Mercurial > octave
view scripts/statistics/corrcoef.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2016-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{r} =} corrcoef (@var{x}) ## @deftypefnx {} {@var{r} =} corrcoef (@var{x}, @var{y}) ## @deftypefnx {} {@var{r} =} corrcoef (@dots{}, @var{param}, @var{value}, @dots{}) ## @deftypefnx {} {[@var{r}, @var{p}] =} corrcoef (@dots{}) ## @deftypefnx {} {[@var{r}, @var{p}, @var{lci}, @var{hci}] =} corrcoef (@dots{}) ## Compute a matrix of correlation coefficients. ## ## @var{x} is an array where each column contains a variable and each row is ## an observation. ## ## If a second input @var{y} (of the same size as @var{x}) is given then ## calculate the correlation coefficients between @var{x} and @var{y}. ## ## @var{param}, @var{value} are optional pairs of parameters and values which ## modify the calculation. Valid options are: ## ## @table @asis ## @item @qcode{"alpha"} ## Confidence level used for the bounds of the confidence interval, @var{lci} ## and @var{hci}. Default is 0.05, i.e., 95% confidence interval. ## ## @item @qcode{"rows"} ## Determine processing of NaN values. Acceptable values are @qcode{"all"}, ## @qcode{"complete"}, and @qcode{"pairwise"}. Default is @qcode{"all"}. ## With @qcode{"complete"}, only the rows without NaN values are considered. ## With @qcode{"pairwise"}, the selection of NaN-free rows is made for each ## pair of variables. ## @end table ## ## Output @var{r} is a matrix of Pearson's product moment correlation ## coefficients for each pair of variables. ## ## Output @var{p} is a matrix of pair-wise p-values testing for the null ## hypothesis of a correlation coefficient of zero. ## ## Outputs @var{lci} and @var{hci} are matrices containing, respectively, the ## lower and higher bounds of the 95% confidence interval of each correlation ## coefficient. ## @seealso{corr, cov} ## @end deftypefn ## FIXME: It would be good to add a definition of the calculation method ## for a Pearson product moment correlation to the documentation. function [r, p, lci, hci] = corrcoef (x, varargin) if (nargin == 0) print_usage (); endif alpha = 0.05; rows = "all"; if (nargin > 1) ## Check for matrix argument y if (isnumeric (varargin{1})) y = varargin{1}; nx = numel (x); ny = numel (y); if (nx > 0 && ny > 0 && nx != ny) error ("corrcoef: X and Y must be the same size"); endif x = [x(:), y(:)]; varargin(1) = []; endif ## Check for Parameter/Value arguments for i = 1:2:numel (varargin) if (! ischar (varargin{i})) error ("corrcoef: parameter %d must be a string", i); endif parameter = varargin{i}; if (i+1 > numel (varargin)) error ('corrcoef: parameter "%s" missing value', parameter); endif value = varargin{i+1}; switch (tolower (parameter)) case "alpha" if (isnumeric (value) && isscalar (value) && value >= 0 && value <= 1) alpha = value; else error ('corrcoef: "alpha" must be a scalar between 0 and 1'); endif case "rows" if (! ischar (value)) error ('corrcoef: "rows" value must be a string'); endif value = tolower (value); switch (value) case {"all", "complete", "pairwise"} rows = value; otherwise error ('corrcoef: "rows" must be "all", "complete", or "pairwise"'); endswitch otherwise error ('corrcoef: Unknown option "%s"', parameter); endswitch endfor endif if (strcmp (rows, "complete")) x(any (isnan (x), 2), :) = []; endif if (isempty (x) || isscalar (x)) r = p = lci = hci = NaN; return; endif ## Flags for calculation pairwise = strcmp (rows, "pairwise"); calc_pval = nargout > 1; if (isrow (x)) x = x(:); endif [m, n] = size (x); r = eye (n); if (calc_pval) p = eye (n); endif if (strcmp (rows, "pairwise")) mpw = m * ones (n); endif for i = 1:n if (! pairwise && any (isnan (x(:,i)))) r(i,i) = NaN; if (nargout > 1) p(i,i) = NaN; endif endif for j = i+1:n xi = x(:,i); xj = x(:,j); if (pairwise) idx = any (isnan ([xi xj]), 2); xi(idx) = xj(idx) = []; mpw(i,j) = mpw(j,i) = m - nnz (idx); endif r(i,j) = r(j,i) = corr (xi, xj); if (calc_pval) df = m - 2; stat = sqrt (df) * r(i,j) / sqrt (1 - r(i,j)^2); cdf = tcdf (stat, df); p(i,j) = p(j,i) = 2 * min (cdf, 1 - cdf); endif endfor endfor if (nargout > 2) if (pairwise) m = mpw; endif CI = sqrt (2) * erfinv (1-alpha) ./ sqrt (m-3); lci = tanh (atanh (r) - CI); hci = tanh (atanh (r) + CI); endif endfunction ## Compute cumulative distribution function for T distribution. function cdf = tcdf (x, n) if (iscomplex (x)) error ("tcdf: X must not be complex"); endif if (isa (x, "single")) cdf = zeros (size (x), "single"); else cdf = zeros (size (x)); endif k = ! isinf (x) & (n > 0); xx = x .^ 2; x_big_abs = (xx > n); ## deal with the case "abs(x) big" kk = k & x_big_abs; cdf(kk) = betainc (n ./ (n + xx(kk)), n/2, 1/2) / 2; ## deal with the case "abs(x) small" kk = k & ! x_big_abs; cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n + xx(kk)), 1/2, n/2)); k &= (x > 0); if (any (k(:))) cdf(k) = 1 - cdf(k); endif k = isnan (x) | !(n > 0); cdf(k) = NaN; k = (x == Inf) & (n > 0); cdf(k) = 1; endfunction %!test %! x = rand (5); %! r = corrcoef (x); %! assert (size (r) == [5, 5]); %!test %! x = [1, 2, 3]; %! r = corrcoef (x); %! assert (size (r) == [1, 1]); %!assert (isnan (corrcoef ([]))) %!assert (isnan (corrcoef (NaN))) %!assert (isnan (corrcoef (1))) %!test %! x = [NaN, NaN]; %! r = corrcoef (x); %! assert (size(r) == [1, 1] && isnan (r)); %!test %! x = rand (5); %! [r, p] = corrcoef (x); %! assert (size (r) == [5, 5] && size (p) == [5 5]); %! assert (diag (r), ones (5,1), eps); %!test %! x = rand (5,1); %! y = rand (5,1); %! R1 = corrcoef (x, y); %! R2 = corrcoef ([x, y]); %! assert (R1, R2); %! R3 = corrcoef (x.', y.'); %! assert (R1, R3); %!test %! x = [1;2;3]; %! y = [1;2;3]; %! r = corrcoef (x, y); %! assert (r, ones (2,2)); %!test %! x = [1;2;3]; %! y = [3;2;1]; %! r = corrcoef (x, y); %! assert (r, [1, -1; -1, 1]); %!test %! x = [1;2;3]; %! y = [1;1;1]; %! r = corrcoef (x, y); %! assert (r, [1, NaN; NaN, 1]); %!error <Invalid call> corrcoef () %!error <parameter 1 must be a string> corrcoef (1, 2, 3) %!error <parameter "alpha" missing value> corrcoef (1, 2, "alpha") %!error <"alpha" must be a scalar> corrcoef (1,2, "alpha", "1") %!error <"alpha" must be a scalar> corrcoef (1,2, "alpha", ones (2,2)) %!error <"alpha" must be a scalar between 0 and 1> corrcoef (1,2, "alpha", -1) %!error <"alpha" must be a scalar between 0 and 1> corrcoef (1,2, "alpha", 2) %!error <"rows" must be "all"...> corrcoef (1,2, "rows", "foobar") %!error <Unknown option "foobar"> corrcoef (1,2, "foobar", 1)