Polynoms.PolyEval Method

Overload List

#	Signature	Description
1	TCplx PolyEval(TCplx Val, TVec Coeff)	Evaluates a polynomial with coefficients Coeff at complex value Val and returns complex results.
2	void PolyEval(TVec Val, TVec Coeff, TMtx R, Int32 DegFreedom, Double L2R, TVec EvalResult, TVec Delta)	Evaluate a polynomial.
3	void PolyEval(TVec Val, TVec Coeff, TVec EvalResult)	Evaluates a polynomial with coefficients Coeff at value Val and returns the results in EvalResult.
4	Double PolyEval(Double Val, TVec Coeff)	Evaluates a polynomial with coefficients Coeff at real value Val and returns real result.

Overload 1: TCplx PolyEval(TCplx Val, TVec Coeff)

Evaluates a polynomial with coefficients Coeff at complex value Val and returns complex results.

#	Name	Type	Description
1	Val	TCplx	scalar
2	Coeff	TVec	source TVec

Returns: TCplx (complex)

Remarks:

Evaluates a polynomial with coefficients Coeff at complex value Val and returns complex results.

Examples

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 Coeff = new Vector(0);

        X.Size(10);
        X.Ramp(-5,1); // X = [-5,-4,-3,-2,-1, 0, 1, 2, 3, 4]
        // construct a parabola
        Coeff.SetIt(false,new double[] {2, -1, 3});
        Polynoms.PolyEval(X,Coeff,Y);

        // Y now holds the values of polynomial, evaluated at all X.Values
        MtxVecTee.DrawIt(X,Y,"Parabola",false);
    }
}

See Also: Polynoms.PolyFit, TPiecePoly

Overload 2: void PolyEval(TVec Val, TVec Coeff, TMtx R, Int32 DegFreedom, Double L2R, TVec EvalResult, TVec Delta)

Evaluate a polynomial.

#	Name	Description
1	Val	Stores values doe which the polynomial will be evaluated (x values).
2	Coeff	Stores polynomial coefficients for which the polynomial will be evaaluted.
3	R	Returns the Cholesky factor of the Vandermonde matrix.
4	DegFreedom	Returns the residuals degree of freedom.
5	L2R	Returns the L2 norm of the residuals.
6	EvalResult	Returns the results P(x), evaluated at Val.
7	Delta	Returns the error estimates for Results.

Result: stored in self (calling object)

Remarks:

Evaluate a polynomial with coefficients Coeff at value Val. The order of polynomial (N) is determined as: N := Coeff.Length - 1. The algorithm employed uses Horners rule. The following formula is used to evaluate the polynomial:

P(x) = coeff[0]*x^n + coeff[1]*x^(n-1) + .. + coeff[n]

To estimate the error of polynomial interpolation after a call to Dew.Math.Units.Polynoms.PolyFit additional parameters have to be passed to the routine.

Overload 3: void PolyEval(TVec Val, TVec Coeff, TVec EvalResult)

Evaluates a polynomial with coefficients Coeff at value Val and returns the results in EvalResult.

#	Name	Type	Description
1	Val	TVec	source TVec
2	Coeff	TVec	source TVec
3	EvalResult	TVec	source TVec

Result: stored in self (calling object)

Remarks:

Evaluates a polynomial with coefficients Coeff at value Val and returns the results in EvalResult.

Overload 4: Double PolyEval(Double Val, TVec Coeff)

Evaluates a polynomial with coefficients Coeff at real value Val and returns real result.

#	Name	Type	Description
1	Val	Double	scalar
2	Coeff	TVec	source TVec

Returns: Double

Remarks:

Evaluates a polynomial with coefficients Coeff at real value Val and returns real result.