Matlab Function - spdiags

spdiags

Extract nonzero diagonals and create sparse band and diagonal matrices

• Bout = spdiags(A) extracts the nonzero diagonals from m-by-n matrix A and returns them as the columns in min(m,n)-by-p matrix Bout, where p is the number of nonzero diagonals.
• S = spdiags(Bin,d,m,n) creates an m-by-n sparse matrix S by taking the columns of Bin and placing them along the diagonals specified by d.
• S = spdiags(Bin,d,A) replaces the diagonals in A specified by d with the columns of Bin.

Examples

Create Tridiagonal Matrix

Create a tridiagonal matrix using three vectors, change some of the matrix diagonals, and then extract the diagonals.

Create a 9-by-1 vector of ones, and then create a tridiagonal matrix using the vector. View the matrix elements.

n = 9;
e = ones(n,1);
A = spdiags([e -2*e e],-1:1,n,n);
full(A)

ans = 9×9

    -2     1     0     0     0     0     0     0     0
     1    -2     1     0     0     0     0     0     0
     0     1    -2     1     0     0     0     0     0
     0     0     1    -2     1     0     0     0     0
     0     0     0     1    -2     1     0     0     0
     0     0     0     0     1    -2     1     0     0
     0     0     0     0     0     1    -2     1     0
     0     0     0     0     0     0     1    -2     1
     0     0     0     0     0     0     0     1    -2

Change the values on the main (d = 0) diagonal of A.

Bin = abs(-(n-1)/2:(n-1)/2)';
d = 0;
A = spdiags(Bin,d,A);
full(A)

ans = 9×9

     4     1     0     0     0     0     0     0     0
     1     3     1     0     0     0     0     0     0
     0     1     2     1     0     0     0     0     0
     0     0     1     1     1     0     0     0     0
     0     0     0     1     0     1     0     0     0
     0     0     0     0     1     1     1     0     0
     0     0     0     0     0     1     2     1     0
     0     0     0     0     0     0     1     3     1
     0     0     0     0     0     0     0     1     4

Finally, recover the diagonals of A as the columns in a matrix.

Bout = spdiags(A);
full(Bout)

ans = 9×3

     1     4     0
     1     3     1
     1     2     1
     1     1     1
     1     0     1
     1     1     1
     1     2     1
     1     3     1
     0     4     1