CubicSpline¶

streaming mode | Standard category

Inputs¶

x (real) - the input coordinate (x-axis)

Outputs¶

y (real) - the value of the spline at x

dy (real) - the first derivative of the spline at x

ddy (real) - the second derivative of the spline at x

Parameters¶

leftBoundaryFlag (integer ∈ {0, 1, 2}, default = 0) :
type of boundary condition for the left boundary

leftBoundaryValue (real ∈ (-∞, ∞), default = 0) :
the value to be used in the left boundary, when leftBoundaryFlag is 1 or 2

rightBoundaryFlag (integer ∈ {0, 1, 2}, default = 0) :
type of boundary condition for the right boundary

rightBoundaryValue (real ∈ (-∞, ∞), default = 0) :
the value to be used in the right boundary, when rightBoundaryFlag is 1 or 2

xPoints (vector_real, default = [0, 1]) :
the x-coordinates where data is specified (the points must be arranged in ascending order and cannot contain duplicates)

yPoints (vector_real, default = [0, 1]) :
the y-coordinates to be interpolated (i.e. the known data)

Description¶

Computes the second derivatives of a piecewise cubic spline. The input value, i.e. the point at which the spline is to be evaluated typically should be between xPoints[0] and xPoints[size-1]. If the value lies outside this range, extrapolation is used. Regarding [left/right] boundary condition flag parameters:

0: the cubic spline should be a quadratic over the first interval

1: the first derivative at the [left/right] endpoint should be [left/right]BoundaryFlag

2: the second derivative at the [left/right] endpoint should be [left/right]BoundaryFlag

References:: [1] Spline interpolation - Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Spline_interpolation

Source code¶

C++ source code

C++ header file