Hot to create a matrix with elements which moves to right as row increases

Question

Ravikumar Gogar 2018-6-26

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评论： Ravikumar Gogar 2018-6-27

Hi, I want to create a Matrix A such that

A = [-1  1  -1  0  0  0  0
-1   1 -1  0  0  0
 0  -1  1 -1  0  0
 0   0 -1  1 -1  0
 0   0  0  -1 1 -1]

Above matrix is a sample with just 5 rows but i want to create a matrix of size 100x100.

I have used following method but failed

a=[-1 2 1];
x=100;
A=convmtx(a,x)

Please help.

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Paolo 2018-6-26

编辑：Paolo 2018-6-26

You mentioned the matrix you want to obtain is a 100x100 matrix. Should the matrix in your example be 5x5, or 8x8?

Ravikumar Gogar 2018-6-27

Sorry I was supposed to type 100x102.

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Answer 1

John D'Errico 2018-6-26

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编辑：John D'Errico 2018-6-26

在 MATLAB Online 中打开

There are MANY ways to solve this. I'm not at all sure what the final dimension of the matrix is expected to be. Is it 100x100? While you say that, the matrix you show is not square.

So, IF you want to create a square matrix with that pattern, then this will do the trick:

n = 10;
toeplitz([-1;zeros(n-1,1)]',[-1 1 -1,zeros(1,n-3)])
ans =
  -1     1    -1     0     0     0     0     0     0     0
   0    -1     1    -1     0     0     0     0     0     0
   0     0    -1     1    -1     0     0     0     0     0
   0     0     0    -1     1    -1     0     0     0     0
   0     0     0     0    -1     1    -1     0     0     0
   0     0     0     0     0    -1     1    -1     0     0
   0     0     0     0     0     0    -1     1    -1     0
   0     0     0     0     0     0     0    -1     1    -1
   0     0     0     0     0     0     0     0    -1     1
   0     0     0     0     0     0     0     0     0    -1

I've shown what it creates for n=10. Make n=100, and you get a 100x100 matrix.

Do you really want to create a non-square matrix? Still easy enough. You could use toeplitz again. Here, I create the matrix you showed in your example.

n = 7;
toeplitz([-1;zeros(n-3,1)]',[-1 1 -1,zeros(1,n-3)])
ans =
  -1     1    -1     0     0     0     0
   0    -1     1    -1     0     0     0
   0     0    -1     1    -1     0     0
   0     0     0    -1     1    -1     0
   0     0     0     0    -1     1    -1

Pick n=100, to get a 98x100 array, IF that is really what you wanted.

Lots of other ways.

n = 5;
A = [-eye(n),zeros(n,2)] + [zeros(n,1),eye(n),zeros(n,1)] + [zeros(n,2),-eye(n)]
A =
  -1     1    -1     0     0     0     0
   0    -1     1    -1     0     0     0
   0     0    -1     1    -1     0     0
   0     0     0    -1     1    -1     0
   0     0     0     0    -1     1    -1

Here is another, using gallery to create a circulant matrix.

n = 10;
A = gallery('circul',[-1 1 -1,zeros(1,n-3)]);
A((n-1):n,1:2) = 0
A =
  -1     1    -1     0     0     0     0     0     0     0
   0    -1     1    -1     0     0     0     0     0     0
   0     0    -1     1    -1     0     0     0     0     0
   0     0     0    -1     1    -1     0     0     0     0
   0     0     0     0    -1     1    -1     0     0     0
   0     0     0     0     0    -1     1    -1     0     0
   0     0     0     0     0     0    -1     1    -1     0
   0     0     0     0     0     0     0    -1     1    -1
   0     0     0     0     0     0     0     0    -1     1
   0     0     0     0     0     0     0     0     0    -1

Or, you could have used spdiags. Or sparse. Lets see, maybe I could get tricky? How about conv2?

n = 10;
A = conv2(diag(ones(1,n),1),[-1 1 -1],'same');
A(end) = -1
A =
  -1     1    -1     0     0     0     0     0     0     0     0
   0    -1     1    -1     0     0     0     0     0     0     0
   0     0    -1     1    -1     0     0     0     0     0     0
   0     0     0    -1     1    -1     0     0     0     0     0
   0     0     0     0    -1     1    -1     0     0     0     0
   0     0     0     0     0    -1     1    -1     0     0     0
   0     0     0     0     0     0    -1     1    -1     0     0
   0     0     0     0     0     0     0    -1     1    -1     0
   0     0     0     0     0     0     0     0    -1     1    -1
   0     0     0     0     0     0     0     0     0    -1     1
   0     0     0     0     0     0     0     0     0     0    -1

So many ways to do this. I can think of at least a couple of other ways as I write this line.

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Answer 2

Image Analyst 2018-6-26

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https://ww2.mathworks.cn/matlabcentral/answers/407562-hot-to-create-a-matrix-with-elements-which-moves-to-right-as-row-increases#answer_326401

在 MATLAB Online 中打开

Try changing the "a" from [1,2,1] to [-1,1,-1] and then cropping to 100x100:

a = [-1, 1, -1];
x = 100;
A = convmtx(a, x);
A = A(:, 1:100)

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Answer 3

Shweta Singh 2018-6-26

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Hi Ravikumar,

The code you provided seems to be working fine. It creates a matrix of 100x102. As per your requirement, with three elements in vector 'a', the resultant matrix would be of size with number of columns two more than the number of rows, and not the square matrix.

Can you provide more details if this is not what you want?

Thanks!