spLDL

Purpose

Computes the \(LDL\) decomposition of a symmetric sparse matrix A.

Format

{ l, d } = spLDL(a)
Parameters:

a (sparse matrix) – NxN symmetric sparse matrix.

Returns:
  • l (NxN lower-triangular sparse matrix) – The lower-triangular sparse matrix \(LDL\) decomposition of A.
  • d (NxN diagonal sparse matrix) – The diagonal sparse matrix \(LDL\) decomposition of A.

Examples

declare sparse matrix a, l, d;

nz = { 142 13 56 57 0,
        13  0  0  0 0,
        56  0 94 47 0,
        57  0 47 35 0,
         0  0  0  0 0 };

 a = densetosp(nz, 0);

 { l, d } = spLDL(a);

Remarks

spLDL() will not check to see if the input matrix is symmetric. The function looks only at the lower triangular portion of the input matrix.

Technical Notes

spLDL() implements functions from the TAUCS library:

TAUCS Version 2.2 Copyright ©2003, by Sivan Toledo, Tel-Aviv University, stoledo@tau.ac.il. All Rights Reserved.

See also

Functions spLU()