³ò jÈKc@s§dZddklZlZddklZlZlZd„Zd„Z d„Z d„Z d„Z d d „Z ed jo%dd kZeiƒZd eGHnd S(s-the Gamma functions: complete and incomplete iÿÿÿÿ(taddtdiv(tlogtexptfabscCsÏ|djotd|‚n|d}|d}||dt|ƒ}dddd d d g}g}tt|ƒƒD]}|||dqy~}tt||ƒ}d tt|ƒ}| td |ƒS(sReturns ln(Gamma(x)). Follows _Numerical Recipes in C_, pp 213-214, but fixes a couple of errors. "You can see that this is sort of a take-off on Stirling's approximation, but with a series of corrections that take into account the first few poles in the left complex plane." isGamma(x): x = %s <= 0ig@gà?g vŸ† S@gV6+W UÀgÆL;ñ›8@gŒÌÍ4µó¿gØìsÍS?gˆ˜¡Ö¾gÇ ð?g'ö“ @(t ValueErrorRtrangetlentmapRtreduceR(txtxTtlxCoft_[1]tntlxDenomtlxtxSer((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pytLnGammas    5cCstt|ƒƒS(sµReturns Gamma(x). If x is a positive integer then Gamma(x) = (x-1)! >>> [int(round(Gamma(n))) for n in range(1,12)] [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] (RR(R ((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pytGamma+scCso|djotd|‚n|djotd|‚n||djot||ƒSnt||ƒSdS(snReturns the incomplete gamma function P(a, x). Follows _Numerical Recipes in C_, pp 216-219, section 6.2. isIGamma(a, x): (a == %s) <= 0sIGamma(a, x): (x == %s) < 0gð?N(Rt IGammaSeriestIGammaCF(taR ((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pytIGamma7s  cCsÏ|djodSnd}|}d|}d|}}x|||jon|d}|||}||}t|ƒt|ƒ|jo+|t| |t|ƒt|ƒƒSq<q<Wtd||f‚dS(Niggvƒ ôõ!”>iegð?isIGammaSeries(%s, %s) fails(tabsRRRR(RR tepsilontxAtxAMaxtxTermtxSum((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pyRAs     0c CsGd}d}d}|d|}d|}d|}}d} xï| |joá| | |} |d}| ||}t|ƒ|jo |}n|| |}t|ƒ|jo |}nd|}||} || }t| dƒ|jo/d|t| |t|ƒt|ƒƒSn| d} qAWtd||f‚dS(Niegvƒ ôõ!”>g ÂëþKH´9gð?ig@sIGammaCF(%s, %s) fails(RRRRR( RR tiMaxRtxTinytbtcthtdtitantt((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pyROs0        /gH¯¼šò×z>cCsÔd}t|ƒ}|d}|djo |}nd}x”||jo†|t||ƒ}t|ƒ|joPnt||dƒt| ƒt|ƒ}|||}|djo |}n|d}q<W|S(Niegð?gi(tfloatRRtpowRR(RtytxEpsilonRR R$R#tm((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pyt InverseIGammafs"    ( t__main__Ns%d tests failed out of %d(t__doc__toperatorRRtmathRRRRRRRRR,t__name__tdoctestttestmodttp(((sr/Users/amos/Documents/Database/Mental/Programming/python/lib/avatar/Personal2/www.amos/Python/lib/mathlib/Gamma.pys s