TVec.TensorProd Methods

Summary

Tensor product between vector and matrix.

Class
TVec

Declaration

Function TensorProd(Vec: TVec; Mtx: TMtx; MtxType: TMtxType = mtGeneral; Operation: TMtxOperation = opNone): TVec;

Description

Calculates the left tensor product between vector and matrix.

Declaration

Function TensorProd(Mtx: TMtx; Vec: TVec; MtxType: TMtxType = mtGeneral; Operation: TMtxOperation = opNone): TVec;

Description

Calculates the right tensor product between matrix and vector. The result is placed in the calling vector. Depending on the TMtxType the following operations are available:

mtSymmetric: y = alfa*a*x + beta*y
mtSymmPosDef: y = alfa*a*x + beta*y
mtHermitian: y = alfa*a*x + beta*y
mtHermPosDef: y = alfa*a*x + beta*y
mtTriangular: y = op(a)*x
mtGeneral: y = alfa*op(a)*x + beta*y

The Alfa and Beta are TVec complex public variables. Their default values are:

Alfa = Cplx(1,0)
Beta = Cplx(0,0).
Note: Each time you call TensorProd the values of Alfa and Beta are reset to default. If the matrix is not complex, only the real part of Alfa and Beta is used. If matrix complex and symmetric the general type is used.

See Also
TensorProd

Example 1

      var a,b,c,t: TMtx;
            d,e,f: TVec;
      begin
        CreateIt(a,b,c,t);
        CreateIt(d,e,f);
        try
          // Test non quadratic general matrix
          a.SetIt(2,3,False,[4,3,3,
                             3,4,2]);
          e.SetIt(false,[1,2]);
          d.TensorProd(e,a);

          f.SetIt(False,[10,11,7]);
          if not f.Equal(d) then raise Exception.Create('Not same');

          // Test on triangular matrices, left
          a.TriangleForm := tfUpper;
          a.TriangleUnit := False;

          a.SetIt(2,2,False,[4,3,
                             0,4]);
          e.SetIt(false,[1,2]);
          d.TensorProd(e,a,mtTriangle);

          f.SetIt(False,[4,11]);
          if not f.Equal(d) then raise Exception.Create('Not same');

          // Test on triangular matrices, right
          a.Reset;
          a.TriangleForm := tfUpper; // data to be referenced is in upper triangle
          a.TriangleUnit := False;  // non unit diagonal
          a.SetIt(2,2,False,[4,3,
                            0,4]);
          e.SetIt(false,[1,2]);
          d.TensorProd(a,e,mtTriangle);

          f.SetIt(False,[10,8]);
          if not f.Equal(d) then raise Exception.Create('Not same');

          // Test on symmetric matrices, right
          a.Reset;
          a.TriangleForm := tfUpper;
          a.SetIt(2,2,False,[4,3,
                            3,4]);
          e.SetIt(false,[1,2]);
          d.TensorProd(e,a,mtSymmetric);

          f.SetIt(False,[10,11]);
          if not f.Equal(d) then raise Exception.Create('Not same');

          // Test on symmetric matrices, Left
          a.Reset;
          a.TriangleForm := tfUpper;
          a.SetIt(2,2,False,[4,3,
                             3,4]);
          e.SetIt(false,[1,2]);
          d.TensorProd(a,e,mtSymmetric);

          f.SetIt(False,[10,11]);
          if not f.Equal(d) then raise Exception.Create('Not same');
        finally
          FreeIt(a,b,c,t);
          FreeIt(d,e,f);
        end;
      end;