Code to generate matrix

bold Hello,

I have this matrix, can someone please adv how to write the code:

A = [ 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
     -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0  -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0  -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0  -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0  -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0  -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0  -1 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0  -1 5 0  0 0 0 0 0 0 0   -1  0 0 0 0 0 0 0 0;
    -1 0 0 0 0 0 0 0  0 4 -1  0 0 0 0 0 0 0  -1  0 0 0 0 0 0 0;
    0 -1 0 0 0 0 0 0 0  -1 4 -1  0 0 0 0 0 0 0 -1  0 0 0 0 0 0;
    0 0 -1 0 0 0 0 0 0 0  -1 4 -1 0 0 0 0 0 0 0 -1   0 0 0 0 0;
    0 0 0 -1 0 0 0 0 0 0 0  -1 4 -1 0 0 0 0 0 0 0 -1   0 0 0 0;
    0 0 0 0 -1 0 0 0 0 0 0 0  -1 4 -1 0 0 0 0 0 0 0 -1   0 0 0;
    0 0 0 0 0 -1 0 0 0 0 0 0 0  -1 4 -1 0 0 0 0 0 0 0 -1   0 0;
    0 0 0 0 0 0 -1 0 0 0 0 0 0 0  -1 4 -1 0 0 0 0 0 0 0 -1   0;
    0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0  -1 4 -1 0 0 0 0 0 0 0 -1  ;
    0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0  -1 5     0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0   0 3 -1    0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0  -1 3 -1    0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0   -1 3 -1    0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0   -1 3 -1    0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0    -1 3 -1   0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0    -1 3 -1   0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0     -1 3 -1 ;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0  0     -1 3   ];

b=[0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;5;0;0;0;0;0;0;0;5];

[Guillaume]

What you have just written is valid matlab code to generate these matrices.

[Aswas]

Sorry, but I'd like to get this matrix by running a code, so I can expand it to a much bigger matrix, for eg following generates 26 x 26 with zeros:

clc;
clear all;
L=1;
nx = 26;
p=linspace(0,L,nx);
dx=p(nx)-p(nx-1);

%==========Matrix Generation=========================
%Matrix with zeros
A=zeros(nx,nx)
rhs=zeros(nx,1)

[Guillaume]

Well, then you have to explain the logic behind the matrix generation.

As far as I can tell b is just a zero column with 5 in two (random?) locations and A is a matrix that could be generated with toeplitz except that some (random?) -1 get replaced by 0 and the main diagonal is either 3, 4 or 5 (depending on ?)

Answer 1

[Walter Roberson]

You can put it together using diag()

d0 = [repmat(4,1,8), 5, repmat(4,1,8), 5, repmat(3,1,8)];
d1 = ones(1, length(d0)-1);
d9 = ones(1, length(d0)-9);

A = diag(d0,0) + diag(d1, -1) + diag(d1, 1) + diag(d9, -9) + diag(d9, 9);

b = [zeros(1,17), 5, zeros(1, 7), 5];

[Aswas]

Walter, awesome, but how do I get -1's please? and zeros after 5's, and before 4 and 3 on rows below 5's.

[Walter Roberson]

d1 = -ones(1, length(d0)-1);
d9 = -ones(1, length(d0)-9);

but watch out, I did not notice that on one of the two 9th diagonals, you end with a 0. That would be

diag([d9(1:end-1),0],9)

[Aswas]

I can get -1's, but cannot get 0's after the two 9th diagonals (5's), and also 0's before the 4's 10th diagonals please.

[Walter Roberson]

d0 = [repmat(4,1,8), 5, repmat(4,1,8), 5, repmat(3,1,8)];
d9 = -ones(1, length(d0)-9);
d1 = [-ones(1,8), 0, -ones(1,8), 0, -ones(1,7)];
A = diag(d0,0) + diag(d1, -1) + diag(d1, 1) + diag(d9, -9) + diag(d9, 9);

For your purpose it might make sense to construct

d1 = one(1,length(d0)-1);
d1(9:9:end) = 0;

[Aswas]

Thanks Walter, much appreciated.