from pylab import *

"""
Original example with two phase transations, but they do not interfere
with the posterior.
"""
seed(123)

t = linspace(0., 100., 1001)
y = sin(2.*pi*t/30.) + sin(2.*pi*t/2. + 1.)
sig = 1.
Y = y + sig*randn(y.size)

data = empty((t.size, 3))
data[:,0], data[:,1], data[:,2] = t, Y, sig

savetxt('fake_data.txt', data)

plot(t, y, 'r')
plot(t, Y, 'bo')
show()


"""
This one has a phase transition at temperature = 1 :-D
"""

t = linspace(0., 100., 1001)
y = sin(2.*pi*t/30.) + 0.3*sin(2.*pi*t/2. + 1.)
sig = 1.
Y = y + sig*randn(y.size)

data = empty((t.size, 3))
data[:,0], data[:,1], data[:,2] = t, Y, sig

savetxt('fake_data.txt', data)

plot(t, y, 'r', linewidth=2, label='Noise-free signal')
plot(t, Y, 'bo', alpha=0.4, label='Noisy measurements')
ylim([-5., 5.])
legend(numpoints=1)
xlabel('Time')
ylabel('Signal')
show()


from pylab import *

"""
Original example with two phase transations, but they do not interfere
with the posterior.
"""
seed(123)

t = linspace(0., 100., 1001)
y = sin(2.*pi*t/30.) + sin(2.*pi*t/2. + 1.)
sig = 1.
Y = y + sig*randn(y.size)

data = empty((t.size, 3))
data[:,0], data[:,1], data[:,2] = t, Y, sig

savetxt('fake_data.txt', data)

plot(t, y, 'r')
plot(t, Y, 'bo')
show()


"""
This one has a phase transition at temperature = 1 :-D
"""

t = linspace(0., 100., 1001)
y = sin(2.*pi*t/30.) + 0.3*sin(2.*pi*t/2. + 1.)
sig = 1.
Y = y + sig*randn(y.size)

data = empty((t.size, 3))
data[:,0], data[:,1], data[:,2] = t, Y, sig

savetxt('fake_data.txt', data)

plot(t, y, 'r', linewidth=2, label='Noise-free signal')
plot(t, Y, 'bo', alpha=0.4, label='Noisy measurements')
ylim([-5., 5.])
legend(numpoints=1)
xlabel('Time')
ylabel('Signal')
savefig('sinewave_data.pdf', bbox_inches='tight')
show()


Save figure