Vectors must be same length help

Hello. I'm trying to make a single plot that overlays the numerical values of all the unknowns of the system of linear equations versus the iterations conducted in the Gauss-Seidel method. However, for some reason it's showing that there's an error and that vectors must be the same length, but I'm confused as to how I can solve this. Can anyone help out?

clear

clc

close all

%Definition of coefficient matrix, vector of constants, and initial solution:

A = [9 2 -3 -1 1; 0 10 -2 5 2; 0 -2 8 4 0; -1 3 0 -6 2; -1 3 2 -1 7];

b = [-34; 23; 60; -23; -39];

x = ones(1,length(b));

%Determines the number of rows (m) and columns (n) in A:

[m,n] = size(A);

%Creates an auxiliary matrix, and auxiliary vectors:

c = zeros(m,n);

d = zeros(m,1);

%Defines initial error (100%), tolerance, and initial iteration:

ea = 100;

tol = 0.01;

iter = 1;

%Prints the header of table to user:

disp('Iter x1 x2 x3 x4 Max_Error')

fprintf('%d %9.4f %9.4f %9.4f %9.4f %9.4f\n', iter-1, x(1),x(2),x(3),x(4),ea)

%Gauss-Seidel iterative method:

while ea > tol

for i = 1:n

%Computes vector of coefficients:

d(i) = b(i)/A(i,i);

%Computation of coefficient matrix "c":

for j = 1:m

if i == j

c(i,j) = 0; %Diagonal of matrix "c" is full of zeros

else

c(i,j) = A(i,j)/A(i,i); %For non-diagonal elements

end

end

%Calculates new solution:

x_new(i) = d(i) -c(i,:)*x(:);

%Calculates new error:

ea_vect(i) = abs((x_new(i) - x(i))/x_new(i)*100);

%Updates to the new solution:

x(i) = x_new(i);

end

%Determines the maximum error among the unknowns, to check convergence:

ea = max(ea_vect);

%Prints results to the user:

fprintf('%d %9.4f %9.4f %9.4f %9.4f %9.4f\n', iter, x(1),x(2),x(3),x(4),ea)

%Updates iteration:

iter = iter + 1;

end

figure;

hold on;

colors = ['r', 'g', 'b', 'm', 'c'];

labels = {'x1', 'x2', 'x3', 'x4', 'x5'};

for i = 1:size(x, 1)

plot(1:iter, x(i, :), 'Color', colors(i));

end

hold off;

grid on;

xlabel('Iterations');

ylabel('Unknowns');

legend(labels);

[Dyuman Joshi]

The value of iter after the while loop is 14, thus 1:iter has 14 elements, whereas x has only 5 columns.

How can you plot 14 points against 5 points?

"I'm trying to make a single plot that overlays the numerical values of all the unknowns of the system of linear equations versus the iterations conducted in the Gauss-Seidel method"

Do you want to plot solution vs no of iterations taken to obtain the solution? If not, please specify / provide more information regarding this.

Answer 1

[Menika]

Hi,

The error you are encountering is due to the mismatch in the dimensions of the x variable. In your code, you have initialized x as a row vector : x = ones(1,length(b));, but later in the while loop, you are updating x as a column vector x(i) = x_new(i);.

You can modify the initialization of x to be a column vector instead in line 7:

x = ones(length(b), 1);

Hope it helps!

[Hunter]

So I tried that and I no longer get the error but it doesn't display the data on the plot as shown in the attachment

[Menika]

Hi, can you specify what the desired plot will look like?