; Êâ"Ic@sndZddlmZddlmZddlmZm Z ddl m Z mZmZmZmZddl mZmZmZmZddlmZ ddl!m"Z#d d d d d ddddddddddddddddddgZ$d ed!ƒed"ƒZ%d"eZ&e d#ƒZ'd$e d%ƒZ(d&Z)d'e) Z*dd(l+Z+Gd)„d e+j,ƒZ,Gd*„de,ƒZ-d+„Z.d,d-„Z/e,ƒZ0e0j1Z1e0j2Z2e0j3Z3e0j4Z4e0j5Z5e0j6Z6e0j7Z7e0j8Z8e0j9Z9e0j:Z:e0j;Z;e0j<Z<e0j=Z=e0j>Z>e0j?Z?e0j@Z@e0jAZAe0jBZBe0jCZCe0jDZDe0jEZEeFd.ko e/ƒnd(S(/u‰Random variable generators. integers -------- uniform within range sequences --------- pick random element pick random sample generate random permutation distributions on the real line: ------------------------------ uniform triangular normal (Gaussian) lognormal negative exponential gamma beta pareto Weibull distributions on the circle (angles 0 to 2pi) --------------------------------------------- circular uniform von Mises General notes on the underlying Mersenne Twister core generator: * The period is 2**19937-1. * It is one of the most extensively tested generators in existence. * The random() method is implemented in C, executes in a single Python step, and is, therefore, threadsafe. i(udivision(uwarn(u MethodTypeuBuiltinMethodType(uloguexpupiueuceil(usqrtuacosucosusin(uurandom(uhexlifyuRandomuseedurandomuuniformurandintuchoiceusampleu randrangeushuffleu normalvariateulognormvariateu expovariateuvonmisesvariateu gammavariateu triangularugaussu betavariateu paretovariateuweibullvariateugetstateusetstateu getrandbitsu SystemRandomigà¿g@g@gð?g@i5iNcs?|EeZdZdZdd„Zd‡fd†Z‡fd†Z‡fd†Zd„Z d„Z d„Z dd e dd e >d „Zd „Zee d e >eed „Zd „Zde d„Zd„Zd„Zdddd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!‡S(uãRandom number generator base class used by bound module functions. Used to instantiate instances of Random to get generators that don't share state. Class Random can also be subclassed if you want to use a different basic generator of your own devising: in that case, override the following methods: random(), seed(), getstate(), and setstate(). Optionally, implement a getrandbits() method so that randrange() can cover arbitrarily large ranges. icCs|j|ƒd|_dS(ueInitialize an instance. Optional argument x controls seeding, as for Random.seed(). N(useeduNoneu gauss_next(uselfux((u#/mit/python/lib/python3.0/random.pyu__init__Ts c s†|dko\ytttdƒƒdƒ}Wqitk o*ddl}t|jƒdƒ}YqiXntƒj|ƒd|_dS(uInitialize internal state from hashable object. None or no argument seeds from current time or from an operating system specific randomness source if available. If a is not None or an int or long, hash(a) is used instead. iiNi( uNoneuintu_hexlifyu_urandomuNotImplementedErrorutimeusuperuseedu gauss_next(uselfuautime(u __class__(u#/mit/python/lib/python3.0/random.pyuseed]s   cs|jtƒjƒ|jfS(u9Return internal state; can be passed to setstate() later.(uVERSIONusuperugetstateu gauss_next(uself(u __class__(u#/mit/python/lib/python3.0/random.pyugetstatepsc sà|d}|dko&|\}}|_tƒj|ƒn |dkoy|\}}|_ytd„|Dƒƒ}Wn0tk o$}zt|‚WYdd}~XnXtt|ƒj|ƒntd||jfƒ‚dS(u:Restore internal state from object returned by getstate().iiicss|]}|dVqdS(ii Nl((u.0ux((u#/mit/python/lib/python3.0/random.pyu sNu?state with version %s passed to Random.setstate() of version %s(u gauss_nextusuperusetstateutupleu ValueErroru TypeErroruRandomuVERSION(uselfustateuversionu internalstateue(u __class__(u#/mit/python/lib/python3.0/random.pyusetstatets   cCs |jƒS(N(ugetstate(uself((u#/mit/python/lib/python3.0/random.pyu __getstate__scCs|j|ƒdS(N(usetstate(uselfustate((u#/mit/python/lib/python3.0/random.pyu __setstate__’scCs|jd|jƒfS(N((u __class__ugetstate(uself((u#/mit/python/lib/python3.0/random.pyu __reduce__•sic Cs||ƒ}||kotdƒ‚n||koM|dko0||ko|j|ƒS||jƒ|ƒStdƒ‚n||ƒ}||kotdƒ‚n||} |dkoQ| dkoD| |ko|||j| ƒƒS||||jƒ| ƒƒS|dkotd||| fƒ‚n||ƒ} | |kotdƒ‚n| dko| | d| } n0| dko| | d| } n tdƒ‚| dkotdƒ‚n| |ko|| |j| ƒS|| ||jƒ| ƒS( uChoose a random item from range(start, stop[, step]). This fixes the problem with randint() which includes the endpoint; in Python this is usually not what you want. Do not supply the 'int', 'default', and 'maxwidth' arguments. u!non-integer arg 1 for randrange()iuempty range for randrange()u non-integer stop for randrange()iu'empty range for randrange() (%d,%d, %d)u non-integer step for randrange()uzero step for randrange()(u ValueErroru _randbelowurandom( uselfustartustopustepuintudefaultumaxwidthuistartuistopuwidthuistepun((u#/mit/python/lib/python3.0/random.pyu randrangešs@                 cCs|j||dƒS(uJReturn random integer in range [a, b], including both end points. i(u randrange(uselfuaub((u#/mit/python/lib/python3.0/random.pyurandintÚsc CsËy |j}Wntk oYnzXt|jƒ|kpt|ƒ|koO|d||ddƒƒ}||ƒ} x| |ko||ƒ} qyW| S||kotdƒn||jƒ|ƒS(u£Return a random int in the range [0,n) Handles the case where n has more bits than returned by a single call to the underlying generator. grÄZ| ð?ig@ugUnderlying random() generator does not supply enough bits to choose from a population range this large(u getrandbitsuAttributeErrorutypeurandomu_warn( uselfunu_loguintu _maxwidthu_Methodu_BuiltinMethodu getrandbitsukur((u#/mit/python/lib/python3.0/random.pyu _randbelowàs )   cCs|t|jƒt|ƒƒS(u2Choose a random element from a non-empty sequence.(uinturandomulen(uselfuseq((u#/mit/python/lib/python3.0/random.pyuchoiceýscCsx|dko |j}nxWttdt|ƒƒƒD]:}||ƒ|dƒ}||||||<|| shuffle list x in place; return None. Optional arg random is a 0-argument function returning a random float in [0.0, 1.0); by default, the standard random.random. iN(uNoneurandomureversedurangeulen(uselfuxurandomuintuiuj((u#/mit/python/lib/python3.0/random.pyushuffles   c CsÔt|ttfƒot|ƒ}nt|dƒ pt|dƒotdƒ‚n|j}t|ƒ}d|ko |knptdƒ‚nt }d g|}d}|dko%|dt t |d dƒƒ7}n||kobt |ƒ}xÏt|ƒD]A} ||ƒ|| ƒ} || || <||| d || !    %        cCs||||jƒS(u(Get a random number in the range [a, b).(urandom(uselfuaub((u#/mit/python/lib/python3.0/random.pyuuniformNsggð?cCs||jƒ}|dkodn||||}||ko%d|}d|}||}}n|||||dS(uÜTriangular distribution. Continuous distribution bounded by given lower and upper limits, and having a given mode value in-between. http://en.wikipedia.org/wiki/Triangular_distribution gà?gð?N(urandomuNone(uselfulowuhighumodeuuuc((u#/mit/python/lib/python3.0/random.pyu triangularTs &   cCsj|j}xR|ƒ}d|ƒ}t|d|}||d}|t|ƒ koPq q |||S(u\Normal distribution. mu is the mean, and sigma is the standard deviation. gð?gà?g@(urandomu NV_MAGICCONSTu_log(uselfumuusigmaurandomuu1uu2uzuzz((u#/mit/python/lib/python3.0/random.pyu normalvariategs   cCst|j||ƒƒS(uûLog normal distribution. If you take the natural logarithm of this distribution, you'll get a normal distribution with mean mu and standard deviation sigma. mu can have any value, and sigma must be greater than zero. (u_expu normalvariate(uselfumuusigma((u#/mit/python/lib/python3.0/random.pyulognormvariate€scCs?|j}|ƒ}x|dko |ƒ}qWt|ƒ |S(uìExponential distribution. lambd is 1.0 divided by the desired mean. (The parameter would be called "lambda", but that is a reserved word in Python.) Returned values range from 0 to positive infinity. gH¯¼šò×z>(urandomu_log(uselfulambdurandomuu((u#/mit/python/lib/python3.0/random.pyu expovariateŒs   cCs7|j}|dko t|ƒSdtdd||ƒ}|td|ƒd|}d||d|}x~|ƒ}tt|ƒ}d||||} ||| } |ƒ} | | d| kp| | td| ƒkoPqsqs|ƒ} | dko|tt| ƒ} n|tt| ƒ} | S(uFCircular data distribution. mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*pi. gíµ ÷Æ°>gð?g@g@gà?(urandomuTWOPIu_sqrtu_cosu_piu_expu_acos(uselfumuukappaurandomuauburuu1uzufucuu2uu3utheta((u#/mit/python/lib/python3.0/random.pyuvonmisesvariateŸs&     0  cCs"|dkp |dkotdƒ‚n|j}|dkoêtd|dƒ}|t}||}x³|ƒ}d|ko dknpqknd|ƒ}t|d|ƒ|} |t| ƒ} |||} ||| | } | td| dkp| t| ƒko | |Sqknõ|dko7|ƒ} x| dko |ƒ} qCWt| ƒ |Sx¥|ƒ} t|t}|| }|dko|d|} nt|||ƒ } |ƒ}|dko|| |dkoPqqq|t| ƒkoPqqqq| |SdS( uxGamma distribution. Not the gamma function! Conditions on the parameters are alpha > 0 and beta > 0. gu*gammavariate: alpha and beta must be > 0.0gð?g@gH¯¼šò×z>gËPÊÿÿï?g@N(u ValueErrorurandomu_sqrtuLOG4u_logu_expu SG_MAGICCONSTu_e(uselfualphaubetaurandomuainvubbbucccuu1uu2uvuxuzuruuubup((u#/mit/python/lib/python3.0/random.pyu gammavariateÑsL       ,         cCs…|j}|j}d|_|dkoQ|ƒt}tdtd|ƒƒƒ}t|ƒ|}t|ƒ||_n|||S(uØGaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function. Not thread-safe without a lock around calls. gÀgð?N(urandomu gauss_nextuNoneuTWOPIu_sqrtu_logu_cosu_sin(uselfumuusigmaurandomuzux2piug2rad((u#/mit/python/lib/python3.0/random.pyugausss     cCs@|j|dƒ}|dkodS|||j|dƒSdS(uBeta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1. gð?igN(u gammavariate(uselfualphaubetauy((u#/mit/python/lib/python3.0/random.pyu betavariateHs  cCs%d|jƒ}dt|d|ƒS(u3Pareto distribution. alpha is the shape parameter.gð?(urandomupow(uselfualphauu((u#/mit/python/lib/python3.0/random.pyu paretovariateZscCs,d|jƒ}|tt|ƒ d|ƒS(ufWeibull distribution. alpha is the scale parameter and beta is the shape parameter. gð?(urandomupowu_log(uselfualphaubetauu((u#/mit/python/lib/python3.0/random.pyuweibullvariatecsN("u__name__u __module__u__doc__uVERSIONuNoneu__init__useedugetstateusetstateu __getstate__u __setstate__u __reduce__uintuBPFu randrangeurandintu_logu _MethodTypeu_BuiltinMethodTypeu _randbelowuchoiceushuffleusampleuuniformu triangularu normalvariateulognormvariateu expovariateuvonmisesvariateu gammavariateugaussu betavariateu paretovariateuweibullvariate(u __locals__((u __class__u#/mit/python/lib/python3.0/random.pyuRandomDs8      ?    ?    2 B 5  cBsB|EeZdZd„Zd„Zd„Zd„ZeZZdS(uÝAlternate random number generator using sources provided by the operating system (such as /dev/urandom on Unix or CryptGenRandom on Windows). Not available on all systems (see os.urandom() for details). cCs!tttdƒƒdƒd?tS(u3Get the next random number in the range [0.0, 1.0).iii(uintu_hexlifyu_urandomu RECIP_BPF(uself((u#/mit/python/lib/python3.0/random.pyurandomxscCsy|dkotdƒ‚n|t|ƒkotdƒ‚n|dd}ttt|ƒƒdƒ}||d|?S(u>getrandbits(k) -> x. Generates a long int with k random bits.iu(number of bits must be greater than zerou#number of bits should be an integeriii(u ValueErroruintu TypeErroru_hexlifyu_urandom(uselfukubytesux((u#/mit/python/lib/python3.0/random.pyu getrandbits|s cOsdS(u<Stub method. Not used for a system random number generator.N(uNone(uselfuargsukwds((u#/mit/python/lib/python3.0/random.pyuseed†scOstdƒ‚dS(uAMethod should not be called for a system random number generator.u*System entropy source does not have state.N(uNotImplementedError(uselfuargsukwds((u#/mit/python/lib/python3.0/random.pyu_notimplementedŠsN( u__name__u __module__u__doc__urandomu getrandbitsuseedu_notimplementedugetstateusetstate(u __locals__((u#/mit/python/lib/python3.0/random.pyu SystemRandomps    c Csddl}t|d|jƒd}d}d}d}|jƒ}xVt|ƒD]H} ||Œ} || 7}|| | }t| |ƒ}t| |ƒ}qPW|jƒ} tt| |dƒddd ƒ||} t||| | ƒ} td | | ||fƒdS( Niutimesgg _ Bg _ Âiusec,uendu u!avg %g, stddev %g, min %g, max %g(utimeuprintu__name__urangeuminumaxuroundu_sqrt(unufuncuargsutimeutotalusqsumusmallestulargestut0uiuxut1uavgustddev((u#/mit/python/lib/python3.0/random.pyu_test_generator‘s(        iÐcCs t|td ƒt|td ƒt|td ƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdƒt|tdddfƒdS(Nggð?g{®Gáz„?gš™™™™™¹?g@gà?gÍÌÌÌÌÌì?g4@gi@g@((ggð?(ggð?(ggð?(g{®Gáz„?gð?(gš™™™™™¹?gð?(gš™™™™™¹?g@(gà?gð?(gÍÌÌÌÌÌì?gð?(gð?gð?(g@gð?(g4@gð?(gi@gð?(ggð?(g@g@gUUUUUUÕ?( u_test_generatorurandomu normalvariateulognormvariateuvonmisesvariateu gammavariateugaussu betavariateu triangular(uN((u#/mit/python/lib/python3.0/random.pyu_test§s u__main__(Gu__doc__u __future__udivisionuwarningsuwarnu_warnutypesu MethodTypeu _MethodTypeuBuiltinMethodTypeu_BuiltinMethodTypeumathulogu_loguexpu_expupiu_piueu_euceilu_ceilusqrtu_sqrtuacosu_acosucosu_cosusinu_sinuosuurandomu_urandomubinasciiuhexlifyu_hexlifyu__all__u NV_MAGICCONSTuTWOPIuLOG4u SG_MAGICCONSTuBPFu RECIP_BPFu_randomuRandomu SystemRandomu_test_generatoru_testu_instuseedurandomuuniformu triangularurandintuchoiceu randrangeusampleushuffleu normalvariateulognormvariateu expovariateuvonmisesvariateu gammavariateugaussu betavariateu paretovariateuweibullvariateugetstateusetstateu getrandbitsu__name__(((u#/mit/python/lib/python3.0/random.pyu%sd("         ÿÿ.!