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
See also
CubicSpline (standard) Spline (standard) Spline (streaming)