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from scipy import stats
import numpy as np
import zipline
import pytz
from datetime import datetime

from pymc.distributions.timeseries import *
from theano.tensor import repeat

from scipy import optimize


# set every possibility to be equally possible
x_coin = np.linspace(0, 1, 101)


with model_randomwalk:
    # First optimize random walk
    start = pm.find_MAP(vars=[alpha, beta], fmin=optimize.fmin_l_bfgs_b)
    
    # Sample
    step = pm.NUTS(scaling=start)
    trace_rw = pm.sample(2000, step, start=start, progressbar=False)

fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, xlabel='Price GDX in \$', ylabel='Price GLD in \$', 
            title='Posterior predictive regression lines')

colors = np.linspace(0.1, 1, len(prices))
colors_sc = np.linspace(0.1, 1, len(trace_rw[-500::10]['alpha'].T))
mymap = plt.get_cmap('winter')
mymap_sc = plt.get_cmap('winter')

xi = np.linspace(prices.GDX.min(), prices.GDX.max(), 50)
for i, (alpha, beta) in enumerate(zip(trace_rw[-500::10]['alpha'].T, trace_rw[-500::10]['beta'].T)):
    for a, b in zip(alpha, beta):
        ax.plot(xi, a + b*xi, alpha=.05, lw=1, c=mymap_sc(colors_sc[i]))
        
sc = ax.scatter(prices.GDX, prices.GLD, label='data', cmap=mymap, c=colors)
cb = plt.colorbar(sc)
cb.ax.set_yticklabels([str(p.date()) for p in prices[::len(prices)//10].index]);
fig.savefig('ppc5.png')