FunctionBasis Class

public abstract class FunctionBasis

Public MustInherit Class FunctionBasis

public ref class FunctionBasis abstract

[<AbstractClassAttribute>]
type FunctionBasis = class end

Inheritance

Object  →  FunctionBasis

Derived

Extreme.Mathematics.Curves.BarycentricBasis

Extreme.Mathematics.Curves.ChebyshevBasis

Extreme.Mathematics.Curves.GeneralFunctionBasis

Extreme.Mathematics.Curves.PolynomialBasis

A FunctionBasis represents a collection of real functions of one real variable. The LinearCombination class implements a Curve that is a linear combination of basis functions in a FunctionBasis.

A function basis is particularly useful for representing a class of functions where the cost of evaluating a series of functions is much less than that of evaluating the functions individually. For example, to evaluate all powers up to degree 10 requires up to 55 multiplications, where only 10 multiplications are required if they are evaluated as a group.

The ValuesAt(Double) and FillValues(Double, DenseVector<Double>) methods evaluate all basis functions for a given value or set of values. The DerivativesAt(Double) and FillDerivatives(Double, DenseVector<Double>) methods evaluate the derivative of all basis functions for a given value or set of values. Derived classes provide optimized implementations of these methods for specific classes of curves.

The curves in a function basis can be combined into a LinearCombination curve using the GetFunction(Vector<Double>) method. The [o:LeastSquaresFit] methods calculate the LinearCombination that is the least squares fit to a set of data points using curves from the function basis.

This is an abstract base class. The following classes derive from FunctionBasis:

Notes to inheritors: When you derive from FunctionBasis, you must override the following members: ValuesAt(Double), DerivativesAt(Double), Length, Item[Int32].

Notes to inheritors:When you inherit from FunctionBasis, you must override the following methods and properties: FillValues(Double, DenseVector<Double>). You should override FillDerivatives(Double, DenseVector<Double>) and Item[Int32].

Reference