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spm_plot_ci.m
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function spm_plot_ci(E,C,x,j,s)
% Plot mean and conditional confidence intervals
% FORMAT spm_plot_ci(E,C,x,j,s)
% E - expectation (structure or array)
% C - variance or covariance (structure or array)
% x - domain
% j - rows of E to plot
% s - string to specify plot type:e.g. '--r' or 'exp'
%
% If E is a row vector with two elements, confidence regions will be
% plotted; otherwise, bar charts with confidence intervals are provided
%__________________________________________________________________________
% Copyright (C) 2008-2015 Wellcome Trust Centre for Neuroimaging
% Karl Friston
% $Id: spm_plot_ci.m 7305 2018-05-07 13:35:06Z karl $
% get axis
%--------------------------------------------------------------------------
ax = gca;
% confidence region (CR) plotting
%--------------------------------------------------------------------------
if size(E,1) == 1 && size(E,2) == 2
E = E';
CR = true;
else
CR = false;
end
% unpack expectations into a matrix
%--------------------------------------------------------------------------
if isstruct(E), E = spm_vec(E); end
if iscell(E), E = spm_vec(E); end
if ~exist('x','var'), x = 1:size(E,2); end
if ~exist('j','var'), j = 1:size(E,1); end
if ~exist('s','var'), s = ''; end
if isempty(x), x = 1:size(E,2); end
if isempty(j), j = 1:size(E,1); end
% order and length of sequence
%--------------------------------------------------------------------------
O = E;
E = E(j,:);
[n,N] = size(E);
% unpack conditional covariances
%--------------------------------------------------------------------------
ci = spm_invNcdf(1 - 0.05); % confidence interval
gr = 0.9; % grey level
if iscell(C)
% try cell array of covariances (from spm_DEM amd spm_LAP)
%----------------------------------------------------------------------
try
for i = 1:N
c(:,i) = ci*sqrt(diag(C{i}(j,j)));
end
catch
% try cell array of variances
%------------------------------------------------------------------
c = ci*sqrt(spm_unvec(spm_vec(C),O));
c = c(j,:);
end
elseif isstruct(C)
% try structure of variances
%----------------------------------------------------------------------
c = ci*sqrt(spm_unvec(spm_vec(C),O));
c = c(j,:);
elseif isnumeric(C)
% try matrix of variances
%----------------------------------------------------------------------
if all(size(C) == size(O))
c = ci*sqrt(C(j,:));
elseif all(size(C') == size(O))
c = ci*sqrt(C(:,j));
else
% try covariance matrix
%------------------------------------------------------------------
C = diag(C);
c = ci*sqrt(C(j,:));
end
end
% set plot parameters
%--------------------------------------------------------------------------
switch lower(get(ax,'NextPlot'))
case 'add'
col = [1 1/4 1/4];
width = .9;
otherwise
col = [1 3/4 3/4];
width = .8;
end
% plot elliptical confidence region
%--------------------------------------------------------------------------
if CR
[x,y] = ellipsoid(E(1),E(2),1,c(1),c(2),0,32);
fill(x(16,:)',y(16,:)',[1 1 1]*gr,'EdgeColor',[1 1 1]*.5,'Parent',ax);
hold(ax,'on');
plot(ax,E(1),E(2),'.','MarkerSize',16);
hold(ax,'off'); drawnow
return
end
% plot bar chart
%--------------------------------------------------------------------------
if N >= 8
% time-series plot
%======================================================================
if strcmpi(s,'exp')
fill([x fliplr(x)],exp([full(E + c) fliplr(full(E - c))]),...
[.95 .95 1],'EdgeColor',[.8 .8 1],'Parent',ax);
hold(ax,'on');
plot(x,exp(E));
else
fill([x fliplr(x)],[full(E + c) fliplr(full(E - c))],...
[.95 .95 1],'EdgeColor',[.8 .8 1],'Parent',ax);
hold(ax,'on');
plot(ax,x,E,s);
end
else
% bar
%======================================================================
if N == 1
if strcmpi(s,'exp')
% conditional means
%--------------------------------------------------------------
bar(ax,exp(E),width,'Edgecolor',[1 1 1]/2,'Facecolor',[1 1 1]*.8);
hold(ax,'on');
% conditional variances
%--------------------------------------------------------------
for k = 1:n
line([k k],exp([-1 1]*c(k) + E(k)),'LineWidth',4,'Color',col,'Parent',ax);
end
else
if n > 1
% conditional means
%----------------------------------------------------------
bar(ax,E,width,'Edgecolor',[1 1 1]/2,'Facecolor',[1 1 1]*.8);
hold(ax,'on');
else
% conditional means
%----------------------------------------------------------
bar(ax,E,'Edgecolor',[1 1 1]/2,'Facecolor',[1 1 1]*.8);
hold(ax,'on');
end
% conditional variances
%--------------------------------------------------------------
for k = 1:n
line([k k],[-1 1]*c(k) + E(k),'LineWidth',4,'Color',col,'Parent',ax);
end
end
box(ax,'off');
set(ax,'XLim',[0 n + 1]);
else
if strcmpi(s,'exp')
% conditional means (exponential)
%------------------------------------------------------------------
h = bar(ax,exp(E)'); hold(ax,'on');
% conditional variances
%------------------------------------------------------------------
for m = 1:n
x = mean(get(get(h(m),'Children'),'Xdata'));
for k = 1:N
line([x(k) x(k)],exp([-1 1]*c(m,k) + E(m,k)),'LineWidth',1,'Color',col,'Parent',ax);
end
end
else
% conditional means
%------------------------------------------------------------------
h = bar(ax,E); hold(ax,'on');
% conditional variances
%------------------------------------------------------------------
for m = 1:N
x = mean(get(get(h(m),'Children'),'Xdata'));
for k = 1:n
line([x(k) x(k)],[-1 1]*c(k,m) + E(k,m),'LineWidth',4,'Color',col,'Parent',ax);
end
end
end
end
end
hold(ax,'off');
drawnow