7`Jc@sddlmZddlmZdZeeZee ZddlZedZdZdZ dZ d Z d d Z d d Z d ZdS(i(texp(tlogiNcCst|}|dkr'tdn|rV|dkrFt||St||Sn&|dkrot||St||SdS(sPPoisson CDF evaluater. This is a more stable CDF function. It can tolerate large lambda value. While the lambda is larger than 700, the function will be a little slower. Parameters: n : your observation lam : lambda of poisson distribution lower : if lower is False, calculate the upper tail CDF gsLambda must > 0iN(tintt Exceptiont__poisson_cdf_large_lambdat __poisson_cdft__poisson_cdf_Q_large_lambdat__poisson_cdf_Q(tntlamtlowertk((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyt poisson_cdfs      cCsw|dkrdSt| }|}x9td|dD]$}|}|||}||}q7W|dkrodS|SdS(sVPoisson CDF For small lambda. If a > 745, this will return incorrect result. iiN(Rtxrange(R tatnexttcdftitlast((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyR1s   c Cs|dkrdSt|t}|t}t| }t}|d8}|}xtd|dD]|}|}|||}||}|tks|tkra|dkr|t9}|t9}|d8}q||9}d}qaqaWxt|D]}|t9}qW||9}|S(s.Slower poisson cdf for large lambda. ii(RtLSTEPRtEXPSTEPR tEXPTHRES( R Rt num_partst last_parttlastexpRRRR((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyRCs.            cCs|dkrdSt| }x/td|dD]}|}|||}q1Wd}|d}x8|dkr|}|||}||7}|d7}qbW|S(sJinternal Poisson CDF evaluater for upper tail with small lambda. ii(RR (R RRRRR((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyRas    c Cs|dkrdSt|t}|t}t| }t}|d8}xqtd|dD]\}|}|||}|tkr[|dkr|t9}|d8}q||9}d}q[q[Wd}|d}x|dkr]|}|||}||7}|d7}|tks|tkr|dkrG|t9}|t9}|d8}qZ||9}d}qqWxt|D]}|t9}qkW||9}|S(sUSlower internal Poisson CDF evaluater for upper tail with large lambda. ii(RRRRR R( R RRRRRRRR((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyRwsD                    icCs|dkst|dks*|dkr9tdn|dkrIdSd}t| }|}x[td|dD]F}|}|}|||}||}||krv||krv|SqvW|S(sinverse poisson distribution. cdf : the CDF lam : the lambda of poisson distribution note: maxmimum return value is 1000 and lambda must be smaller than 740. iiisCDF must >= 0 and <= 1(tAssertionErrorRRR (RR tmaximumtsum2tnewvalRtsumoldR((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pytpoisson_cdf_invs    cCs|dkst|dks*|dkr9tdn|dkrIdSd}t| }|}x[td|dD]F}|}|}|||}||}||krv||krv|SqvW|S(sinverse poisson distribution. cdf : the CDF lam : the lambda of poisson distribution note: maxmimum return value is 1000 and lambda must be smaller than 740. iiisCDF must >= 0 and <= 1(RRRR (RR RRRRRR((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pytpoisson_cdf_Q_invs    cCs2|dkrdSt| t||t|S(sPoisson PDF. PDF(K,A) is the probability that the number of events observed in a unit time period will be K, given the expected number of events in a unit time. i(Rtpowt factorial(R R((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyt poisson_pdfs (tmathRRRRRtTrueR RRRRRRR"(((s=/woldlab/castor/data00/home/georgi/programs/NPS-1.3.2/Prob.pyts        , $