Mercurial > hg > octave-lyh
annotate scripts/general/quadv.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> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | 5d3a684236b0 |
rev | line source |
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1 ## Copyright (C) 2008-2012 David Bateman |
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2 ## Copyright (C) 2012 Alexander Klein |
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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{q} =} quadv (@var{f}, @var{a}, @var{b}) |
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22 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}) |
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23 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}) |
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24 ## @deftypefnx {Function File} {@var{q} =} quadv (@var{f}, @var{a}, @var{b}, @var{tol}, @var{trace}, @var{p1}, @var{p2}, @dots{}) |
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25 ## @deftypefnx {Function File} {[@var{q}, @var{nfun}] =} quadv (@dots{}) |
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26 ## |
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27 ## Numerically evaluate the integral of @var{f} from @var{a} to @var{b} |
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28 ## using an adaptive Simpson's rule. |
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29 ## @var{f} is a function handle, inline function, or string |
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30 ## containing the name of the function to evaluate. |
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31 ## @code{quadv} is a vectorized version of @code{quad} and the function |
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32 ## defined by @var{f} must accept a scalar or vector as input and return a |
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33 ## scalar, vector, or array as output. |
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34 ## |
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35 ## @var{a} and @var{b} are the lower and upper limits of integration. Both |
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36 ## limits must be finite. |
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37 ## |
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38 ## The optional argument @var{tol} defines the tolerance used to stop |
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39 ## the adaptation procedure. The default value is @math{1e^{-6}}. |
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40 ## |
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41 ## The algorithm used by @code{quadv} involves recursively subdividing the |
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42 ## integration interval and applying Simpson's rule on each subinterval. |
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43 ## If @var{trace} is true then after computing each of these partial |
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44 ## integrals display: (1) the total number of function evaluations, |
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45 ## (2) the left end of the subinterval, (3) the length of the subinterval, |
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46 ## (4) the approximation of the integral over the subinterval. |
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47 ## |
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48 ## Additional arguments @var{p1}, etc., are passed directly to the function |
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49 ## @var{f}. To use default values for @var{tol} and @var{trace}, one may pass |
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50 ## empty matrices ([]). |
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51 ## |
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52 ## The result of the integration is returned in @var{q}. @var{nfun} indicates |
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53 ## the number of function evaluations that were made. |
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54 ## |
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55 ## Note: @code{quadv} is written in Octave's scripting language and can be |
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56 ## used recursively in @code{dblquad} and @code{triplequad}, unlike the |
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57 ## similar @code{quad} function. |
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58 ## @seealso{quad, quadl, quadgk, quadcc, trapz, dblquad, triplequad} |
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59 ## @end deftypefn |
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60 |
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61 function [q, nfun] = quadv (f, a, b, tol, trace, varargin) |
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62 ## TODO: Make norm for convergence testing configurable |
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63 |
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64 if (nargin < 3) |
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65 print_usage (); |
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66 endif |
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67 if (nargin < 4) |
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68 tol = []; |
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69 endif |
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70 if (nargin < 5) |
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71 trace = []; |
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72 endif |
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73 if (isa (a, "single") || isa (b, "single")) |
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74 myeps = eps ("single"); |
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75 else |
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76 myeps = eps; |
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77 endif |
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78 if (isempty (tol)) |
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79 tol = 1e-6; |
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80 endif |
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81 if (isempty (trace)) |
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82 trace = 0; |
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83 endif |
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84 |
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85 ## Split the interval into 3 abscissa, and apply a 3 point Simpson's rule |
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86 c = (a + b) / 2; |
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87 fa = feval (f, a, varargin{:}); |
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88 fc = feval (f, c, varargin{:}); |
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89 fb = feval (f, b, varargin{:}); |
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90 nfun = 3; |
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91 |
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92 ## If have edge singularities, move edge point by eps*(b-a) as |
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93 ## discussed in Shampine paper used to implement quadgk |
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94 if (any (isinf (fa(:)))) |
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95 fa = feval (f, a + myeps * (b-a), varargin{:}); |
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96 endif |
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97 if (any (isinf (fb(:)))) |
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98 fb = feval (f, b - myeps * (b-a), varargin{:}); |
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99 endif |
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100 |
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101 h = (b - a); |
8507 | 102 q = (b - a) / 6 * (fa + 4 * fc + fb); |
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103 |
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104 [q, nfun, hmin] = simpsonstp (f, a, b, c, fa, fb, fc, q, nfun, abs (h), |
10549 | 105 tol, trace, varargin{:}); |
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106 |
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107 if (nfun > 10000) |
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109 elseif (any (isnan (q)(:) | isinf (q)(:))) |
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111 elseif (hmin < (b - a) * myeps) |
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113 endif |
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114 endfunction |
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115 |
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116 function [q, nfun, hmin] = simpsonstp (f, a, b, c, fa, fb, fc, q0, |
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117 nfun, hmin, tol, trace, varargin) |
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118 if (nfun > 10000) |
8507 | 119 q = q0; |
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120 else |
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121 d = (a + c) / 2; |
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122 e = (c + b) / 2; |
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123 fd = feval (f, d, varargin{:}); |
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124 fe = feval (f, e, varargin{:}); |
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125 nfun += 2; |
8507 | 126 q1 = (c - a) / 6 * (fa + 4 * fd + fc); |
127 q2 = (b - c) / 6 * (fc + 4 * fe + fb); | |
128 q = q1 + q2; | |
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129 |
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130 if (abs(a - c) < hmin) |
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131 hmin = abs (a - c); |
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132 endif |
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133 |
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134 if (trace) |
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135 disp ([nfun, a, b-a, q]); |
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136 endif |
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137 |
8507 | 138 ## Force at least one adpative step. |
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139 ## Not vectorizing q-q0 in the norm provides a more rigid criterion for |
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140 ## matrix-valued functions. |
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141 if (nfun == 5 || norm (q - q0, Inf) > tol) |
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142 [q1, nfun, hmin] = simpsonstp (f, a, c, d, fa, fc, fd, q1, nfun, hmin, |
10549 | 143 tol, trace, varargin{:}); |
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144 [q2, nfun, hmin] = simpsonstp (f, c, b, e, fc, fb, fe, q2, nfun, hmin, |
10549 | 145 tol, trace, varargin{:}); |
8507 | 146 q = q1 + q2; |
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147 endif |
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148 endif |
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149 endfunction |
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150 |
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151 |
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152 %!assert (quadv (@sin, 0, 2 * pi), 0, 1e-5) |
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153 %!assert (quadv (@sin, 0, pi), 2, 1e-5) |
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154 |
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155 %% Handles weak singularities at the edge |
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156 %!assert (quadv (@(x) 1 ./ sqrt(x), 0, 1), 2, 1e-5) |
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157 |
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158 %% Handles vector-valued functions |
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159 %!assert (quadv (@(x) [(sin (x)), (sin (2 * x))], 0, pi), [2, 0], 1e-5) |
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160 |
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161 %% Handles matrix-valued functions |
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162 %!assert (quadv (@(x) [ x, x, x; x, 1./sqrt(x), x; x, x, x ], 0, 1 ), [0.5, 0.5, 0.5; 0.5, 2, 0.5; 0.5, 0.5, 0.5], 1e-5) |
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163 |