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java.lang.Object umontreal.iro.lecuyer.functionfit.SmoothingCubicSpline
public class SmoothingCubicSpline
Represents a cubic spline with nodes at (x_{i}, y_{i}) computed with the smoothing cubic spline algorithm of Schoenberg. A smoothing cubic spline is made of n + 1 cubic polynomials. The ith polynomial of such a spline, for i = 1,…, n  1, is defined as S_{i}(x) while the complete spline is defined as
The spline is computed with a smoothing parameter ρ∈[0, 1] which represents its accuracy with respect to the initial (x_{i}, y_{i}) nodes. The smoothing spline minimizes
Constructor Summary  

SmoothingCubicSpline(double[] x,
double[] y,
double rho)
Constructs a spline with nodes at (x_{i}, y_{i}), with weights = 1 and smoothing factor ρ = rho. 

SmoothingCubicSpline(double[] x,
double[] y,
double[] w,
double rho)
Constructs a spline with nodes at (x_{i}, y_{i}), with weights w_{i} and smoothing factor ρ = rho. 
Method Summary  

double 
derivative(double z)
Evaluates and returns the value of the first derivative of the spline at z. 
double 
derivative(double z,
int n)
Evaluates and returns the value of the nth derivative of the spline at z. 
double 
evaluate(double z)
Evaluates and returns the value of the spline at z. 
int 
getFitPolynomialIndex(double x)
Returns the index of P, the Polynomial instance used to evaluate
x, in an ArrayList table instance returned by
getSplinePolynomials(). 
double 
getRho()
Returns the smoothing factor used to construct the spline. 
Polynomial[] 
getSplinePolynomials()
Returns a table containing all fitting polynomials. 
double[] 
getWeights()
Returns the weights of the points. 
double[] 
getX()
Returns the x_{i} coordinates for this spline. 
double[] 
getY()
Returns the y_{i} coordinates for this spline. 
double 
integral(double a,
double b)
Evaluates and returns the value of the integral of the spline from a to b. 
Methods inherited from class java.lang.Object 

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 

public SmoothingCubicSpline(double[] x, double[] y, double[] w, double rho)
x
 the x_{i} coordinates.y
 the y_{i} coordinates.w
 the weight for each point, must be > 0.rho
 the smoothing parameter
IllegalArgumentException
 if x, y and
z do not have the same length, if rho has wrong value, or if
the spline cannot be calculated.public SmoothingCubicSpline(double[] x, double[] y, double rho)
x
 the x_{i} coordinates.y
 the y_{i} coordinates.rho
 the smoothing parameter
IllegalArgumentException
 if x and y do
not have the same length, if rho has wrong value, or if the spline
cannot be calculated.Method Detail 

public double evaluate(double z)
evaluate
in interface MathFunction
z
 argument of the spline.
public double integral(double a, double b)
integral
in interface MathFunctionWithIntegral
a
 lower limit of integral.b
 upper limit of integral.
public double derivative(double z)
derivative
in interface MathFunctionWithFirstDerivative
z
 argument of the spline.
public double derivative(double z, int n)
derivative
in interface MathFunctionWithDerivative
z
 argument of the spline.n
 order of the derivative.
public double[] getX()
public double[] getY()
public double[] getWeights()
public double getRho()
public Polynomial[] getSplinePolynomials()
public int getFitPolynomialIndex(double x)
Polynomial
instance used to evaluate
x, in an ArrayList table instance returned by
getSplinePolynomials(). This index k gives also the interval in
table X which contains the value x
(i.e. such that
x_{k} < x <= x_{k+1}).

SSJ V. 2.6. 

PREV CLASS NEXT CLASS  FRAMES NO FRAMES  
SUMMARY: NESTED  FIELD  CONSTR  METHOD  DETAIL: FIELD  CONSTR  METHOD 