how can i compute Aij?

Question

Gurpreet 2024-2-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2081271-how-can-i-compute-aij

评论： Les Beckham 2024-2-12

采纳的回答： Les Beckham

this is the question i have. my instructor is not really helpful with this and i need help.

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Gurpreet 2024-2-12

编辑：Torsten 2024-2-12

在 MATLAB Online 中打开

this is the code i have so far: as per my instructor:

% Function to generate n x n matrix with pseudo-random entries between 0 and 1

generateMatrix = @(n) rand(n);

% Parameters

delta_n = 200;

k_values = 1:10;

% Initialize arrays to store condition numbers

condition_numbers_A = zeros(size(k_values));

condition_numbers_B = zeros(size(k_values));

condition_numbers_C = zeros(size(k_values));

condition_numbers_D = zeros(size(k_values));

% Loop over k values

for k = k_values

n = k * delta_n;

% Generate matrix A

A = generateMatrix(n);

% Generate matrices B, C, D based on the rules

B = A;

C = A;

D = A;

% Modify elements based on rules

for i = 1:n

B(i, i) = 10;

C(i, i) = 20;

D(i, i) = 100;

end

% Calculate condition numbers

condition_numbers_A(k) = cond(A);

condition_numbers_B(k) = cond(B);

condition_numbers_C(k) = cond(C);

condition_numbers_D(k) = cond(D);

end

% Plot results using semilogy

figure;

semilogy(k_values * delta_n, condition_numbers_A, 'b', 'LineWidth', 2, 'DisplayName', 'A');

hold on;

semilogy(k_values * delta_n, condition_numbers_B, 'g', 'LineWidth', 2, 'DisplayName', 'B');

semilogy(k_values * delta_n, condition_numbers_C, 'r', 'LineWidth', 2, 'DisplayName', 'C');

semilogy(k_values * delta_n, condition_numbers_D, 'm', 'LineWidth', 2, 'DisplayName', 'D');

xlabel('Matrix Size (nk)');

ylabel('Condition Number (log scale)');

title('Condition Numbers of Matrices A, B, C, D');

legend('Location', 'Best');

grid on;

hold off;

it doesnt run however, and i am really confused

Torsten 2024-2-12

Works for me (at least up to k=10) (see above).

Gurpreet 2024-2-12

移动：Torsten 2024-2-12

this is what im getting:

In untitled2 (line 32)

condition_numbers_A(k) = cond(A);

In untitled2 (line 33)

condition_numbers_B(k) = cond(B);

i ran it four times and then came to answers :(

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Answer 1

Les Beckham 2024-2-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2081271-how-can-i-compute-aij#answer_1407241

在 MATLAB Online 中打开

It appears to work. I ran it for only 2 values of k as it was timing out here in Answers when running with 20 values of k.

What do you mean "it doesn't run"? What are you seeing? Are you getting an error message? If so, cut and paste it here (all of the red or orange text in the command window.

% Function to generate n x n matrix with pseudo-random entries between 0 and 1

generateMatrix = @(n) rand(n);

% Parameters

delta_n = 200;

k_values = 1:2; % was 1:20

% Initialize arrays to store condition numbers

condition_numbers_A = zeros(size(k_values));

condition_numbers_B = zeros(size(k_values));

condition_numbers_C = zeros(size(k_values));

condition_numbers_D = zeros(size(k_values));

% Loop over k values

for k = k_values

n = k * delta_n;

% Generate matrix A

A = generateMatrix(n);

% Generate matrices B, C, D based on the rules

B = A;

C = A;

D = A;

% Modify elements based on rules

for i = 1:n

B(i, i) = 10;

C(i, i) = 20;

D(i, i) = 100;

end

% Calculate condition numbers

condition_numbers_A(k) = cond(A);

condition_numbers_B(k) = cond(B);

condition_numbers_C(k) = cond(C);

condition_numbers_D(k) = cond(D);

end

% Plot results using semilogy

figure;

semilogy(k_values * delta_n, condition_numbers_A, 'b', 'LineWidth', 2, 'DisplayName', 'A');

hold on;

semilogy(k_values * delta_n, condition_numbers_B, 'g', 'LineWidth', 2, 'DisplayName', 'B');

semilogy(k_values * delta_n, condition_numbers_C, 'r', 'LineWidth', 2, 'DisplayName', 'C');

semilogy(k_values * delta_n, condition_numbers_D, 'm', 'LineWidth', 2, 'DisplayName', 'D');

xlabel('Matrix Size (nk)');

ylabel('Condition Number (log scale)');

title('Condition Numbers of Matrices A, B, C, D');

legend('Location', 'Best');

grid on;

hold off;

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Gurpreet 2024-2-12

i tried on a different computer and it ran!!!

thank you all for your help :)

Les Beckham 2024-2-12

You are quite welcome.

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how can i compute Aij?

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