NMath User's Guide

17.3 Sparse Matrix Factorizations (.NET, C#, CSharp, Visual Basic, VB.NET)

NMath provides classes for computing and storing factorizations of general sparse matrices. Instances of the factorization classes calculate solutions to the equation where A is a sparse matrix and B is a single vector, or multiple vectors.

Once a factorization is constructed, it can be reused to solve for different right-hand sides.

Factorization Classes

The factorization classes associated with each general sparse matrix type are shown in Table 13.

Note that there are two factorization classes for symmetric and Hermitian types: one for indefinite matrices, and one for positive definite (PD) matrices.

SparseMatrixFact is the base class for sparse matrix factorizations, and is parameterized on the type, T, of values stored in the vector.

Creating Factorizations

You can create an instance of a factorization class by supplying the constructor with a matrix to factor. The following code creates a symmetric sparse matrix from the given data, then factors the matrix:

DoubleSymCsrSparseMatrix sA =
  new DoubleSymCsrSparseMatrix( sparseData);
DoubleSparseSymFact fact = new DoubleSparseSymFact( sA );

You can also use an existing instance to factor other matrices with the provided Factor() method. Thus, if sB is another DoubleSymCsrSparseMatrix:

fact.Factor( sB );

The read-only ErrorStatus property gets an Error enumerated value. For example:

if ( fact.ErrorStatus == DoubleSparseSymFact.Error.NoError )
{
   // Do something here...
}

Using Factorizations

Once a factorization is constructed from a matrix, it can be used to solve for different right hand sides. For instance, this code solves for one right-hand side:

DoubleVector b = new DoubleVector( 8, 1 );
DoubleVector x = fact.Solve( b );

Similarly, you can use the Solve() method to solve for multiple right-hand sides. This code solves for 3 right-hand sides:

int nrhs = 3;
DoubleMatrix B = new DoubleMatrix( 8, nrhs, new RandGenBeta() );
DoubleMatrix X = fact.Solve( B );

The right-hand sides are the columns of matrix B, and the corresponding solutions are the columns of matrix X.

NOTE- Be sure to check the ErrorStatus property on the factorization before calling Solve() to confirm that the factorization is valid.

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