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

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