CODEWITHSUNDEEP
matlabmatrix
user3508294
user3508294

Reputation: 3

100x100 Matrix MATLAB coding

I would like to generate a 100x100 Matrix that is similar to this whereby the first line and last line are different and the middle ones are all the same but shifted along by 1.

Here is what I have for a 10x10 matrix:

>> A=[0.8 -0.2 0 0 0 0 0 0 0 0;
-0.3 0.5 -0.2 0 0 0 0 0 0 0;
0 -0.3 0.5 -0.2 0 0 0 0 0 0;
0 0 -0.3 0.5 -0.2 0 0 0 0 0;
0 0 0 -0.3 0.5 -0.2 0 0 0 0;
0 0 0 0 -0.3 0.5 -0.2 0 0 0;
0 0 0 0 0 -0.3 0.5 -0.2 0 0;
 0 0 0 0 0 -0.3 0.5 -0.2 0;
0 0 0 0 0 0 0 -0.3 0.5 -0.2;
0 0 0 0 0 0 0 0 -0.3 0.7;]

B= [62; 0; 0; 0; 0; 0; 0; 0; 0; 82]

>> solution=inv(A)*B

Any help is much appreciated.

Many thanks.

Upvotes: 0

Views: 2027

Answers (3)

Mathias
Mathias

Reputation: 1500

What you want is called a Band Matrix also see this

n=10;
e=ones(n,1);
A=spdiags([-0.3*e 0.5*e -0.2*e],-1:1,n,n)

now this is a sparse Matrix, where the zeros are not stored which can improve storage and speed. If you want a full matrix, simply use A=full(spdiags(...)).

For B do:

B=ones(10,1)*0.8;
B(1) =62;
B(10)=82;

Upvotes: 4

Divakar
Divakar

Reputation: 221624

Approach 1: 

%%// Only this part would change when you go from your sample size of 10 to 100
N = 100; 

A = zeros(N); %%// Initialize
A(1:size(A,1)+1:end) = 0.5; %%// Diagonal values
A(2:size(A,1)+1:end) = -0.3;%%// Left-to-diagonal values
A(size(A,1)+1:size(A,1)+1:end) = -0.2;%%// Right-to-diagonal values
A([1 end]) = [0.8 0.7]; %% Different scalars at the top and end

Approach 2:

N = 100; %%// Size of matrix

L = -0.3; %%// Left to diagonal values
D = 0.5;  %%// Diagonal values
R = -0.2;  %%// Right to diagonal values

A = D*diag(ones(N,1)) + R*diag(ones(N-1,1),1) + L*diag(ones(N-1,1),-1);
A([1 end]) = [0.8 0.7]; %% Different scalars at the top and end

Upvotes: 0

honi
honi

Reputation: 968

code to create A is:

A = zeros(100);
A(1,1:2) = [0.8 -0.2];
for i = 2:99
    A(i,i-1:i+1) = [-0.3 0.5 -0.2];
end
A(100,99:100) = [-0.3 0.7];

you can then do B with the same template.

Upvotes: 0

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