MtxExpr.AddScaled Method

MtxExpr

Overload List

#SignatureDescription
1function AddScaled(const X: TMtx; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx): Matrix;Result = X*xScale + Y*yScale, where X is a Matrix
2function AddScaled(const X: TMtx; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Matrix;Result = X*xScale + Y*yScale + Z*zScale, where X is a Matrix
3function AddScaled(const X: TMtx; const Y: TMtx; const aScale: TCplx): Matrix;Computes X + Y*Ascale
4function AddScaled(const X: TMtx; const Y: TMtx; aScale: Double): Matrix;Computes X + Y*Ascale
5function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: TCplx): Matrix;Result = X + Y*yScale, where X is a Matrix
6function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Matrix;Result = X + Y*yScale + Z*zScale, where X is a Matrix
7function AddScaled(const X: TMtx; const Y: TMtxVec; const Z: TMtxVec; const zScale: TCplx): Matrix;Result = X + Y + Z*zScale, where X is a Matrix
8function AddScaled(const X: TMtx; const Y: TMtxVec; const Z: TMtxVec; const zScale: Double): Matrix;Result = X + Y + Z*zScale, where X is a Matrix
9function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: Double): Matrix;Result = X + Y*yScale, where X is a Matrix
10function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Matrix;Result = X + Y*yScale + Z*zScale, where X is a Matrix
11function AddScaled(const X: TMtx; const xScale: Double; const Y: TMtxVec; const yScale: Double): Matrix;Result = X*xScale + Y*yScale, when X is a Matrix
12function AddScaled(const X: TMtx; const xScale: Double; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Matrix;Result = X*xScale + Y*yScale + Z*zScale
13function AddScaled(const X: TVec; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx): Vector;Result = X*xScale + Y*yScale
14function AddScaled(const X: TVec; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Vector;Result = X*xScale + Y*yScale + Z*zScale
15function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: TCplx): Vector;Result = X + Y*yScale
16function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Vector;Result = X + Y*yScale + Z*zScale
17function AddScaled(const X: TVec; const Y: TMtxVec; const Z: TMtxVec; const zScale: TCplx): Vector;Result = X + Y + Z*zScale
18function AddScaled(const X: TVec; const Y: TMtxVec; const Z: TMtxVec; const zScale: Double): Vector;Result = X + Y + Z*zScale
19function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: Double): Vector;Result = X + Y*yScale
20function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Vector;Result = X + Y*yScale + Z*zScale
21function AddScaled(const X: TVec; const Y: TVec; const aScale: TCplx): Vector;Computes X + Y*Ascale
22function AddScaled(const X: TVec; const Y: TVec; aScale: Double): Vector;Computes X + Y*Ascale
23function AddScaled(const X: TVec; const xScale: Double; const Y: TMtxVec; const yScale: Double): Vector;Result = X*xScale + Y*yScale
24function AddScaled(const X: TVec; const xScale: Double; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Vector;Result = X*xScale + Y*yScale + Z*zScale

Overload 1: function AddScaled(const X: TMtx; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx): Matrix;

Compute X*xScale + Y*yScale, where X is a Matrix

#NameTypeDescription
1XTMtx
2xScaleTCplx
3YTMtxVec
4yScaleTCplx

Returns: Matrix

Overload 2: function AddScaled(const X: TMtx; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Matrix;

Compute X*xScale + Y*yScale + Z*zScale, where X is a Matrix

#NameTypeDescription
1XTMtx
2xScaleTCplx
3YTMtxVec
4yScaleTCplx
5ZTMtxVec
6zScaleTCplx

Returns: Matrix

Overload 3: function AddScaled(const X: TMtx; const Y: TMtx; const aScale: TCplx): Matrix;

Computes X + Y*Ascale

#NameTypeDescription
1XTMtx
2YTMtx
3aScaleTCplx

Returns: Matrix

Remarks:

Internally calls Matrix.AddScaled

Overload 4: function AddScaled(const X: TMtx; const Y: TMtx; aScale: Double): Matrix;

Computes X + Y*Ascale

#NameTypeDescription
1XTMtx
2YTMtx
3aScaleDoublescalar

Returns: Matrix

Remarks:

Internally calls Matrix.AddScaled

Overload 5: function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: TCplx): Matrix;

Compute X + Y*yScale, where X is a Matrix.

#NameTypeDescription
1XTMtx
2YTMtxVec
3yScaleTCplx

Returns: Matrix

Overload 6: function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Matrix;

Compute X + Y*yScale + Z*zScale, where X is a Matrix.

#NameTypeDescription
1XTMtx
2YTMtxVec
3yScaleTCplx
4ZTMtxVec
5zScaleTCplx

Returns: Matrix

Overload 7: function AddScaled(const X: TMtx; const Y: TMtxVec; const Z: TMtxVec; const zScale: TCplx): Matrix;

Compute X + Y + Z*zScale, where X is a Matrix.

#NameTypeDescription
1XTMtx
2YTMtxVec
3ZTMtxVec
4zScaleTCplx

Returns: Matrix

Overload 8: function AddScaled(const X: TMtx; const Y: TMtxVec; const Z: TMtxVec; const zScale: Double): Matrix;

Compute X + Y + Z*zScale, where X is a Matrix.

#NameTypeDescription
1XTMtx
2YTMtxVec
3ZTMtxVec
4zScaleDouble

Returns: Matrix

Overload 9: function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: Double): Matrix;

Compute X + Y*yScale, where X is a Matrix.

#NameTypeDescription
1XTMtx
2YTMtxVec
3yScaleDouble

Returns: Matrix

Overload 10: function AddScaled(const X: TMtx; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Matrix;

Compute X + Y*yScale + Z*zScale, where X is a Matrix.

#NameTypeDescription
1XTMtx
2YTMtxVec
3yScaleDouble
4ZTMtxVec
5zScaleDouble

Returns: Matrix

Overload 11: function AddScaled(const X: TMtx; const xScale: Double; const Y: TMtxVec; const yScale: Double): Matrix;

Compute X*xScale + Y*yScale, when X is a Matrix

#NameTypeDescription
1XTMtx
2xScaleDouble
3YTMtxVec
4yScaleDouble

Returns: Matrix

Remarks:

The operation does only per-element math.

Overload 12: function AddScaled(const X: TMtx; const xScale: Double; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Matrix;

Compute X*xScale + Y*yScale + Z*zScale

#NameTypeDescription
1XTMtx
2xScaleDouble
3YTMtxVec
4yScaleDouble
5ZTMtxVec
6zScaleDouble

Returns: Matrix

Overload 13: function AddScaled(const X: TVec; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx): Vector;

Compute X*xScale + Y*yScale

#NameTypeDescription
1XTVec
2xScaleTCplx
3YTMtxVec
4yScaleTCplx

Returns: Vector

Overload 14: function AddScaled(const X: TVec; const xScale: TCplx; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Vector;

Compute X*xScale + Y*yScale + Z*zScale

#NameTypeDescription
1XTVec
2xScaleTCplx
3YTMtxVec
4yScaleTCplx
5ZTMtxVec
6zScaleTCplx

Returns: Vector

Overload 15: function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: TCplx): Vector;

Compute X + Y*yScale

#NameTypeDescription
1XTVec
2YTMtxVec
3yScaleTCplx

Returns: Vector

Overload 16: function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: TCplx; const Z: TMtxVec; const zScale: TCplx): Vector;

Compute X + Y*yScale + Z*zScale

#NameTypeDescription
1XTVec
2YTMtxVec
3yScaleTCplx
4ZTMtxVec
5zScaleTCplx

Returns: Vector

Overload 17: function AddScaled(const X: TVec; const Y: TMtxVec; const Z: TMtxVec; const zScale: TCplx): Vector;

Compute X + Y + Z*zScale

#NameTypeDescription
1XTVec
2YTMtxVec
3ZTMtxVec
4zScaleTCplx

Returns: Vector

Overload 18: function AddScaled(const X: TVec; const Y: TMtxVec; const Z: TMtxVec; const zScale: Double): Vector;

Compute X + Y + Z*zScale

#NameTypeDescription
1XTVec
2YTMtxVec
3ZTMtxVec
4zScaleDouble

Returns: Vector

Remarks:

Computes the sum of X and Y plus Z scaled by zScale without creating temporary objects.

Examples
var
    zScale: Double;
    X, Y, Z, A1, A2, A3: Vector;
begin
zScale := 2.0;
X := [1, 2, 3, 4];
Y := [2, 3, 4, 5];
Z := [3, 4, 5, 6];
A1 := X + Y + Z * zScale;
A2 := AddScaled(X, Y, Z, zScale);
A3.AddScaled(X, Y, Z, zScale);
if not A2.IsEqual(A1) then ERaise('Problem');
if not A3.IsEqual(A1) then ERaise('Problem');
end;

Overload 19: function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: Double): Vector;

Compute X + Y*yScale

#NameTypeDescription
1XTVec
2YTMtxVec
3yScaleDouble

Returns: Vector

Remarks:

Computes the sum of two vector-based operands, X and Y, where Y is first scaled by yScale. This operation is performed without creating temporary objects.

Examples
var
    yScale: Double;
    X, Y, A1, A2, A3: Vector;
begin
yScale := 1.5;
X := [1, 2, 3, 4];
Y := [2, 3, 4, 5];
A1 := X + Y * yScale;
A2 := AddScaled(X, Y, yScale);
A3.AddScaled(X, Y, yScale);
if not A2.IsEqual(A1) then ERaise('Problem');
if not A3.IsEqual(A1) then ERaise('Problem');
end;

Overload 20: function AddScaled(const X: TVec; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Vector;

Compute X + Y*yScale + Z*zScale

#NameTypeDescription
1XTVec
2YTMtxVec
3yScaleDouble
4ZTMtxVec
5zScaleDouble

Returns: Vector

Remarks:

Computes the sum of X and Y scaled by yScale plus Z scaled by zScale without temporary objects.

Examples
var
    yScale: Double;
    X, Y, Z, A1, A2, A3: Vector;
begin
yScale := 1.5, zScale = 2.0;
X := [1, 2, 3, 4];
Y := [2, 3, 4, 5];
Z := [3, 4, 5, 6];
A1 := X + Y * yScale + Z * zScale;
A2 := AddScaled(X, Y, yScale, Z, zScale);
A3.AddScaled(X, Y, yScale, Z, zScale);
if not A2.IsEqual(A1) then ERaise('Problem');
if not A3.IsEqual(A1) then ERaise('Problem');
end;

Overload 21: function AddScaled(const X: TVec; const Y: TVec; const aScale: TCplx): Vector;

Computes X + Y*Ascale

#NameTypeDescription
1XTVec
2YTVec
3aScaleTCplx

Returns: Vector

Remarks:

Internally calls Vector.AddScaled

Overload 22: function AddScaled(const X: TVec; const Y: TVec; aScale: Double): Vector;

Computes X + Y*Ascale

#NameTypeDescription
1XTVec
2YTVec
3aScaleDoublescalar

Returns: Vector

Remarks:

Internally calls Vector.AddScaled

Overload 23: function AddScaled(const X: TVec; const xScale: Double; const Y: TMtxVec; const yScale: Double): Vector;

Compute X*xScale + Y*yScale

#NameTypeDescription
1XTVec
2xScaleDouble
3YTMtxVec
4yScaleDouble

Returns: Vector

Remarks:

Computes the specified expression without temporary objects and at the same speed as computing only X + Y.

Examples
var
    xScale, yScale: Double;
    X, Y, A1, A2, A3: Vector;
begin
xScale := 1.5;
yScale := -1.5;
X := [1, 2, 3, 4];
Y := [2, 3, 4, 5];
A1 := X * xScale + Y * yScale;
A2 := AddScaled(X, xScale, Y, yScale);
A3.AddScaled(X, xScale, Y, yScale);
if not A2.IsEqual(A1) then ERaise('Problem');
if not A3.IsEqual(A1) then ERaise('Problem');
end;

Overload 24: function AddScaled(const X: TVec; const xScale: Double; const Y: TMtxVec; const yScale: Double; const Z: TMtxVec; const zScale: Double): Vector;

Compute X*xScale + Y*yScale + Z*zScale

#NameTypeDescription
1XTVec
2xScaleDouble
3YTMtxVec
4yScaleDouble
5ZTMtxVec
6zScaleDouble

Returns: Vector

Remarks:

Computes the weighted sum of X, Y, and Z without temporary objects.

Examples
var
    xScale: Double;
    X, Y, Z, A1, A2, A3: Vector;
begin
xScale := 1.0, yScale = 2.0, zScale = 3.0;
X := [1, 2, 3, 4];
Y := [2, 3, 4, 5];
Z := [3, 4, 5, 6];
A1 := X * xScale + Y * yScale + Z * zScale;
A2 := AddScaled(X, xScale, Y, yScale, Z, zScale);
A3.AddScaled(X, xScale, Y, yScale, Z, zScale);
if not A2.IsEqual(A1) then ERaise('Problem');
if not A3.IsEqual(A1) then ERaise('Problem');
end;