`speye`

Sparse identity matrix.

Syntax

S = speye(n)

Returns the n-by-n sparse identity.

S = speye(m, n)

Returns an m-by-n sparse matrix with ones on the main diagonal.

S = speye([m n])

Same, with the size given as a vector.

Description

speye(n) is the sparse counterpart of eye(n). It is the natural building block for shifted matrices such as A + sigma*speye(n), where using a full identity would destroy the sparsity of the sum.

Input arguments

m, n: Number of rows and columns.

Output arguments

S: Sparse matrix with min(m,n) stored nonzeros.

Example

Identity and a shifted matrix

I = speye(3)
full(speye(2, 3))
S = 2*speye(2) + sparse([0 1; 0 0]);
full(S)

Output

I = 

   (1,1)        1
   (2,2)        1
   (3,3)        1
ans = 2×3

     1     0     0
     0     1     0
ans = 2×2

     2     1
     0     2

Notes

MatLivre stores sparse matrices densely, so they save no memory, and sizes above 200 million elements are rejected. Results and display match MATLAB for ordinary sizes.

speye