Serves as an abstract base class for collections of
functions.
SystemObject Extreme.Mathematics.CurvesFunctionBasis Extreme.Mathematics.CurvesBarycentricBasis Extreme.Mathematics.CurvesChebyshevBasis Extreme.Mathematics.CurvesGeneralFunctionBasis Extreme.Mathematics.CurvesPolynomialBasis
Namespace:
Extreme.Mathematics.Curves
Assembly:
Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
public abstract class FunctionBasis
Public MustInherit Class FunctionBasis
public ref class FunctionBasis abstract
[<AbstractClassAttribute>]
type FunctionBasis = class end
The FunctionBasis type exposes the following members.
|
| Name | Description |
|---|
 | FunctionBasis |
Constructs a new FunctionBasis with the specified number of basis
functions.
|
Top
|
| Name | Description |
|---|
 | Item |
Gets an element of the collection as a
function of one variable.
|
| Length |
Gets the number of items in this FunctionBasis.
|
Top
|
| Name | Description |
|---|
 | DerivativesAt |
Evaluates the derivatives of the member functions of this
FunctionBasis at a specified value.
|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
| FillDerivatives(Double, DenseVectorDouble) |
Fills a vector with the derivatives of the
member functions at a specified value.
|
| FillDerivatives(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.
|
| FillValues(Double, DenseVectorDouble) |
Fills a dense vector with the values of the
member functions of a FunctionBasis at a specified value.
|
| FillValues(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.
|
| Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetFunction(Double) | Obsolete. |
| GetFunction(VectorDouble) | |
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetType | Gets the Type of the current instance. |
| LeastSquaresFit(VectorDouble, VectorDouble) |
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(Double, Double, Int32) |
Gets the least squares fit of target data in terms of
the components of the FunctionBasis.
|
| LeastSquaresFit(VectorDouble, VectorDouble, VectorDouble) |
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 | Returns a string that represents the current object. (Inherited from Object.) |
| ValuesAt |
Evaluates the member functions of this
FunctionBasis at a specified value.
|
Top
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, DenseVectorDouble)
methods evaluate all basis functions for a given value or set of
values. The DerivativesAt(Double) and FillDerivatives(Double, DenseVectorDouble)
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(VectorDouble)
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, ItemInt32.
Notes to inheritors:When you inherit from
FunctionBasis, you must override the
following methods and properties: FillValues(Double, DenseVectorDouble).
You should override FillDerivatives(Double, DenseVectorDouble)
and ItemInt32.
Reference