TSparseMtx.Solve Methods

Summary

Vector version of Solve.

Class
TSparseMtx

Declaration

Procedure Solve(B, X: TVec; MtxType: TMtxType = mtGeneral);

Declaration

Procedure Solve(B, X: TMtx; MtxType: TMtxType = mtGeneral);

Summary

Direct solve.

Description

Solve the system A*X = B, where A is the calling matrix. The actual system being solved is defined by SparseSystem property. A is sparse and unsymmetric. It is based on the Unsymmetric MultiFrontal method, which factorizes PAQ into the product LU, where L and U are lower and upper triangular, respectively, and P are Q are permutation matrices. Both P and Q are chosen to reduce fill-in (new nonzeros in L and U that are not present in A). The permutation P has the dual role of reducing fill-in and maintaining numerical accuracy (via relaxed partial pivoting and row interchanges).

The Solve method uses BLAS level 3 dgeem matrix multiply routine and takes full advantage of CPU specific optimized code and symmetric multiprocessing.

See Also
SparseSolver

Example 1

          uses MtxExpr, MtxVecTee, Sparse;

          procedure Example;
          var x,b: Vector;
            SparseA: TSparseMtx;
          begin
            // load data
            SparseA.LoadFromMatrixFile('system.mtx');
            b.LoadFromFile('coefficients.vec');
            // set solution size
            x.Size(b);
            // solve
            SparseA.SparseSolver := ssUmfPack;
            SparseA.Solve(b,x);
            //view solution
            ViewValues(x);
          end;

          #include "MtxVecCpp.h"
          #include "Sparse.hpp"
          #include "MtxVecTee.hpp"

          void  __fastcall Example()
          {
            Vector x,b;
            TSparseMtx *SparseA = new TSparseMtx();
            try
            {
              // load data
              SparseA->LoadFromMatrixFile("system.mtx");
              b->LoadFromFile("coefficients.vec");
              // set solution size
              x->Size(b);
              // solve
              SparseA->SparseSolver = ssUmfPack;
              SparseA->Solve(b,x);
              //view solution
              ViewValues(x);
            }
            __finally
            {
              delete SparseA;
            }
          }