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Orthogonal Spline Basis provides allows computing and fitting splines and penalized splines using orthogonalized bases. It also provides easy functions for exact computation of integrals and derivatives.
orthogonalsplinebasis releases are available from CRAN and can be installed by running install.package("orthongalsplinebasis") from inside a running R session.
The standard basis functions for B splines are shown in the plot
The standard basis functions for cubic splines.
Sometimes it is desireable to work with the basis after they have been transformed to be orthogonl
The basis functions after being transformed to be orthogonal.
Through creative matrix representations this orthogonalizing transformation can be computed very fast without any calculations more that matrix multiplication, meaning that calculations are acurate to machine precision. Other caculus computation are similarly just as easy such as derivatives and integrals.
The integrated orthogonal basis functions.
The script for generating these functions
The project summary page you can find here.