PolyharmonicSpline (FsODE)

FsODE

Documentation for 0.0.2

PolyharmonicSpline Type

Namespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore.Redist.dll
Base Type: obj

Interpolation method for scattered data in any dimension based on radial basis functions. In 2D this is the so called Thin Plate Spline, which is an interpolation method that finds a "minimally bended" smooth surface that passes through all given points. The polyharmonic spline has an arbitrary number of dimensions and arbitrary derivative order. Note: The allocation space requirement is in the order (N+3)*(N+3), where N is the number of control points. Thus it is not applicable for too many points.

Literature: http://en.wikipedia.org/wiki/Polyharmonic_spline Extension to any number of dimensions: TIM GUTZMER AND JENS MARKUS MELENK, MATHEMATICS OF COMPUTATION, Volume 70, Number 234, Pages 699{703, S 0025-5718(00)01299-0, Article electronically published on October 18, 2000

Constructors

Constructor	Description
`PolyharmonicSpline()` Full Usage: `PolyharmonicSpline()`	Initializes the spline with a regularization parameter of zero and an derivative order of 2.

Instance members

Instance member	Description
`this.Construct` Full Usage: `this.Construct` Parameters: x : `IReadOnlyList<float>` - X coordinates of the points. h : `IReadOnlyList<float>` - Values of the points that should be interpolated.	Constructs the interpolation (1 dimensional). The values and the corresponding coordinates of the values are given in separate vectors. x : `IReadOnlyList<float>` X coordinates of the points. h : `IReadOnlyList<float>` Values of the points that should be interpolated.
`this.Construct` Full Usage: `this.Construct` Parameters: x : `IReadOnlyList<float>` - X coordinates of the points. y : `IReadOnlyList<float>` - Y coordinates of the points. h : `IReadOnlyList<float>` - Values of the points that should be interpolated.	Constructs the interpolation (2 dimensional). The values and the corresponding coordinates of the values are given in separate vectors. x : `IReadOnlyList<float>` X coordinates of the points. y : `IReadOnlyList<float>` Y coordinates of the points. h : `IReadOnlyList<float>` Values of the points that should be interpolated.
`this.Construct` Full Usage: `this.Construct` Parameters: x : `IReadOnlyList<float>` - X coordinates of the points. y : `IReadOnlyList<float>` - Y coordinates of the points. z : `IReadOnlyList<float>` - Z coordinates of the points. h : `IReadOnlyList<float>` - Values of the points that should be interpolated.	Constructs the interpolation (3 dimensional). The values and the corresponding coordinates of the values are given in separate vectors. x : `IReadOnlyList<float>` X coordinates of the points. y : `IReadOnlyList<float>` Y coordinates of the points. z : `IReadOnlyList<float>` Z coordinates of the points. h : `IReadOnlyList<float>` Values of the points that should be interpolated.
`this.Construct` Full Usage: `this.Construct` Parameters: x : `IReadOnlyList<float>[]` - X coordinates of the points. h : `IReadOnlyList<float>` - Values of the points that should be interpolated.	Constructs the interpolation (any dimension). The values and the corresponding coordinates of the values are given in separate vectors. x : `IReadOnlyList<float>[]` X coordinates of the points. h : `IReadOnlyList<float>` Values of the points that should be interpolated.
`this.DerivativeOrder` Full Usage: `this.DerivativeOrder`	Derivative order of the spline. Effectively, the L2-norm of this derivative is minimized.
`this.GetBendingEnergy` Full Usage: `this.GetBendingEnergy` Returns: `float`	Gets the bending energy of the interpolation. Returns: `float`
`this.GetInterpolatedValue` Full Usage: `this.GetInterpolatedValue` Parameters: x : `float[]` - The x coordinate of the point. Returns: `float` The interpolated value at the point (x,y).	Gets the interpolation value of given coordinates x and y. x : `float[]` The x coordinate of the point. Returns: `float` The interpolated value at the point (x,y).
`this.NumberOfControlPoints` Full Usage: `this.NumberOfControlPoints` Returns: `int`	Number of control points. Returns: `int`
`this.NumberOfDimensions` Full Usage: `this.NumberOfDimensions` Returns: `int`	Number of dimensions of the control points. Returns: `int`
`this.RegularizationParameter` Full Usage: `this.RegularizationParameter`	Regularization parameter (>=0). If the regularization parameter is zero, interpolation is exact. As it approaches infinity, the resulting spline is reduced to a least squares linear fit (in 2D this is a plane, the bending energy is 0).