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Theta_D_F_H.py2.py
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Theta_D_F_H.py2.py
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# -*- coding: utf-8 -*-
#####################################################################################################
## By: Pan Yuwen, 05/2021
## Contact: [email protected]
#####################################################################################################
import numpy as np
import pandas
import gzip
import re
from functools import reduce
import math
from math import sqrt
import argparse
import sys
import socket
import os
import time
import gc
from scipy import integrate
from scipy.special import gamma
#from rpy2.robjects.packages import importr
#from rpy2.robjects.vectors import FloatVector
#stats = importr('stats')
## 1993-Statistical tests of neutrality of mutations
## under the neutral model
## E(s) = an * theta;
## E(pi) = theta
## E(η) = n/(n-1) * theta
## FU & Li's D: K vs. singleton
## FU & Li's F: pi vs. singleton
## Fay & Wu's H: pi vs. sum(#mutant^2)
## Tajima's D: pi vs. K
## Fu and Li's D, with or without outgroup
## #singletons may overestimate the #mutations in the external branches without outgroup
def calculate_Dfuli_outgroup(s,n,m):
## s: num of segregating sites
## n: num of DNA sequences
## m: num of derived singletons
an = reduce(lambda x,y: x+1.0/y, range(1,n))
bn = reduce(lambda x,y: x+1.0/pow(y,2), range(1,n))
if n==2:
cn = 1
else:
cn = 2.0 * (n*an - 2.0*(n-1.0)) / ((n-1.0)*(n-2.0))
v = 1.0 + (pow(an,2) / (bn+pow(an,2))) * (cn - (n+1.0)/(n-1.0))
u = an - 1.0 - v
D = (s - m*an) / sqrt(u*s + v*pow(s,2))
return D
def calculate_Dfuli_no_outgroup(s,n,m):
## s: num of segregating sites
## n: num of DNA sequences
## m: num of singletons
an = reduce(lambda x,y: x+1.0/y, range(1,n))
an1 = an + 1.0/n
bn = reduce(lambda x,y: x+1.0/pow(y,2), range(1,n))
if n==2:
cn = 1
else:
cn = 2.0 * (n*an - 2.0*(n-1.0)) / ((n-1.0)*(n-2.0))
dn = cn + (n-2.0)/pow(n-1.0,2) + 2.0/(n-1.0)*(3.0/2-(2.0*an1-3.0)/(n-2.0)-1.0/n)
v = (pow(n*1.0/(n-1.0),2)*bn + pow(an,2)*dn - 2.0*n*an*(an+1.0)/pow(n-1,2)) / (pow(an,2)+bn)
u = n*1.0/(n-1.0) * (an-n*1.0/(n-1.0)) - v
D = (s*n*1.0 / (n-1.0) - an*m) / sqrt(u*s + v*pow(s,2))
return D
def calculate_Ffuli_outgroup(s,n,m,pi):
## s: num of segregating sites
## n: num of DNA sequences
## m: num of derived singletons
an = reduce(lambda x,y: x+1.0/y, range(1,n))
an1 = an + 1.0/n
bn = reduce(lambda x,y: x+1.0/pow(y,2), range(1,n))
if n==2:
cn = 1
else:
cn = 2.0 * (n*an - 2.0*(n-1.0)) / ((n-1.0)*(n-2.0))
v = (cn+2.0*(pow(n,2)+n+3.0)/(9.0*n*(n-1.0))-2.0/(n-1.0)) / (pow(an,2)+bn)
u = (1.0 + (n+1.0)/(3.0*(n-1.0)) - 4.0*(n+1.0)/pow(n-1,2)*(an1-2.0*n/(n+1.0))) / an - v
F = (pi - m) / sqrt(u*s + v*pow(s,2))
return F
## 1995-Properties of Statistical Tests of Neutrality for DNA Polymorphism Data
def calculate_Ffuli_no_outgroup(s,n,m,pi):
## s: num of segregating sites
## n: num of DNA sequences
## m: num of singletons
an = reduce(lambda x,y: x+1.0/y, range(1,n))
an1 = an + 1.0/n
bn = reduce(lambda x,y: x+1.0/pow(y,2), range(1,n))
#v = (dn + 2.0*(pow(n,2)+n+3.0)/(9.0*n*(n-1.0)) - 2.0/(n-1.0)*(4.0*bn-6.0+8.0/n)) / (pow(an,2) + bn)
#u = (n*1.0/(n-1.0)+(n+1.0)/(3.0*(n-1.0))-4.0/(n*(n-1.0))+2.0*(n+1.0)/pow(n-1,2)*(an1-2.0*n/(n+1.0))) / an -v
v = ((2.0*pow(n,3)+110.0*pow(n,2)-255.0*n+153.0) / (9.0*pow(n,2)*(n-1.0)) + 2.0*(n-1.0)*an/pow(n,2) - 8.0*bn/n) / (pow(an,2) + bn)
u = (4.0*pow(n,2)+19.0*n+3.0-12.0*(n+1.0)*an1) / (3.0*n*(n-1)) / an - v
F = (pi - m*1.0*(n-1.0)/n) / sqrt(u*s + v*pow(s,2))
return F
## ancestral stat required
## 2000-Hitchhiking Under Positive Darwinian Selection
## 2006-Statistical Tests for Detecting Positive Selection by Utilizing High-Frequency Variants, (8, 11, 12)
def calculate_Hfaywu(s,n,pi,hapcount):
## s: num of segregating sites
## n: num of DNA sequences
## original Fay and Wu's H
#count = pandas.value_counts(hapcount['1'])
#thetaH = 2.0*(count.values * np.power(np.array(count.index),2)).sum() / (n*(n-1))
thetaH = 2.0 * np.power(hapcount['1'].values,2).sum() / (n*(n-1.0))
H = pi - thetaH
## normalized Fay and Wu's H
thetaL = hapcount['1'].sum()*1.0 / (n-1.0)
an = reduce(lambda x,y: x+1.0/y, range(1,n))
bn = reduce(lambda x,y: x+1.0/pow(y,2), range(1,n))
bn1 = bn + 1.0/pow(n,2)
thetaW = s*1.0 / an
theta_squre = s*1.0*(s-1.0) / (pow(an,2)+bn)
var = thetaW*(n-2.0)/(6.0*(n-1.0)) + theta_squre * (18.0*pow(n,2)*(3.0*n+2.0)*bn1 - (88.0*pow(n,3)+9.0*pow(n,2)-13.0*n+6.0)) / (9.0*n*pow(n-1,2))
normH = (pi - thetaL)*1.0 / sqrt(var)
return H, normH
## 1989-Statistical Method for Testing the Neutral Mutation Hypothesis by DNA Polymorphism
def calculate_Dtajima(s,n,pi):
## s: num of segregating sites
## n: num of DNA sequences
## Tajima's D
a1 = reduce(lambda x,y: x+1.0/y, range(1,n)); a2 = reduce(lambda x,y: x+1.0/pow(y,2), range(1,n))
b1 = (n+1.0)/(3.0*n-3.0); b2 = 2.0*(pow(n,2)+n+3.0)/(9.0*n*(n-1.0))
c1 = b1-1.0/a1; c2 = b2-(n+2.0)/(a1*n)+a2/pow(a1,2)
e1 = c1/a1; e2 = c2/(pow(a1,2)+a2)
D = (pi-s/a1)/sqrt(e1*s+e2*s*(s-1.0))
## P value for Tajima's D, assuming that D follows the beta distribution
if n%2 == 0:
Dmax = (n/(2.0*(n-1))-1.0/a1)/sqrt(e2)
else:
Dmax = ((n+1.0)/(2.0*n)-1.0/a1)/sqrt(e2)
Dmin = (2.0/n-1.0/a1)/sqrt(e2)
a = Dmin; b = Dmax
alpha = -(1.0+a*b)*b/(b-a); beta = (1.0+a*b)*a/(b-a)
func = lambda d: gamma(alpha+beta)*pow(b-d,alpha-1.0)*pow(d-a,beta-1.0)/(gamma(alpha)*gamma(beta)*pow(b-a,alpha+beta-1.0))
pvalue = 2*min(integrate.quad(func, Dmin, D)[0], integrate.quad(func, D, Dmax)[0])
#pvalue = np.nan
return D, pvalue
## Nei, M., and Li, W.H. (1979). MATHEMATICAL-MODEL FOR STUDYING GENETIC-VARIATION IN TERMS OF RESTRICTION ENDONUCLEASES. Proc Natl Acad Sci U S A 76, 5269-5273
def theta_pi_k(hapcount,s,n):
pi = (hapcount['0'].values * hapcount['1'].values).sum() * 1.0/(n*(n-1.0)/2.0)
k = s * 1.0 / reduce(lambda x,y: x+1.0/y, range(1,n))
return pi, k
## Nei, M., and Tajima, F. (1981). DNA POLYMORPHISM DETECTABLE BY RESTRICTION ENDONUCLEASES. Genetics 97, 145-163
def haplotype_diversity(haps):
## Haplotype Diversity (H), H = N/(N-1) * (1-sigma(x^2))
## x is the haplotype frequency of each haplotype
## N is the sample size (haplotypes)
## This measure of gene diversity is analogous to the heterozygosity at a single locus
haplist = haps.apply(lambda x: "".join(list(x)),axis=0) # assemble each hap to string
nsample = haps.shape[1]
sigmax2 = reduce(lambda x,y: x+pow(y,2), [0]+[z*1.0/nsample for z in list(haplist.value_counts())])
nhap = len(set(haplist))
H = nsample*1.0/(nsample-1.0)*(1.0-sigmax2)
return nhap, H
def calculate_one_region_stat(hap_df,hapcount_df,nseq,chromid,start,end,outgroup):
## info in the given region
haps = hap_df[(hap_df['#CHROM']==str(chromid)) & (hap_df['POS']>=int(start)) & (hap_df['POS']<=int(end))].copy()
hapcount = hapcount_df[(hapcount_df['#CHROM']==str(chromid)) & (hapcount_df['POS']>=int(start)) & (hapcount_df['POS']<=int(end))].copy()
if haps.empty:
nmarker = 0; sigtn = 0; thetaPI = 0; thetaK = 0; seg = 0; nhap = 0; H = 0;
Dtajima = np.nan; DtajimaP = np.nan;
Hfaywu = np.nan; normHfaywu = np.nan;
Ffuli = np.nan; Dfuli = np.nan
return nmarker, sigtn, thetaPI, thetaK, seg, nhap, H, Hfaywu, normHfaywu, Ffuli, Dfuli, Dtajima, DtajimaP
else:
nmarker = hapcount.shape[0]
haps.drop(['#CHROM','POS'],axis=1,inplace=True); hapcount.drop(['#CHROM','POS'],axis=1,inplace=True)
## check non-biallelic (or missing) sites + homozygotes
site2rm = list(hapcount[((hapcount['0']+hapcount['1']) <nseq) | (hapcount['1']==0) | (hapcount['0']==0)].index)
if len(site2rm) == nmarker:
sigtn = 0; thetaPI = 0; thetaK = 0; seg = 0; nhap = 0; H = 0;
Dtajima = np.nan; DtajimaP = np.nan;
Hfaywu = np.nan; normHfaywu = np.nan;
Ffuli = np.nan; Dfuli = np.nan
return nmarker, sigtn, thetaPI, thetaK, seg, nhap, H, Hfaywu, normHfaywu, Ffuli, Dfuli, Dtajima, DtajimaP
else:
if len(site2rm) >0:
haps.drop(site2rm,inplace=True)
hapcount.drop(site2rm,inplace=True)
else:
pass
seg = hapcount.shape[0] ## num of segregating site
thetaPI, thetaK = theta_pi_k(hapcount,seg,nseq)
nhap, H = haplotype_diversity(haps)
Dtajima, DtajimaP = calculate_Dtajima(seg,nseq,thetaPI)
if outgroup == 'Y':
sigtn = hapcount[(hapcount['1']==1)].shape[0] ## num of derived singleton
Hfaywu, normHfaywu = calculate_Hfaywu(seg,nseq,thetaPI,hapcount)
Ffuli = calculate_Ffuli_outgroup(seg,nseq,sigtn,thetaPI)
Dfuli = calculate_Dfuli_outgroup(seg,nseq,sigtn)
else:
sigtn = hapcount[(hapcount['0']==1) | (hapcount['1']==1)].shape[0] ## num of singleton
Hfaywu, normHfaywu = np.nan, np.nan
Ffuli = calculate_Ffuli_no_outgroup(seg,nseq,sigtn,thetaPI)
Dfuli = calculate_Dfuli_no_outgroup(seg,nseq,sigtn)
return nmarker, sigtn, thetaPI, thetaK, seg, nhap, H, Hfaywu, normHfaywu, Ffuli, Dfuli, Dtajima, DtajimaP
## remain required geno data
## convert to ped format
## count alleles
def convert_vcf(vcf,regionfile,window_shift,info,haplist):
if window_shift == 'target_region':
windowsize = 5000
else:
windowsize = int(window_shift.split('@')[0])
region = pandas.read_csv(regionfile,sep='\s+',header=None,usecols=[0,1,2,3],names=['regionID','chr','start','end'])
region['chr'] = region['chr'].astype(str)
region['start'] = region['start'] - windowsize
region['end'] = region['end'] + windowsize
region.sort_values(by=['chr','start','end'],ascending=True,inplace=True)
region.reset_index(inplace=True,drop=True)
## merge regions
if region.shape[0] == 1:
pass
else:
for index in list(region.index)[:-1]:
chrom1, start1, end1 = list(region.loc[index])[1:]
chrom2, start2, end2 = list(region.loc[index+1])[1:]
if ((chrom2 == chrom1) & (start2 <= end1+1)):
new_end = max(end1,end2)
region.loc[index+1,'start'] = start1
region.loc[index+1,'end'] = new_end
region.drop(index,inplace=True)
else:
pass
## extract vcf, and convert format
geno = pandas.concat(list(region.apply(lambda x: vcf[(vcf['#CHROM']==x['chr']) & (vcf['POS']>=x['start']) & (vcf['POS']<=x['end'])].copy(), axis=1)),ignore_index=True)
if geno.empty:
haps = pandas.DataFrame()
hapcount = pandas.DataFrame()
nseq = 0
return haps, hapcount, nseq
else:
slist = list(geno.columns)[2:]
mlist = [s for s in slist if info[s]==1]
## convert format, for male individuals
if ((len(mlist) >0) & (('X' in list(geno['#CHROM'].unique())) | ('chrX' in list(geno['#CHROM'].unique())))):
geno[mlist] = geno[mlist].applymap(lambda x: x[0]).astype('category')
hapnames = []
for s in slist:
if info[s] == 1:
hapnames += [s+'_1']
else:
hapnames += [s+'_1',s+'_2']
else:
hapnames = [s+'_'+i for s in slist for i in ['1','2']]
## to ped format, as type of category
haps = pandas.DataFrame(geno.apply(lambda x: '|'.join(x[2:]).split('|'),axis=1).tolist(),columns=hapnames).astype('category')
if (len(set(hapnames) & set(haplist)) < len(hapnames)):
hapnames = [h for h in hapnames if h in haplist]
haps = haps[hapnames]
else:
pass
nseq = len(hapnames)
haps.columns = ['hap'+str(x) for x in range(1,nseq+1)]
#haps = pandas.DataFrame(geno.apply(lambda x: list(''.join(x[2:]).replace('|','')),axis=1).tolist(),columns=['hap'+str(x) for x in range(1,nseq+1)]).astype('category')
## allele count, using bool types to speed up (the same as summing up numbers)
#hapcount = haps.apply(pandas.value_counts,axis=1) # Matrix[#site number, 2]
count1 = (haps=='1').apply(sum,axis=1); count0 = (haps=='0').apply(sum,axis=1)
hapcount = pandas.concat([count0, count1],axis=1).astype('int64')
hapcount.rename(columns=lambda x: str(x),inplace=True)
haps['#CHROM'] = hapcount['#CHROM'] = geno['#CHROM'].values
haps['POS'] = hapcount['POS'] = geno['POS'].values
## compress
haps = haps.astype({'#CHROM':'category','POS':'int32'})
hapcount = hapcount.astype({'#CHROM':'category','POS':'int32'})
return haps, hapcount, nseq
def split_window(regionID,chromID,start,end,window_shift):
windowsize = int(window_shift.split('@')[0])
stepsize = int(window_shift.split('@')[1])
overlapsize = windowsize - stepsize
length = end - start + 1
bin_num = max(int(math.ceil((length - overlapsize)*1.0 / stepsize)),1)
ex_len = bin_num * stepsize + overlapsize
ex_start = int(max(start-(ex_len-length)/2.0, 1.0))
ex_end = int(end + (ex_len-length)/2.0)
region = pandas.DataFrame(columns=['regionID','chr','start','end'])
region['regionID'] = [regionID] * bin_num
region['chr'] = chromID
region['start'] = [ex_start + num*stepsize for num in range(bin_num)]
region['end'] = region['start'] + windowsize - 1
return region
def make_regions(regionfile,window_shift):
region = pandas.read_csv(regionfile,sep='\s+',header=None,usecols=[0,1,2,3],names=['regionID','chr','start','end'])
region['chr'] = region['chr'].astype(str)
if window_shift == 'target_region':
pass
else:
region['tmp'] = region.apply(lambda x: split_window(x['regionID'],x['chr'],x['start'],x['end'],window_shift),axis=1)
region = pandas.concat(list(region['tmp']),ignore_index=True)
region.sort_values(by=['chr','start','end'],ascending=True,inplace=True)
return region
def fdr(pvaluelist):
## numpy.array format
## should be sorted, decreasing order (ascending Pvalues)
n = len(pvaluelist)
pvalues = pvaluelist[~np.isnan(pvaluelist)]
if len(pvalues) <= 1:
return list(pvaluelist)
else:
num = len(pvalues)
adj_pvalues = pvalues * num / range(1,num+1)
if adj_pvalues[-1] > 1.0:
adj_pvalues[-1] = 1.0
for i in range(num-2,-1,-1):
adj_pvalues[i] = min(adj_pvalues[i+1],adj_pvalues[i])
adj_pvalues = list(adj_pvalues) + [np.nan] * (n-num)
return adj_pvalues
def make_sample_hap(samplefile, hapfile, allsamplelist):
if samplefile == 'all':
sampleinfo = pandas.DataFrame(columns=[0,1])
sampleinfo[0] = allsamplelist
sampleinfo[1] = 2
else:
sampleinfo = pandas.read_csv(samplefile,header=None,sep='\s+')
if sampleinfo.shape[1] == 1:
sampleinfo[1] = 2
else:
pass
sampleinfo[1] = sampleinfo[1].astype(int)
if len(set([1,2]) | set(sampleinfo[1])) == 2:
pass
else:
print('something wrong with the genders. only accept 1 and 2.')
exit()
if hapfile == 'all':
hapinfo = pandas.DataFrame(columns=[0,1])
hapinfo[0] = allsamplelist + allsamplelist
hapinfo[1] = [1]*len(allsamplelist) + [2]*len(allsamplelist)
else:
hapinfo = pandas.read_csv(hapfile,header=None,sep='\s+')
hapinfo[1] = hapinfo[1].astype(int)
if len(set([1,2]) | set(hapinfo[1])) == 2:
pass
else:
print('something wrong with the hap index. only accept 1 and 2.')
exit()
s2r = list(set(sampleinfo[0]) & set(hapinfo[0]) & set(allsamplelist))
if len(s2r) == 0:
print('NO sample included.')
exit()
else:
pass
samplelist = [s for s in allsamplelist if s in s2r]
sampleinfo = sampleinfo[sampleinfo[0].isin(s2r)]
sampleinfo = dict(zip(list(sampleinfo[0]), list(sampleinfo[1])))
hapinfo = hapinfo[hapinfo[0].isin(s2r)]
haplist = list(hapinfo.apply(lambda x: '{}_{}'.format(x[0],x[1]), axis=1))
haplist = [s+'_'+i for s in samplelist for i in ['1','2'] if s+'_'+i in haplist]
return samplelist, sampleinfo, haplist
def main():
parser = argparse.ArgumentParser()
parser.add_argument("--gzvcf", type=str, required = True, \
help="/path/to/phased.vcf.gz, format:GT, do not combine autosome and X chromosome")
parser.add_argument("--samples", type=str, required = False, default='all', \
help="/included/sample/ID/list, 1 or 2 column: <sample ID> <gender 1/2, optional>, no header")
parser.add_argument("--haps", type=str, required = False, default='all', \
help="/included/sample-hap_index, 2 column: <sample ID> <haplotype index, 1/2, first/second hap>, no header")
parser.add_argument("--region", type=str, required = True, \
help="/path/to/region/file, 4 columns: <region ID> <chrom ID> <start pos> <end pos>, no header line, tab or space sperated")
parser.add_argument("--window_shift", type=str, required = False, default='target_region', \
help="windowsize@increment, for example, 50000@10000.")
parser.add_argument("--outgroup",type=str, required = False, choices=['Y','N'], default='N', \
help="whether the state of ancestral/derived allele is determined, required for FU&Li's and Fay&Wu's tests")
parser.add_argument("--out", type=str, required = False, default='out.txt', \
help="/out/file/name")
args = parser.parse_args()
## log
with open(args.out+'.logfile','w') as log:
log.write('python {}\n'.format(sys.argv[0]))
log.write('{}--gzvcf {}\n'.format(' '*8, args.gzvcf))
log.write('{}--samples {}\n'.format(' '*8, args.samples))
log.write('{}--haps {}\n'.format(' '*8, args.haps))
log.write('{}--region {}\n'.format(' '*8, args.region))
log.write('{}--window_shift {}\n'.format(' '*8, args.window_shift))
log.write('{}--outgroup {}\n'.format(' '*8, args.outgroup))
log.write('{}--out {}\n\n'.format(' '*8, args.out))
log.write('Hostname: '+socket.gethostname()+'\n')
log.write('Working directory: '+os.getcwd()+'\n')
log.write('Start time: '+time.strftime("%Y-%m-%d %X",time.localtime())+'\n\n')
## sample info
with gzip.open(args.gzvcf) as f:
headerline = 0
line = f.readline()
while line[:2] == "##":
headerline += 1
line = f.readline()
allsamplelist = line.strip().split('\t')[9:]
samplelist, sampleinfo, haplist = make_sample_hap(args.samples, args.haps, allsamplelist) ## gender not consider for haplist
if ((len(samplelist) <=1) | (len(haplist) <=3)):
print('No enough sequences, at least 4 sequences are required.')
exit()
else:
pass
## input
## read str using Categorical dtypes, to save memory
datatype = dict(zip(['#CHROM','POS']+samplelist, ['category','int32']+['category']*len(samplelist)))
vcfdata = pandas.read_csv(args.gzvcf,sep='\t',skiprows=range(headerline),usecols=['#CHROM','POS']+samplelist,dtype=datatype)
if ((vcfdata.shape[0] <=1) | (vcfdata.shape[1] <=4)):
print('There may be something wrong with the input data.')
print('Plz check the #sites and #samples.')
else:
pass
## convert
hapdata, hapcountdata, nseq = convert_vcf(vcfdata, args.region, args.window_shift, sampleinfo, haplist)
if nseq <=3:
print('No enough sequences, at least 4 sequences are required.')
exit()
else:
pass
## get output
result = make_regions(args.region, args.window_shift)
result['#sequence'] = nseq
result['tmp'] = result.apply(lambda x: calculate_one_region_stat(hapdata,hapcountdata,nseq, x['chr'],x['start'],x['end'],args.outgroup),axis=1)
result = pandas.concat([result[['regionID','chr','start','end','#sequence']], pandas.DataFrame(result['tmp'].tolist(),columns=['#marker','#singleton','ThetaPI','ThetaK','#segregating','#haplotype','Hap_diversity',"Hfaywu","norm_Hfaywu","Ffuli","Dfuli","Dtajima",'Dtajima_P'], index=list(result.index))],axis=1)
result.sort_values(by='Dtajima_P',ascending=True,inplace=True)
#result['Dtajima_adj.P'] = stats.p_adjust(FloatVector(result['Dtajima_P']), method='BH')
result['Dtajima_adj.P'] = fdr(result['Dtajima_P'].values)
result.sort_values(by=['chr','start','end'],ascending=True,inplace=True)
result.to_csv(args.out+'.gz',sep='\t',index=None,compression='gzip',na_rep='NA')
with open(args.out+'.logfile','a') as log:
log.write("Done.\n")
log.write("Output "+args.out+'.gz\n')
log.write('End time: '+time.strftime("%Y-%m-%d %X",time.localtime())+'\n\n')
print('Done.')
print('Have a Nice Day!')
if __name__ == '__main__':
main()