Mercurial > octave-antonio
annotate scripts/statistics/base/cov.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 | 34af9f9ff98b |
children | 5d3a684236b0 |
rev | line source |
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1 ## Copyright (C) 1995-2012 Kurt Hornik |
3426 | 2 ## |
3922 | 3 ## This file is part of Octave. |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
3426 | 9 ## |
3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
3426 | 13 ## General Public License for more details. |
14 ## | |
3200 | 15 ## You should have received a copy of the GNU General Public License |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
3200 | 18 |
3367 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} cov (@var{x}) |
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21 ## @deftypefnx {Function File} {} cov (@var{x}, @var{opt}) |
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22 ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}) |
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23 ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}, @var{opt}) |
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24 ## Compute the covariance matrix. |
6754 | 25 ## |
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26 ## If each row of @var{x} and @var{y} is an observation, and each column is |
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27 ## a variable, then the @w{(@var{i}, @var{j})-th} entry of |
3367 | 28 ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th |
6754 | 29 ## variable in @var{x} and the @var{j}-th variable in @var{y}. |
30 ## @tex | |
31 ## $$ | |
32 ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) | |
33 ## $$ | |
34 ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$. | |
35 ## @end tex | |
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36 ## @ifnottex |
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37 ## |
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38 ## @example |
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39 ## cov (x) = 1/N-1 * SUM_i (x(i) - mean(x)) * (y(i) - mean(y)) |
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40 ## @end example |
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41 ## |
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42 ## @end ifnottex |
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43 ## |
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44 ## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the |
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45 ## covariance between the columns of @var{x}. |
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46 ## |
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47 ## The argument @var{opt} determines the type of normalization to use. |
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48 ## Valid values are |
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49 ## |
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50 ## @table @asis |
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51 ## @item 0: |
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52 ## normalize with @math{N-1}, provides the best unbiased estimator of the |
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53 ## covariance [default] |
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54 ## |
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55 ## @item 1: |
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56 ## normalize with @math{N}, this provides the second moment around the mean |
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57 ## @end table |
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58 ## @seealso{corr} |
3367 | 59 ## @end deftypefn |
3200 | 60 |
5428 | 61 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 62 ## Description: Compute covariances |
3200 | 63 |
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64 function c = cov (x, y = [], opt = 0) |
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65 |
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66 if (nargin < 1 || nargin > 3) |
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67 print_usage (); |
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68 endif |
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69 |
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70 if ( ! (isnumeric (x) || islogical (x)) |
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71 || ! (isnumeric (y) || islogical (y))) |
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72 error ("cov: X and Y must be numeric matrices or vectors"); |
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73 endif |
3200 | 74 |
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75 if (ndims (x) != 2 || ndims (y) != 2) |
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76 error ("cov: X and Y must be 2-D matrices or vectors"); |
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77 endif |
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78 |
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79 if (nargin == 2 && isscalar (y)) |
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80 opt = y; |
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81 endif |
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82 |
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83 if (opt != 0 && opt != 1) |
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84 error ("cov: normalization OPT must be 0 or 1"); |
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85 endif |
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86 |
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87 ## Special case, scalar has zero covariance |
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88 if (isscalar (x)) |
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89 if (isa (x, "single")) |
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90 c = single (0); |
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91 else |
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92 c = 0; |
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93 endif |
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94 return; |
3200 | 95 endif |
96 | |
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97 if (isrow (x)) |
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98 x = x.'; |
3200 | 99 endif |
100 n = rows (x); | |
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101 |
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102 if (nargin == 1 || isscalar (y)) |
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103 x = center (x, 1); |
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104 c = conj (x' * x / (n - 1 + opt)); |
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105 else |
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106 if (isrow (y)) |
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107 y = y.'; |
3200 | 108 endif |
109 if (rows (y) != n) | |
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110 error ("cov: X and Y must have the same number of observations"); |
3200 | 111 endif |
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112 x = center (x, 1); |
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113 y = center (y, 1); |
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114 c = conj (x' * y / (n - 1 + opt)); |
3200 | 115 endif |
116 | |
117 endfunction | |
7411 | 118 |
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119 |
7411 | 120 %!test |
121 %! x = rand (10); | |
122 %! cx1 = cov (x); | |
123 %! cx2 = cov (x, x); | |
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124 %! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]); |
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125 %! assert (cx1, cx2, 1e1*eps); |
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126 |
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127 %!test |
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128 %! x = [1:3]'; |
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129 %! y = [3:-1:1]'; |
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130 %! assert (cov (x, y), -1, 5*eps); |
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131 %! assert (cov (x, flipud (y)), 1, 5*eps); |
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132 %! assert (cov ([x, y]), [1 -1; -1 1], 5*eps); |
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133 |
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134 %!test |
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135 %! x = single ([1:3]'); |
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136 %! y = single ([3:-1:1]'); |
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137 %! assert (cov (x, y), single (-1), 5*eps); |
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138 %! assert (cov (x, flipud (y)), single (1), 5*eps); |
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139 %! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps); |
7411 | 140 |
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141 %!test |
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142 %! x = [1:5]; |
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143 %! c = cov (x); |
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144 %! assert (isscalar (c)); |
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145 %! assert (c, 2.5); |
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146 |
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147 %!assert(cov (5), 0) |
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148 %!assert(cov (single(5)), single(0)) |
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149 |
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150 %!test |
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151 %! x = [1:5]; |
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152 %! c = cov (x, 0); |
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153 %! assert(c, 2.5); |
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154 %! c = cov (x, 1); |
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155 %! assert(c, 2); |
7411 | 156 |
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157 %% Test input validation |
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158 %!error cov () |
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159 %!error cov (1, 2, 3, 4) |
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160 %!error cov ([1; 2], ["A", "B"]) |
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161 %!error cov (ones (2,2,2)) |
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162 %!error cov (ones (2,2), ones (2,2,2)) |
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163 %!error cov (1, 3) |
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164 %!error cov (ones (2,2), ones (3,2)) |
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165 |