Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
---|
[SerializableAttribute] public class Spline2DLeastSquares : Spline2D |
Visual Basic (Declaration) |
---|
<SerializableAttribute> _ Public Class Spline2DLeastSquares _ Inherits Spline2D |
Visual C++ |
---|
[SerializableAttribute] public ref class Spline2DLeastSquares : public Spline2D |
Remarks
The Spline2DLeastSquares class computes a tensor-product spline
least-squares approximation to weighted tensor-product data. The input
consists of data vectors to specify the tensor-product grid for the
data, two vectors with the weights, the values of the surface on the
grid, and the specification for the tensor-product spline. The grid is
specified by the two vectors x = xData and y
= yData of length
n = xData.Length and
m = yData.Length, respectively. A two-dimensional array
f = fData contains the data values which are to be fit.
The two vectors = xWeights and
= yWeights contain the weights for the
weighted least-squares problem. The information for the approximating
tensor-product spline can be provided using the SetXOrder,
SetYOrder, SetXKnots and SetYKnots methods. This
information is contained in = xOrder,
= xKnots, and N =
xSplineSpaceDim for the spline in the first variable, and in
= yOrder, =
yKnots and M = ySplineSpaceDim for the spline in
the second variable. This class computes coefficients for the
tensor-product spline by solving the normal equations in tensor-product
form as discussed in de Boor (1978, Chapter 17). The interested reader
might also want to study the paper by Grosse (1980).
As the computation proceeds, we obtain coefficients c minimizing
where the function is the tensor-product of two B-splines of order and . Specifically, we have The spline and its partial derivatives can be evaluated using the Value method.