Spline

streaming mode | Standard category

Inputs

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

Outputs

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

Parameters

  • beta1 (real ∈ [0, ∞], default = 1) :
    the skew or bias parameter (only available for type beta)
  • beta2 (real ∈ [0, ∞), default = 0) :
    the tension parameter
  • type (string ∈ {b, beta, quadratic}, default = b) :
    the type of spline to be computed
  • 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

Evaluates a piecewise spline of type b, beta or quadratic. The input value, i.e. the point at which the spline is to be evaluated typically should be between xPoins[0] and xPoinst[size-1]. If the value lies outside this range, extrapolation is used. Regarding spline types:

  • B: evaluates a cubic B spline approximant.
  • Beta: evaluates a cubic beta spline approximant. For beta splines parameters 'beta1' and 'beta2' can be supplied. For no bias set beta1 to 1 and for no tension set beta2 to 0. Note that if beta1=1 and beta2=0, the cubic beta becomes a cubic B spline. On the other hand if beta1=1 and beta2 is large the beta spline turns into a linear spline.
  • Quadratic: evaluates a piecewise quadratic spline at a point. Note that size of input must be odd.
References:
[1] Spline interpolation - Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Spline_interpolation

Streaming algorithms

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