BarycentricBasis Class

Represents a barycentric basis for a set of rational functions.

Definition

Namespace: Numerics.NET.Curves
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4
C#
public class BarycentricBasis : FunctionBasis
Inheritance
Object  →  FunctionBasis  →  BarycentricBasis

Remarks

Use the BarycentricBasis class to represent the basis of a set of rational functions in barycentric form. All functions in the set have the same support points or nodes and corresponding weights.

The rational functions that can be represented in the basis are linear combinations of the basis functions.

For a specific set of support points, there is one set of weights for which all basis functions are polynomials. A barycentric basis is therefore a generalization of a polynomial basis.

Constructors

BarycentricBasis Constructs a new barycentric basis with the specified set of support points and corresponding weights.

Properties

Item Gets an element of the collection as a function of one variable.
(Inherited from FunctionBasis)
Length Gets the number of items in this FunctionBasis.
(Inherited from FunctionBasis)
SupportPoints Gets the support points of the basis.
Weights Gets the weights of the basis.

Methods

Chebyshev(Int32) Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the specified degree over the interval [-1, 1].
Chebyshev(Double, Double, Int32) Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the specified degree over the specified interval.
Chebyshev2(Int32) Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the second kind of the specified degree over the interval [-1, 1].
Chebyshev2(Double, Double, Int32) Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the second kind of the specified degree over the specified interval.
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 of a FunctionBasis 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)
FloaterHormann(Vector<Double>, Int32) Constructs a new barycentric basis for Floater-Hormann rational interpolation of the specified order through the specified support points.
FloaterHormann(Double, Double, Int32, Int32) Constructs a new barycentric basis for Floater-Hormann rational interpolation through a set of equidistant support points.
GetFunction Constructs a new LinearCombination from the functions in this instance.
(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)
Polynomial(Vector<Double>) Constructs a new barycentric basis equivalent to Lagrange polynomial interpolation through the specified support points.
Polynomial(Double, Double, Int32) Returns a new BarycentricBasis equivalent to a basis of Lagrange polynomials over an equidistant set of points.
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