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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,
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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,
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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,
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vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m,
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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 | 721a4a83cba6 |
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## Copyright (C) 2001-2012 Kai Habel ## ## 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} =} pchip (@var{x}, @var{y}) ## @deftypefnx {Function File} {@var{yi} =} pchip (@var{x}, @var{y}, @var{xi}) ## Return the Piecewise Cubic Hermite Interpolating Polynomial (pchip) of ## points @var{x} and @var{y}. ## ## If called with two arguments, return the piecewise polynomial @var{pp} ## that may be used with @code{ppval} to evaluate the polynomial at specific ## points. When called with a third input argument, @code{pchip} evaluates ## the pchip polynomial at the points @var{xi}. The third calling form is ## equivalent to @code{ppval (pchip (@var{x}, @var{y}), @var{xi})}. ## ## The variable @var{x} must be a strictly monotonic vector (either ## increasing or decreasing) of length @var{n}. @var{y} can be either a ## vector or array. If @var{y} is a vector then it must be the same length ## @var{n} as @var{x}. If @var{y} is an array then the size of @var{y} must ## have the form ## @tex ## $$[s_1, s_2, \cdots, s_k, n]$$ ## @end tex ## @ifnottex ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n}]} ## @end ifnottex ## The array is reshaped internally to a matrix where the leading ## dimension is given by ## @tex ## $$s_1 s_2 \cdots s_k$$ ## @end tex ## @ifnottex ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}} ## @end ifnottex ## and each row of this matrix is then treated separately. Note that this ## is exactly opposite to @code{interp1} but is done for @sc{matlab} ## compatibility. ## ## @seealso{spline, ppval, mkpp, unmkpp} ## @end deftypefn ## Author: Kai Habel <kai.habel@gmx.de> ## Date: 9. mar 2001 ## ## S_k = a_k + b_k*x + c_k*x^2 + d_k*x^3; (spline polynom) ## ## 4 conditions: ## S_k(x_k) = y_k; ## S_k(x_k+1) = y_k+1; ## S_k'(x_k) = y_k'; ## S_k'(x_k+1) = y_k+1'; function ret = pchip (x, y, xi) if (nargin < 2 || nargin > 3) print_usage (); endif ## make row vector x = x(:).'; n = length (x); ## Check the size and shape of y if (isvector (y)) y = y(:).'; ##row vector szy = size (y); if !(size_equal (x, y)) error ("pchip: length of X and Y must match") endif else szy = size (y); if (n != szy(end)) error ("pchip: length of X and last dimension of Y must match") endif y = reshape (y, [prod(szy(1:end-1)), szy(end)]); endif h = diff (x); if (all (h < 0)) x = fliplr (x); h = diff (x); y = fliplr (y); elseif (any (h <= 0)) error("pchip: X must be strictly monotonic"); endif f1 = y(:, 1:n-1); ## Compute derivatives. d = __pchip_deriv__ (x, y, 2); d1 = d(:, 1:n-1); d2 = d(:, 2:n); ## This is taken from SLATEC. h = diag (h); delta = diff (y, 1, 2) / h; del1 = (d1 - delta) / h; del2 = (d2 - delta) / h; c3 = del1 + del2; c2 = -c3 - del1; c3 = c3 / h; coeffs = cat (3, c3, c2, d1, f1); ret = mkpp (x, coeffs, szy(1:end-1)); if (nargin == 3) ret = ppval (ret, xi); endif endfunction %!demo %! x = 0:8; %! y = [1, 1, 1, 1, 0.5, 0, 0, 0, 0]; %! xi = 0:0.01:8; %! yspline = spline (x,y,xi); %! ypchip = pchip (x,y,xi); %! title ("pchip and spline fit to discontinuous function"); %! plot (xi,yspline, xi,ypchip,"-", x,y,"+"); %! legend ("spline", "pchip", "data"); %! %------------------------------------------------------------------- %! % confirm that pchip agreed better to discontinuous data than spline %!shared x,y,y2,pp,yi1,yi2,yi3 %! x = 0:8; %! y = [1, 1, 1, 1, 0.5, 0, 0, 0, 0]; %!assert (pchip (x,y,x), y) %!assert (pchip (x,y,x'), y') %!assert (pchip (x',y',x'), y') %!assert (pchip (x',y',x), y) %!assert (isempty (pchip(x',y',[]))) %!assert (isempty (pchip(x,y,[]))) %!assert (pchip (x,[y;y],x), [pchip(x,y,x);pchip(x,y,x)]) %!assert (pchip (x,[y;y],x'), [pchip(x,y,x);pchip(x,y,x)]) %!assert (pchip (x',[y;y],x), [pchip(x,y,x);pchip(x,y,x)]) %!assert (pchip (x',[y;y],x'), [pchip(x,y,x);pchip(x,y,x)]) %!test %! x = (0:8)*pi/4; y = [sin(x); cos(x)]; %! y2(:,:,1) = y; y2(:,:,2) = y+1; y2(:,:,3) = y-1; %! pp = pchip (x, shiftdim (y2,2)); %! yi1 = ppval (pp, (1:4)*pi/4); %! yi2 = ppval (pp, repmat ((1:4)*pi/4, [5,1])); %! yi3 = ppval (pp, [pi/2,pi]); %!assert (size (pp.coefs), [48,4]) %!assert (pp.pieces, 8) %!assert (pp.order, 4) %!assert (pp.dim, [3,2]) %!assert (ppval (pp,pi), [0,-1;1,0;-1,-2], 1e-14) %!assert (yi3(:,:,2), ppval (pp,pi), 1e-14) %!assert (yi3(:,:,1), [1,0;2,1;0,-1], 1e-14) %!assert (squeeze (yi1(1,2,:)), [1/sqrt(2); 0; -1/sqrt(2);-1], 1e-14) %!assert (size (yi2), [3,2,5,4]) %!assert (squeeze (yi2(1,2,3,:)), [1/sqrt(2); 0; -1/sqrt(2);-1], 1e-14)