% TEST_AO_LSCOV tests the lscov method of the AO class.
%
% M Hueller 19-03-10
%
% $Id: test_ao_lscov.m,v 1.7 2010/03/19 11:25:36 mauro Exp $
%
% function test_ao_lscov()

%% 1) Determine the coefficients of a linear combination of noises:
%
% Make some data
fs    = 10;
nsecs = 10;
B1 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
B2 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
B3 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
n  = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'm'));
c = [ao(1,plist('yunits','m/T')) ao(2,plist('yunits','m/T')) ao(3,plist('yunits','m T^-1'))];
y = c(1)*B1 + c(2)*B2 + c(3)*B3 + n;
y.simplifyYunits;
% Get a fit for c
p_s = lscov(B1, B2, B3, y);
% do linear combination: using lincom
yfit1 = lincom(B1, B2, B3, p_s);
yfit1.simplifyYunits;
% do linear combination: using eval
yfit2 = p_s.eval(B1, B2, B3);

% Plot (compare data with fit)
iplot(y, yfit1, yfit2, plist('Linestyles', {'-','--'}))

%% 2) Determine the coefficients of a linear combination of noises:
%
% Make some data
fs    = 10;
nsecs = 10;
x1 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'T'));
x2 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'm'));
x3 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'C'));
n  = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', nsecs, 'yunits', 'm'));
c = [ao(1,plist('yunits','m/T')) ao(2,plist('yunits','m/m')) ao(3,plist('yunits','m C^-1'))];
y = c(1)*x1 + c(2)*x2 + c(3)*x3 + n;
y.simplifyYunits;
% Get a fit for c
p_m = lscov(x1, x2, x3, y);
% do linear combination: using lincom
yfit1 = lincom(x1, x2, x3, p_m);
% do linear combination: using eval
pl_split = plist('times', [1 5]);
yfit2 = p_m.eval(plist('Xdata', {split(x1, pl_split), split(x2, pl_split), split(x3, pl_split)}));
% Plot (compare data with fit)
iplot(y, yfit1, yfit2, plist('Linestyles', {'-','--'}))