Mercurial > octave-nkf
view scripts/polynomial/splinefit.m @ 17281:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m,
scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m,
scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m,
scripts/general/dblquad.m, scripts/general/display.m,
scripts/general/genvarname.m, scripts/general/idivide.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m,
scripts/general/profexplore.m, scripts/general/profile.m,
scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/triplequad.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m,
scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m,
scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m,
scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m,
scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m,
scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m,
scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m,
scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m,
scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 19 Aug 2013 20:46:38 -0700 |
parents | b10a23fe80bb |
children | 6dbc866379e2 |
line wrap: on
line source
## Copyright (C) 2012 Ben Abbott, Jonas Lundgren ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pp} =} splinefit (@var{x}, @var{y}, @var{breaks}) ## @deftypefnx {Function File} {@var{pp} =} splinefit (@var{x}, @var{y}, @var{p}) ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "periodic", @var{periodic}) ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "robust", @var{robust}) ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "beta", @var{beta}) ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "order", @var{order}) ## @deftypefnx {Function File} {@var{pp} =} splinefit (@dots{}, "constraints", @var{constraints}) ## ## Fit a piecewise cubic spline with breaks (knots) @var{breaks} to the ## noisy data, @var{x} and @var{y}. @var{x} is a vector, and @var{y} ## is a vector or N-D array. If @var{y} is an N-D array, then @var{x}(j) ## is matched to @var{y}(:,@dots{},:,j). ## ## The fitted spline is returned as a piecewise polynomial, @var{pp}, and ## may be evaluated using @code{ppval}. ## ## @var{p} is a positive integer defining the number of intervals along @var{x}, ## and @var{p}+1 is the number of breaks. The number of points in each interval ## differ by no more than 1. ## ## The optional property @var{periodic} is a logical value which specifies ## whether a periodic boundary condition is applied to the spline. The ## length of the period is @code{max (@var{breaks}) - min (@var{breaks})}. ## The default value is @code{false}. ## ## The optional property @var{robust} is a logical value which specifies ## if robust fitting is to be applied to reduce the influence of outlying ## data points. Three iterations of weighted least squares are performed. ## Weights are computed from previous residuals. The sensitivity of outlier ## identification is controlled by the property @var{beta}. The value of ## @var{beta} is stricted to the range, 0 < @var{beta} < 1. The default ## value is @var{beta} = 1/2. Values close to 0 give all data equal ## weighting. Increasing values of @var{beta} reduce the influence of ## outlying data. Values close to unity may cause instability or rank ## deficiency. ## ## The splines are constructed of polynomials with degree @var{order}. ## The default is a cubic, @var{order}=3. A spline with P pieces has ## P+@var{order} degrees of freedom. With periodic boundary conditions ## the degrees of freedom are reduced to P. ## ## The optional property, @var{constaints}, is a structure specifying ## linear constraints on the fit. The structure has three fields, @qcode{"xc"}, ## @qcode{"yc"}, and @qcode{"cc"}. ## ## @table @asis ## @item @qcode{"xc"} ## Vector of the x-locations of the constraints. ## ## @item @qcode{"yc"} ## Constraining values at the locations @var{xc}. ## The default is an array of zeros. ## ## @item @qcode{"cc"} ## Coefficients (matrix). The default is an array of ones. The number of ## rows is limited to the order of the piecewise polynomials, @var{order}. ## @end table ## ## Constraints are linear combinations of derivatives of order 0 to ## @var{order}-1 according to ## ## @example ## @group ## @tex ## $cc(1,j) \cdot y(xc(j)) + cc(2,j) \cdot y\prime(xc(j)) + ... = yc(:,\dots,:,j)$. ## @end tex ## @ifnottex ## cc(1,j) * y(xc(j)) + cc(2,j) * y'(xc(j)) + ... = yc(:,...,:,j). ## @end ifnottex ## @end group ## @end example ## ## @seealso{interp1, unmkpp, ppval, spline, pchip, ppder, ppint, ppjumps} ## @end deftypefn function pp = splinefit (x, y, breaks, varargin) if (nargin > 3) n = cellfun (@ischar, varargin, "uniformoutput", true); varargin(n) = lower (varargin(n)); try props = struct (varargin{:}); catch print_usage (); end_try_catch else props = struct (); endif fields = fieldnames (props); for f = 1:numel (fields) if (! any (strcmp (fields{f}, {"periodic", "robust", "beta", "order", "constraints"}))) error ("splinefit:invalidproperty", "unrecognized property '%s'", fields{f}); endif endfor args = {}; if (isfield (props, "periodic") && props.periodic) args{end+1} = "p"; endif if (isfield (props, "robust") && props.robust) args{end+1} = "r"; endif if (isfield (props, "beta")) if (0 < props.beta && props.beta < 1) args{end+1} = props.beta; else error ("splinefit:invalidbeta", "invalid beta parameter (0 < beta < 1)"); endif endif if (isfield (props, "order")) if (props.order >= 0) args{end+1} = props.order + 1; else error ("splinefit:invalidorder", "invalid order"); endif endif if (isfield (props, "constraints")) args{end+1} = props.constraints; endif if (nargin < 3) print_usage (); elseif (! isnumeric (breaks) || ! isvector (breaks)) print_usage (); endif pp = __splinefit__ (x, y, breaks, args{:}); endfunction %!demo %! % Noisy data %! x = linspace (0, 2*pi, 100); %! y = sin (x) + 0.1 * randn (size (x)); %! % Breaks %! breaks = [0:5, 2*pi]; %! % Fit a spline of order 5 %! pp = splinefit (x, y, breaks, "order", 4); %! clf () %! plot (x, y, "s", x, ppval (pp, x), "r", breaks, ppval (pp, breaks), "+r") %! xlabel ("Independent Variable") %! ylabel ("Dependent Variable") %! title ("Fit a piece-wise polynomial of order 4"); %! legend ({"data", "fit", "breaks"}) %! axis tight %! ylim auto %!demo %! % Noisy data %! x = linspace (0,2*pi, 100); %! y = sin (x) + 0.1 * randn (size (x)); %! % Breaks %! breaks = [0:5, 2*pi]; %! % Fit a spline of order 3 with periodic boundary conditions %! pp = splinefit (x, y, breaks, "order", 2, "periodic", true); %! clf () %! plot (x, y, "s", x, ppval (pp, x), "r", breaks, ppval (pp, breaks), "+r") %! xlabel ("Independent Variable") %! ylabel ("Dependent Variable") %! title ("Fit a periodic piece-wise polynomial of order 2"); %! legend ({"data", "fit", "breaks"}) %! axis tight %! ylim auto %!demo %! % Noisy data %! x = linspace (0, 2*pi, 100); %! y = sin (x) + 0.1 * randn (size (x)); %! % Breaks %! breaks = [0:5, 2*pi]; %! % Constraints: y(0) = 0, y'(0) = 1 and y(3) + y"(3) = 0 %! xc = [0 0 3]; %! yc = [0 1 0]; %! cc = [1 0 1; 0 1 0; 0 0 1]; %! con = struct ("xc", xc, "yc", yc, "cc", cc); %! % Fit a cubic spline with 8 pieces and constraints %! pp = splinefit (x, y, 8, "constraints", con); %! clf () %! plot (x, y, "s", x, ppval (pp, x), "r", breaks, ppval (pp, breaks), "+r") %! xlabel ("Independent Variable") %! ylabel ("Dependent Variable") %! title ("Fit a cubic spline with constraints") %! legend ({"data", "fit", "breaks"}) %! axis tight %! ylim auto %!demo %! % Noisy data %! x = linspace (0, 2*pi, 100); %! y = sin (x) + 0.1 * randn (size (x)); %! % Breaks %! breaks = [0:5, 2*pi]; %! xc = [0 0 3]; %! yc = [0 1 0]; %! cc = [1 0 1; 0 1 0; 0 0 1]; %! con = struct ("xc", xc, "yc", yc, "cc", cc); %! % Fit a spline of order 6 with constraints and periodicity %! pp = splinefit (x, y, breaks, "constraints", con, "order", 5, "periodic", true); %! clf () %! plot (x, y, "s", x, ppval (pp, x), "r", breaks, ppval (pp, breaks), "+r") %! xlabel ("Independent Variable") %! ylabel ("Dependent Variable") %! title ("Fit a 5th order piece-wise periodic polynomial with constraints") %! legend ({"data", "fit", "breaks"}) %! axis tight %! ylim auto %!shared xb, yb, x %! xb = 0:2:10; %! yb = 2*rand (size (xb)) - 1; %! x = 0:0.1:10; %!test %! y = interp1 (xb, yb, x, "linear"); %! assert (ppval (splinefit (x, y, xb, "order", 1), x), y, 15 * eps ()); %!test %! y = interp1 (xb, yb, x, "spline"); %! assert (ppval (splinefit (x, y, xb, "order", 3), x), y, 15 * eps ()); %!test %! y = interp1 (xb, yb, x, "spline"); %! assert (ppval (splinefit (x, y, xb), x), y, 15 * eps ());