Systems Optimization Laboratory

lusolZ: Nullspace of sparse matrix via SPQR or LUSOL

• AUTHORS: Nick Henderson, San Kim, Ding Ma, Michael Saunders, Yuekai Sun, Ronan Fleming, Ines Thiele.

• CONTENTS:
  Matlab software for computing a nullspace operator \(Z\) of the transpose of a sparse matrix \(S\) (so that \(S^T Z = 0\)) using sparse QR factors of either \(S\) or \(S^T\) computed by SuiteSparseQR, or sparse LU factors of either \(S\) or \(S^T\) computed by LUSOL. MATLAB routines {spqrZ, spqrZv, spqrZt} and {lusolZ, lusolZv, lusolZt} are provided to factorize \(S\) or \(S^T\) and to compute products of the form \(w = Zv\) and \(s = Z^T t\) for given vectors \(v\) and \(t\).
  

• REFERENCES:
  [1] T. A. Davis, Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization, ACM TOMS 38(1), 8:1-8:22, 2011.
  [2] N. W. Henderson, S. Kim, D. Ma, M. A. Saunders, Y. Sun, R. M. T. Fleming, and I. Thiele, Conservation analysis of genome-scale biochemical networks, Bioinformatics, in preparation, Feb 2016.

• RELEASE:
  19 Jan 2016: First version of lusolZ software.
  02 Feb 2016: spqrZ routines added.
  16 Feb 2016: Updated.
  02 Mar 2016: Updated M-file help.

• MATLAB files: lusolZ.zip.