www.pudn.com > dspproject.rar > pcamat.m, change:2003-12-15,size:12075b

```function [E, D] = pcamat(vectors, firstEig, lastEig, s_interactive, ...
s_verbose);
%PCAMAT - Calculates the pca for data
%
% [E, D] = pcamat(vectors, firstEig, lastEig, ...
%                 interactive, verbose);
%
% Calculates the PCA matrices for given data (row) vectors. Returns
% the eigenvector (E) and diagonal eigenvalue (D) matrices containing the
% selected subspaces. Dimensionality reduction is controlled with
% the parameters 'firstEig' and 'lastEig' - but it can also be done
% interactively by setting parameter 'interactive' to 'on' or 'gui'.
%
% ARGUMENTS
%
% vectors       Data in row vectors.
% firstEig      Index of the largest eigenvalue to keep.
%               Default is 1.
% lastEig       Index of the smallest eigenvalue to keep.
%               Default is equal to dimension of vectors.
% interactive   Specify eigenvalues to keep interactively. Note that if
%               you set 'interactive' to 'on' or 'gui' then the values
%               for 'firstEig' and 'lastEig' will be ignored, but they
%               still have to be entered. If the value is 'gui' then the
%               same graphical user interface as in FASTICAG will be
%               used. Default is 'off'.
% verbose       Default is 'on'.
%
%
% EXAMPLE
%       [E, D] = pcamat(vectors);
%
% Note
%       The eigenvalues and eigenvectors returned by PCAMAT are not sorted.
%
% This function is needed by FASTICA and FASTICAG

% For historical reasons this version does not sort the eigenvalues or
% the eigen vectors in any ways. Therefore neither does the FASTICA or
% FASTICAG. Generally it seams that the components returned from
% whitening is almost in reversed order. (That means, they usually are,
% but sometime they are not - depends on the EIG-command of matlab.)

% @(#)\$Id: pcamat.m,v 1.5 2003/12/15 18:24:32 jarmo Exp \$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Default values:
if nargin < 5, s_verbose = 'on'; end
if nargin < 4, s_interactive = 'off'; end
if nargin < 3, lastEig = size(vectors, 1); end
if nargin < 2, firstEig = 1; end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Check the optional parameters;
switch lower(s_verbose)
case 'on'
b_verbose = 1;
case 'off'
b_verbose = 0;
otherwise
error(sprintf('Illegal value [ %s ] for parameter: ''verbose''\n', s_verbose));
end

switch lower(s_interactive)
case 'on'
b_interactive = 1;
case 'off'
b_interactive = 0;
case 'gui'
b_interactive = 2;
otherwise
error(sprintf('Illegal value [ %s ] for parameter: ''interactive''\n', ...
s_interactive));
end

oldDimension = size (vectors, 1);
if ~(b_interactive)
if lastEig < 1 | lastEig > oldDimension
error(sprintf('Illegal value [ %d ] for parameter: ''lastEig''\n', lastEig));
end
if firstEig < 1 | firstEig > lastEig
error(sprintf('Illegal value [ %d ] for parameter: ''firstEig''\n', firstEig));
end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculate PCA

% Calculate the covariance matrix.
if b_verbose, fprintf ('Calculating covariance...\n'); end
covarianceMatrix = cov(vectors', 1);

% Calculate the eigenvalues and eigenvectors of covariance
% matrix.
[E, D] = eig (covarianceMatrix);

% The rank is determined from the eigenvalues - and not directly by
% using the function rank - because function rank uses svd, which
% in some cases gives a higher dimensionality than what can be used
% with eig later on (eig then gives negative eigenvalues).
rankTolerance = 1e-7;
maxLastEig = sum (diag (D) > rankTolerance);
if maxLastEig == 0,
fprintf (['Eigenvalues of the covariance matrix are' ...
' all smaller than tolerance [ %g ].\n' ...
' nonzero values.\nIf the values are very small,' ...
' try rescaling the data matrix.\n'], rankTolerance);
error ('Unable to continue, aborting.');
end

% Sort the eigenvalues - decending.
eigenvalues = flipud(sort(diag(D)));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Interactive part - command-line
if b_interactive == 1

% Show the eigenvalues to the user
hndl_win=figure;
bar(eigenvalues);
title('Eigenvalues');

% ask the range from the user...
% ... and keep on asking until the range is valid :-)
areValuesOK=0;
while areValuesOK == 0
firstEig = input('The index of the largest eigenvalue to keep? (1) ');
lastEig = input(['The index of the smallest eigenvalue to keep? (' ...
int2str(oldDimension) ') ']);
% Check the new values...
% if they are empty then use default values
if isempty(firstEig), firstEig = 1;end
if isempty(lastEig), lastEig = oldDimension;end
% Check that the entered values are within the range
areValuesOK = 1;
if lastEig < 1 | lastEig > oldDimension
fprintf('Illegal number for the last eigenvalue.\n');
areValuesOK = 0;
end
if firstEig < 1 | firstEig > lastEig
fprintf('Illegal number for the first eigenvalue.\n');
areValuesOK = 0;
end
end
% close the window
close(hndl_win);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Interactive part - GUI
if b_interactive == 2

% Show the eigenvalues to the user
hndl_win = figure('Color',[0.8 0.8 0.8], ...
'PaperType','a4letter', ...
'Units', 'normalized', ...
'Name', 'FastICA: Reduce dimension', ...
'NumberTitle','off', ...
'Tag', 'f_eig');
h_frame = uicontrol('Parent', hndl_win, ...
'BackgroundColor',[0.701961 0.701961 0.701961], ...
'Units', 'normalized', ...
'Position',[0.13 0.05 0.775 0.17], ...
'Style','frame', ...
'Tag','f_frame');

b = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'BackgroundColor',[0.701961 0.701961 0.701961], ...
'HorizontalAlignment','left', ...
'Position',[0.142415 0.0949436 0.712077 0.108507], ...
'String','Give the indices of the largest and smallest eigenvalues of the covariance matrix to be included in the reduced data.', ...
'Style','text', ...
'Tag','StaticText1');
e_first = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'Callback',[ ...
'f=round(str2num(get(gcbo, ''String'')));' ...
'if (f < 1), f=1; end;' ...
'l=str2num(get(findobj(''Tag'',''e_last''), ''String''));' ...
'if (f > l), f=l; end;' ...
'set(gcbo, ''String'', int2str(f));' ...
], ...
'BackgroundColor',[1 1 1], ...
'HorizontalAlignment','right', ...
'Position',[0.284831 0.0678168 0.12207 0.0542535], ...
'Style','edit', ...
'String', '1', ...
'Tag','e_first');
b = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'BackgroundColor',[0.701961 0.701961 0.701961], ...
'HorizontalAlignment','left', ...
'Position',[0.142415 0.0678168 0.12207 0.0542535], ...
'String','Range from', ...
'Style','text', ...
'Tag','StaticText2');
e_last = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'Callback',[ ...
'l=round(str2num(get(gcbo, ''String'')));' ...
'lmax = get(gcbo, ''UserData'');' ...
'if (l > lmax), l=lmax; fprintf([''The selected value was too large, or the selected eigenvalues were close to zero\n'']); end;' ...
'f=str2num(get(findobj(''Tag'',''e_first''), ''String''));' ...
'if (l < f), l=f; end;' ...
'set(gcbo, ''String'', int2str(l));' ...
], ...
'BackgroundColor',[1 1 1], ...
'HorizontalAlignment','right', ...
'Position',[0.467936 0.0678168 0.12207 0.0542535], ...
'Style','edit', ...
'String', int2str(maxLastEig), ...
'UserData', maxLastEig, ...
'Tag','e_last');
% in the first version oldDimension was used instead of
% maxLastEig, but since the program would automatically
% drop the eigenvalues afte maxLastEig...
b = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'BackgroundColor',[0.701961 0.701961 0.701961], ...
'HorizontalAlignment','left', ...
'Position',[0.427246 0.0678168 0.0406901 0.0542535], ...
'String','to', ...
'Style','text', ...
'Tag','StaticText3');
b = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'Callback','uiresume(gcbf)', ...
'Position',[0.630697 0.0678168 0.12207 0.0542535], ...
'String','OK', ...
'Tag','Pushbutton1');
b = uicontrol('Parent',hndl_win, ...
'Units','normalized', ...
'Callback',[ ...
'gui_help(''pcamat'');' ...
], ...
'Position',[0.767008 0.0678168 0.12207 0.0542535], ...
'String','Help', ...
'Tag','Pushbutton2');

h_axes = axes('Position' ,[0.13 0.3 0.775 0.6]);
set(hndl_win, 'currentaxes',h_axes);
bar(eigenvalues);
title('Eigenvalues');

uiwait(hndl_win);
firstEig = str2num(get(e_first, 'String'));
lastEig = str2num(get(e_last, 'String'));

% close the window
close(hndl_win);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% See if the user has reduced the dimension enought

if lastEig > maxLastEig
lastEig = maxLastEig;
if b_verbose
fprintf('Dimension reduced to %d due to the singularity of covariance matrix\n',...
lastEig-firstEig+1);
end
else
% Reduce the dimensionality of the problem.
if b_verbose
if oldDimension == (lastEig - firstEig + 1)
fprintf ('Dimension not reduced.\n');
else
fprintf ('Reducing dimension...\n');
end
end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Drop the smaller eigenvalues
if lastEig < oldDimension
lowerLimitValue = (eigenvalues(lastEig) + eigenvalues(lastEig + 1)) / 2;
else
lowerLimitValue = eigenvalues(oldDimension) - 1;
end

lowerColumns = diag(D) > lowerLimitValue;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Drop the larger eigenvalues
if firstEig > 1
higherLimitValue = (eigenvalues(firstEig - 1) + eigenvalues(firstEig)) / 2;
else
higherLimitValue = eigenvalues(1) + 1;
end
higherColumns = diag(D) < higherLimitValue;

% Combine the results from above
selectedColumns = lowerColumns & higherColumns;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% print some info for the user
if b_verbose
fprintf ('Selected [ %d ] dimensions.\n', sum (selectedColumns));
end
if sum (selectedColumns) ~= (lastEig - firstEig + 1),
error ('Selected a wrong number of dimensions.');
end

if b_verbose
fprintf ('Smallest remaining (non-zero) eigenvalue [ %g ]\n', eigenvalues(lastEig));
fprintf ('Largest remaining (non-zero) eigenvalue [ %g ]\n', eigenvalues(firstEig));
fprintf ('Sum of removed eigenvalues [ %g ]\n', sum(diag(D) .* ...
(~selectedColumns)));
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Select the colums which correspond to the desired range
% of eigenvalues.
E = selcol(E, selectedColumns);
D = selcol(selcol(D, selectedColumns)', selectedColumns);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if b_verbose
sumAll=sum(eigenvalues);
sumUsed=sum(diag(D));
retained = (sumUsed / sumAll) * 100;
fprintf('[ %g ] %% of (non-zero) eigenvalues retained.\n', retained);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
% Selects the columns of the matrix that marked by one in the given vector.
% The maskVector is a column vector.

% 15.3.1998

if size(maskVector, 1) ~= size(oldMatrix, 2),
error ('The mask vector and matrix are of uncompatible size.');
end

numTaken = 0;

for i = 1 : size (maskVector, 1),