Mercurial > octave-libtiff
view scripts/statistics/base/cov.m @ 20174:d9341b422488 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed statistics/ and @ftp/ in scripts directory.
* scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m,
scripts/@ftp/dir.m, scripts/@ftp/ftp.m, scripts/@ftp/mget.m,
scripts/@ftp/mput.m, scripts/statistics/base/center.m,
scripts/statistics/base/cloglog.m, scripts/statistics/base/cov.m,
scripts/statistics/base/gls.m, scripts/statistics/base/histc.m,
scripts/statistics/base/iqr.m, scripts/statistics/base/kendall.m,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/logit.m,
scripts/statistics/base/lscov.m, scripts/statistics/base/mahalanobis.m,
scripts/statistics/base/mean.m, scripts/statistics/base/meansq.m,
scripts/statistics/base/median.m, scripts/statistics/base/mode.m,
scripts/statistics/base/moment.m, scripts/statistics/base/ols.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/prctile.m,
scripts/statistics/base/probit.m, scripts/statistics/base/range.m,
scripts/statistics/base/ranks.m, scripts/statistics/base/run_count.m,
scripts/statistics/base/runlength.m, scripts/statistics/base/skewness.m,
scripts/statistics/base/spearman.m, scripts/statistics/base/statistics.m,
scripts/statistics/base/std.m, scripts/statistics/base/table.m,
scripts/statistics/base/var.m, scripts/statistics/base/zscore.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_inv.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_inv.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normcdf.m,
scripts/statistics/distributions/norminv.m,
scripts/statistics/distributions/normpdf.m,
scripts/statistics/distributions/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidinv.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifcdf.m,
scripts/statistics/distributions/unifinv.m,
scripts/statistics/distributions/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 10 May 2015 16:07:41 -0700 |
parents | 9fc020886ae9 |
children | 516bb87ea72e |
line wrap: on
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## Copyright (C) 1995-2015 Kurt Hornik ## ## 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} {} cov (@var{x}) ## @deftypefnx {Function File} {} cov (@var{x}, @var{opt}) ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}) ## @deftypefnx {Function File} {} cov (@var{x}, @var{y}, @var{opt}) ## Compute the covariance matrix. ## ## If each row of @var{x} and @var{y} is an observation, and each column is ## a variable, then the @w{(@var{i}, @var{j})-th} entry of ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th ## variable in @var{x} and the @var{j}-th variable in @var{y}. ## @tex ## $$ ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) ## $$ ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$. ## @end tex ## @ifnottex ## ## @example ## cov (x) = 1/N-1 * SUM_i (x(i) - mean(x)) * (y(i) - mean(y)) ## @end example ## ## @end ifnottex ## ## If called with one argument, compute @code{cov (@var{x}, @var{x})}, the ## covariance between the columns of @var{x}. ## ## The argument @var{opt} determines the type of normalization to use. ## Valid values are ## ## @table @asis ## @item 0: ## normalize with @math{N-1}, provides the best unbiased estimator of the ## covariance [default] ## ## @item 1: ## normalize with @math{N}, this provides the second moment around the mean ## @end table ## ## Compatibility Note:: Octave always computes the covariance matrix. ## For two inputs, however, @sc{matlab} will calculate ## @code{cov (@var{x}(:), @var{y}(:))} whenever the number of elements in ## @var{x} and @var{y} are equal. This will result in a scalar rather than ## a matrix output. Code relying on this odd definition will need to be ## changed when running in Octave. ## @seealso{corr} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Compute covariances function c = cov (x, y = [], opt = 0) if (nargin < 1 || nargin > 3) print_usage (); endif if ( ! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y))) error ("cov: X and Y must be numeric matrices or vectors"); endif if (ndims (x) != 2 || ndims (y) != 2) error ("cov: X and Y must be 2-D matrices or vectors"); endif if (nargin == 2 && isscalar (y)) opt = y; endif if (opt != 0 && opt != 1) error ("cov: normalization OPT must be 0 or 1"); endif ## Special case, scalar has zero covariance if (isscalar (x)) if (isa (x, "single")) c = single (0); else c = 0; endif return; endif if (isrow (x)) x = x.'; endif n = rows (x); if (nargin == 1 || isscalar (y)) x = center (x, 1); c = conj (x' * x / (n - 1 + opt)); else if (isrow (y)) y = y.'; endif if (rows (y) != n) error ("cov: X and Y must have the same number of observations"); endif x = center (x, 1); y = center (y, 1); c = conj (x' * y / (n - 1 + opt)); endif endfunction %!test %! x = rand (10); %! cx1 = cov (x); %! cx2 = cov (x, x); %! assert (size (cx1) == [10, 10] && size (cx2) == [10, 10]); %! assert (cx1, cx2, 1e1*eps); %!test %! x = [1:3]'; %! y = [3:-1:1]'; %! assert (cov (x, y), -1, 5*eps); %! assert (cov (x, flipud (y)), 1, 5*eps); %! assert (cov ([x, y]), [1 -1; -1 1], 5*eps); %!test %! x = single ([1:3]'); %! y = single ([3:-1:1]'); %! assert (cov (x, y), single (-1), 5*eps); %! assert (cov (x, flipud (y)), single (1), 5*eps); %! assert (cov ([x, y]), single ([1 -1; -1 1]), 5*eps); %!test %! x = [1:5]; %! c = cov (x); %! assert (isscalar (c)); %! assert (c, 2.5); %!assert (cov (5), 0) %!assert (cov (single (5)), single (0)) %!test %! x = [1:5]; %! c = cov (x, 0); %! assert (c, 2.5); %! c = cov (x, 1); %! assert (c, 2); ## Test input validation %!error cov () %!error cov (1, 2, 3, 4) %!error cov ([1; 2], ["A", "B"]) %!error cov (ones (2,2,2)) %!error cov (ones (2,2), ones (2,2,2)) %!error cov (1, 3) %!error cov (ones (2,2), ones (3,2))