Packages

class B_Spline extends Error

The B_Spline class provides B-Spline basis functions for various orders 'm', where the order is one more than the degree. A spline function is a piecewise polynomial function where the pieces are stitched together at knots with the goal of maintaining continuity and differentability. B-Spline basis functions form a popular form of basis functions used in Functional Data Analysis.

See also

open.uct.ac.za/bitstream/item/16664/thesis_sci_2015_essomba_rene_franck.pdf?sequence=1 -----------------------------------------------------------------------------

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Instance Constructors

  1. new B_Spline(ττ: VectorD, mMax: Int = 4)

    ττ

    the time-points of the original knots in the time dimension

    mMax

    the maximum order, allowing splines orders from 1 to mMax

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  5. def b1(j: Int, t: Double): Double

    Order one 'm = 1' B-Spline basis functions (flat functions).

    Order one 'm = 1' B-Spline basis functions (flat functions).

    j

    indicates which spline function 0 to l-1

    t

    the time parameter

  6. def b2(j: Int, t: Double): Double

    Order two 'm = 2' B-Spline basis functions (linear functions).

    Order two 'm = 2' B-Spline basis functions (linear functions).

    j

    indicates which spline function

    t

    the time parameter

  7. def b3(j: Int, t: Double): Double

    Order three 'm = 3' B-Spline basis functions (quadratic functions).

    Order three 'm = 3' B-Spline basis functions (quadratic functions).

    j

    indicates which spline function

    t

    the time parameter

  8. def b4(j: Int, t: Double): Double

    Order four 'm = 4' B-Spline basis functions (cubic functions).

    Order four 'm = 4' B-Spline basis functions (cubic functions). FIX: missing first interesting spline, see B_SplineTest

    j

    indicates which spline function

    t

    the time parameter

  9. def bb(m: Int)(j: Int, t: Double): Double

    Order 'm' B-Spline basis functions (general recurrence).

    Order 'm' B-Spline basis functions (general recurrence).

    m

    the order of the spline function (degree = order - 1)

    j

    indicates which spline function

    t

    the time parameter

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