B-Spline Interpolation and Regression
nD B-curve governed by (x,y,...) control points.
Basis matrix and knot Jacobian for B-spline of order 0 (step function)...
Calculate B-spline values from their coefficients qw and knots xk
bspline: build and use B-splines for interpolation and regression.
Retrieve parameters of B-splines
Derivative of B-spline
Finite differences
Differentiation matrix
Indefinite integral of B-spline
Estimate internal knot positions equalizing jumps in n-th derivative
Intervals of points in knot intervals
Knot Jacobian of B-spline with weights
Convert parameters to B-spline function
Polynomial formulation of B-spline
Polynomial B-spline Calculation of Basis Matrix
Smoothing B-spline of order n >= 0
Build and use B-splines for interpolation and regression. In case of regression, equality constraints as well as monotonicity and/or positivity of B-spline weights can be imposed. Moreover, knot positions (not only spline weights) can be part of optimized parameters too. For this end, 'bspline' is able to calculate Jacobian of basis vectors as function of knot positions. User is provided with functions calculating spline values at arbitrary points. These functions can be differentiated and integrated to obtain B-splines calculating derivatives/integrals at any point. B-splines of this package can simultaneously operate on a series of curves sharing the same set of knots. 'bspline' is written with concern about computing performance that's why the basis and Jacobian calculation is implemented in C++. The rest is implemented in R but without notable impact on computing speed.