Polynoms.PolyEval Method

Overload List

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

Overload 1: function PolyEval(Val: TCplx; Coeff: TVec): TCplx;

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.

See Also: Polynoms.PolyFit, TPiecePoly

Overload 2: procedure PolyEval(Val: TVec; Coeff: TVec; R: TMtx; DegFreedom: Integer; L2R: Double; EvalResult: TVec; Delta: TVec);

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 Polynoms.PolyFit additional parameters have to be passed to the routine.

Examples

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

procedure TForm1.Button1Click(Sender: TObject);
var X, Y, Coeff: Vector;
begin
    X := Ramp(10,-5,1); // X = [-5,-4,-3,-2,-1, 0, 1, 2, 3, 4]

    // construct a parabola

    Coeff.SetIt(false,[2, -1, 3]);
    PolyEval(X,Coeff,Y);

    // Y now holds the values of polynomial, evaluated at all X.Values

    DrawIt(X,Y,'Parabola');
end;

Overload 3: procedure PolyEval(Val: TVec; Coeff: TVec; EvalResult: TVec);

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: function PolyEval(Val: Double; Coeff: TVec): Double;

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.