pbsc {bspline}

Polynomial B-spline Calculation of Basis Matrix

Description

Polynomial B-spline Calculation of Basis Matrix

Usage

pbsc(x, xk, coeffs)

Arguments

x

Numeric,vector, abscissa points

xk

Numeric vector, knots

coeffs

Numeric 3D array, polynomial coefficients such as calculated by parr

Details

Polynomials are calculated recursively by Cox-de Boor formula. However, it is not applied to final values but to polynomial coefficients. Multiplication by a linear functions gives a raise of polynomial degree by 1.
Polynomial coefficients stored in the first dimension of coeffs are used as in the following formula p[1]*x^n + p[1]*x^(n-1) + ... + p[n+1].
Resulting matrix is the same as returned by bsc(x, xk, n=dim(coeffs)[1]-1)

Value

Numeric matrix, basis vectors, one per column. Row number is length(x).

See Also

bsc

Examples

  n=3
  x=seq(0, 5, length.out=101)
  xk=c(rep(0, n+1), 1:4, rep(5, n+1))
  # cubic polynomial coefficients
  coeffs=parr(xk)
  # basis matrix
  m=pbsc(x, xk, coeffs)
  matplot(x, m, t="l")
  stopifnot(all.equal.numeric(c(m), c(bsc(x, xk))))