|Returns a sparse orthonormal basis for the null space|
|Other toolboxes required||none|
|Function category||Helper functions|
|This is a helper function that only exists to aid other functions in QETLAB. If you are an end-user of QETLAB, you likely will never have a reason to use this function.|
spnull is a function that computes an orthonormal basis for the null space of a full or sparse matrix. When the matrix is sparse, this computation is performed via the QR decomposition and is typically much faster than using null(full(S)).
- Z = spnull(S)
- Z = spnull(S,varargin)
- S: The matrix to have its null space computed.
- varargin (optional): Extra arguments that, if S is full, will be passed to MATLAB's null function.
The following example gives a 4-by-4 matrix whose null space is spanned by the two vectors $[0,0,1,0]^T$ and $[0,0,0,1]^T$:
>> S = sparse(4,4); >> S(1,1) = 1; S(3,2) = 1; >> spnull(S) ans = (3,1) 1 (4,2) 1
Note that the output is sparse because S is sparse. If the input is full then the output will be full as well:
>> spnull(full(S)) ans = 0 0 0 0 1 0 0 1
Click on "expand" to the right to view the MATLAB source code for this function.
- Sparse null space and orthogonal: The source of this file on MATLAB File Exchange