# scenario2: alpha, beta, p1, and p2 are given, p2>p1
# what's the minimum sample size needed to reject h0: p1>=p2 in favor of p2>p1
# we return a matrix of options
import numpy as np, pandas as pd, array as a, math as m
from scipy.stats import norm
params=pd.read_csv("./scen2_params.csv", sep=",", names=['alpha', 'beta', 'p1', 'p2'])
alpha=float(params.alpha[params.alpha.index[0]])
beta=float(params.beta[params.beta.index[0]])
p1=float(params.p1[params.p1.index[0]])
p2=float(params.p2[params.p2.index[0]])
# s = pd.Series(np.randn(10), index=np.arange(10))
# print s
# print alpha 
z_alpha_div2=norm.ppf(alpha/2)
z_1_minus_beta=norm.ppf(1-beta)
# print z_alpha_div2, z_1_minus_beta
c=((p2-p1)**2)/((z_1_minus_beta-z_alpha_div2)**2)
c1=p1-p1**2
c2=p2-p2**2
# print c, c1, c2
# First case is n1=n2
n1=int(m.ceil(((c1)+(c2))/c))
# print 'n1', n1
S=2*n1
# print 'S', S
# res=[{'S':pd.Series([S, S], index=[0, 1]), 'n1':pd.Series([n1, n1], index=[0, 1]), 'n2':pd.Series([n1, n1], index=[0, 1])}]
# res=[S, n1, n1]
res = np.zeros((1,),dtype=[('S', 'f4'),('n1', 'f4'),('n2', 'f4')])
# print 'res', res

res[:] = [(S, n1, n1)]
# print 'res', res
res=pd.DataFrame(res, columns=['S', 'n1', 'n2'])
print 'res', res
# 
# if n1>60 & n1<500:
# 	cn1=n1
# 	shape_res=0
# 	# print 'cn1', cn1
# 	while True:
# 		cn1=cn1-1
# 		if S-cn1>3*n1:
# 			break
# 		S=int(m.ceil(((cn1**2*c+n1*(-c1+c2)))/(cn1*c-c1)))
# 		shape_res+=1
# 		
# 		tmp=np.zeros((1,),dtype=[('S', 'f4'),('n1', 'f4'),('n2', 'f4')])
# 		tmp[:]=[(S, cn1, S-cn1)]
# 		tmp=pd.DataFrame(tmp, columns=['S', 'n1', 'n2'], index=[shape_res])
# 		# print 'tmp', tmp
# 		res=res.append(tmp)
# 	cn1=n1
# 	while True:
# 		cn1=cn1+1
# 		if cn1>=3*n1:
# 			break
# 		S=int(m.ceil(((cn1**2*c+n1*(-c1+c2)))/(cn1*c-c1)))
# 		shape_res+=1
# 		
# 		tmp=np.zeros((1,),dtype=[('S', 'f4'),('n1', 'f4'),('n2', 'f4')])
# 		tmp[:]=[(S, cn1, S-cn1)]
# 		tmp=pd.DataFrame(tmp, columns=['S', 'n1', 'n2'], index=[shape_res])
# 		# print 'tmp', tmp
# 		res=res.append(tmp)
# 
# res.to_csv("scen2_out.csv")
# 		
# #