Code to generate matrix

2016 5 12
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更新时间：2016 5 12
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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];

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Guillaume
Guillaume 2016-5-12
What you have just written is valid matlab code to generate these matrices.
Aswas
Aswas 2016-5-12
编辑：Walter Roberson 2016-5-12
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
Guillaume 2016-5-12
编辑：Guillaume 2016-5-12
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 ?)

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Walter Roberson
Walter Roberson 2016-5-12

0 个投票

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];

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Aswas
Aswas 2016-5-12
编辑：Aswas 2016-5-12
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
Walter Roberson 2016-5-12
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
Aswas 2016-5-12
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
Walter Roberson 2016-5-12
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
Aswas 2016-5-12
Thanks Walter, much appreciated.

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