Linear1D Routines

Summary

Linear interpolation.

Declaration

Procedure Linear1D(X, Y: TVec; PiecePoly: TPiecePoly);

Description

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 Interpolate routine. X values must be monotonic or the result will not be valid.

Declaration

Procedure Linear1D(Y: TVec; PiecePoly: TPiecePoly);

Description

Assumes that Y is evaluated at [0,1,2,...] i.e. X values are [0,1,2,...]

See Also
Interpolate
Spline1D
PolyFit
TPiecePoly

Example 1

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

procedure TForm1.Button1Click(Sender: TObject);
var   X,Y,Y2: Vector;
      PP    : TPiecePoly;
      i     : Integer;
      YVal  : TSample;
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.Destroy;
	end;
end;

  #include "MtxVecCPP.h" //MtxVecCPP.cpp must be included in the project
  #include "Polynoms.hpp"
  #include "MtxVecTee.hpp"
  #include "MtxVecEdit.hpp"

  void __fastcall TForm1::BitBtn1Click(TObject *Sender)
  {
      Vector X,Y,Y2;
      TPiecePoly *PP;
      int i;
      double YVal;

      PP = new TPiecePoly();
      try
      {
         // generate function - note that X values are monotonical
         X->Size(100);
         Y->Size(100);
         Y2->Size(100);

         X->Ramp(0,1);
         Y->RandUniform(0,50);
         Y2->Ramp(100,0.25);
         Y += Y2;

     //   construct cubic splines, but do not evaluate them

         Linear1D(X,Y,PP);

         X->Size(800);
         X->Ramp(0,0.125); //get interpolation points
         PP->Evaluate(X,Y2); // evaluate

         DrawIt(Y,"Original",false);
         DrawIt(Y2,"Interpolated",false);
    }
    __finally
    {
         delete PP;
    }
  }

  using Dew.Math;
  using Dew.Math.Units;
  using Dew.Math.Tee;

  namespace Dew.Examples
  {
    private void Example()
    {
      Vector X = new Vector(0);
      Vector Y = new Vector(0);
      Vector Y2 = new Vector(0);
      TPiecePoly PP = new TPiecePoly();
      int i;
      double YVal;

      // generate function - note that X values are monotonical
      X.Size(100);
      Y.Size(100);
      Y2.Size(100);

      X.Ramp(0,1);
      Y.RandUniform(0,50);
      Y2-Ramp(100,0.25);
      Y += Y2;

     //   construct cubic splines, but do not evaluate them

     Polynoms.Linear1D(X,Y,PP);

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

     TeeChart.DrawIt(Y,"Original",false);
     TeeChart.DrawIt(Y2,"Interpolated",false);
    }
  }