para comentarios, propuestas y correcciones. Resalto los casos de estudio
Creo que el libro les puede dar un buen panorama del área con la posibilidad de experimentar de manera interactiva con todo el material de MATLAB disponible en formato Live Script. Lo mejor es que se pueden formular preguntas en el blog y hacer propuestas al autor de ejercicios resueltos.
Son bienvenidos los comentarios, sugerencias y correcciones al texto.
Simulink has been an essential tool for modeling and simulating dynamic systems in MATLAB. With the continuous advancements in AI, automation, and real-time simulation, I’m curious about what the future holds for Simulink.
What improvements or new features do you think Simulink will have in the coming years? Will AI-driven modeling, cloud-based simulation, or improved hardware integration shape the next generation of Simulink?
I am very pleased to share my book, with coauthors Professor Richard Davis and Associate Professor Sam Toan, titled "Chemical Engineering Analysis and Optimization Using MATLAB" published by Wiley: https://www.wiley.com/en-us/Chemical+Engineering+Analysis+and+Optimization+Using+MATLAB-p-9781394205363
Also in The MathWorks Book Program:
Chemical Engineering Analysis and Optimization Using MATLAB® introduces cutting-edge, highly in-demand skills in computer-aided design and optimization. With a focus on chemical engineering analysis, the book uses the MATLAB platform to develop reader skills in programming, modeling, and more. It provides an overview of some of the most essential tools in modern engineering design.
Chemical Engineering Analysis and Optimization Using MATLAB® readers will also find:
- Case studies for developing specific skills in MATLAB and beyond
- Examples of code both within the text and on a companion website
- End-of-chapter problems with an accompanying solutions manual for instructors
This textbook is ideal for advanced undergraduate and graduate students in chemical engineering and related disciplines, as well as professionals with backgrounds in engineering design.
You've probably heard about the DeepSeek AI models by now. Did you know you can run them on your own machine (assuming its powerful enough) and interact with them on MATLAB?
In my latest blog post, I install and run one of the smaller models and start playing with it using MATLAB.
Larger models wouldn't be any different to use assuming you have a big enough machine...and for the largest models you'll need a HUGE machine!
Even tiny models, like the 1.5 billion parameter one I demonstrate in the blog post, can be used to demonstrate and teach things about LLM-based technologies.
Have a play. Let me know what you think.
My following code works running Matlab 2024b for all test cases. However, 3 of 7 tests fail (#1, #4, & #5) the QWERTY Shift Encoder problem. Any ideas what I am missing?
Thanks in advance.
keyboardMap1 = {'qwertyuiop[;'; 'asdfghjkl;'; 'zxcvbnm,'};
keyboardMap2 = {'QWERTYUIOP{'; 'ASDFGHJKL:'; 'ZXCVBNM<'};
if length(s) == 0
se = s;
end
for i = 1:length(s)
if double(s(i)) >= 65 && s(i) <= 90
row = 1;
col = 1;
while ~strcmp(s(i), keyboardMap2{row}(col))
if col < length(keyboardMap2{row})
col = col + 1;
else
row = row + 1;
col = 1;
end
end
se(i) = keyboardMap2{row}(col + 1);
elseif double(s(i)) >= 97 && s(i) <= 122
row = 1;
col = 1;
while ~strcmp(s(i), keyboardMap1{row}(col))
if col < length(keyboardMap1{row})
col = col + 1;
else
row = row + 1;
col = 1;
end
end
se(i) = keyboardMap1{row}(col + 1);
else
se(i) = s(i);
end
% if ~(s(i) = 65 && s(i) <= 90) && ~(s(i) >= 97 && s(i) <= 122)
% se(i) = s(i);
% end
end
ı m tryna prepare a battery simulation with simulink but when ı push right click on "battery-table based" , and then ı go simscape button, and ı just only see "log simulation data" . Have you any reccomend for this problem? It s probably an easy solution, but ı can't
私の場合、前の会社が音楽認識アプリの会社で、アルゴリズム開発でFFTが使われていたことがきっかけでした。でも、MATLABのすごさが分かったのは、機械学習のオンライン講座で、Andrew Ngが、線型代数を使うと、数式と非常に近い構文のコードで問題が処理できることを学んだ時でした。
Dears,
I am running a MS-DSGE model using RISE toolbox. I want to add a fiscal shock and examine its effect on output, price...
%fiscal shock
shock_type = {'eps_G'};
%here is my variable list of a cell array of character variables and not a struct.
var_list={'log_y','C','pi_ann','B_nominal','B','sp','i_ann','r_real_ann','P'};
% EXOGENOUS SWITCHING
myirfs1=irf(m1,'irf_periods',24,'irf_shock_sign',1);
myirfs1 = struct()
myirfs1.eps_CP = struct();
myirfs1.eps_G = struct();
myirfs1.eps_T = struct();
myirfs1.eps_a = struct();
myirfs1.eps_nu = struct();
myirfs1.eps_z = struct();
var_aux = {'log_y','C','pi_ann','B_nominal','B','sp','i_ann','r_real_ann','P'};
var_aux3 = {'eps_G_log_y','eps_G_C','eps_G_pi_ann','eps_G_B_nominal','eps_G_B','eps_G_sp','eps_G_i_ann','eps_G_r_real_ann','eps_G_P'};
fieldnames(myirfs1)
myirfs1.eps_G.var = var_aux3 % assign the data array to the struct variable
irf_fisc = struct();
for i = 1:numel(var_aux)
irf_fisc.var_aux{i} = [0,myirfs1.eps_G.var{i}]';
end
irf_fisc.var_aux(1)
irf_fisc
% what is the write syntax to assign value (simulated data) to the struct?
myirfs1.eps_G.logy = data(:,1)/10; %Is the suggested code. but where is the data variable located? should I create it data = randn(TMax, N); or it is already simulated?
Dears,
I need your help. hocan I access the subfields within eps_G, where eps_G is a structure.
whos myirfs1
Name Size Bytes Class Attributes
myirfs1 1x1 374094 struct
%% disp(fieldnames(myirfs1))
>> disp(fieldnames(myirfs1))
{'eps_CP'}
{'eps_G' }
{'eps_T' }
{'eps_a' }
{'eps_nu'}
{'eps_z' }
% choose 1 or 2 below
shock_type = {'eps_G','eps_nu'};
var_aux = {'log_y','C','pi_ann','B_nominal','B','sp','i_ann','r_real_ann','P'};
var_aux2 = {'log_y_eps_nu','C_eps_nu','pi_ann_eps_nu','B_nominal_eps_nu','B_eps_nu','sp_eps_nu','i_ann_eps_nu','r_real_ann_eps_nu','P_eps_nu'};
var_aux3 = {'eps_G_log_y','eps_G_C','eps_G_pi_ann','eps_G_B_nominal','eps_G_B','eps_G_sp','eps_G_i_ann','eps_G_r_real_ann','eps_G_P'};
%Irfs of monetary and fiscal policy
irf_mon = struct();
irf_fisc = struct();
%% disp(fieldnames(myirfs1))
>> disp(fieldnames(myirfs1))
{'eps_CP'}
{'eps_G' }
{'eps_T' }
{'eps_a' }
{'eps_nu'}
{'eps_z' }
% when i run the following code it is unrecognized. can you suggest me what to do?
for i = 1:numel(var_aux)
irf_mon.(var_aux{i}) = [0,myirfs1(1).(var_aux3{i})]';
irf_fisc.(var_aux{i}) = [0,myirfs1(1).(var_aux3{i})]';
end
Unrecognized field name "log_y_eps_G".
Overview
Authors:
- Narayanaswamy P.R. Iyer
- Provides Simulink models for various PWM techniques used for inverters
- Presents vector and direct torque control of inverter-fed AC drives and fuzzy logic control of converter-fed AC drives
- Includes examples, case studies, source codes of models, and model projects from all the chapters.
About this book
Successful development of power electronic converters and converter-fed electric drives involves system modeling, analyzing the output voltage, current, electromagnetic torque, and machine speed, and making necessary design changes before hardware implementation. Inverters and AC Drives: Control, Modeling, and Simulation Using Simulink offers readers Simulink models for single, multi-triangle carrier, selective harmonic elimination, and space vector PWM techniques for three-phase two-level, multi-level (including modular multi-level), Z-source, Quasi Z-source, switched inductor, switched capacitor and diode assisted extended boost inverters, six-step inverter-fed permanent magnet synchronous motor (PMSM), brushless DC motor (BLDCM) and induction motor (IM) drives, vector-controlled PMSM, IM drives, direct torque-controlled inverter-fed IM drives, and fuzzy logic controlled converter-fed AC drives with several examples and case studies. Appendices in the book include source codes for all relevant models, model projects, and answers to selected model projects from all chapters.
This textbook will be a valuable resource for upper-level undergraduate and graduate students in electrical and electronics engineering, power electronics, and AC drives. It is also a hands-on reference for practicing engineers and researchers in these areas.
I want to share a new book "Introduction to Digital Control - An Integrated Approach, Springer, 2024" available through https://link.springer.com/book/10.1007/978-3-031-66830-2.
This textbook presents an integrated approach to digital (discrete-time) control systems covering analysis, design, simulation, and real-time implementation through relevant hardware and software platforms. Topics related to discrete-time control systems include z-transform, inverse z-transform, sampling and reconstruction, open- and closed-loop system characteristics, steady-state accuracy for different system types and input functions, stability analysis in z-domain-Jury’s test, bilinear transformation from z- to w-domain, stability analysis in w-domain- Routh-Hurwitz criterion, root locus techniques in z-domain, frequency domain analysis in w-domain, control system specifications in time- and frequency- domains, design of controllers – PI, PD, PID, phase-lag, phase-lead, phase-lag-lead using time- and frequency-domain specifications, state-space methods- controllability and observability, pole placement controllers, design of observers (estimators) - full-order prediction, reduced-order, and current observers, system identification, optimal control- linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) estimator (Kalman filter), implementation of controllers, and laboratory experiments for validation of analysis and design techniques on real laboratory scale hardware modules. Both single-input single-output (SISO) and multi-input multi-output (MIMO) systems are covered. Software platform of MATLAB/Simlink is used for analysis, design, and simulation and hardware/software platforms of National Instruments (NI)/LabVIEW are used for implementation and validation of analysis and design of digital control systems. Demonstrating the use of an integrated approach to cover interdisciplinary topics of digital control, emphasizing theoretical background, validation through analysis, simulation, and implementation in physical laboratory experiments, the book is ideal for students of engineering and applied science across in a range of concentrations.
I am excited to share my new book "Introduction to Mechatronics - An Integrated Approach, Springer, 2023" available through https://link.springer.com/book/10.1007/978-3-031-29320-7.
This textbook presents mechatronics through an integrated approach covering instrumentation, circuits and electronics, computer-based data acquisition and analysis, analog and digital signal processing, sensors, actuators, digital logic circuits, microcontroller programming and interfacing. The use of computer programming is emphasized throughout the text, and includes MATLAB for system modeling, simulation, and analysis; LabVIEW for data acquisition and signal processing; and C++ for Arduino-based microcontroller programming and interfacing. The book provides numerous examples along with appropriate program codes, for simulation and analysis, that are discussed in detail to illustrate the concepts covered in each section. The book also includes the illustration of theoretical concepts through the virtual simulation platform Tinkercad to provide students virtual lab experience.
I had originally planned on publishing my book via a traditional publisher, but am now reconsidering whether to use Amazon.com. I use Matlab and Latex in my book. It appears that it is not possible to publish is with Amazon due to this. Advice? Thanks. Kevin Passino
Let's celebrate what made 2024 memorable! Together, we made big impacts, hosted exciting events, and built new apps.
Resource links:
can i add TMS320F28P55SJ launch pad to matlab simulik
