Vector.AddScaledSqr Method

Overload List

#	Signature	Description
1	function AddScaledSqr(const X: TMtxVec; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx): TMtxVec;	self = sqr(XxScale + YyScale)
	└ indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const xScale: TCplx; const Y: TMtxVec; YIndex: Integer; const yScale: TCplx; Index: Integer; Len: Integer): TMtxVec;
2	function AddScaledSqr(const X: TMtxVec; const Y: TMtxVec; const yScale: TCplx): TMtxVec;	self = sqr(X + Y*yScale)
	└ indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const Y: TMtxVec; YIndex: Integer; const yScale: TCplx; Index: Integer; Len: Integer): TMtxVec;
3	function AddScaledSqr(const X: TMtxVec; const Y: TMtxVec; const yScale: Double): TMtxVec;	self = sqr(X + Y*yScale)
	└ indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const Y: TMtxVec; YIndex: Integer; const yScale: Double; Index: Integer; Len: Integer): TMtxVec;
4	function AddScaledSqr(const X: TMtxVec; const xScale: Double; const Y: TMtxVec; const yScale: Double): TMtxVec;	self = sqr(XxScale + YyScale)
	└ indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const xScale: Double; const Y: TMtxVec; YIndex: Integer; const yScale: Double; Index: Integer; Len: Integer): TMtxVec;

Overload 1: function AddScaledSqr(const X: TMtxVec; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx): TMtxVec;

Compute sqr(X*xScale + Y*yScale)

#	Name	Type
1	X	TMtxVec
2	xScale	TCplx
3	Y	TMtxVec
4	yScale	TCplx

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

Indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const xScale: TCplx; const Y: TMtxVec; YIndex: Integer; const yScale: TCplx; Index: Integer; Len: Integer): TMtxVec;

Compute sqr(X*xScale + Y*yScale) on sub arrays

#	Name	Type	Description
1	X	TMtxVec
2	XIndex	Integer	X start index
3	xScale	TCplx
4	Y	TMtxVec
5	YIndex	Integer	Y start index
6	yScale	TCplx
7	Index	Integer	start index
8	Len	Integer	element count

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

Overload 2: function AddScaledSqr(const X: TMtxVec; const Y: TMtxVec; const yScale: TCplx): TMtxVec;

Compute sqr(X + Y*yScale)

#	Name	Type
1	X	TMtxVec
2	Y	TMtxVec
3	yScale	TCplx

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

Examples

uses MtxVec, MtxExpr, Math387;

var
    X, Y, A1, A2, A3: Vector;
    yScale: Double;
begin
    yScale := 1.5;
    X := [1,2,3,4];
    Y := [2,3,4,5];
    A1 := Sqr(X + Y * yScale);
    A2 := AddScaledSqr(X, Y, yScale);
    A3.AddScaledSqr(X, Y, yScale);

    if not A2.IsEqual(A1) then ERaise('Problem');
    if not A3.IsEqual(A1) then ERaise('Problem');
end;

Indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const Y: TMtxVec; YIndex: Integer; const yScale: TCplx; Index: Integer; Len: Integer): TMtxVec;

Compute sqr(X + Y*yScale) on sub arrays

#	Name	Type	Description
1	X	TMtxVec
2	XIndex	Integer	X start index
3	Y	TMtxVec
4	YIndex	Integer	Y start index
5	yScale	TCplx
6	Index	Integer	start index
7	Len	Integer	element count

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

Overload 3: function AddScaledSqr(const X: TMtxVec; const Y: TMtxVec; const yScale: Double): TMtxVec;

Compute sqr(X + Y*yScale)

#	Name	Type
1	X	TMtxVec
2	Y	TMtxVec
3	yScale	Double

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

Remarks:

By making use of yScale, it is also possible to compute the following (at the same or higher speed):

(X - Y)^2 = X^2 - 2XY +Y^2

Examples

uses MtxVec, MtxExpr, Math387;

var
    X, Y, A1, A2, A3: Vector;
    xScale, yScale: Double;
begin
    xScale := 1.5;
    yScale := -1.5;
    X := [1,2,3,4];
    Y := [2,3,4,5];
    A1 := Sqr(X * xScale + Y * yScale);
    A2 := AddScaledSqr(X, xScale, Y, yScale);
    A3.AddScaledSqr(X, xScale, Y, yScale);

    if not A2.IsEqual(A1) then ERaise('Problem');
    if not A3.IsEqual(A1) then ERaise('Problem');
end;

Indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const Y: TMtxVec; YIndex: Integer; const yScale: Double; Index: Integer; Len: Integer): TMtxVec;

Compute sqr(X + Y*yScale) on sub arrays

#	Name	Type	Description
1	X	TMtxVec
2	XIndex	Integer	X start index
3	Y	TMtxVec
4	YIndex	Integer	Y start index
5	yScale	Double
6	Index	Integer	start index
7	Len	Integer	element count

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

Overload 4: function AddScaledSqr(const X: TMtxVec; const xScale: Double; const Y: TMtxVec; const yScale: Double): TMtxVec;

Compute sqr(X*xScale + Y*yScale)

#	Name	Type
1	X	TMtxVec
2	xScale	Double
3	Y	TMtxVec
4	yScale	Double

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

Indexed: function AddScaledSqr(const X: TMtxVec; XIndex: Integer; const xScale: Double; const Y: TMtxVec; YIndex: Integer; const yScale: Double; Index: Integer; Len: Integer): TMtxVec;

Compute sqr(X*xScale + Y*yScale) on sub arrays

#	Name	Type	Description
1	X	TMtxVec
2	XIndex	Integer	X start index
3	xScale	Double
4	Y	TMtxVec
5	YIndex	Integer	Y start index
6	yScale	Double
7	Index	Integer	start index
8	Len	Integer	element count

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