import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
from scipy.stats import hypergeom
from scipy.stats import binned_statistic as binsta
from scipy.special import logsumexp
from util import *
import palettable as pal
clrx = pal.cartocolors.qualitative.Prism_10.mpl_colors
clr = tuple(x for n,x in enumerate(clrx) if n in [1,2,4,5,6])
clr2 = pal.cartocolors.sequential.agSunset_7.mpl_colors
import matplotlib.gridspec as gridspec
import matplotlib.patches as patches

import plotly.graph_objects as go
import plotly.tools as tls
from plotly.offline import plot, iplot, init_notebook_mode
from IPython.core.display import display, HTML
init_notebook_mode(connected = True)
config={'showLink': False, 'displayModeBar': False}

# CCP, the Coupon Collector's Problem
def ccp_sample(c,pool=60):
    return len(set(np.random.choice(pool,c)))

# Draw overlap
def nab_sample(s,na,nb,pool=60):
    sa = np.random.hypergeometric(s,pool-s,na)
    nab = np.random.hypergeometric(sa,pool-sa,nb)
    return nab

# Overlap between two PCRs of depth c and overlap s
def pcr_sample(c,s):
    na = ccp_sample(c)
    nb = ccp_sample(c)
    return nab_sample(s,na,nb),na,nb

# Draw na and nb samples from two populations of size pool_a and pool_b, with true overlap s
# and return empirical overlap between na and nb
# note that this is basically the same as nab_sample, but with two different size pools!
def nab_sample_unequal(s,na,nb,pool_a,pool_b):
    sa = np.random.hypergeometric(s,pool_a-s,na)
    nab = np.random.hypergeometric(sa,pool_b-sa,nb)
    return nab


def p_ccp(c, pool=60):
    p = np.zeros([c+1,pool+1])
    p[0,0] = 1;
    for row in range(1,c+1):
        for k in range(1,np.min([row+2,pool+1])):
            p[row,k] = p[row-1,k]*k/pool + p[row-1,k-1]*(1-(k-1)/pool)
    return p[-1,:]

def p_overlap(na,nb,nab,pool=60):
    p_s = np.zeros(pool+1)
    # reference: hypergeom.pmf(outcome, Total, hits, Draws, loc=0)
    for s in np.arange(pool+1):
        # p_sa is the probability that we'd get sa from the overlap (s), just in na draws of a
        p_sa = hypergeom.pmf(np.arange(pool+1),pool,s,na)
        # p_nab_given_sa is the probability of getting that nab, given sa
        p_nab_given_sa = hypergeom.pmf(nab,pool,np.arange(pool+1),nb)
        p_s[s] = np.dot(p_sa,p_nab_given_sa)
    return p_s/np.sum(p_s)

def e_overlap(na,nb,nab,pool=60):
    p_s = p_overlap(na,nb,nab,pool=pool)
    return np.dot(np.arange(pool+1),p_s)


def credible_interval(na,nb,nab,pct=90,pool=60):
    p_s = p_overlap(na,nb,nab,pool=pool)
    cdf = np.cumsum(p_s)
    ccdf = np.flipud(np.cumsum(np.flipud(p_s)))
    # adjust for fractions vs percents; put everything as a fraction
    if pct > 1:
        pct = pct/100
    cutoff = (1-pct)/2
    # get the lower bound. 
    # it's the first index at which cdf ≥ cutoff
    try:
        lower = np.where(cdf >= cutoff)[0][0]
    except IndexError:
        lower = 0
    # get the upper bound
    # it's the first index at which ccdf ≥ 0.05
    try:
        upper = np.where(ccdf >= cutoff)[0][-1]
    except IndexError:
        upper=pool
    expectation = np.dot(np.arange(pool+1),p_s)
    # Sanity and indexing check: uncomment this line to see true tail probability ≤ 0.05
    # print([cdf[lower-1],(1-ccdf[upper+1])])
    return lower,expectation,upper


def p_nab_given_c(s,c,pool=60):
    pna = p_ccp(c)
    pnb = p_ccp(c)
    nas = np.arange(1,len(pna))
    nbs = np.arange(1,len(pnb))
    p_gen = np.zeros([pool+1,pool+1,pool+1])
    for na in nas:
        p_sa = hypergeom.pmf(np.arange(pool+1),pool,s,na)
        for nb in nbs:
            pna_pnb = pna[na] * pnb[nb]
            for nab in range(0,np.minimum(na,nb)):
                p_nab_given_sa = hypergeom.pmf(nab,pool,np.arange(pool+1),nb)
                p_nab_given_s = np.dot(p_sa,p_nab_given_sa)
                p_gen[na,nb,nab] = p_nab_given_s * pna_pnb
    return p_gen

def p_shat_given_sc(s,c,shat,pool=60):
    masses = p_nab_given_c(s,c,pool=pool)
    if np.sum(masses)<0.99:
        print('Swapping to Monte Carlo')
        return p_shat_given_sc_montecarlo(s,c,shat,pool=pool)
    hist = binsta(np.ravel(shat),np.ravel(masses),statistic='sum',bins=(np.arange(pool+2)-0.5))
    return hist

def p_shat_given_sc_montecarlo(s,c,shat,pool=60,n_mc=int(1e5)):
    masses = np.zeros([pool+1,pool+1,pool+1])
    for ii in range(n_mc):
        nab,na,nb = pcr_sample(c,s)
        masses[na,nb,nab] += 1
    hist = binsta(np.ravel(shat),np.ravel(masses/n_mc),statistic='sum',bins=(np.arange(pool+2)-0.5))
    return hist

def compute_all_estimates(pool=60):
    shat = np.zeros([pool+1,pool+1,pool+1])
    for na in range(1,pool+1):
        for nb in range(1,pool+1):
            for nab in range(0,np.minimum(na+1,nb+1)):
                shat[na,nb,nab] = e_overlap(na,nb,nab,pool=pool)
    return shat

def p_overlap_unequal(na,nb,nab,pool_a,pool_b):
    # all loops are in terms of pool_a, which is assumed to be ≤ pool_b. 
    p_s = np.zeros(pool_a+1)
    # reference: hypergeom.pmf(outcome, Total, hits, Draws, loc=0)
    for s in np.arange(pool_a+1):
        # p_sa is the probability that we'd get sa from the overlap (s), just in na draws of a
        p_sa = hypergeom.pmf(np.arange(pool_a+1),pool_a,s,na)
        # p_nab_given_sa is the probability of getting that nab, given sa
        p_nab_given_sa = hypergeom.pmf(nab,pool_b,np.arange(pool_a+1),nb)
        p_s[s] = np.dot(p_sa,p_nab_given_sa)
    return p_s/np.sum(p_s)

def e_overlap_unequal(na,nb,nab,pool_a,pool_b):
    # TODO. Code expects that pool_b > pool_a...
    p_s = p_overlap_unequal(na,nb,nab,pool_a,pool_b)
    return np.dot(np.arange(pool_a+1),p_s)

# shat = compute_all_estimates(pool=60)
# np.save('shat_60.npy',shat)
shat = np.load('shat_60.npy')

pool=60
shat = np.load('shat_60.npy')
planted2 = np.zeros([6,6,pool+1])
recovered2 = np.zeros([6,6,pool+1])
lower = np.zeros([6,6,pool+1])
upper = np.zeros([6,6,pool+1])

nas = [30,40,50]
for idxa,na in enumerate(nas):
    nb = na
    idxb = idxa
    for s in np.arange(0,pool+1,1):
        planted2[idxa,idxb,s] = s
        nab = nab_sample(s,na,nb)
        lower[idxa,idxb,s], recovered2[idxa,idxb,s], upper[idxa,idxb,s] = credible_interval(na,nb,nab)
        es = e_overlap(na,nb,nab)
        recovered2[idxa,idxb,s] = es

sub = np.arange(0,pool+1,2)

z = np.zeros(60)
d = np.arange(1,60)

fig4 = go.Figure()

fig4.add_trace(go.Scatter(x = d , y = d, line = dict(width=1, dash='dash', color = 'rgb(0,0,0)'), name = 'Reference' ))

fig4.add_trace(go.Scatter(x = planted2[0,0,sub], y = recovered2[0,0,sub], 
                         mode = 'markers', 
                         name = "overlap ± cred. interval",
                         line = dict(color = 'rgb(104, 75, 163)'),
                         error_y=dict(
                                    type='data',
                                    symmetric=False,
                                    arrayminus=recovered2[0,0,sub]-lower[0,0,sub],
                                    array=upper[0,0,sub]-recovered2[0,0,sub])))

fig4.add_trace(go.Scatter(x = planted2[1,1,sub], y = recovered2[1,1,sub], mode = 'markers', 
                              name = "overlap ± cred. interval",
                              line = dict(color = 'rgb(137, 47, 163)'),
                              visible = False,
                              error_y=dict(
                                    type='data',
                                    symmetric=False,
                                    arrayminus=recovered2[1,1,sub]-lower[1,1,sub],
                                    array=upper[1,1,sub]-recovered2[1,1,sub])))

fig4.add_trace(go.Scatter(x = planted2[2,2,sub], y = recovered2[2,2,sub], mode = 'markers', 
                              name = "overlap ± cred. interval",
                              line = dict(color = 'rgb(192, 54, 157)'),
                              visible = False,
                              error_y=dict(
                                    type='data',
                                    symmetric=False,
                                    arrayminus=recovered2[2,2,sub]-lower[2,2,sub],
                                    array=upper[2,2,sub]-recovered2[2,2,sub])))

fig4.update_layout(
    updatemenus=[
        dict(
            active=0,
            buttons=list([
                dict(label="30 samples",
                     method="update",
                     args=[{"visible": [True,True, False, False]},
                           {"title": ""}]),
                dict(label="40 samples",
                     method="update",
                     args=[{"visible": [True,False, True, False]},
                           {"title": ""
                            }]),
                dict(label="50 samples",
                     method="update",
                     args=[{"visible": [True, False, False,True]},
                           {"title": ""}]),
               
            ]),
                x=0.2,
                y = 1.2
        )
])

fig4.update_layout(plot_bgcolor='rgb(255,255,255)',xaxis_title="True overlap s",
    yaxis_title='Estimated overlap \u015D', legend=dict(x=.85, y=.1))

fig4.update_xaxes(ticks = 'outside', showline=True, linecolor='black')
fig4.update_yaxes(ticks = 'outside', showline=True, linecolor='black')

# Plot figure
plot(fig4, filename = 'plotly_figures/fig4.html', config = config)
display(HTML('plotly_figures/fig4.html'))