#!/usr/bin/env python
# coding: utf-8

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
import numpy as np
import matplotlib.pyplot as plt
import pymc as pm


# Sample data

# In[2]:


x = (-5, -4.9, -4.8, -4.7, -4.6, -4.5, -4.4, -4.3, -4.2, -4.1, -4, 
-3.9, -3.8, -3.7, -3.6, -3.5, -3.4, -3.3, -3.2, -3.1, -3, -2.9, 
-2.8, -2.7, -2.6, -2.5, -2.4, -2.3, -2.2, -2.1, -2, -1.9, -1.8, 
-1.7, -1.6, -1.5, -1.4, -1.3, -1.2, -1.1, -1, -0.9, -0.8, -0.7, 
-0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3, 0.4, 0.5, 
0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 
1.9, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3, 3.1, 
3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1, 4.2, 4.3, 4.4, 
4.5, 4.6, 4.7, 4.8, 4.9, 5)

y = (1.04442478194401, 0.948306088493654, 0.357037759697332, 0.492336514646604, 
0.520651364364746, 0.112629866592809, 0.470995468454158, -0.168442254267804, 
0.0720344402575861, -0.188108980535916, -0.0160163306512027, 
-0.0388792158617705, -0.0600673630622568, 0.113568725264636, 
0.447160403837629, 0.664421188556779, -0.139510743820276, 0.458823971660986, 
0.141214654640904, -0.286957663528091, -0.466537724021695, -0.308185884317105, 
-1.57664872694079, -1.44463024170082, -1.51206214603847, -1.49393593601901, 
-2.02292464164487, -1.57047488853653, -1.22973445533419, -1.51502367058357, 
-1.41493587255224, -1.10140254663611, -0.591866485375275, -1.08781838696462, 
-0.800375653733931, -1.00764767602679, -0.0471028950122742, -0.536820626879737, 
-0.151688056391446, -0.176771681318393, -0.240094952335518, -1.16827876746502, 
-0.493597351974992, -0.831683011472805, -0.152347043914137, 0.0190364158178343, 
-1.09355955218051, -0.328157917911376, -0.585575679802941, -0.472837120425201, 
-0.503633622750049, -0.0124446353828312, -0.465529814250314, 
-0.101621725887347, -0.26988462590405, 0.398726664193302, 0.113805181040188, 
0.331353802465398, 0.383592361618461, 0.431647298655434, 0.580036473774238, 
0.830404669466897, 1.17919105883462, 0.871037583886711, 1.12290553424174, 
0.752564860804382, 0.76897960270623, 1.14738839410786, 0.773151715269892, 
0.700611498974798, 0.0412951045437818, 0.303526087747629, -0.139399513324585, 
-0.862987735433697, -1.23399179134008, -1.58924289116396, -1.35105117911049, 
-0.990144529089174, -1.91175364127672, -1.31836236129543, -1.65955735224704, 
-1.83516148300526, -2.03817062501248, -1.66764011409214, -0.552154350554687, 
-0.547807883952654, -0.905389222477036, -0.737156477425302, -0.40211249920415, 
0.129669958952991, 0.271142753510592, 0.176311762529962, 0.283580281859344, 
0.635808289696458, 1.69976647982837, 1.10748978734239, 0.365412229181044, 
0.788821368082444, 0.879731888124867, 1.02180766619069, 0.551526067300283
)

N = len(x)


# In[3]:


plt.plot(x, y, 'r.')


# Kernel function

# In[4]:


squared_exponential = lambda x, y, η2, ρ2: η2 * np.exp(-ρ2 * (x - y)**2)


# Parameters of kernel function

# In[5]:


eta2 = pm.HalfCauchy('eta2', 0, 5, value=1)
rho2 = pm.HalfCauchy('rho2', 0, 5, value=1)
sigma2 = pm.HalfCauchy('sigma2', 0, 5, value=1)


# Points on which to evaluate GP

# In[6]:


x_pred = np.append(x, np.linspace(-6, 6, 10))


# Covariance

# In[7]:


@pm.deterministic
def Sigma(eta2=eta2, rho2=rho2, sigma2=sigma2):
    S = np.array([[squared_exponential(xi, yi, eta2, rho2) for xi in x_pred] for yi in x_pred])
    # Add variance to 
    S[np.diag_indices_from(S)] += sigma2
    return S


# Default mean

# In[8]:


mu = np.zeros(len(x_pred))


# Use masked array to make predictions on linear mesh along with observed values

# In[9]:


y_masked = np.ma.masked_equal(np.append(y, np.zeros(10)), value=0)


# In[10]:


y_masked


# In[11]:


gp = pm.MvNormalCov('gp', mu, Sigma, value=y_masked, observed=True)


# In[12]:


M = pm.MCMC(locals())
#M.use_step_method(pm.AdaptiveMetropolis, y)


# In[13]:


M.sample(2000, 1000)


# In[14]:


pm.Matplot.summary_plot(gp)


# Plot predictions (blue points)

# In[17]:


plt.plot(x, y, 'r.')
plt.plot(np.linspace(-6, 6, 10), gp.value[-10:], 'bo')


# In[18]:


pm.Matplot.plot(rho2)


# In[19]:


pm.Matplot.plot(eta2)


# In[20]:


pm.Matplot.plot(sigma2)