Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public NotInheritable Class ChebyshevBasis _ Inherits FunctionBasis |
| C# |
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public sealed class ChebyshevBasis : FunctionBasis |
| C++ |
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public ref class ChebyshevBasis sealed : public FunctionBasis |
Methods
| Icon | Type | Description |
|---|---|---|
 | DerivativesAt(Double) |
Evaluates the derivatives of the member functions of this
FunctionBasis at a specified value.
|
| Equals(Object) | |
| FillDerivatives(Double, GeneralVector) |
Fills a Vector with the derivatives of the
member functions at a specified value.
|
| FillDerivatives(Vector, GeneralMatrix) |
Fills the rows of a GeneralMatrix with the values
of the member functions of a FunctionBasis evaluated for each element
in a Vector.
|
| FillValues(Double, GeneralVector) |
Fills a GeneralVector with the values of the
member functions at a specified value.
|
| FillValues(Vector, GeneralMatrix) |
Fills the rows of a GeneralMatrix with the values
of the member functions of a FunctionBasis evaluated for each element
in a Vector.
|
 | Finalize() | |
| GetFunction(Double[]()) |
Constructs a new ChebyshevSeries with the
specified coefficients.
|
| GetFunction(Vector) |
Constructs a new ChebyshevSeries with the
specified coefficients.
|
| GetHashCode() | Serves as a hash function for a particular type. |
| GetType() | Gets the Type of the current instance. |
| LeastSquaresFit(Double[](), Double[](), Int32) |
Gets the least squares fit of target data in terms of
the components of the FunctionBasis.
|
| LeastSquaresFit(Double[](), Double[](), Double[]()) |
Gets the least squares fit of target data in terms of
the components of the FunctionBasis.
|
| LeastSquaresFit(Vector, Vector) |
Gets the least squares fit of target data in terms of
the components of the FunctionBasis.
|
| LeastSquaresFit(Vector, Vector, Vector) |
Gets the least squares fit of target data in terms of
the components of the FunctionBasis.
|
| MemberwiseClone() | Creates a shallow copy of the current Object. |
| ToString() | |
| ValuesAt(Double) |
Evaluates the member functions of this
FunctionBasis at a specified value.
|
Constructors
| Icon | Type | Description |
|---|---|---|
| ChebyshevBasisNew(Int32) |
Constructs a new ChebyshevBasis of Chebyshev
polynomials up to a specified degree over the interval [-1, 1].
|
| ChebyshevBasisNew(Double, Double, Int32) |
Constructs a new ChebyshevBasis
over a specified interval from an array of RealFunction
delegates.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | Item(Int32) |
Gets an element of the collection as a
RealFunction.
|
| Length |
Gets the number of items in this FunctionBasis.
|
| LowerBound |
Gets or sets the lower bound of the interval over which this ChebyshevBasis is defined.
|
| UpperBound |
Gets or sets the upper bound of the interval over which this ChebyshevBasis is defined.
|
Remarks
Chebyshev polynomials have these special properties only over the interval [-1,1]. However, rescaling is applied transparently to allow a ChebyshevBasis to be defined over any finite interval.
Only in rare cases will it be necessary to construct a ChebyshevBasis, as most functionality is available through the ChebyshevSeries class. The most useful members are the FillValues(Double, GeneralVector) and FillDerivatives(Double, GeneralVector) methods, which allow for efficient calculation of multiple values or derivatives of the polynomials.
Note: The first function (the constant term) is equal to 0.5 instead of the value of 1 of the Chebyshev polynomial of degree 0. The reason is that Chebyshev series are commonly expressed with the constant term multiplied by 0.5. The ChebyshevSeries class follows this convention.
Inheritance Hierarchy
See Also
