MATLAB: Define a series of matrices

matrices

How do I define the next series of matrices

A=[0,1;sigma,0].

where

sigma=[-5:0.01:-4]

And I want the label to be as follows

A1=[0,1;sigma(1),0]

Best Answer

Using numbered variables is not going to be neat or efficient. The MATLAB approach would be to use one array, e.g.:

sigma = -5:0.01:-4; % the square brackets are superfluous
N = numel(sigma);
A = [zeros(N,1),ones(N,1),sigma(:),zeros(N,1)]

Each row of A is one of your output vectors, e.g.:

A(1,:)

Related Solutions

MATLAB: How to use loop to reduce the code

you can try with cell

clc
clear
syms t sigma
r = -4;
w = 2;
a = 1;
b = 1;
W = 1;
x_2 = 1
A_sin = 1;
A_sigma = [0,1;-w^2,-a*((A_sin*sin(W*sigma)^2)/w^4)-b*x_2+r];
B=0;
A{1} = int((A_sigma),sigma, 0, t);
for n = 2:5
    A{n} = int((A_sigma*A{n-1}),sigma, 0, t);
    B = A{n}+B;
end
    phi = [1 0; 0 1]+A{1}+B;

MATLAB: How to get the t=infinity values of an ODE against one of the parameters and then plot those infinity values to a different parameter

You can create a nested for-loop and then create a surf plot between beta, sigma, and x. Note that consider decreasing the step size for B and Sigma from 0.01 to some higher value. It can take a long time to run

B = 0:0.01:1;
gamma = 0.1;
Sigma = 0:0.01:1;
t_inf_values1 = zeros(numel(B), numel(Sigma));
t_inf_values2 = zeros(numel(B), numel(Sigma));
for i = 1:numel(B)
    for j = 1:numel(Sigma)
        beta = B(i);
        sigma = Sigma(j);
        fprintf('beta = %f,\t sigma = %f\n', beta, sigma) 
        f = @(t,x) [-beta.*x(1)*x(2) + sigma.*x(3); beta.*x(1)*x(2)-gamma.*x(2); gamma.*x(2)-sigma.*x(3)];
        [t,xa] = ode45(f, [0 1000], [950 50 0]);
        t_inf_values1(i, j) = xa(end,3);
        t_inf_values2(i, j) = xa(end,2);
    end
end
subplot(2,1,1);
surf(B, Sigma, t_inf_values1);
shading interp
xlabel('beta');
ylabel('Sigma');
zlabel('x_3(t_{inf})');
subplot(2,1,2);
surf(B, Sigma, t_inf_values2);
shading interp
xlabel('beta');
ylabel('Sigma');
zlabel('x_2(t_{inf})');

Best Answer

Related Solutions

MATLAB: How to use loop to reduce the code

MATLAB: How to get the t=infinity values of an ODE against one of the parameters and then plot those infinity values to a different parameter

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