Vector.DotProdc Method

Overload List

#	Signature	Description
1	function DotProdc(const Vec: TMtxVec): TCplx;	Scalar product of two complex arrays.
	└ indexed: function DotProdc(const Vec: TMtxVec; VecIndex: Integer; Index: Integer; Len: Integer): TCplx;
2	function DotProdc(const Vec: TMtxVec; ConjVec: Boolean): TCplx;	Returns the scalar product between Vec and calling object complex elements.
	└ indexed: function DotProdc(const Vec: TMtxVec; ConjVec: Boolean; VecIndex: Integer; Index: Integer; Len: Integer): TCplx;

Overload 1: function DotProdc(const Vec: TMtxVec): TCplx;

Scalar product of two complex arrays.

#	Name	Type	Description
1	Vec	TMtxVec

Returns: TCplx (complex)

Remarks:

Calculates the dot product (scalar value) of the calling object and Vec object and returns a complex scalar value. An exception is raised if calling or Vec object Vector.Complex property is false. The dot product is defined by the equation:

\text{V}\cdot \text{V} = \sum _{k=0} ^{\text{Length}-1}\text{V}[k]\cdot \text{V}[k]

Note
Both objects must be of equal size. If they are not, the method will return the dot product of the largest sub-array.

Examples

var a,b: Vector;
prod: TCplx;
begin
    a.SetIt(True,[1,2,3,4]);
    b.SetIt(True,[5,6,7,8]);
    prod := a.DotProdc(b); //= (1+2i)*(5+6i)+(3+4i)*(7+8i)
end;

See Also: Vector.DotProd

Indexed: function DotProdc(const Vec: TMtxVec; VecIndex: Integer; Index: Integer; Len: Integer): TCplx;

Returns the scalar product between Vec (complex) elements [VecIndex]..[VecIndex+Len-1] and calling object (complex) elements [Index]..[Index+Len-1].

#	Name	Type	Description
1	Vec	TMtxVec
2	VecIndex	Integer
3	Index	Integer	start index
4	Len	Integer	element count

Returns: TCplx (complex)

Remarks:

An exception is raised if Vec and calling object Vector.Complex property is False. An exception is raised if Vector.ConditionCheck is True and array borders are overrun or underrun.

Overload 2: function DotProdc(const Vec: TMtxVec; ConjVec: Boolean): TCplx;

Returns the scalar product between Vec and calling object complex elements.

#	Name	Type	Description
1	Vec	TMtxVec
2	ConjVec	Boolean

Returns: TCplx (complex)

Remarks:

If ConjVec is True, scalar product between calling object and conjugated Vec object elements is calculated. An exception is raised if Vec and calling object Vector.Complex property is False.

Indexed: function DotProdc(const Vec: TMtxVec; ConjVec: Boolean; VecIndex: Integer; Index: Integer; Len: Integer): TCplx;

Returns the scalar product between Vec (complex) elements [VecIndex]..[VecIndex+Len-1] and calling object (complex) elements [Index]..[Index+Len-1].

#	Name	Type	Description
1	Vec	TMtxVec
2	ConjVec	Boolean
3	VecIndex	Integer
4	Index	Integer	start index
5	Len	Integer	element count

Returns: TCplx (complex)

Remarks:

If ConjVec is True, scalar product between calling object and conjugated Vec object elements is calculated. An exception is raised if Vec and calling object Vector.Complex property is False. An exception is raised if Vector.ConditionCheck is True and array borders are overrun or underrun.