CsPeriodic Class |
Namespace: Imsl.Math
The CsPeriodic type exposes the following members.
Name | Description | |
---|---|---|
CsPeriodic |
Constructs a cubic spline that interpolates the given data points
with periodic boundary conditions.
|
Name | Description | |
---|---|---|
Derivative(Double) |
Returns the value of the first derivative of the spline at a point.
(Inherited from Spline.) | |
Derivative(Double, Int32) |
Returns the value of the derivative of the spline at a point.
(Inherited from Spline.) | |
Derivative(Double, Int32) |
Returns the value of the derivative of the spline at each point of an
array.
(Inherited from Spline.) | |
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Eval(Double) |
Returns the value of the spline at a point.
(Inherited from Spline.) | |
Eval(Double) |
Returns the value of the spline at each point of an array.
(Inherited from Spline.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetBreakpoints |
Returns a copy of the breakpoints.
(Inherited from Spline.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
Integral |
Returns the value of an integral of the spline.
(Inherited from Spline.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Class CsPeriodic computes a cubic spline interpolant to a set of data points for . The breakpoints of the spline are the abscissas. The program enforces periodic endpoint conditions. This means that the spline s satisfies s(a) = s(b), , and , where a is the leftmost abscissa and b is the rightmost abscissa. If the ordinate values corresponding to a and b are not equal, then a warning message is issued. The ordinate value at b is set equal to the ordinate value at a and the interpolant is computed.
If the data points arise from the values of a smooth (say ) periodic function f, i.e. , then the error will behave in a predictable fashion. Let be the breakpoint vector for the above spline interpolant. Then, the maximum absolute error satisfies
whereFor more details, see de Boor (1978, pages 320-322).