function spm_DEM_qH(qH,pH)

% Report on conditional estimates of hyperparameters

% FORMAT spm_DEM_qH(qH,pH)

%

% qH.h - conditional estimate of log-precision (causes)

% qH.g - conditional of log-precision (state)

% qH.V - conditional variance (causes)

% qH.W - conditional (states)

%

% qH.p - time-dependent estimates from Laplace scheme

% qH.c - time-dependent covariances

%

% pH - option true log-precisions

%__________________________________________________________________________

% Karl Friston

% Copyright (C) 2005-2022 Wellcome Centre for Human Neuroimaging

% unpack conditional covariances

%--------------------------------------------------------------------------

try, qH = qH.qH; end

try, pH = pH.pH; end

% [Re]ML estimates - h

%==========================================================================

ci = spm_invNcdf(1 - 0.05);

h = spm_vec(qH.h);

c = spm_vec(qH.V);

c = sqrt(c)*ci;

subplot(2,2,1)

bar(full(h),'Edgecolor',[1 1 1]/2,'Facecolor',[1 1 1]*.8)

title({'log-precision';'noise and causes'},'FontSize',16);

axis square

set(gca,'XLim',[0 length(c) 1])

hlabel = {};

for i = 1:length(qH.h)

for j = 1:length(qH.h{i})

hlabel{end 1} = sprintf('h:level %i',i);

end

end

set(gca,'XTickLabel',hlabel)

% conditional covariances

%--------------------------------------------------------------------------

for i = 1:length(c)

line([i i],[-1 1]*c(i) h(i),'LineWidth',4,'Color','r');

end

% prior or true means

%--------------------------------------------------------------------------

try

p = spm_vec(pH.h);

for i = 1:length(h)

line([-1 1]/2 i,[0 0] p(i),'LineWidth',4,'Color','k');

end

end

% [Re]ML estimates - g

%==========================================================================

h = spm_vec(qH.g);

c = spm_vec(qH.W);

c = sqrt(c)*spm_invNcdf(1 - 0.05);

if h

subplot(2,2,2)

bar(full(h),'Edgecolor',[1 1 1]/2,'Facecolor',[1 1 1]*.8)

title({'log-precision';'states'},'FontSize',16);

axis square

set(gca,'XLim',[0 length(c) 1])

% conditional covariances

%----------------------------------------------------------------------

for i = 1:length(c)

line([i i],[-1 1]*c(i) h(i),'LineWidth',4,'Color','r');

end

% prior or true means

%----------------------------------------------------------------------

try

p = spm_vec(pH.g);

for i = 1:length(h)

line([-1 1]/2 i,[0 0] p(i),'LineWidth',4,'Color','k');

end

end

glabel = {};

for i = 1:length(qH.h)

for j = 1:length(qH.h{i})

glabel{end 1} = sprintf('g:level %i',i);

end

end

set(gca,'XTickLabel',glabel)

else

glabel = {};

end

% conditional covariance and correlations

%--------------------------------------------------------------------------

subplot(2,2,3)

imagesc(qH.C)

title({'covariances among','hyperparameters'},'FontSize',16)

axis square

set(gca,'YTickLabel',{hlabel{:} glabel{:}},'YTick',[1:length(qH.C)])

% plot evolution of hyperparameters if supplied

%==========================================================================

subplot(2,2,4)

try

% confidence interval and expectations

%----------------------------------------------------------------------

ns = length(qH.p);

t = 1:ns;

for i = 1:ns

v(:,i) = sqrt(diag(qH.c{i}));

end

c = ci*v;

h = spm_cat(qH.p);

% plot

%----------------------------------------------------------------------

hold on

nh = size(h,1);

for i = 1:nh

fill([t fliplr(t)],[(h(i,:) c(i,:)) fliplr(h(i,:) - c(i,:))],...

[1 1 1]*.8,'EdgeColor',[1 1 1]/2)

plot(t,h(i,:))

end

set(gca,'XLim',[1 ns])

title({'dynamics of','hyperparameters'},'FontSize',16)

xlabel('time')

axis square

hold off

catch

imagesc(spm_cov2corr(qH.C))

title({'correlations among','hyperparameters'},'FontSize',16)

axis square

end