how to create a diagonal matrix with the semibandwidth of 4

how to create a matrix like this:

Answer 1

[Niels]

Hi Lin Hongbin

not sure if your picture contains some errors, A(3,1) looks suspicious to me...

look at this and tell me if it fits your wishes :)

a=1:10;
b=11:20;
c=21:30;
d=31:40;
n=length(a);
A=zeros(n);

% set the rest
for i=1:n % rows
        A(i,i:i+3)=[a(i),b(i),c(i),d(i)];
end
>> A
A =
     1    11    21    31     0     0     0     0     0     0     0     0     0
     0     2    12    22    32     0     0     0     0     0     0     0     0
     0     0     3    13    23    33     0     0     0     0     0     0     0
     0     0     0     4    14    24    34     0     0     0     0     0     0
     0     0     0     0     5    15    25    35     0     0     0     0     0
     0     0     0     0     0     6    16    26    36     0     0     0     0
     0     0     0     0     0     0     7    17    27    37     0     0     0
     0     0     0     0     0     0     0     8    18    28    38     0     0
     0     0     0     0     0     0     0     0     9    19    29    39     0
     0     0     0     0     0     0     0     0     0    10    20    30    40

if u cut off the first and last column it looks more like your picture (beside A(3,1) and A(3,4) etc is not d3 ...)

B=A(1:n,2:n+2)
B =
  11    21    31     0     0     0     0     0     0     0     0
   2    12    22    32     0     0     0     0     0     0     0
   0     3    13    23    33     0     0     0     0     0     0
   0     0     4    14    24    34     0     0     0     0     0
   0     0     0     5    15    25    35     0     0     0     0
   0     0     0     0     6    16    26    36     0     0     0
   0     0     0     0     0     7    17    27    37     0     0
   0     0     0     0     0     0     8    18    28    38     0
   0     0     0     0     0     0     0     9    19    29    39
   0     0     0     0     0     0     0     0    10    20    30

so either matrix A or B might be the answer.

But neither A nor B are quadratic. A has size n x n+3 and B: n x n+1

[Niels]

there are also two other ways to do the same thing:

first and best one:

A = spdiags(B,d,m,n) creates an m-by-n sparse matrix by taking the
columns of B and placing them along the diagonals specified by d.

example:

a=1:10;
b=11:20;
c=21:30;
d=31:40;
n=length(a);
B=[a',b',c',d'];
d=[-1 0 1 2];
A=full(spdiags(B,d,n,n+1))

or use diag yourself:

a=1:10;
b=11:20;
c=21:30;
d=31:40;
n=length(a);

A=diag(a(2:n),-1);
A(1,n+1)=0;
B=diag(b,0);
B(1,n+1)=0;
C=diag(c,1);
C=C(1:n,1:n+1);
D=diag(d(1:n-1),2);
D=D(1:n,1:n+1);

Sum= A+B+C+D

[LIN Hongbin]

Thank you Niels, you did help me solve this problem.Appreciate you a lot.

[LIN Hongbin]

The answer in your comment is what I want.