188 lines
4.6 KiB
Matlab
188 lines
4.6 KiB
Matlab
function retval = corr(x, y) % --*-- Unitary tests --*--
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%@info:
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%! @deftypefn {Function File} {} corr (@var{x})
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%! @deftypefnx {Function File} {} corr (@var{x}, @var{y})
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%! Compute matrix of correlation coefficients.
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%! @anchor{corr}
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%!
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%! If each row of @var{x} and @var{y} is an observation and each column is
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%! a variable, then the @w{(@var{i}, @var{j})-th} entry of
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%! @code{corr (@var{x}, @var{y})} is the correlation between the
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%! @var{i}-th variable in @var{x} and the @var{j}-th variable in @var{y}.
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%! @tex
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%! $$
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%! {\rm corr}(x,y) = {{\rm cov}(x,y) \over {\rm std}(x) {\rm std}(y)}
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%! $$
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%! @end tex
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%! @ifnottex
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%!
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%! @example
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%! corr (x,y) = cov (x,y) / (std (x) * std (y))
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%! @end example
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%!
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%! @end ifnottex
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%! If called with one argument, compute @code{corr (@var{x}, @var{x})},
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%! the correlation between the columns of @var{x}.
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%! @end deftypefn
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%@eod:
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%
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% Notes: - the original Octave code has been rewritten to avoid calling cov, since
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% there is a long-standing incompatiblity between Matlab's cov and Octave's cov
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% (see https://savannah.gnu.org/bugs/?40751)
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% - For compatibility with Matlab, the correlation of a constant
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% is defined as NaN, not 1
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%
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% Adapted for Matlab (R) from GNU Octave 4.0.1
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% Original files: statistics\base\corr.m, statistics\base\cov.m, and packages\stk-2.3.4\misc\mole\corr\corr.m
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% Original authors: Kurt Hornik <hornik@wu-wien.ac.at> and Julien Bect <julien.bect@supelec.fr>
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% Copyright (C) 1993-1996 Kurt Hornik
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% Copyright (C) 1996-2015 John W. Eaton
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% Copyright (C) 2013-2015 Julien Bect
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% Copyright (C) 2016-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if (nargin < 1 || nargin > 2)
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error('corr needs to be called with 1 or 2 input arguments')
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end
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% Input validation
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if (nargin==1 && ~(isnumeric (x) || islogical (x))) || ...
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(nargin==2 && ~(isnumeric (x) || islogical (x) || isnumeric (y) || islogical (y)))
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error ('corr: X and Y must be numeric matrices or vectors');
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end
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if (nargin==1 && ~ismatrix(x)) || (nargin==2 && (~ismatrix(y) || ~ismatrix(x)))
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error ('corr: X and Y must be 2-D matrices or vectors');
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end
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if (nargin == 2)
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if size(y,1)~=size(x,1)
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error('corr: X and Y must have the same length')
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end
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end
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% Special case, correlation with scalar is NaN in Matlab
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if isscalar(x)
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if nargin==1
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retval = NaN;
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else
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retval = NaN(size(y));
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end
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return
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end
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if nargin==2 && isscalar(y)
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retval = NaN(size(x'));
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return
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end
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n = size (x, 1);
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x = x - repmat(mean(x),n,1); %demean
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sx = std(x,1); %standard deviation
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sx(sx==0)=NaN; %take care of constant vectors
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if (nargin == 2)
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y = y - repmat (mean (y), n, 1);
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sy = std (y, 1);
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sy (sy == 0) = nan;
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else
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y = x;
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sy = sx;
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end
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c = x'*y;
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s = sx'*sy;
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retval = c./(n * s);
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end
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%@test:1
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%$ x = rand (10);
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%$ cc1 = corr(x);
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%$ cc2 = corr(x, x);
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%$ t(1) = dassert(size(cc1),[10, 10]);
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%$ t(2) = dassert(size (cc2),[10, 10]);
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%$ t(3) = dassert(cc1, cc2, sqrt (eps));
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%$ T = all(t);
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%@eof:1
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%@test:2
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%$ x = [1:3]';
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%$ y = [3:-1:1]';
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%$ t = zeros(3,1);
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%$ t(1) = dassert(corr(x, y), -1, 5*eps);
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%$ t(2) = dassert(corr(x, flipud (y)), 1, 5*eps);
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%$ t(3) = dassert(corr([x, y]), [1 -1; -1 1], 5*eps);
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%$ T = all(t);
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%@eof:2
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%@test:3
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%$ if ~isoctave()
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%$ t = zeros(3,1);
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%$ t(1) = dassert(corr(5), NaN);
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%$ t(2) = dassert(corr([1 2 3],5),NaN(3,1));
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%$ t(3) = dassert(corr(5,[1 2 3]),NaN(1,3));
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%$ else
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%$ t = 1;
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%$ end
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%$ T = all(t);
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%@eof:3
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%@test:4
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%$ t = zeros(6,1);
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%$ try
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%$ corr()
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%$ t(1) = false;
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%$ catch
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%$ t(1) = true;
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%$ end
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%$ try
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%$ corr(1, 2, 3)
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%$ t(2) = false;
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%$ catch
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%$ t(2) = true;
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%$ end
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%$ try
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%$ corr([1; 2], ['A', 'B'])
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%$ t(3) = false;
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%$ catch
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%$ t(3) = true;
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%$ end
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%$ try
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%$ corr([1; 2], ['A', 'B'])
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%$ t(4) = false;
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%$ catch
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%$ t(4) = true;
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%$ end
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%$ try
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%$ corr(ones (2,2,2))
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%$ t(5) = false;
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%$ catch
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%$ t(5) = true;
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%$ end
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%$ try
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%$ corr(ones (2,2), ones (2,2,2))
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%$ t(6) = false;
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%$ catch
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%$ t(6) = true;
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%$ end
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%$ T = all(t);
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%@eof:4 |