PolynomialBasis Class

Represents a FunctionBasis for the polynomials up to a specified degree.

Definition

Namespace: Extreme.Mathematics.Curves
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C#
[SerializableAttribute]
public class PolynomialBasis : FunctionBasis
Inheritance
Object  →  FunctionBasis  →  PolynomialBasis

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.

Constructors

PolynomialBasis Constructs a new GeneralFunctionBasis from an array of function of one variable delegates.

Properties

Item Gets an element of the collection as a function of one variable.
(Overrides FunctionBasis.Item[Int32])
Length Gets the number of items in this FunctionBasis.
(Inherited from FunctionBasis)

Methods

DerivativesAt Evaluates the derivatives of the member functions of this FunctionBasis at a specified value.
(Inherited from FunctionBasis)
EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FillDerivatives(Double, DenseVector<Double>) Fills a vector with the derivatives of the member functions at a specified value.
(Overrides FunctionBasis.FillDerivatives(Double, DenseVector<Double>))
FillDerivatives(Vector<Double>, DenseMatrix<Double>) Fills the rows of a DenseMatrix<T> with the values of the member functions of a FunctionBasis evaluated for each element in a Vector.
(Inherited from FunctionBasis)
FillValues(Double, DenseVector<Double>) Fills a dense vector with the values of the member functions at a specified value.
(Overrides FunctionBasis.FillValues(Double, DenseVector<Double>))
FillValues(Vector<Double>, DenseMatrix<Double>) Fills the rows of a DenseMatrix<T> with the values of the member functions of a FunctionBasis evaluated for each element in a Vector.
(Inherited from FunctionBasis)
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
GetFunction(Double[]) Constructs a new LinearCombination from the functions in this instance.
(Inherited from FunctionBasis)
Obsolete.
GetFunction(Vector<Double>) Constructs a new Polynomial with the specified coefficients.
(Overrides FunctionBasis.GetFunction(Vector<Double>))
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetTypeGets the Type of the current instance.
(Inherited from Object)
LeastSquaresFit(Vector<Double>, Vector<Double>) Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis)
LeastSquaresFit(Double[], Double[], Double[]) Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis)
LeastSquaresFit(Double[], Double[], Int32) Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis)
LeastSquaresFit(Vector<Double>, Vector<Double>, Vector<Double>) Gets the least squares fit of target data in terms of the components of the FunctionBasis.
(Inherited from FunctionBasis)
MemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
ToStringReturns a string that represents the current object.
(Inherited from Object)
ValuesAt Evaluates the member functions of this FunctionBasis at a specified value.
(Inherited from FunctionBasis)

See Also