Matlab/ Scilab/ R : Creating a block tridiagonal matrix in Scilab

Question

I need to create a block tridiagonal matrix in Scilab. More explicitly I would like to set up a M^2 X M^2 matrix of the format:

  B  C   0 ... 0  0 
  D  B   C  0 ... 0 
  0  D   B  C ... 0
  0 ... ... ... ...  
  0  0  ... D  B  C 
  0  0   0 ... D  B

where B,C and D are M X M matrices.

I know how to create a block diagonal matrix with help of the "sysdiag" function but I haven't found any reference for easily creating a block tridiagonal one.

By the way given the matrices B,C and D I know how to create the matrix above.

 auxA = sysdiag(B,B);
  auxC = C;
  auxD = D;
  for i=1:2*M-1
     auxA = sysdiag(auxA,B);
     auxC = sysdiag(auxC,C);
     auxD = sysdiag(auxD,D);
  end
  A = auxA + [zeros((2*M+1)^2 -(2*M+1),2*M+1) auxC ;zeros(2*M+1,2*M+1) zeros(2*M+1,(2*M+1)^2 -(2*M+1)) ] + [zeros(2*M+1,(2*M+1)^2 -(2*M+1)) zeros(2*M+1,2*M+1); auxD zeros((2*M+1)^2 -(2*M+1),2*M+1)];

I would still like to knwo if there is a function that does it directly in Scilab, Matlab or R. Could someone help me with that please?

All advices are appreciated.

Many thanks

Doesn't look like there is. The only utility I know generating a tri-diagonal matrix, but not with the elements being matrices... only scalars. However, this submission to MATLAB FEX by John D'Errico is of particular interest: mathworks.com/matlabcentral/fileexchange/… — rayryeng

Unknown Unknown · Accepted Answer · 2015-01-09T01:44:13

The Kronecker product, realized as .*. in Scilab, can help. Given M, B, C, D as in your post, Kronecker product with identity matrix creates the block-diagonal matrix like what you'd get with sysdiag:

eye(M,M).*.B

But the Kronecker product can also be taken with other matrices. Put 1s above the main diagonal, and take Kronecker product with C to obtain the C blocks in the desired locations:

diag(ones(M-1,1),1).*.C

Similarly for D:

diag(ones(M-1,1),-1).*.D

In one line,

A = eye(M,M).*.B + diag(ones(M-1,1),1).*.C + diag(ones(M-1,1),-1).*.D

does the job.

Matlab/ Scilab/ R : Creating a block tridiagonal matrix in Scilab

1 Answers