Polynoms::Spline1D Function

Polynoms Namespace

Overload List

#SignatureDescription
1void Spline1D(TVec *X, TVec *Y, TPiecePoly *PiecePoly);Cubic spline interpolation.
2void Spline1D(TVec *Y, TPiecePoly *PiecePoly, bool Knots = false);Interpolates cubic splines between consecutive Y points.

Overload 1: void Spline1D(TVec *X, TVec *Y, TPiecePoly *PiecePoly);

Cubic spline interpolation.

#NameTypeDescription
1XTVec *
2YTVec *
3PiecePolyTPiecePoly *
Remarks:

The procedure interpolates cubic splines between consequtive (X,Y) pairs. The rotine does not return interpolated points. It constructs piece-wise polynomial, which in term can be used for evaluating (by using the TPiecePoly.Evaluate method) cubic splines. To directly obtain interpolated values, use the Polynoms::Interpolate routine.

Note
If X.Length=Y.Length, then the "not-a-knot" end conditions are used. If Y.Length = X.Length +2 then the "knot" end conditions are used. X values must be monotonic or the result will not be valid.

Examples
#include "MtxExpr.h"
#include "Polynoms.h"
#include "Units.MtxExpr.h"
#include "Units.Polynoms.h"

using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Math::Units::MtxExpr;
using namespace Dew::Math::Units::Polynoms;

void Example()
{
    Vector X, Y, Y2;
    TPiecePoly* PP;
    int i;
    double YVal;
    PP = new TPiecePoly();
    // generate function - note that X values are monotonical
    X = Ramp(100, TMtxFloatPrecision::mvDouble, 0, 1);
    Y = RandUniform(100, TMtxFloatPrecision::mvDouble, 0, 50) + Ramp(100, TMtxFloatPrecision::mvDouble, 100, 0.25);

    //   construct cubic splines, but do not evaluate them

    Spline1D(X, Y, PP);

    X = Ramp(800, TMtxFloatPrecision::mvDouble, 0, 0.125); //get interpolation points
    PP->Evaluate(X, Y2); // evaluate

    delete PP;
}
Declared in Dew::Math::Units::Polynoms · Dew.Math/Units.Polynoms.h · Cross-compiler

Overload 2: void Spline1D(TVec *Y, TPiecePoly *PiecePoly, bool Knots = false);

Interpolates cubic splines between consecutive Y points.

#NameTypeDescription
1YTVec *
2PiecePolyTPiecePoly *
3Knots = falsebool
Remarks:

Interpolates cubic splines between consecutive Y points. The assumption is that Y is evaluated at [0,1,2,...] -> X values are [0,1,2,...]. If the Knot parameter is true then the first and the last Y value will be used for the end conditions. In this case Y.Length = X.Length + 2.

Examples
#include "MtxExpr.h"
#include "Polynoms.h"
#include "Units.Polynoms.h"

using namespace Dew;
using namespace Dew::Math;
using namespace Dew::Math::Units;

void Example()
{
    Vector X(0);
    Vector Y(0);
    Vector Y2(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 = Y + Y2;

    //   construct cubic splines, but do not evaluate them
    Polynoms::Spline1D(X, Y, PP);
    X.Size(800);
    X.Ramp(0, 0.125); //get interpolation points
    PP->Evaluate(X, Y2); // evaluate
    delete PP;
}
See Also: Polynoms::Interpolate, Polynoms::Linear1D, Polynoms::PolyFit, TPiecePoly
Declared in Dew::Math::Units::Polynoms · Dew.Math/Units.Polynoms.h · Cross-compiler