/usr/share/octave/packages/statistics-1.2.3/princomp.m is in octave-statistics 1.2.3-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | ## Copyright (C) 2013 Fernando Damian Nieuwveldt <fdnieuwveldt@gmail.com>
##
## This program 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.
##
## This program is distributed in the hope that it will be useful,
## 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
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{COEFF}]} = princomp(@var{X})
## @deftypefnx {Function File} {[@var{COEFF},@var{SCORE}]} = princomp(@var{X})
## @deftypefnx {Function File} {[@var{COEFF},@var{SCORE},@var{latent}]} = princomp(@var{X})
## @deftypefnx {Function File} {[@var{COEFF},@var{SCORE},@var{latent},@var{tsquare}]} = princomp(@var{X})
## @deftypefnx {Function File} {[...]} = princomp(@var{X},'econ')
## @itemize @bullet
## @item
## princomp performs principal component analysis on a NxP data matrix X
## @item
## @var{COEFF} : returns the principal component coefficients
## @item
## @var{SCORE} : returns the principal component scores, the representation of X
## in the principal component space
## @item
## @var{LATENT} : returns the principal component variances, i.e., the
## eigenvalues of the covariance matrix X.
## @item
## @var{TSQUARE} : returns Hotelling's T-squared Statistic for each observation in X
## @item
## [...] = princomp(X,'econ') returns only the elements of latent that are not
## necessarily zero, and the corresponding columns of COEFF and SCORE, that is,
## when n <= p, only the first n-1. This can be significantly faster when p is
## much larger than n. In this case the svd will be applied on the transpose of
## the data matrix X
##
## @end itemize
##
## @subheading References
##
## @enumerate
## @item
## Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002
##
## @end enumerate
## @end deftypefn
function [COEFF,SCORE,latent,tsquare] = princomp(X,varargin)
if (nargin < 1 || nargin > 2)
print_usage ();
endif
if (nargin == 2 && ! strcmpi (varargin{:}, "econ"))
error ("princomp: if a second input argument is present, it must be the string 'econ'");
endif
[nobs nvars] = size(X);
# Center the columns to mean zero
Xcentered = bsxfun(@minus,X,mean(X));
# Check if there are more variables then observations
if nvars <= nobs
[U,S,COEFF] = svd(Xcentered);
else
# Calculate the svd on the transpose matrix, much faster
if (nargin == 2 && strcmpi ( varargin{:} , "econ"))
[COEFF,S,V] = svd(Xcentered' , 'econ');
else
[COEFF,S,V] = svd(Xcentered');
endif
endif
if nargout > 1
# Get the Scores
SCORE = Xcentered*COEFF;
# Get the rank of the SCORE matrix
r = rank(SCORE);
# Only use the first r columns, pad rest with zeros if economy != 'econ'
SCORE = SCORE(:,1:r) ;
if !(nargin == 2 && strcmpi ( varargin{:} , "econ"))
SCORE = [SCORE, zeros(nobs , nvars-r)];
else
COEFF = COEFF(: , 1:r);
endif
endif
if nargout > 2
# This is the same as the eigenvalues of the covariance matrix of X
latent = (diag(S'*S)/(size(Xcentered,1)-1))(1:r);
if !(nargin == 2 && strcmpi ( varargin{:} , "econ"))
latent= [latent;zeros(nvars-r,1)];
endif
endif
if nargout > 3
# Calculate the Hotelling T-Square statistic for the observations
tsquare = sumsq(zscore(SCORE(:,1:r)),2);
endif
endfunction
%!shared COEFF,SCORE,latent,tsquare,m,x
%!test
%! x=[1,2,3;2,1,3]';
%! [COEFF,SCORE,latent,tsquare] = princomp(x);
%! m=[sqrt(2),sqrt(2);sqrt(2),-sqrt(2);-2*sqrt(2),0]/2;
%! m(:,1) = m(:,1)*sign(COEFF(1,1));
%! m(:,2) = m(:,2)*sign(COEFF(1,2));
%!assert(COEFF,m(1:2,:),10*eps);
%!assert(SCORE,-m,10*eps);
%!assert(latent,[1.5;.5],10*eps);
%!assert(tsquare,[4;4;4]/3,10*eps);
%!test
%! x=x';
%! [COEFF,SCORE,latent,tsquare] = princomp(x);
%! m=[sqrt(2),sqrt(2),0;-sqrt(2),sqrt(2),0;0,0,2]/2;
%! m(:,1) = m(:,1)*sign(COEFF(1,1));
%! m(:,2) = m(:,2)*sign(COEFF(1,2));
%! m(:,3) = m(:,3)*sign(COEFF(3,3));
%!assert(COEFF,m,10*eps);
%!assert(SCORE(:,1),-m(1:2,1),10*eps);
%!assert(SCORE(:,2:3),zeros(2),10*eps);
%!assert(latent,[1;0;0],10*eps);
%!xtest
%! assert(tsquare,[0.5;0.5],10*eps)
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