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Free-knot spline approximation

17 Nov 2009 (Updated 10 Jun 2010)

Code covered by the BSD License

Least squares approximation of 1D data using free-knots spline

File Information
Description	The purpose of this function is to provide a flexible and robust fit to one-dimensional data using free-knot splines. The knots are free and able to cope with rapid change in the underlying model. Knot removal strategy is used to fit with only a small number of knots. Optional L2-regularization on the derivative of the spline function can be used to enforce the smoothness. Shape preserving approximation can be enforced by specifying the lower and upper bounds of the derivative(s) of the spline function on sub-intervals. Furthermore specific values of the spline function and its derivative can be specified on a set of discrete data points. I did not test QUADPROG engine, but I have implemented it. Any feedback is welcome.
Acknowledgements	The author wishes to acknowledge the following in the creation of this submission: Pseudo-inverse, Multiple same-size linear solver, Min/Max filter
MATLAB release	MATLAB 7.9 (2009b)
Other requirements	optimization toolbox or QP solvers available at: http://sigpromu.org/quadprog/index.html (QPC) http://www.mat.univie.ac.at/~neum/software/minq/ QPC solver is strongly recommended.
Zip File Content
Other Files	BSFKFolder/BBspline.m, BSFKFolder/BSFK.m, BSFKFolder/BSFK_install.m, BSFKFolder/example.png, BSFKFolder/MinMaxFilterFolder/benchminmax.m, BSFKFolder/MinMaxFilterFolder/Contents.txt, BSFKFolder/MinMaxFilterFolder/demolena.m, BSFKFolder/MinMaxFilterFolder/KramerBruckner.m, BSFKFolder/MinMaxFilterFolder/lemire_engine.c, BSFKFolder/MinMaxFilterFolder/lemire_engine.m, BSFKFolder/MinMaxFilterFolder/lemire_engine.mexw32, BSFKFolder/MinMaxFilterFolder/lemire_nd_engine.c, BSFKFolder/MinMaxFilterFolder/lemire_nd_engine.mexw32, BSFKFolder/MinMaxFilterFolder/lemire_nd_maxengine.c, BSFKFolder/MinMaxFilterFolder/lemire_nd_maxengine.m, BSFKFolder/MinMaxFilterFolder/lemire_nd_maxengine.mexw32, BSFKFolder/MinMaxFilterFolder/lemire_nd_minengine.c, BSFKFolder/MinMaxFilterFolder/lemire_nd_minengine.m, BSFKFolder/MinMaxFilterFolder/lemire_nd_minengine.mexw32, BSFKFolder/MinMaxFilterFolder/minmaxfilt.m, BSFKFolder/MinMaxFilterFolder/minmaxfilt1.m, BSFKFolder/MinMaxFilterFolder/minmaxfilter_install.m, BSFKFolder/MinMaxFilterFolder/slowminmaxfilt_algo.m, BSFKFolder/MinMaxFilterFolder/testminmaxfilt.m, BSFKFolder/MinMaxFilterFolder/vanherk.m, BSFKFolder/MultiSolverFolder/MultiProd.m, BSFKFolder/MultiSolverFolder/MultiSolver.m, BSFKFolder/MultiSolverFolder/SliceMultiProd.m, BSFKFolder/MultiSolverFolder/SliceMultiSolver.m, BSFKFolder/private/BernKnotDeriv.m, BSFKFolder/private/Bernstein.m, BSFKFolder/private/Bspline.m, BSFKFolder/private/Bspline2pp.m, BSFKFolder/private/BsplineKnotDeriv.m, BSFKFolder/private/DerivB.m, BSFKFolder/private/DerivBKnotDeriv.m, BSFKFolder/private/derivchol.m, BSFKFolder/private/DGD.m, BSFKFolder/private/getoption.m, BSFKFolder/private/Gram.m, BSFKFolder/private/qpmin.m, BSFKFolder/private/qrnull.m, BSFKFolder/PseudoInverseFolder/@pseudoinverse/private/getoption.m, BSFKFolder/PseudoInverseFolder/@pseudoinverse/private/lowercase.m, BSFKFolder/PseudoInverseFolder/@pseudoinverse/pseudoinverse.m, BSFKFolder/testBSFK.m, license.txt

Tags for This File
Everyone's Tags	bspline(2), data compression, fitting, free knots(2), knot removal, least squares, shape preserving, spline
Tags I've Applied
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Comments and Ratings (3)
09 Jan 2010	x yuij
01 Jun 2010	Bruno Luong	Periodic spline is now available
08 Jun 2010	Bruno Luong	Just discover an issue with continuous regularization. In the mean time, please use the discrete regularization

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Updates
18 Nov 2009	Update description, more options added to control the fit, discrete regularization
19 Nov 2009	Remove NaN data before fitting, change TRY/CATCH ME syntax for better compatibility (tested under 2006B), estimate automatic of the noise standard deviation
28 Nov 2009	Change title and description
04 Dec 2009	A major enhancement with shape preserving splines
08 Dec 2009	Point-wise constraints. Discover an error of the Jacobian formula in [Schutze/Schwetlick 97] paper, modify the calculation accordingly. This concern only the constrained fitting.
09 Dec 2009	Correct another bug in the Jacobian calculation (constrained case)
09 Dec 2009	Change the description.
10 Dec 2009	Singular constraints will issue a warning (instead of an error). Refine the Gauss-Newton direction. Fix few minor bugs.
14 Dec 2009	Correct a bug in UpdateConstraints that did not update the knot positions. Precasting data to double. Update more frequently the scaling matrix. Reduce the Lagrange's tolerance to detect active set of QPC solver
18 Mar 2010	fixed small bug when calling QP engine minqdef
10 Apr 2010	fix a bug with parsing k and nknots Spline order can be as low as k=1 (piecewise constant fit)
31 May 2010	New feature: Periodic spline
01 Jun 2010	Remove some redundant code, modify test program
07 Jun 2010	A more robust conversion in pp form is implemented
07 Jun 2010	Fix a small bug (eigs with 'sa' option requires true symmetric matrix, which is now always the case by symmetrizing)
10 Jun 2010	Fix the bug for continuous regularization

Tag Activity for this File
Tag	Applied By	Date/Time
fitting	Bruno Luong	17 Nov 2009 13:09:10
bspline	Bruno Luong	17 Nov 2009 13:09:10
free knots	Bruno Luong	17 Nov 2009 13:09:10
knot removal	Bruno Luong	17 Nov 2009 13:09:10
data compression	Bruno Luong	17 Nov 2009 13:09:10
least squares	Bruno Luong	18 Nov 2009 10:17:14
shape preserving	Bruno Luong	04 Dec 2009 09:49:00
spline	Bruno Luong	10 Dec 2009 12:09:06
bspline	Jon	09 Mar 2010 09:50:15
free knots	Jon	09 Mar 2010 12:39:13