spLU

Purpose

Computes the \(LU\) decomposition of a sparse matrix A with partial pivoting.

Format

{ l, u } = spLU(a)
Parameters:

a (sparse matrix) – N x N non-singular sparse matrix.

Returns:
  • l (NxN sparse matrix) – . This is a “scrambled” lower-triangular, sparse matrix that has been reordered based upon the row pivoting.
  • u (NxN sparse matrix) – . This is an “scrambled” upper-triangular, sparse matrix that has been reordered based upon column pivoting to preserve sparsity.

Examples

declare sparse matrix a, l, u;

nz = {-5.974       0  -13.37   6.136       0,
           0   5.932   7.712       0  -6.549,
           0  -5.728       0  14.227       0,
           0 -12.164   9.916  13.902   6.182,
      13.425       0 -12.654 -16.534       0 };

a = densetosp(nz, 0);
{ l, u } = spLU(a);

Remarks

If the input matrix or either of the factors \(L\) and \(U\) are singular, the function will either terminate the program with an error message or return an error code which can be tested for with the scalerr() function.

This depends on the trap state as follows:

trap 1 return error code: 50
trap 0 terminate with error message: Matrix singular

Technical Notes

spLU() implements functions from the SuperLU 4.0 library written by James W. Demmel, John R. Gilbert and Xiaoye S. Li.

Copyright ©2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy). All rights reserved.

See also

Functions spLDL()