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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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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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
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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
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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
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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
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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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