public class BsLeastSquares extends BSpline
Let's make the identifications
n = xData.length
x = xData
f = yData
m = nCoef
k = order
For convenience, we assume that the sequence x is increasing, although the class does not require this.
By default, k = 4, and the knot sequence we select equally distributes the knots through the distinct . In particular, the m + k knots will be generated in with k knots stacked at each of the extreme values. The interior knots will be equally spaced in the interval.
Once knots and weights w are determined, then the spline leastsquares fit to the data is computed by minimizing over the linear coefficients
where the are a (Bspline) basis for the spline subspace.
This algorithm is based on the routine L2APPR by deBoor (1978, p. 255).
Modifier and Type  Field and Description 

protected int 
nCoef
Number of Bspline coefficients.

protected double[] 
weight
The weight array of length n, where
n is the number of data points fit.

Constructor and Description 

BsLeastSquares(double[] xData,
double[] yData,
int nCoef)
Constructs a least squares Bspline approximation to the given data points.

BsLeastSquares(double[] xData,
double[] yData,
int nCoef,
int order)
Constructs a least squares Bspline approximation to the given data points.

BsLeastSquares(double[] xData,
double[] yData,
int nCoef,
int order,
double[] weight,
double[] knot)
Constructs a least squares Bspline approximation to the given data points.

protected int nCoef
protected double[] weight
public BsLeastSquares(double[] xData, double[] yData, int nCoef)
xData
 A double
array containing the xcoordinates of the data.yData
 A double
array containing the ycoordinates of the data.
The arrays xData and yData must have the same length.nCoef
 An int
denoting the linear dimension of the spline
subspace. It should be smaller than the number of data points
and greater than or equal to the order of the spline (whose default value is 4).public BsLeastSquares(double[] xData, double[] yData, int nCoef, int order)
xData
 A double
array containing the xcoordinates of the data.yData
 A double
array containing the ycoordinates of the data.
The arrays xData and yData must have the same length.nCoef
 An int
denoting the linear dimension of the spline
subspace. It should be smaller than the number of data points
and greater than or equal to the order of the spline.order
 An int
denoting the order of the spline.public BsLeastSquares(double[] xData, double[] yData, int nCoef, int order, double[] weight, double[] knot)
xData
 A double
array containing the xcoordinates of the data.yData
 A double
array containing the ycoordinates of the data.
The arrays xData and yData must have the same length.nCoef
 An int
denoting the linear dimension of the spline
subspace. It should be smaller than the number of data points
and greater than or equal to the order of the spline.order
 An int
denoting the order of the spline.weight
 A double
array containing the weights for the data.
The arrays xData, yData and weights must have the same length.knot
 A double
array containing the knot sequence for the spline.Copyright © 19702015 Rogue Wave Software
Built October 13 2015.