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    • BarycentricBasis Class
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  • PolynomialBasis Class
    • PolynomialBasis Constructor
    • Properties
    • Methods

PolynomialBasis Class

Extreme Optimization Numerical Libraries for .NET Professional
Represents a FunctionBasis for the polynomials up to a specified degree.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.CurvesFunctionBasis
    Extreme.Mathematics.CurvesPolynomialBasis

Namespace:  Extreme.Mathematics.Curves
Assembly:  Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
Syntax

C#
VB
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[SerializableAttribute]
public class PolynomialBasis : FunctionBasis
<SerializableAttribute>
Public Class PolynomialBasis
	Inherits FunctionBasis
[SerializableAttribute]
public ref class PolynomialBasis : public FunctionBasis
[<SerializableAttribute>]
type PolynomialBasis =  
    class
        inherit FunctionBasis
    end

The PolynomialBasis type exposes the following members.

Constructors

  NameDescription
Public methodPolynomialBasis
Constructs a new GeneralFunctionBasis from an array of function of one variable delegates.
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Properties

  NameDescription
Public propertyItem
Gets an element of the collection as a function of one variable.
(Overrides FunctionBasisItemInt32.)
Public propertyLength
Gets the number of items in this FunctionBasis.
(Inherited from FunctionBasis.)
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Methods

  NameDescription
Public methodDerivativesAt
Evaluates the derivatives of the member functions of this FunctionBasis at a specified value.
(Inherited from FunctionBasis.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodFillDerivatives(Double, DenseVectorDouble)
Fills a vector with the derivatives of the member functions at a specified value.
(Overrides FunctionBasisFillDerivatives(Double, DenseVectorDouble).)
Public methodFillDerivatives(VectorDouble, DenseMatrixDouble)
Fills the rows of a DenseMatrixT with the values of the member functions of a FunctionBasis evaluated for each element in a Vector.
(Inherited from FunctionBasis.)
Public methodFillValues(Double, DenseVectorDouble)
Fills a dense vector with the values of the member functions at a specified value.
(Overrides FunctionBasisFillValues(Double, DenseVectorDouble).)
Public methodFillValues(VectorDouble, DenseMatrixDouble)
Fills the rows of a DenseMatrixT with the values of the member functions of a FunctionBasis evaluated for each element in a Vector.
(Inherited from FunctionBasis.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetFunction(Double) Obsolete.
Constructs a new LinearCombination from the functions in this instance.
(Inherited from FunctionBasis.)
Public methodGetFunction(VectorDouble)
Constructs a new Polynomial with the specified coefficients.
(Overrides FunctionBasisGetFunction(VectorDouble).)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodLeastSquaresFit(VectorDouble, VectorDouble)
Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis.)
Public methodLeastSquaresFit(Double, Double, Double)
Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis.)
Public methodLeastSquaresFit(Double, Double, Int32)
Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis.)
Public methodLeastSquaresFit(VectorDouble, VectorDouble, VectorDouble)
Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Public methodValuesAt
Evaluates the member functions of this FunctionBasis at a specified value.
(Inherited from FunctionBasis.)
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Remarks

Use a PolynomialBasis object to represent a basis for the polynomials. Only in rare cases will it be necessary to construct a PolynomialBasis, as most functionality is available through the Polynomial class.

The basis functions of a PolynomialBasis are the monomials of degree 0 up to and including the specified degree.

The Chebyshev polynomials form an alternate basis for the polynomials and have many desirable numerical properties.

See Also

Reference

Extreme.Mathematics.Curves Namespace
Extreme.Mathematics.CurvesFunctionBasis
Extreme.Mathematics.CurvesBarycentricBasis
Extreme.Mathematics.CurvesChebyshevBasis
Extreme.Mathematics.CurvesPolynomial

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