Implement the Gauss-Seidel method for solving a system of linear equations from scratch in MATLAB and walk me through your thought process in constructing the code. Additionally, demonstrate that your implementation works by applying it to the following system. 2x +3y −z =7 , x −2y+4z =1 , 3x +y+2z =8
%Gauss seidel
A=input(‘Enter a co-efficient matrix A: ‘);
B=input(‘Enter source vector B: ‘);
P=input(‘Enter initial guess vector: ‘);
n=input(‘Enter number of iterations: ‘);
e=input(‘Enter tolerance: ‘);
N=length(B);
X=zeros(N,1);
Y=zeros(N,1); %for stopping criteria
for j=1:n
for i=1:N
x(i)=(B(i)/A(i,i))-(A(i,[1:i-1,i+1:N])*P([1:i-1,i+1:N]))/A(i,i);
P(i)=X(i);
end
fprintf(‘Iterations no %d n’ ,j)
X
if abs (Y-X)<e
break
end
Y=X;
end
This is my code is this correct? please help meImplement the Gauss-Seidel method for solving a system of linear equations from scratch in MATLAB and walk me through your thought process in constructing the code. Additionally, demonstrate that your implementation works by applying it to the following system. 2x +3y −z =7 , x −2y+4z =1 , 3x +y+2z =8
%Gauss seidel
A=input(‘Enter a co-efficient matrix A: ‘);
B=input(‘Enter source vector B: ‘);
P=input(‘Enter initial guess vector: ‘);
n=input(‘Enter number of iterations: ‘);
e=input(‘Enter tolerance: ‘);
N=length(B);
X=zeros(N,1);
Y=zeros(N,1); %for stopping criteria
for j=1:n
for i=1:N
x(i)=(B(i)/A(i,i))-(A(i,[1:i-1,i+1:N])*P([1:i-1,i+1:N]))/A(i,i);
P(i)=X(i);
end
fprintf(‘Iterations no %d n’ ,j)
X
if abs (Y-X)<e
break
end
Y=X;
end
This is my code is this correct? please help me Implement the Gauss-Seidel method for solving a system of linear equations from scratch in MATLAB and walk me through your thought process in constructing the code. Additionally, demonstrate that your implementation works by applying it to the following system. 2x +3y −z =7 , x −2y+4z =1 , 3x +y+2z =8
%Gauss seidel
A=input(‘Enter a co-efficient matrix A: ‘);
B=input(‘Enter source vector B: ‘);
P=input(‘Enter initial guess vector: ‘);
n=input(‘Enter number of iterations: ‘);
e=input(‘Enter tolerance: ‘);
N=length(B);
X=zeros(N,1);
Y=zeros(N,1); %for stopping criteria
for j=1:n
for i=1:N
x(i)=(B(i)/A(i,i))-(A(i,[1:i-1,i+1:N])*P([1:i-1,i+1:N]))/A(i,i);
P(i)=X(i);
end
fprintf(‘Iterations no %d n’ ,j)
X
if abs (Y-X)<e
break
end
Y=X;
end
This is my code is this correct? please help me @wantquickhelp MATLAB Answers — New Questions

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clc
clear all
close all
image_org=imread(‘C:UserspcOneDriveDesktopmemoirechapitre 3image for test’,’JPG’);
% Gaussian white noise
X = double(image_org) / 255;
NG = imnoise(X, ‘gaussian’, 0, 0.01);%NG=gaussian noise
figure(1);subplot(231); imshow(image_org);title (‘image org’)
subplot(233); imshow(NG) ; title (‘Gaussian additive noise’)
NG_gray = rgb2gray(NG);
%averaging filter
f_m = fspecial (‘average’, 3)%f_m=averaging filter
NGmoy = imfilter (NG, f_m,’replicate’);
%gaussian filter
f_g = fspecial (‘gaussian’,3,0.8)%f_g=gaussian filter
NGg = imfilter(NG,f_g,’replicate’);
%median filter
NGmed = medfilt2( NG_gray ,[3 3]);
%the show
subplot(234); imshow(NGmoy);title(‘ avraging Filter ‘)
subplot(235); imshow(NGg);title(‘ gaussien Filtre ‘)
subplot(236); imshow(NGmed);title(‘ median Filtre’)
%PSNR
EQMb=mean2((X-NG).^2 );PSNRb=-10*log10(EQMb);
EQMmoy=mean2( (NG-NGmoy).^2 );PSNRmoy=-10*log10(EQMmoy);
EQMg=mean2( (NG-NGg).^2 );PSNRg=-10*log10(EQMg);
EQMmed=mean2( (NG_gray-NGmed).^2 );PSNRmed=-10*log10(EQMmed);

% Resize the original image to match the input size of the CNN
image_resized = imresize(image_org, [299 450]);

% Add Gaussian noise to the original image
X = double(image_resized) / 255;
NG = imnoise(X, ‘gaussian’, 0, 0.03); % Add Gaussian noise

% Display the original and noisy images
figure(1);
subplot(1, 2, 1);
imshow(image_resized);
title(‘Original Image’);
subplot(1, 2, 2);
imshow(NG);
title(‘Noisy Image’);

% Prepare data for training (noisy images as input, original images as target)
inputData = NG; % Noisy images
targetData = X; % Original clean images

% Define the CNN architecture for image denoising
layers = [
imageInputLayer([299 450 3]) % Input layer with the size of the input images
convolution2dLayer(3, 64, ‘Padding’, ‘same’) % Convolutional layer with 64 filters of size 3×3
reluLayer % ReLU activation layer
convolution2dLayer(3, 64, ‘Padding’, ‘same’) % Another convolutional layer
reluLayer % ReLU activation layer
convolution2dLayer(3, 3, ‘Padding’, ‘same’) % Output convolutional layer with 3 channels (RGB)
regressionLayer % Regression layer
];

% Define training options
options = trainingOptions(‘adam’, … % Adam optimizer
‘MaxEpochs’, 50, … % Increase the number of epochs
‘MiniBatchSize’, 16, … % Decrease the mini-batch size
‘InitialLearnRate’, 1e-4, … % Decrease the initial learning rate
‘Plots’, ‘training-progress’); % Plot training progress

% Train the network
net = trainNetwork(inputData, targetData, layers, options);

% Denoise the image using the trained CNN
denoisedImage = predict(net, inputData);

% Display the original noisy image and the denoised image
figure;
subplot(1, 2, 1);
imshow(inputData);
title(‘Noisy Image’);
subplot(1, 2, 2);
imshow(denoisedImage);
title(‘Denoised Image’);clc
clear all
close all
image_org=imread(‘C:UserspcOneDriveDesktopmemoirechapitre 3image for test’,’JPG’);
% Gaussian white noise
X = double(image_org) / 255;
NG = imnoise(X, ‘gaussian’, 0, 0.01);%NG=gaussian noise
figure(1);subplot(231); imshow(image_org);title (‘image org’)
subplot(233); imshow(NG) ; title (‘Gaussian additive noise’)
NG_gray = rgb2gray(NG);
%averaging filter
f_m = fspecial (‘average’, 3)%f_m=averaging filter
NGmoy = imfilter (NG, f_m,’replicate’);
%gaussian filter
f_g = fspecial (‘gaussian’,3,0.8)%f_g=gaussian filter
NGg = imfilter(NG,f_g,’replicate’);
%median filter
NGmed = medfilt2( NG_gray ,[3 3]);
%the show
subplot(234); imshow(NGmoy);title(‘ avraging Filter ‘)
subplot(235); imshow(NGg);title(‘ gaussien Filtre ‘)
subplot(236); imshow(NGmed);title(‘ median Filtre’)
%PSNR
EQMb=mean2((X-NG).^2 );PSNRb=-10*log10(EQMb);
EQMmoy=mean2( (NG-NGmoy).^2 );PSNRmoy=-10*log10(EQMmoy);
EQMg=mean2( (NG-NGg).^2 );PSNRg=-10*log10(EQMg);
EQMmed=mean2( (NG_gray-NGmed).^2 );PSNRmed=-10*log10(EQMmed);

% Resize the original image to match the input size of the CNN
image_resized = imresize(image_org, [299 450]);

% Add Gaussian noise to the original image
X = double(image_resized) / 255;
NG = imnoise(X, ‘gaussian’, 0, 0.03); % Add Gaussian noise

% Display the original and noisy images
figure(1);
subplot(1, 2, 1);
imshow(image_resized);
title(‘Original Image’);
subplot(1, 2, 2);
imshow(NG);
title(‘Noisy Image’);

% Prepare data for training (noisy images as input, original images as target)
inputData = NG; % Noisy images
targetData = X; % Original clean images

% Define the CNN architecture for image denoising
layers = [
imageInputLayer([299 450 3]) % Input layer with the size of the input images
convolution2dLayer(3, 64, ‘Padding’, ‘same’) % Convolutional layer with 64 filters of size 3×3
reluLayer % ReLU activation layer
convolution2dLayer(3, 64, ‘Padding’, ‘same’) % Another convolutional layer
reluLayer % ReLU activation layer
convolution2dLayer(3, 3, ‘Padding’, ‘same’) % Output convolutional layer with 3 channels (RGB)
regressionLayer % Regression layer
];

% Define training options
options = trainingOptions(‘adam’, … % Adam optimizer
‘MaxEpochs’, 50, … % Increase the number of epochs
‘MiniBatchSize’, 16, … % Decrease the mini-batch size
‘InitialLearnRate’, 1e-4, … % Decrease the initial learning rate
‘Plots’, ‘training-progress’); % Plot training progress

% Train the network
net = trainNetwork(inputData, targetData, layers, options);

% Denoise the image using the trained CNN
denoisedImage = predict(net, inputData);

% Display the original noisy image and the denoised image
figure;
subplot(1, 2, 1);
imshow(inputData);
title(‘Noisy Image’);
subplot(1, 2, 2);
imshow(denoisedImage);
title(‘Denoised Image’); clc
clear all
close all
image_org=imread(‘C:UserspcOneDriveDesktopmemoirechapitre 3image for test’,’JPG’);
% Gaussian white noise
X = double(image_org) / 255;
NG = imnoise(X, ‘gaussian’, 0, 0.01);%NG=gaussian noise
figure(1);subplot(231); imshow(image_org);title (‘image org’)
subplot(233); imshow(NG) ; title (‘Gaussian additive noise’)
NG_gray = rgb2gray(NG);
%averaging filter
f_m = fspecial (‘average’, 3)%f_m=averaging filter
NGmoy = imfilter (NG, f_m,’replicate’);
%gaussian filter
f_g = fspecial (‘gaussian’,3,0.8)%f_g=gaussian filter
NGg = imfilter(NG,f_g,’replicate’);
%median filter
NGmed = medfilt2( NG_gray ,[3 3]);
%the show
subplot(234); imshow(NGmoy);title(‘ avraging Filter ‘)
subplot(235); imshow(NGg);title(‘ gaussien Filtre ‘)
subplot(236); imshow(NGmed);title(‘ median Filtre’)
%PSNR
EQMb=mean2((X-NG).^2 );PSNRb=-10*log10(EQMb);
EQMmoy=mean2( (NG-NGmoy).^2 );PSNRmoy=-10*log10(EQMmoy);
EQMg=mean2( (NG-NGg).^2 );PSNRg=-10*log10(EQMg);
EQMmed=mean2( (NG_gray-NGmed).^2 );PSNRmed=-10*log10(EQMmed);

% Resize the original image to match the input size of the CNN
image_resized = imresize(image_org, [299 450]);

% Add Gaussian noise to the original image
X = double(image_resized) / 255;
NG = imnoise(X, ‘gaussian’, 0, 0.03); % Add Gaussian noise

% Display the original and noisy images
figure(1);
subplot(1, 2, 1);
imshow(image_resized);
title(‘Original Image’);
subplot(1, 2, 2);
imshow(NG);
title(‘Noisy Image’);

% Prepare data for training (noisy images as input, original images as target)
inputData = NG; % Noisy images
targetData = X; % Original clean images

% Define the CNN architecture for image denoising
layers = [
imageInputLayer([299 450 3]) % Input layer with the size of the input images
convolution2dLayer(3, 64, ‘Padding’, ‘same’) % Convolutional layer with 64 filters of size 3×3
reluLayer % ReLU activation layer
convolution2dLayer(3, 64, ‘Padding’, ‘same’) % Another convolutional layer
reluLayer % ReLU activation layer
convolution2dLayer(3, 3, ‘Padding’, ‘same’) % Output convolutional layer with 3 channels (RGB)
regressionLayer % Regression layer
];

% Define training options
options = trainingOptions(‘adam’, … % Adam optimizer
‘MaxEpochs’, 50, … % Increase the number of epochs
‘MiniBatchSize’, 16, … % Decrease the mini-batch size
‘InitialLearnRate’, 1e-4, … % Decrease the initial learning rate
‘Plots’, ‘training-progress’); % Plot training progress

% Train the network
net = trainNetwork(inputData, targetData, layers, options);

% Denoise the image using the trained CNN
denoisedImage = predict(net, inputData);

% Display the original noisy image and the denoised image
figure;
subplot(1, 2, 1);
imshow(inputData);
title(‘Noisy Image’);
subplot(1, 2, 2);
imshow(denoisedImage);
title(‘Denoised Image’); deep learning, neural network MATLAB Answers — New Questions

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I have a control loop such that:
The loop starts by calculating the error between the desired and measured temperature.
The relay block turns the heating system on or off based on this error, with a hysteresis of ±5 degrees to prevent frequent switching.
The output from the relay (on/off signal) is passed through a transfer function to simulate the dynamics of the system (introducing a delay or lag in the heating response).
The scaled output from the transfer function (now a power signal) is converted into a physical signal.
Finally, the physical signal controls the heat source, which in turn affects the system’s temperature.
I want to use PID controller block instead of this, how can I achieve that?I have a control loop such that:
The loop starts by calculating the error between the desired and measured temperature.
The relay block turns the heating system on or off based on this error, with a hysteresis of ±5 degrees to prevent frequent switching.
The output from the relay (on/off signal) is passed through a transfer function to simulate the dynamics of the system (introducing a delay or lag in the heating response).
The scaled output from the transfer function (now a power signal) is converted into a physical signal.
Finally, the physical signal controls the heat source, which in turn affects the system’s temperature.
I want to use PID controller block instead of this, how can I achieve that? I have a control loop such that:
The loop starts by calculating the error between the desired and measured temperature.
The relay block turns the heating system on or off based on this error, with a hysteresis of ±5 degrees to prevent frequent switching.
The output from the relay (on/off signal) is passed through a transfer function to simulate the dynamics of the system (introducing a delay or lag in the heating response).
The scaled output from the transfer function (now a power signal) is converted into a physical signal.
Finally, the physical signal controls the heat source, which in turn affects the system’s temperature.
I want to use PID controller block instead of this, how can I achieve that? simulink, pid, simscape MATLAB Answers — New Questions

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Hello all,
I am using a System Object (SO) in combination with Simulink to simulate some stuff. Within that SO multiple objects of normal Matlab classes are instantiated in the setupImpl method. From one stepImpl to the next it seems that Matlab/Simulink clears/re-initializes the properties of those Matlab objects which in return costs time. How can I prevent this from happening? I want the memory of the Matlab Objects to be untouched because the size of their properties is large and don’t change over time. I thought of using persistent variables but I fail in defining persistent properties. Is that possible and if so, how?
Any hint is highly appreciated!Hello all,
I am using a System Object (SO) in combination with Simulink to simulate some stuff. Within that SO multiple objects of normal Matlab classes are instantiated in the setupImpl method. From one stepImpl to the next it seems that Matlab/Simulink clears/re-initializes the properties of those Matlab objects which in return costs time. How can I prevent this from happening? I want the memory of the Matlab Objects to be untouched because the size of their properties is large and don’t change over time. I thought of using persistent variables but I fail in defining persistent properties. Is that possible and if so, how?
Any hint is highly appreciated! Hello all,
I am using a System Object (SO) in combination with Simulink to simulate some stuff. Within that SO multiple objects of normal Matlab classes are instantiated in the setupImpl method. From one stepImpl to the next it seems that Matlab/Simulink clears/re-initializes the properties of those Matlab objects which in return costs time. How can I prevent this from happening? I want the memory of the Matlab Objects to be untouched because the size of their properties is large and don’t change over time. I thought of using persistent variables but I fail in defining persistent properties. Is that possible and if so, how?
Any hint is highly appreciated! persistent memory, simulink, class MATLAB Answers — New Questions

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I am using this optimizer tool since Matlab obliterated the old one —->

It has all these options, shown in the image bellow, to display many different values per iteration, except an option to display each value of the solution, x, at each iteration – which is what I need.

I have noticed that a lot of people have already asked the same question, but all the answers don’t seem to apply to the code I’m using (generated by the new optimization tool). While answers related to the old tool box do not apply anymore. The code the new tool generates looks a bit like this:
% Pass fixed parameters to objfun
objfun19 = @(x)LDR(x);

% Set nondefault solver options
options20 = optimoptions("gamultiobj","ConstraintTolerance",1e-05,"Display",…
"iter");

% Solve
[solution0,objectiveValue0] = gamultiobj(objfun19,v0,[],[],[],[],min,max,[],[],…
options20);
Where x is an array. I have been using multi-objective genetic algorithm, pareto search, and fmincon, which all look almost the same.
Appreciate any help. Please and thank you.I am using this optimizer tool since Matlab obliterated the old one —->

It has all these options, shown in the image bellow, to display many different values per iteration, except an option to display each value of the solution, x, at each iteration – which is what I need.

I have noticed that a lot of people have already asked the same question, but all the answers don’t seem to apply to the code I’m using (generated by the new optimization tool). While answers related to the old tool box do not apply anymore. The code the new tool generates looks a bit like this:
% Pass fixed parameters to objfun
objfun19 = @(x)LDR(x);

% Set nondefault solver options
options20 = optimoptions("gamultiobj","ConstraintTolerance",1e-05,"Display",…
"iter");

% Solve
[solution0,objectiveValue0] = gamultiobj(objfun19,v0,[],[],[],[],min,max,[],[],…
options20);
Where x is an array. I have been using multi-objective genetic algorithm, pareto search, and fmincon, which all look almost the same.
Appreciate any help. Please and thank you. I am using this optimizer tool since Matlab obliterated the old one —->

It has all these options, shown in the image bellow, to display many different values per iteration, except an option to display each value of the solution, x, at each iteration – which is what I need.

I have noticed that a lot of people have already asked the same question, but all the answers don’t seem to apply to the code I’m using (generated by the new optimization tool). While answers related to the old tool box do not apply anymore. The code the new tool generates looks a bit like this:
% Pass fixed parameters to objfun
objfun19 = @(x)LDR(x);

% Set nondefault solver options
options20 = optimoptions("gamultiobj","ConstraintTolerance",1e-05,"Display",…
"iter");

% Solve
[solution0,objectiveValue0] = gamultiobj(objfun19,v0,[],[],[],[],min,max,[],[],…
options20);
Where x is an array. I have been using multi-objective genetic algorithm, pareto search, and fmincon, which all look almost the same.
Appreciate any help. Please and thank you. optimization MATLAB Answers — New Questions

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I want to determine the surrounding(corresponding) vertices of all the nodes of the voronoi cells. Please help adding to the program below.
x=[2 2 3 3 4 5 5 5 6 7 8];
y=[1 3 1 3 4 4 5 6 5 4 2];
N=[x’ y’];
axis([0 10 0 10]);
hold on;
scatter(x,y, [], ‘filled’);
%Labelling the nodes
labels = cellstr( num2str([1:length(x)]’) );
plot(N(:,1), N(:,2), ‘bx’)
text(N(:,1), N(:,2), labels, ‘VerticalAlignment’,’bottom’, …
‘HorizontalAlignment’,’right’)
%Voronoi
voronoi(x,y,’green’);
[vx,vy]=voronoi(x,y);
plot(vx,vy,’rx’);
grid on
[V C]=voronoin(N); %
%Labelling the vertices
labels = cellstr( num2str([1:length(V)]’) );
plot(V(:,1), V(:,2), ‘rx’)
text(V(:,1), V(:,2), labels, ‘VerticalAlignment’,’bottom’, …
‘HorizontalAlignment’,’right’)I want to determine the surrounding(corresponding) vertices of all the nodes of the voronoi cells. Please help adding to the program below.
x=[2 2 3 3 4 5 5 5 6 7 8];
y=[1 3 1 3 4 4 5 6 5 4 2];
N=[x’ y’];
axis([0 10 0 10]);
hold on;
scatter(x,y, [], ‘filled’);
%Labelling the nodes
labels = cellstr( num2str([1:length(x)]’) );
plot(N(:,1), N(:,2), ‘bx’)
text(N(:,1), N(:,2), labels, ‘VerticalAlignment’,’bottom’, …
‘HorizontalAlignment’,’right’)
%Voronoi
voronoi(x,y,’green’);
[vx,vy]=voronoi(x,y);
plot(vx,vy,’rx’);
grid on
[V C]=voronoin(N); %
%Labelling the vertices
labels = cellstr( num2str([1:length(V)]’) );
plot(V(:,1), V(:,2), ‘rx’)
text(V(:,1), V(:,2), labels, ‘VerticalAlignment’,’bottom’, …
‘HorizontalAlignment’,’right’) I want to determine the surrounding(corresponding) vertices of all the nodes of the voronoi cells. Please help adding to the program below.
x=[2 2 3 3 4 5 5 5 6 7 8];
y=[1 3 1 3 4 4 5 6 5 4 2];
N=[x’ y’];
axis([0 10 0 10]);
hold on;
scatter(x,y, [], ‘filled’);
%Labelling the nodes
labels = cellstr( num2str([1:length(x)]’) );
plot(N(:,1), N(:,2), ‘bx’)
text(N(:,1), N(:,2), labels, ‘VerticalAlignment’,’bottom’, …
‘HorizontalAlignment’,’right’)
%Voronoi
voronoi(x,y,’green’);
[vx,vy]=voronoi(x,y);
plot(vx,vy,’rx’);
grid on
[V C]=voronoin(N); %
%Labelling the vertices
labels = cellstr( num2str([1:length(V)]’) );
plot(V(:,1), V(:,2), ‘rx’)
text(V(:,1), V(:,2), labels, ‘VerticalAlignment’,’bottom’, …
‘HorizontalAlignment’,’right’) aida MATLAB Answers — New Questions

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