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: