hmm based speech recognition

function h=error_ellipse(varargin) % ERROR_ELLIPSE - plot an error ellipse, or ellipsoid, defining confidence region % ERROR_ELLIPSE(C22) - Given a 2x2 covariance matrix, plot the % associated error ellipse, at the origin. It returns a graphics handle % of the ellipse that was drawn. % % ERROR_ELLIPSE(C33) - Given a 3x3 covariance matrix, plot the % associated error ellipsoid, at the origin, as well as its projections % onto the three axes. Returns a vector of 4 graphics handles, for the % three ellipses (in the X-Y, Y-Z, and Z-X planes, respectively) and for % the ellipsoid. % % ERROR_ELLIPSE(C,MU) - Plot the ellipse, or ellipsoid, centered at MU, % a vector whose length should match that of C (which is 2x2 or 3x3). % % ERROR_ELLIPSE(...,'Property1',Value1,'Name2',Value2,...) sets the % values of specified properties, including: % 'C' - Alternate method of specifying the covariance matrix % 'mu' - Alternate method of specifying the ellipse (-oid) center % 'conf' - A value betwen 0 and 1 specifying the confidence interval. % the default is 0.5 which is the 50% error ellipse. % 'scale' - Allow the plot the be scaled to difference units. % 'style' - A plotting style used to format ellipses. % 'clip' - specifies a clipping radius. Portions of the ellipse, -oid, % outside the radius will not be shown. % % NOTES: C must be positive definite for this function to work properly. default_properties = struct(... 'C', [], ... % The covaraince matrix (required) 'mu', [], ... % Center of ellipse (optional) 'conf', 0.5, ... % Percent confidence/100 'scale', 1, ... % Scale factor, e.g. 1e-3 to plot m as km 'style', '', ... % Plot style 'clip', inf); % Clipping radius if length(varargin) >= 1 & isnumeric(varargin{1}) default_properties.C = varargin{1}; varargin(1) = []; end if length(varargin) >= 1 & isnumeric(varargin{1}) default_properties.mu = varargin{1}; varargin(1) = []; end if length(varargin) >= 1 & isnumeric(varargin{1}) default_properties.conf = varargin{1}; varargin(1) = []; end if length(varargin) >= 1 & isnumeric(varargin{1}) default_properties.scale = varargin{1}; varargin(1) = []; end if length(varargin) >= 1 & ~ischar(varargin{1}) error('Invalid parameter/value pair arguments.') end prop = getopt(default_properties, varargin{:}); C = prop.C; if isempty(prop.mu) mu = zeros(length(C),1); else mu = prop.mu; end conf = prop.conf; scale = prop.scale; style = prop.style; if conf <= 0 | conf >= 1 error('conf parameter must be in range 0 to 1, exclusive') end [r,c] = size(C); if r ~= c | (r ~= 2 & r ~= 3) error(['Don''t know what to do with ',num2str(r),'x',num2str(c),' matrix']) end x0=mu(1); y0=mu(2); % Compute quantile for the desired percentile k = sqrt(qchisq(conf,r)); % r is the number of dimensions (degrees of freedom) hold_state = get(gca,'nextplot'); if r==3 & c==3 z0=mu(3); % Make the matrix has positive eigenvalues - else it's not a valid covariance matrix! if any(eig(C) <=0) error('The covariance matrix must be positive definite (it has non-positive eigenvalues)') end % C is 3x3; extract the 2x2 matricies, and plot the associated error % ellipses. They are drawn in space, around the ellipsoid; it may be % preferable to draw them on the axes. Cxy = C(1:2,1:2); Cyz = C(2:3,2:3); Czx = C([3 1],[3 1]); [x,y,z] = getpoints(Cxy,prop.clip); h1=plot3(x0+k*x,y0+k*y,z0+k*z,prop.style);hold on [y,z,x] = getpoints(Cyz,prop.clip); h2=plot3(x0+k*x,y0+k*y,z0+k*z,prop.style);hold on [z,x,y] = getpoints(Czx,prop.clip); h3=plot3(x0+k*x,y0+k*y,z0+k*z,prop.style);hold on [eigvec,eigval] = eig(C); [X,Y,Z] = ellipsoid(0,0,0,1,1,1); XYZ = [X(:),Y(:),Z(:)]*sqrt(eigval)*eigvec'; X(:) = scale*(k*XYZ(:,1)+x0); Y(:) = scale*(k*XYZ(:,2)+y0); Z(:) = scale*(k*XYZ(:,3)+z0); h4=surf(X,Y,Z); colormap gray alpha(0.3) camlight if nargout h=[h1 h2 h3 h4]; end elseif r==2 & c==2 % Make the matrix has positive eigenvalues - else it's not a valid covariance matrix! if any(eig(C) <=0) error('The covariance matrix must be positive definite (it has non-positive eigenvalues)') end [x,y,z] = getpoints(C,prop.clip); h1=plot(scale*(x0+k*x),scale*(y0+k*y),prop.style); set(h1,'zdata',z+1) if nargout h=h1; end else error('C (covaraince matrix) must be specified as a 2x2 or 3x3 matrix)') end %axis equal set(gca,'nextplot',hold_state); %--------------------------------------------------------------- % getpoints - Generate x and y points that define an ellipse, given a 2x2 % covariance matrix, C. z, if requested, is all zeros with same shape as % x and y. function [x,y,z] = getpoints(C,clipping_radius) n=100; % Number of points around ellipse p=0:pi/n:2*pi; % angles around a circle [eigvec,eigval] = eig(C); % Compute eigen-stuff xy = [cos(p'),sin(p')] * sqrt(eigval) * eigvec'; % Transformation x = xy(:,1); y = xy(:,2); z = zeros(size(x)); % Clip data to a bounding radius if nargin >= 2 r = sqrt(sum(xy.^2,2)); % Euclidian distance (distance from center) x(r > clipping_radius) = nan; y(r > clipping_radius) = nan; z(r > clipping_radius) = nan; end %--------------------------------------------------------------- function x=qchisq(P,n) % QCHISQ(P,N) - quantile of the chi-square distribution. if nargin<2 n=1; end s0 = P==0; s1 = P==1; s = P>0 & P<1; x = 0.5*ones(size(P)); x(s0) = -inf; x(s1) = inf; x(~(s0|s1|s))=nan; for ii=1:14 dx = -(pchisq(x(s),n)-P(s))./dchisq(x(s),n); x(s) = x(s)+dx; if all(abs(dx) < 1e-6) break; end end %--------------------------------------------------------------- function F=pchisq(x,n) % PCHISQ(X,N) - Probability function of the chi-square distribution. if nargin<2 n=1; end F=zeros(size(x)); if rem(n,2) == 0 s = x>0; k = 0; for jj = 0:n/2-1; k = k + (x(s)/2).^jj/factorial(jj); end F(s) = 1-exp(-x(s)/2).*k; else for ii=1:numel(x) if x(ii) > 0 F(ii) = quadl(@dchisq,0,x(ii),1e-6,0,n); else F(ii) = 0; end end end %--------------------------------------------------------------- function f=dchisq(x,n) % DCHISQ(X,N) - Density function of the chi-square distribution. if nargin<2 n=1; end f=zeros(size(x)); s = x>=0; f(s) = x(s).^(n/2-1).*exp(-x(s)/2)./(2^(n/2)*gamma(n/2)); %--------------------------------------------------------------- function properties = getopt(properties,varargin) %GETOPT - Process paired optional arguments as 'prop1',val1,'prop2',val2,... % % getopt(properties,varargin) returns a modified properties structure, % given an initial properties structure, and a list of paired arguments. % Each argumnet pair should be of the form property_name,val where % property_name is the name of one of the field in properties, and val is % the value to be assigned to that structure field. % % No validation of the values is performed. % % EXAMPLE: % properties = struct('zoom',1.0,'aspect',1.0,'gamma',1.0,'file',[],'bg',[]); % properties = getopt(properties,'aspect',0.76,'file','mydata.dat') % would return: % properties = % zoom: 1 % aspect: 0.7600 % gamma: 1 % file: 'mydata.dat' % bg: [] % % Typical usage in a function: % properties = getopt(properties,varargin{:}) % Process the properties (optional input arguments) prop_names = fieldnames(properties); TargetField = []; for ii=1:length(varargin) arg = varargin{ii}; if isempty(TargetField) if ~ischar(arg) error('Propery names must be character strings'); end f = find(strcmp(prop_names, arg)); if length(f) == 0 error('%s ',['invalid property ''',arg,'''; must be