Matlab programs for the computation of univariate and bivariate
splines with free knots
by T.Schuetze, January 1996 - April 1999
schuetze@math.tu-dresden.de
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Overview
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univar routines for univariate approximation
mainfree.m main program
bivar routines for bivariate approximation
mainbiv main program
both routines that will be used by univariate and bivariate
algorithms
Required software
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non-free:
Matlab v5.3
Optimization Toolbox v2.0
Spline Toolbox v2.0.1
optional non-free software:
NPSOL, LSSOL, NLSSOL licensed software from Stanford
lpsol.m, npsol.m, nlssol.m
lssolmex.mexlx, npsolMex.mexlx, nlssolMex.mexlx or mex-files
for other platforms *.mexrs6, *.mexsol
free:
Regularization Toolbox v3.0 by P.C.Hansen
Contents
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both routines that will be used by univariate and bivariate
algorithms
absconst.m compute matrix C and vector h for linear constraints
g(t)=C*t-h >= 0 which avoid the coalescing of knots
for an absolute measure of distance
relconst.m compute matrix C and vector h for linear constraints
g(t)=C*t-h >= 0 which avoid the coalescing of knots
for a relative measure of distance
deriv.m Computation of a matrix D, so that alpha^{r} = D_r
alpha are the coefficients of the r-th order
derivative of the given spline of order k with
coefficients alpha belonging to the knotsequence t
smooth.m Computation of a matrix S, so that
\left\| S \alpha \right|^2 is an upper bound for the
smoothing term \int_a^b [ s^{r} (x)]^2 dx
This approximation of the smoothing term results from
replacing the L_2 - norm by its discrete equivalent
l_2.
readchar.m
readnum.m auxiliary routines: read character/number from
terminal with output text and default value
lssol.m
lssolmexm.* Convex quadratic programming and linear least-square
code LSSOL by Gill et. al.
npsol.m
npsolMex.* Sequential quadratic programming code NPSOL by Gill
et. al.
nlssol.m
nlssolMex.* NLSSOL by Gill et. al. solves constrained least
squares problems using a sequential quadratic
programming algorithm, with a positive-definite
quasi-Newton approximation to the transformed Hessian
QHQ of the Lagrangian function code
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univar routines for univariate approximation
mainfree.m univariate splines with free knots, main program
menupara.m set parameter
menuload.m load data points, spline parameter, free knots, constraints
menusave.m save data points, spline parameter, parameter, residual
menuap.m l2-approximation with fixed knots (with Matlab
Optimization toolbox)
menuapls.m l2-approximation with fixed knots (with LSSOL)
menufree.m l2-approximation with free knots (with Matlab
Optimization toolbox)
menunp.m l2-approximation with free knots (with NPSOL)
menunls.m l2-approximation with free knots (with NLSSOL)
menuregu.m compute regularization (smoothing) parameter
menuplot.m plot approximant, derivative, residual, print to file
menu3d.m plot 3d-data file produced by Pascal program FREE
inpbounds.m input bounds on derivatives
chbounds.m check consistency of bounds on coefficients for p-th
derivatives
trbounds.m transform bounds on derivatives
uncapp.m unconstrained spline approximation, fixed knots
uncsmo.m unconstrained spline smoothing, fixed knots
uncappls.m unconstrained spline approximation with LSSOL, fixed
knots
uncsmols.m unconstrained spline smoothing with LSSOL, fixed knots
conapp.m constrained spline approximation, fixed knots
consmo.m constrained spline smoothing, fixed knots
conappls.m constrained spline approximation with LSSOL, fixed
knots
consmols.m constrained spline smoothing with LSSOL, fixed knots
npfun.m compute residual of reduced functional and set dummy
gradient
npcon.m compute nonlinear constraints and the Jacobian
nlsfun.m compute residual function of reduced functional and
set dummy Jacobian
nlscon.m compute nonlinear constraints and the Jacobian
plotrun.m
plotart.m auxiliary routines to plot figures for article
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bivar routines for bivariate approximation
mainbiv.m bivariate splines with free knots, main program
menuload.m load data points, spline parameter, free knots
menusave.m save data points, spline parameter, parameter
menuap.m l2-approximation with fixed knots (with Matlab
Optimization toolbox)
menufree.m l2-approximation with free knots (with Matlab
Optimization toolbox)
menunp.m l2-approximation with free knots (with NPSOL)
menunls.m l2-approximation with free knots (with NLSSOL)
menuplot.m plot data, approximant, approximant with data,
derivative, contour plot with knots, residual, print
to file
uncapp.m unconstrained spline approximation, fixed knots
uncsmo.m unconstrained spline smoothing, fixed knots
npfun.m compute residual of reduced functional and set dummy
gradient
npcon.m compute nonlinear constraints and the Jacobian
nlsfun.m compute residual function of reduced functional and
set dummy Jacobian
nlscon.m compute nonlinear constraints and the Jacobian
bititan.m bivariate Titanium test data set
dierckx.m test data set by Dierckx for bivariate splines with
free knots
eosalu.m test data set by Carlson/Fritsch
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