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fastBSpline - A fast, lightweight class that implements non-uniform B splines of any order Matlab's spline functions are very general. This generality comes at the price of speed. For large-scale applications, including model fitting where some components of the model are defined in terms of splines, such as generalized additive models, a faster solution is desirable. The fastBSpline class implements a lightweight set of B-spline features, including evaluation, differentiation, and parameter fitting. The hard work is done by C code, resulting in up to 10x acceleration for evaluating splines and up to 50x acceleration when evaluating of spline derivatives. Nevertheless, fastBSplines are manipulated using an intuitive, high- level object-oriented interface, thus allowing C-level performance without the messiness. Use CompileMexFiles to compile the required files. If mex files are not available, evaluation will be done in .m code, so you may still use the code if you can't use a compiler for your platform. B splines are defined in terms of basis functions: y(x) = sum_i B_i(x,knots)*weights_i B (the basis) is defined in terms of knots, a non-decreasing sequence of values. Each basis function is a piecewise polynomial of order length(knots)-length(weights)-1. The most commonly used B-spline is the cubic B-spline. In that case there are 4 more knots than there are weights. Another commonly used B-spline is the linear B-spline, whose basis function are shaped like tents, and whose application results in piecewise linear interpolation. The class offers two static functions to fit the weights of a spline: lsqspline and pspline. It includes facilities for computing the basis B and the derivatives of the spline at all points. Constructor: sp = fastBSpline(knots,weights); Example use: %Fit a noisy measurement with a smoothness-penalized spline (p-spline) x = (0:.5:10)'; y = sin(x*pi*.41-.9)+randn(size(x))*.2; knots = [0,0,0,0:.5:10,10,10,10]; %Notice there are as many knots as observations %Because there are so many knots, this is an exact interpolant sp1 = fastBSpline.lsqspline(knots,3,x,y); %Fit penalized on the smoothness of the spline sp2 = fastBSpline.pspline(knots,3,x,y,.7); clf; rg = -2:.005:12; plot(x,y,'o',rg,sp1.evalAt(rg),rg,sp2.evalAt(rg)); legend('measured','interpolant','smoothed'); fastBSpline properties: outOfRange - Determines how the spline is extrapolated outside the range of the knots knots - The knots of the spline (read only) weights - The weights of the spline (read only) fastBSpline Methods: fastBSpline - Construct a B spline from weights at the knots lsqspline - Construct a least-squares spline from noisy measurements pspline - Construct a smoothness-penalized spline from noisy measurements evalAt - Evaluate a spline at the given points getBasis - Get the values of the underlying basis at the given points Btimesy - Evaluate the product getBasis(x)'*y dx - Returns another fastBSpline object which computes the derivative of the original spline Disclaimer: fastBSpline is not meant to replace Matlab's spline functions; it does not include any code from the Mathworks
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Windows Software
Albina Merfyn - I find this to be really easy to use. I can...
