% Test script for ao/confint
% 
% L Ferraioli 20-03-09
% 
% $Id: test_ao_confint.m,v 1.4 2011/04/29 14:03:08 luigi Exp $

%% params

fs = 1; % Hz

%% Set the model

d = [1 -1.1 0.5];
h11 = miir([1 -0.5],d,fs);
h12 = miir([0 -0.5],d,fs);
h21 = miir([0 0.4],d,fs);
h22 = miir([1 -0.6],d,fs);

%% Theoretical sectra

f = logspace(-5,log10(0.5),300);
f = f.';

plresp = plist('f',f);

rh11 = resp(h11,plresp);
rh12 = resp(h12,plresp);
rh21 = resp(h21,plresp);
rh22 = resp(h22,plresp);

% psd11
G11 = rh11.y.*conj(rh11.y) + rh12.y.*conj(rh12.y);
G11 = ao(plist('xvals', f, 'yvals', G11, 'fs', fs, 'type', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G11.setName;

% psd 22
G22 = rh21.y.*conj(rh21.y) + rh22.y.*conj(rh22.y);
G22 = ao(plist('xvals', f, 'yvals', G22, 'fs', fs, 'type', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G22.setName;

% cpsd
G12 = conj(rh11.y).*rh21.y + conj(rh12.y).*rh22.y;
G12 = ao(plist('xvals', f, 'yvals', G12, 'fs', fs, 'type', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G12.setName;

% mscohere
sK12 = (G12.y.*conj(G12.y))./(G11.y.*G22.y);
sK12 = ao(plist('xvals', f, 'yvals', sK12, 'fs', fs, 'type', 'fsdata'));
sK12.setName;

%% Noise generation

w1 = ao(plist('tsfcn','randn(size(t))','fs',1,'nsecs',1e5,'yunits','m'));
w2 = ao(plist('tsfcn','randn(size(t))','fs',1,'nsecs',1e5,'yunits','m'));

x11 = filter(w1,h11);
x12 = filter(w2,h12);
x21 = filter(w1,h21);
x22 = filter(w2,h22);

x1 = x11 + x12;
x2 = x21 + x22;

%% mslcohere

sk12log = lcohere(x1,x2,plist('type','MS'));
if numel(sk12log)>1
  sk12log = sk12log(1,2);
end

% iplot(sK12,sk12log,plist('Yscales',{'All','linear'}))

out = confint(sk12log,plist('method','mslcohere'));
lc = out.getObjectAtIndex(1);
uc = out.getObjectAtIndex(2);
var = out.getObjectAtIndex(3);

iplot(sK12,sk12log,lc,uc,plist('Yscales',{'All','linear'}))

dof = getdof(sk12log,plist('method','mslcohere'));

%% shaded plot

x = lc.data.x;
y1 = lc.data.y;
y2 = uc.data.y;
mod = sK12;

figure
y = [y1 (y2-y1)]; % y1 and y2 are columns
ha = area(x, y);
set(ha(1), 'FaceColor', 'none') % this makes the bottom area invisible
set(ha(2), 'FaceColor', 'r')
set(ha, 'LineStyle', 'none')
grid on

% plot the line edges
hold on 
hb = plot(x, y1, 'LineWidth', 1, 'Color', 'r');
hc = plot(x, y2, 'LineWidth', 1, 'Color', 'r');
hd = plot(mod.data.x, mod.data.y);
hf = plot(sk12log.data.x,sk12log.data.y,'Color', 'g');

set(gca,'xscale','log','yscale','lin');
% set(gca,'Layer','top')
ylabel('Magnitude Squared Coherence');
xlabel('Frequency [Hz]');
legend([hd hf ha(2)],{'Model MSC','Sample MSC','95% Conf. level'});

%% lpsd

g11lpsd = lpsd(x1);

% iplot(2.*G11,g11lpsd)

outlpsd = confint(g11lpsd,plist('method','lpsd'));
lclpsd = outlpsd.getObjectAtIndex(1);
uclpsd = outlpsd.getObjectAtIndex(2);
varlpsd = outlpsd.getObjectAtIndex(3);

iplot(2.*G11,g11lpsd,lclpsd,uclpsd)

doflpsd = getdof(g11lpsd,plist('method','lpsd'));

%% shaded plot

x = lclpsd.data.x;
y1 = lclpsd.data.y;
y2 = uclpsd.data.y;
mod = 2.*G11;

figure
y = [y1 (y2-y1)]; % y1 and y2 are columns
ha = area(x, y);
set(ha(1), 'FaceColor', 'none') % this makes the bottom area invisible
set(ha(2), 'FaceColor', 'r')
set(ha, 'LineStyle', 'none')
grid on

% plot the line edges
hold on 
hb = plot(x, y1, 'LineWidth', 1, 'Color', 'r');
hc = plot(x, y2, 'LineWidth', 1, 'Color', 'r');
hd = plot(mod.data.x, mod.data.y);
hf = plot(g11lpsd.data.x,g11lpsd.data.y,'Color', 'g');

set(gca,'xscale','log','yscale','log');
% set(gca,'Layer','top')
ylabel('Power Spectral Density [m^{2} / Hz]');
xlabel('Frequency [Hz]');
legend([hd hf ha(2)],{'Model Spectrum','Sample Spectrum','95% Conf. level'});

%% mscohere

sk12lin = cohere(x1,x2,plist('Nfft',1e3,'type','MS'));
if numel(sk12lin)>1
  sk12lin = sk12lin(1,2);
end

iplot(sK12,sk12lin,plist('Yscales',{'All','linear'}))

outlin = confint(sk12lin,plist('method','mscohere'));
lclin = outlin.getObjectAtIndex(1);
uclin = outlin.getObjectAtIndex(2);
varlin = outlin.getObjectAtIndex(3);

iplot(sK12,sk12lin,lclin,uclin,plist('Yscales',{'All','linear'}))

doflin = getdof(sk12lin,plist('method','mscohere'));

%% shaded plot

x = lclin.data.x;
y1 = lclin.data.y;
y2 = uclin.data.y;
mod = sK12;

figure
y = [y1 (y2-y1)]; % y1 and y2 are columns
ha = area(x, y);
set(ha(1), 'FaceColor', 'none') % this makes the bottom area invisible
set(ha(2), 'FaceColor', 'r')
set(ha, 'LineStyle', 'none')
grid on

% plot the line edges
hold on 
hb = plot(x, y1, 'LineWidth', 1, 'Color', 'r');
hc = plot(x, y2, 'LineWidth', 1, 'Color', 'r');
hd = plot(mod.data.x, mod.data.y);
hf = plot(sk12lin.data.x,sk12lin.data.y,'Color', 'g');

set(gca,'xscale','log','yscale','lin');
% set(gca,'Layer','top')
ylabel('Magnitude Squared Coherence');
xlabel('Frequency [Hz]');
legend([hd hf ha(2)],{'Model MSC','Sample MSC','95% Conf. level'});

%% psd

g11psd = psd(x1,plist('Nfft',1e4));

iplot(2.*G11,g11psd)

outpsd = confint(g11psd,plist('method','psd'));
lcpsd = outpsd.getObjectAtIndex(1);
ucpsd = outpsd.getObjectAtIndex(2);
varpsd = outpsd.getObjectAtIndex(3);

iplot(2.*G11,g11psd,lcpsd,ucpsd)

dofpsd = getdof(g11psd,plist('method','psd'));

%% shaded plot

x = lcpsd.data.x;
y1 = lcpsd.data.y;
y2 = ucpsd.data.y;
mod = 2.*G11;

figure
y = [y1 (y2-y1)]; % y1 and y2 are columns
ha = area(x, y);
set(ha(1), 'FaceColor', 'none') % this makes the bottom area invisible
set(ha(2), 'FaceColor', 'r')
set(ha, 'LineStyle', 'none')
grid on

% plot the line edges
hold on 
hb = plot(x, y1, 'LineWidth', 1, 'Color', 'r');
hc = plot(x, y2, 'LineWidth', 1, 'Color', 'r');
hd = plot(mod.data.x, mod.data.y);
hf = plot(g11psd.data.x,g11psd.data.y,'Color', 'g');

set(gca,'xscale','log','yscale','log');
% set(gca,'Layer','top')
ylabel('Power Spectral Density [m^{2} / Hz]');
xlabel('Frequency [Hz]');
legend([hd hf ha(2)],{'Model Spectrum','Sample Spectrum','95% Conf. level'});

%% Shaded plot 2

x = [lcpsd.data.x; flipud(lcpsd.data.x)];
y = [ucpsd.data.y; flipud(lcpsd.data.y)];
mod = 2.*G11;

figure
ha = fill(x,y,'r');
set(ha,'EdgeColor','r');

grid on
hold on

hd = plot(mod.data.x, mod.data.y);
hf = plot(g11psd.data.x,g11psd.data.y,'Color','g');

set(gca,'xscale','log','yscale','log');
% set(gca,'Layer','top')
ylabel('Power Spectral Density [m^{2} / Hz]');
xlabel('Frequency [Hz]');
legend([hd hf ha],{'Model Spectrum','Sample Spectrum','95% Conf. level'});

%% Test it is working also with processed data

g11psd = psd(x1,plist('Nfft',1e4));

g11psd.setName('psd');

plsp = plist('samples',[5 numel(g11psd.x)]);
g11psds = split(g11psd,plsp);

outpsd = confint(g11psds,plist('method','psd'));
lcpsd = outpsd.getObjectAtIndex(1);
ucpsd = outpsd.getObjectAtIndex(2);
varpsd = outpsd.getObjectAtIndex(3);

iplot(2.*G11,g11psds,lcpsd,ucpsd)

dofpsd = getdof(g11psd,plist('method','psd'));