Struct rgsl::types::basis_spline::BSpLineWorkspace

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pub struct BSpLineWorkspace { /* private fields */ }

Implementations

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impl BSpLineWorkspace

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pub fn new(k: usize, nbreak: usize) -> Option<Self>

This function allocates a workspace for computing B-splines of order k.

The number of breakpoints is given by nbreak. This leads to n = nbreak + k - 2 basis functions.

Cubic B-splines are specified by k = 4. The size of the workspace is O(5k + nbreak).

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pub fn knots(&mut self, breakpts: &VectorF64) -> Value

This function computes the knots associated with the given breakpoints and stores them internally in w->knots.

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pub fn knots_uniform(&mut self, a: f64, b: f64) -> Value

This function assumes uniformly spaced breakpoints on [a,b] and constructs the corresponding knot vector using the previously specified nbreak parameter. The knots are stored in w->knots.

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pub fn eval(&mut self, x: f64, B: &mut VectorF64) -> Value

This function evaluates all B-spline basis functions at the position x and stores them in the vector B, so that the i-th element is B_i(x).

The vector B must be of length n = nbreak + k - 2. This value may also be obtained by calling gsl_bspline_ncoeffs.

Computing all the basis functions at once is more efficient than computing them individually, due to the nature of the defining recurrence relation.

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pub fn eval_non_zero(
    &mut self,
    x: f64,
    Bk: &mut VectorF64
) -> (Value, usize, usize )

This function evaluates all potentially nonzero B-spline basis functions at the position x and stores them in the vector Bk, so that the i-th element is B_(istart+i)(x).

The last element of Bk is B_(iend)(x). The vector Bk must be of length k. By returning only the nonzero basis functions, this function allows quantities involving linear combinations of the B_i(x) to be computed without unnecessary terms (such linear combinations occur, for example, when evaluating an interpolated function).

Returns (Value, istart, iend).

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pub fn ncoeffs(&mut self) -> usize

This function returns the number of B-spline coefficients given by n = nbreak + k - 2.

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pub fn greville_abscissa(&mut self, i: usize) -> f64

The Greville abscissae are defined to be the mean location of k-1 consecutive knots in the knot vector for each basis spline function of order k.

With the first and last knots in the gsl_bspline_workspace knot vector excluded, there are gsl_bspline_ncoeffs Greville abscissae for any given B-spline basis.

These values are often used in B-spline collocation applications and may also be called Marsden-Schoenberg points.

Returns the location of the i-th Greville abscissa for the given B-spline basis. For the ill-defined case when k=1, the implementation chooses to return breakpoint interval midpoints.