annotate scripts/polynomial/spline.m @ 14363:f3d52523cde1

Use Octave coding conventions in all m-file %!test blocks * wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m, csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m, accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m, celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m, cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m, flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m, interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m, isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m, narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m, polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m, randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m, structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m, griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m, get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m, imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m, textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m, duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m, issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m, qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m, bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m, fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m, ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m, news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m, setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m, warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m, pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m, __plt_get_axis_arg__.m, ancestor.m, cla.m, clf.m, close.m, colorbar.m, colstyle.m, comet3.m, contourc.m, figure.m, gca.m, gcbf.m, gcbo.m, gcf.m, ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m, ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m, orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m, refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m, stem3.m, subplot.m, title.m, uigetfile.m, view.m, whitebg.m, compan.m, conv.m, deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m, polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m, ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m, sinewave.m, unwrap.m, bicg.m, bicgstab.m, gmres.m, gplot.m, nonzeros.m, pcg.m, pcr.m, spaugment.m, spconvert.m, spdiags.m, speye.m, spfun.m, spones.m, sprand.m, sprandsym.m, spstats.m, spy.m, svds.m, treelayout.m, bessel.m, beta.m, betaln.m, factor.m, factorial.m, isprime.m, lcm.m, legendre.m, nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m, realsqrt.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, rosser.m, vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m, iqr.m, kendall.m, kurtosis.m, logit.m, mahalanobis.m, mean.m, meansq.m, median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m, range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m, statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m, betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m, cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m, chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m, expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m, gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m, hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m, laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m, logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m, lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m, norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m, poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m, tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m, unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m, wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m, bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m, strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m, substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m, asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m, eomday.m, etime.m, is_leap_year.m, now.m: Use Octave coding conventions in all m-file %!test blocks
author Rik <octave@nomad.inbox5.com>
date Mon, 13 Feb 2012 07:29:44 -0800
parents 11949c9795a0
children 2e23cd0a9e40
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rev   line source
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1 ## Copyright (C) 2000-2012 Kai Habel
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2 ## Copyright (C) 2006 David Bateman
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{pp} =} spline (@var{x}, @var{y})
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22 ## @deftypefnx {Function File} {@var{yi} =} spline (@var{x}, @var{y}, @var{xi})
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23 ## Return the cubic spline interpolant of points @var{x} and @var{y}.
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24 ##
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25 ## When called with two arguments, return the piecewise polynomial @var{pp}
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26 ## that may be used with @code{ppval} to evaluate the polynomial at specific
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27 ## points. When called with a third input argument, @code{spline} evaluates
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28 ## the spline at the points @var{xi}. The third calling form @code{spline
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29 ## (@var{x}, @var{y}, @var{xi})} is equivalent to @code{ppval (spline
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30 ## (@var{x}, @var{y}), @var{xi})}.
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31 ##
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32 ## The variable @var{x} must be a vector of length @var{n}. @var{y} can be
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33 ## either a vector or array. If @var{y} is a vector it must have a length of
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34 ## either @var{n} or @code{@var{n} + 2}. If the length of @var{y} is
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35 ## @var{n}, then the "not-a-knot" end condition is used. If the length of
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36 ## @var{y} is @code{@var{n} + 2}, then the first and last values of the
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37 ## vector @var{y} are the values of the first derivative of the cubic spline
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38 ## at the endpoints.
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39 ##
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40 ## If @var{y} is an array, then the size of @var{y} must have the form
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41 ## @tex
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42 ## $$[s_1, s_2, \cdots, s_k, n]$$
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43 ## @end tex
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44 ## @ifnottex
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45 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n}]}
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46 ## @end ifnottex
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47 ## or
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48 ## @tex
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49 ## $$[s_1, s_2, \cdots, s_k, n + 2].$$
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50 ## @end tex
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51 ## @ifnottex
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52 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}.
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53 ## @end ifnottex
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54 ## The array is reshaped internally to a matrix where the leading
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55 ## dimension is given by
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56 ## @tex
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57 ## $$s_1 s_2 \cdots s_k$$
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58 ## @end tex
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59 ## @ifnottex
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60 ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}}
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61 ## @end ifnottex
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62 ## and each row of this matrix is then treated separately. Note that this
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63 ## is exactly opposite to @code{interp1} but is done for @sc{matlab}
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64 ## compatibility.
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65 ##
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66 ## @seealso{pchip, ppval, mkpp, unmkpp}
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67 ## @end deftypefn
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68
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69 ## This code is based on csape.m from octave-forge, but has been
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70 ## modified to use the sparse solver code in octave that itself allows
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71 ## special casing of tri-diagonal matrices, modified for NDArrays and
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72 ## for the treatment of vectors y 2 elements longer than x as complete
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73 ## splines.
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74
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75 function ret = spline (x, y, xi)
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76
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77 x = x(:);
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78 n = length (x);
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79 if (n < 2)
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80 error ("spline: requires at least 2 points");
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81 endif
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82
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83 ## Check the size and shape of y
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84 ndy = ndims (y);
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85 szy = size (y);
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86 if (ndy == 2 && (szy(1) == n || szy(2) == n))
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87 if (szy(2) == n)
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88 a = y.';
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89 else
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90 a = y;
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91 szy = fliplr (szy);
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92 endif
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93 else
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94 a = shiftdim (reshape (y, [prod(szy(1:end-1)), szy(end)]), 1);
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parents:
diff changeset
95 endif
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11536
diff changeset
96
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11536
diff changeset
97 for k = (1:columns (a))(any (isnan (a)))
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11536
diff changeset
98 ok = ! isnan (a(:,k));
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11536
diff changeset
99 a(!ok,k) = spline (x(ok), a(ok,k), x(!ok));
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11536
diff changeset
100 endfor
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11536
diff changeset
101
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
102 complete = false;
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
103 if (size (a, 1) == n + 2)
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
104 complete = true;
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
105 dfs = a(1,:);
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
106 dfe = a(end,:);
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
107 a = a(2:end-1,:);
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
108 endif
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
109
14222
190952239c2c Use '!' for not operation in preference to '~'.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
110 if (! issorted (x))
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
111 [x, idx] = sort(x);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
112 a = a(idx,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
113 endif
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
114
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
115 b = c = zeros (size (a));
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
116 h = diff (x);
5838
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe]
jwe
parents: 5837
diff changeset
117 idx = ones (columns (a), 1);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
118
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
119 if (complete)
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
120
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
121 if (n == 2)
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
122 d = (dfs + dfe) / (x(2) - x(1)) ^ 2 + ...
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
123 2 * (a(1,:) - a(2,:)) / (x(2) - x(1)) ^ 3;
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
124 c = (-2 * dfs - dfe) / (x(2) - x(1)) - ...
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
125 3 * (a(1,:) - a(2,:)) / (x(2) - x(1)) ^ 2;
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
126 b = dfs;
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
127 a = a(1,:);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
128
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
129 d = d(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
130 c = c(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
131 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
132 a = a(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
133 else
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
134 if (n == 3)
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
135 dg = 1.5 * h(1) - 0.5 * h(2);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
136 c(2:n-1,:) = 1/dg(1);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
137 else
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
138 dg = 2 * (h(1:n-2) .+ h(2:n-1));
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
139 dg(1) = dg(1) - 0.5 * h(1);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
140 dg(n-2) = dg(n-2) - 0.5 * h(n-1);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
141
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
142 e = h(2:n-2);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
143
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
144 g = 3 * diff (a(2:n,:)) ./ h(2:n-1,idx) ...
5838
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe]
jwe
parents: 5837
diff changeset
145 - 3 * diff (a(1:n-1,:)) ./ h(1:n-2,idx);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
146 g(1,:) = 3 * (a(3,:) - a(2,:)) / h(2) ...
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
147 - 3 / 2 * (3 * (a(2,:) - a(1,:)) / h(1) - dfs);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
148 g(n-2,:) = 3 / 2 * (3 * (a(n,:) - a(n-1,:)) / h(n-1) - dfe) ...
5838
376e02b2ce70 [project @ 2006-06-01 20:23:53 by jwe]
jwe
parents: 5837
diff changeset
149 - 3 * (a(n-1,:) - a(n-2,:)) / h(n-2);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
150
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
151 c(2:n-1,:) = spdiags ([[e(:); 0], dg, [0; e(:)]],
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9768
diff changeset
152 [-1, 0, 1], n-2, n-2) \ g;
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
153 endif
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
154
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
155 c(1,:) = (3 / h(1) * (a(2,:) - a(1,:)) - 3 * dfs
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
156 - c(2,:) * h(1)) / (2 * h(1));
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
157 c(n,:) = - (3 / h(n-1) * (a(n,:) - a(n-1,:)) - 3 * dfe
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
158 + c(n-1,:) * h(n-1)) / (2 * h(n-1));
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
159 b(1:n-1,:) = diff (a) ./ h(1:n-1, idx) ...
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9768
diff changeset
160 - h(1:n-1,idx) / 3 .* (c(2:n,:) + 2 * c(1:n-1,:));
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
161 d = diff (c) ./ (3 * h(1:n-1, idx));
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
162
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
163 d = d(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
164 c = c(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
165 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
166 a = a(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
167 endif
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
168 else
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
169
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
170 if (n == 2)
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
171 b = (a(2,:) - a(1,:)) / (x(2) - x(1));
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
172 a = a(1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
173 d = [];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
174 c = [];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
175 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
176 a = a(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
177 elseif (n == 3)
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
178
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
179 n = 2;
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
180 c = (a(1,:) - a(3,:)) / ((x(3) - x(1)) * (x(2) - x(3))) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
181 + (a(2,:) - a(1,:)) / ((x(2) - x(1)) * (x(2) - x(3)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
182 b = (a(2,:) - a(1,:)) * (x(3) - x(1)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
183 / ((x(2) - x(1)) * (x(3) - x(2))) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
184 + (a(1,:) - a(3,:)) * (x(2) - x(1)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
185 / ((x(3) - x(1)) * (x(3) - x(2)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
186 a = a(1,:);
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
187 d = [];
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
188 x = [min(x), max(x)];
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
189
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
190 c = c(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
191 b = b(1:n-1,:);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
192 a = a(1:n-1,:);
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
193 else
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
194
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
195 g = zeros (n-2, columns (a));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
196 g(1,:) = 3 / (h(1) + h(2)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
197 * (a(3,:) - a(2,:) - h(2) / h(1) * (a(2,:) - a(1,:)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
198 g(n-2,:) = 3 / (h(n-1) + h(n-2)) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
199 * (h(n-2) / h(n-1) * (a(n,:) - a(n-1,:)) - (a(n-1,:) - a(n-2,:)));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
200
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
201 if (n > 4)
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
202
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
203 g(2:n - 3,:) = 3 * diff (a(3:n-1,:)) ./ h(3:n-2,idx) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
204 - 3 * diff (a(2:n-2,:)) ./ h(2:n - 3,idx);
5824
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
205
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
206 dg = 2 * (h(1:n-2) .+ h(2:n-1));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
207 dg(1) = dg(1) - h(1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
208 dg(n-2) = dg(n-2) - h(n-1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
209
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
210 ldg = udg = h(2:n-2);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
211 udg(1) = udg(1) - h(1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
212 ldg(n - 3) = ldg(n-3) - h(n-1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
213 c(2:n-1,:) = spdiags ([[ldg(:); 0], dg, [0; udg(:)]],
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9768
diff changeset
214 [-1, 0, 1], n-2, n-2) \ g;
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diff changeset
215
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
216 elseif (n == 4)
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
217
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
218 dg = [h(1) + 2 * h(2); 2 * h(2) + h(3)];
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
219 ldg = h(2) - h(3);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
220 udg = h(2) - h(1);
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
221 c(2:n-1,:) = spdiags ([[ldg(:);0], dg, [0; udg(:)]],
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
222 [-1, 0, 1], n-2, n-2) \ g;
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223
11196
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
224 endif
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
225
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
226 c(1,:) = c(2,:) + h(1) / h(2) * (c(2,:) - c(3,:));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
227 c(n,:) = c(n-1,:) + h(n-1) / h(n-2) * (c(n-1,:) - c(n-2,:));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
228 b = diff (a) ./ h(1:n-1, idx) ...
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
229 - h(1:n-1, idx) / 3 .* (c(2:n,:) + 2 * c(1:n-1,:));
d17cb8a1271d spline.m: Fix algorithm for input with 3 elements (bug #31098)
Marco Caliari <marco.caliari@univr.it>
parents: 10793
diff changeset
230 d = diff (c) ./ (3 * h(1:n-1, idx));
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231
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Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
232 d = d(1:n-1,:);d = d.'(:);
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
233 c = c(1:n-1,:);c = c.'(:);
59e2460acae1 make piecewise polynomial (pp) functions more compatible
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parents: 12444
diff changeset
234 b = b(1:n-1,:);b = b.'(:);
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
235 a = a(1:n-1,:);a = a.'(:);
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parents:
diff changeset
236 endif
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
237
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
238 endif
12608
59e2460acae1 make piecewise polynomial (pp) functions more compatible
Kai Habel <kai.habel@gmx.de>
parents: 12444
diff changeset
239 ret = mkpp (x, cat (2, d, c, b, a), szy(1:end-1));
5824
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diff changeset
240
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
241 if (nargin == 3)
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
242 ret = ppval (ret, xi);
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
243 endif
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
244
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
245 endfunction
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
246
14237
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
247
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parents:
diff changeset
248 %!demo
14237
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parents: 14222
diff changeset
249 %! x = 0:10; y = sin (x);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14237
diff changeset
250 %! xspline = 0:0.1:10; yspline = spline (x,y,xspline);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
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parents: 14237
diff changeset
251 %! title ("spline fit to points from sin (x)");
14237
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parents: 14222
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252 %! plot (xspline,sin(xspline),"r", xspline,yspline,"g-", x,y,"b+");
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
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parents: 14222
diff changeset
253 %! legend ("original", "interpolation", "interpolation points");
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diff changeset
254 %! %--------------------------------------------------------
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
255 %! % confirm that interpolated function matches the original
448f9982e7fb [project @ 2006-05-19 06:53:31 by jwe]
jwe
parents:
diff changeset
256
6686
2aad75fcc93a [project @ 2007-06-03 20:58:28 by dbateman]
dbateman
parents: 6248
diff changeset
257 %!shared x,y,abserr
14237
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
258 %! x = [0:10]; y = sin (x); abserr = 1e-14;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
259 %!assert (spline (x,y,x), y, abserr)
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Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
260 %!assert (spline (x,y,x'), y', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
261 %!assert (spline (x',y',x'), y', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
262 %!assert (spline (x',y',x), y, abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
263 %!assert (isempty (spline (x',y',[])))
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
264 %!assert (isempty (spline (x,y,[])))
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
265 %!assert (spline (x,[y;y],x), [spline(x,y,x);spline(x,y,x)], abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
266 %!assert (spline (x,[y;y],x'), [spline(x,y,x);spline(x,y,x)], abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
267 %!assert (spline (x',[y;y],x), [spline(x,y,x);spline(x,y,x)], abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
268 %!assert (spline (x',[y;y],x'), [spline(x,y,x);spline(x,y,x)], abserr)
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14237
diff changeset
269 %! y = cos (x) + i*sin (x);
14237
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parents: 14222
diff changeset
270 %!assert (spline (x,y,x), y, abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
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parents: 14222
diff changeset
271 %!assert (real (spline (x,y,x)), real (y), abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
272 %!assert (real (spline (x,y,x.')), real (y).', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
273 %!assert (real (spline (x.',y.',x.')), real (y).', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
274 %!assert (real (spline (x.',y,x)), real (y), abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
275 %!assert (imag (spline (x,y,x)), imag (y), abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
276 %!assert (imag (spline (x,y,x.')), imag (y).', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
277 %!assert (imag (spline (x.',y.',x.')), imag (y).', abserr)
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
278 %!assert (imag (spline (x.',y,x)), imag (y), abserr)
10658
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
279 %!test
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
280 %! xnan = 5;
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
281 %! y(x==xnan) = NaN;
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
282 %! ok = ! isnan (y);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
283 %! assert (spline (x, y, x(ok)), y(ok), abserr);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
284 %!test
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
285 %! ok = ! isnan (y);
c66a4657d764 spline.m: Ignore NaNs within input vectors.
Ben Abbott <bpabbott@mac.com>
parents: 10549
diff changeset
286 %! assert (! isnan (spline (x, y, x(!ok))));
12444
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
287 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
288 %! x = [1,2];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
289 %! y = [1,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
290 %! assert (spline (x,y,x), [1,4], abserr);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
291 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
292 %! x = [2,1];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
293 %! y = [1,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
294 %! assert (spline (x,y,x), [1,4], abserr);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
295 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
296 %! x = [1,2];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
297 %! y = [1,2,3,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
298 %! pp = spline (x,y);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
299 %! [x,P] = unmkpp (pp);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
300 %! assert (norm (P-[3,-3,1,2]), 0, abserr);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
301 %!test
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
302 %! x = [2,1];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
303 %! y = [1,2,3,4];
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
304 %! pp = spline (x,y);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
305 %! [x,P] = unmkpp (pp);
07e102029d2a spline.m: Allow length(x) == 2 and unsorted x values.
Ben Abbott <bpabbott@mac.com>
parents: 11587
diff changeset
306 %! assert (norm (P-[7,-9,1,3]), 0, abserr);
14237
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc.
Rik <octave@nomad.inbox5.com>
parents: 14222
diff changeset
307