Vector.TensorProd Method

Overload List

#	Signature	Description
1	TVec TensorProd(TMtx Mtx, TVec Vec, TMtxType MtxType, TMtxOperation Operation)	Tensor product between vector and matrix.
2	TVec TensorProd(TVec Vec, TMtx Mtx, TMtxType MtxType, TMtxOperation Operation)	Calculates the left tensor product between vector and matrix.

Overload 1: TVec TensorProd(TMtx Mtx, TVec Vec, TMtxType MtxType, TMtxOperation Operation)

Tensor product between vector and matrix.

#	Name	Type	Description
1	Mtx	TMtx	source TMtx
2	Vec	TVec	source TVec
3	MtxType	TMtxType
4	Operation	TMtxOperation

Result: stored in self (calling object), returns self for chaining

Remarks:

Calculates the right tensor product between matrix and vector. The result is placed in the calling vector. Depending on the Dew.Math.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 Dew.Math.Vector.Alfa and Dew.Math.Vector.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.

Examples

Matrix a;
Matrix b;
Matrix c;
Matrix t;
Vector d;
Vector e;
Vector f;
// Test non quadratic general matrix
a.SetIt(2,3,false,[4,3,3,
3,4,2]);
e.SetIt(false,new double[] {1,2});
d.TensorProd(e,a);

f.SetIt(false,new double[] {10,11,7});
if !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,new double[] {1,2});
d.TensorProd(e,a,mtTriangle);

f.SetIt(false,new double[] {4,11});
if !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,new double[] {1,2});
d.TensorProd(a,e,mtTriangle);

f.SetIt(false,new double[] {10,8});
if !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,new double[] {1,2});
d.TensorProd(e,a,mtSymmetric);

f.SetIt(false,new double[] {10,11});
if !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,new double[] {1,2});
d.TensorProd(a,e,mtSymmetric);

f.SetIt(false,new double[] {10,11});
if !f.Equal(d) then raise Exception.Create(@"Not same");

See Also: Vector.TensorProd

Overload 2: TVec TensorProd(TVec Vec, TMtx Mtx, TMtxType MtxType, TMtxOperation Operation)

Calculates the left tensor product between vector and matrix.

#	Name	Type	Description
1	Vec	TVec	source TVec
2	Mtx	TMtx	source TMtx
3	MtxType	TMtxType
4	Operation	TMtxOperation

Result: stored in self (calling object), returns self for chaining