Polynoms.Linear1D Method

Overload List

#	Signature	Description
1	procedure Linear1D(Y: TVec; PiecePoly: TPiecePoly);	Perform interpolation assuming that Y is evaluated at [0,1,2,...].
2	procedure Linear1D(X: TVec; Y: TVec; PiecePoly: TPiecePoly);	Linear interpolation.

Overload 1: procedure Linear1D(Y: TVec; PiecePoly: TPiecePoly);

Perform interpolation assuming that Y is evaluated at [0,1,2,...].

#	Name	Type	Description
1	Y	TVec	source TVec
2	PiecePoly	TPiecePoly

Result: stored in self (calling object)

See Also: Polynoms.Interpolate, Polynoms.Spline1D, Polynoms.PolyFit, TPiecePoly

Overload 2: procedure Linear1D(X: TVec; Y: TVec; PiecePoly: TPiecePoly);

Linear interpolation.

#	Name	Type	Description
1	X	TVec	source TVec
2	Y	TVec	source TVec
3	PiecePoly	TPiecePoly

Result: stored in self (calling object)

Remarks:

The Linear1D procedure interpolates lines between consecutive (X,Y) pairs. Linear1D does not return interpolated points. It constructs piece-wise polynomial, which can be used to evaluate ( by using the PiecePoly.Evaluate method) the linear functions. To directly obtain interpolated values, use the Polynoms.Interpolate routine.

Note:
X values must be monotonic or the result will not be valid.

Examples

uses MtxExpr, Math387, MtxVec, MtxVecEdit, MtxVecTee,Polynoms;

procedure TForm1.Button1Click(Sender: TObject);
var   X,Y,Y2: Vector;
PP    : TPiecePoly;
i     : Integer;
YVal  : double;
begin
    PP := TPiecePoly.Create;
    try
        // generate function - note that X values are monotonical
        X := Ramp(100,0,1);
        Y := RandUniform(100,0,50) + Ramp(100,100,0.25);

        //   construct cubic splines, but do not evaluate them

        Linear1D(X,Y,PP);

        X := Ramp(800,0,0.125); //get interpolation points
        PP.Evaluate(X,Y2); // evaluate

        DrawIt(Y,'Original');
        DrawIt(Y2,'Interpolated');

    finally
        PP.Free;
    end;
end;