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statistics.cpython-311.opt-2.pyc
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Z4d>d"Z5d# Z6d$ Z7d% Z8d@d'Z9d( Z:d) Z;d*d+d,d-Z<d>d.Z=d>d/Z>d>d0Z?d>d1Z@d2 ZAd3 ZBd4 ZC e d5d6 ZDd7d8d9ZEd: ZF dd;lGmFZF n # eH$ r Y nw xY w G d< d= ZIdS )A) NormalDistStatisticsError correlation covariancefmeangeometric_mean harmonic_meanlinear_regressionmeanmedianmedian_grouped median_high median_lowmode multimodepstdev pvariance quantilesstdevvariance NFraction)Decimal)groupbyrepeat) bisect_left bisect_right)hypotsqrtfabsexperftaulogfsum)reduce)mul)Counter namedtuple defaultdict @c e Zd ZdS )r N)__name__ __module__ __qualname__ //opt/alt/python311/lib/python3.11/statistics.pyr r s Dr1 r c d}t }|j }i }|j }t | t D ]B\ }} || t t | D ] \ }} |dz } || d |z || < Cd |v r |d } n+t d | D } t t |t } | | |fS )Nr c 3 < K | ]\ }}t || V d S Nr .0dns r2 <genexpr>z_sum.<locals>.<genexpr> s. @@tq!HQNN@@@@@@r1 ) setaddgetr typemap _exact_ratiosumitemsr& _coerceint) datacounttypes types_addpartials partials_gettypvaluesr: r9 totalTs r2 _sumrP s > E EEE IH<L tT** 1 1 V # f-- 1 1DAq QJE&,q!,,q0HQKK 1 x @@x~~/?/?@@@@@ws##A ue r1 c &t fd| D \ }}}|||fS d}t }|j }t t }t t }t | t D ]S\ } } || t t | D ]-\ } |dz }|xx | z cc< |xx | | z z cc< .T|st d x}nxd |v r |d x}nit d | D } t d | D } || z | | z z |z }| |z t t |t }|||fS )Nc 3 , K | ]}|z xz V d S r6 r0 )r8 xcr9 s r2 r; z_ss.<locals>.<genexpr> s0 < <!1q5jaA - < < < < < <r1 r r4 c 3 < K | ]\ }}t || V d S r6 r r7 s r2 r; z_ss.<locals>.<genexpr> s. @@DAq!Q @@@@@@r1 c 3 B K | ]\ }}t |||z V d S r6 r r7 s r2 r; z_ss.<locals>.<genexpr> s4 DDtq!(1ac""DDDDDDr1 )rP r< r= r* rE r r? r@ rA r rB rC r& rD )rF rT rO ssdrG rH rI sx_partials sxx_partialsrL rM r: sxsxxr9 s ` @r2 _ssr\ s } < < < < <t < < <<< 335!! E EEE I c""K s##L tT** % % V # f-- % %DAq QJE NNNa NNN OOOq1u $OOOO % 1++ aa d##aa @@K,=,=,?,?@@@ @ @DD|/A/A/C/CDDDDD s{R"W$- Jws##A sAu r1 c t | S # t $ r t j | cY S w xY wr6 ) is_finiteAttributeErrormathisfinite)rS s r2 _isfiniterb sF {{}} }Q s 77c | |u r| S |t u s |t u r| S | t u r|S t || r|S t | | r| S t | t r|S t |t r| S t | t rt |t r|S t | t rt |t r| S d}t || j |j fz )Nz"don't know how to coerce %s and %s)rE bool issubclassr float TypeErrorr- )rO Smsgs r2 rD rD s AvvqCxx199axCxx(!Q"(!Q"(!S$1H!S$1H!X :a#7#7 !U 1h 7 7 .C C1:qz22 3 33r1 c | S # t $ r Y nt t f$ r | d fcY S w xY w | j | j fS # t $ r( dt | j d}t | w xY w)Nzcan't convert type 'z' to numerator/denominator) as_integer_ratior_ OverflowError ValueError numerator denominatorr? r- rg )rS ri s r2 rA rA s :!!### : & 4y Q]++ QT!WW%5QQQnn s ::: A 2A>c t | |u r| S t |t r| j dk rt } || S # t $ r: t |t r# || j || j z cY S w xY w)Nr4 )r? re rE ro rf rg r rn )valuerO s r2 _convertrr M s 0 E{{a !S e /1 4 4 qxx a ! ! 1U_%%%*;(<(<< < < < s A A B B negative valuec # H K | D ]}|dk rt | |V d S )Nr )r )rM errmsgrS s r2 _fail_negrv _ sD A q55!&)) ) r1 r: mreturnc P t j | |z }|||z |z | k z S r6 )r` isqrt)r: rw as r2 _integer_sqrt_of_frac_rtor| g s/ P 16A !A r1 _sqrt_bit_widthc | | z t z dz }|dk r t | |d|z z |z }d}n t | d|z z | }d| z }||z S )Nr} r r4 ) bit_lengthr r| )r: rw qrn ro s r2 _float_sqrt_of_fracr s s ; !,,.. (? :q@AAvv-aa!e<<A -a26k1== A2g { ""r1 c | dk r| st d S | | }} t | t | z }| \ }}| }| \ }}d| z ||z dz z |||z ||z z dz z k r|S | }| \ } } d| z || z dz z ||| z | |z z dz z k r|S |S )Nr z0.0 r} )r r rk next_plus next_minus) r: rw rootnrdrplusnpdpminusnmdms r2 _decimal_sqrt_of_fracr s# = Avv "5>> !rA21 AJJ # ) ) + +D " " $ $FB >> D " " $ $FB1u2zABB 2 222 OO E # # % %FB1u2zABB 2 222 Kr1 c z t | \ }}}|dk rt d t ||z | S )Nr4 z%mean requires at least one data point)rP r rr )rF rO rN r: s r2 r r sF t**KAua1uu EFFF EAIq ! !!r1 c t | n"# t $ r dfd} || } Y nw xY w|%t | }st d |z S t | }n.# t $ r! t | }t | }Y nw xY wt t t | | }|k rt d t | }|st d ||z S )Nr c 3 B K t | d D ] \ }|V d S )Nr4 )start) enumerate)iterablerS r: s r2 rG zfmean.<locals>.count s< !(!444 1 r1 z&fmean requires at least one data pointz(data and weights must be the same lengthz sum of weights must be non-zero)lenrg r% r listr@ r' )rF weightsrG rN num_weightsnumdenr: s @r2 r r sC II uT{{ T L!"JKK Kqy#'ll # # #w--'ll # s3g&& ' 'CK HIII w--C A ?@@@ 9s 33 A. .(BBc t t t t | S # t $ r t d d w xY w)NzGgeometric mean requires a non-empty dataset containing positive numbers)r! r r@ r$ rm r )rF s r2 r r se G5S$ (())) G G G < = =BF GGs .2 A c . t | | u rt | } d}t | }|dk rt d |dk rQ|O| d }t |t j t f r|dk rt | |S t d |t d| }|}nmt | |u rt | }t | |k rt d t d t || D \ }}} t | | } t d t || D \ }}} n# t $ r Y dS w xY w|dk rt d t ||z | S ) Nz.harmonic mean does not support negative valuesr4 z.harmonic_mean requires at least one data pointr zunsupported typez*Number of weights does not match data sizec 3 K | ]}|V d S r6 r0 )r8 ws r2 r; z harmonic_mean.<locals>.<genexpr> s" G Gq G G G G G Gr1 c 3 . K | ]\ }}|r||z nd V dS )r Nr0 )r8 r rS s r2 r; z harmonic_mean.<locals>.<genexpr> s3 P PTQ 0q1uuq P P P P P Pr1 z Weighted sum must be positive)iterr r r isinstancenumbersRealr rg r rP rv zipZeroDivisionErrorrr ) rF r ru r: rS sum_weights_rO rN rG s r2 r r s , DzzTDzz =F D A1uu NOOO aGO G a',0 1 1 01uu%f---H .// /A,, ==G # #7mmG w<<1 !"NOO O G GIgv,F,F G G G G G;v&& P PS$=O=O P P PPP5%% qq zz =>>> K%' + ++s ";E E,+E,c t | } t | }|dk rt d |dz dk r | |dz S |dz }| |dz | | z dz S Nr no median for empty datar} r4 sortedr r )rF r: is r2 r r % sw $<<D D AAvv 89991uzzAF| FQU d1g%**r1 c t | } t | }|dk rt d |dz dk r | |dz S | |dz dz S r r rF r: s r2 r r = se $<<D D AAvv 89991uzzAF|AFQJ r1 c t | } t | }|dk rt d | |dz S )Nr r r} r r s r2 r r S sE $<<D D AAvv 8999 Q<r1 ?c v t | } t | }|st d | |dz }t | | }t | || } t | }t | }n # t $ r t d w xY w||dz z }|}||z }|||dz |z z |z z S )Nr r} )loz$Value cannot be converted to a floatr+ )r r r r r rf rm rg ) rF intervalr: rS r jLcffs r2 r r f s )T $<<D D A : 8999 Q!V A D! AT1###AA?? !HH A A A?@@@A HsNA B AA x1q52:&* **s A> >Bc t t | d } |d d S # t $ r t d d w xY w)Nr4 r zno mode for empty data)r( r most_common IndexErrorr )rF pairss r2 r r sn , DJJ + +A . .EBQx{ B B B 677TABs A Ac t t | }|sg S t | fd| D S )Nc & g | ] \ }}|k |S r0 r0 )r8 rq rG maxcounts r2 <listcomp>z multimode.<locals>.<listcomp> s' J J JleU8I8IE8I8I8Ir1 )r( r maxrM rC )rF countsr s @r2 r r sa T$ZZ F 6==??##H J J J Jfllnn J J JJr1 r exclusive)r: methodc |dk rt d t | } t | }|dk rt d |dk rg|dz }g }t d| D ]M}t ||z | \ }}| | ||z z | |dz |z z |z } | | N|S |dk r||dz }g }t d| D ]b}||z |z }|dk rdn||dz k r|dz n|}||z ||z z }| |dz ||z z | | |z z |z } | | c|S t d| )Nr4 zn must be at least 1r} z"must have at least two data points inclusiver zUnknown method: )r r r rangedivmodappendrm ) rF r: r ldrw resultr r delta interpolateds r2 r r s 1uu 4555 $<<D TB Avv BCCC Fq! ( (A a!eQ''HAu Gq5y 1DQK%4G G1LL MM, ' ' ' ' Fq! ( (AA AUUBqD1aAaC!A#IE QK1u9 5Q% G1LL MM, ' ' ' ' 222 3 33r1 c t | | \ }}}}|dk rt d t ||dz z | S )Nr} z*variance requires at least two data pointsr4 r\ r rr )rF xbarrO ssrT r: s r2 r r 6 sO $J dD//KAr1a1uu JKKK B!a%L! $ $$r1 c ~ t | | \ }}}}|dk rt d t ||z | S )Nr4 z*pvariance requires at least one data pointr )rF murO r rT r: s r2 r r b sK !D dB--KAr1a1uu JKKK BFA r1 c t | | \ }}}}|dk rt d ||dz z }t |t rt |j |j S t |j |j S Nr} z'stdev requires at least two data pointsr4 r\ r re r r rn ro r )rF r rO r rT r: msss r2 r r s~ dD//KAr1a1uu GHHH A,C!W E$S]CODDD s}co > >>r1 c t | | \ }}}}|dk rt d ||z }t |t rt |j |j S t |j |j S )Nr4 z'pstdev requires at least one data pointr )rF r rO r rT r: r s r2 r r sz dB--KAr1a1uu GHHH q&C!W E$S]CODDD s}co > >>r1 c 6 t | \ }}}}|dk rt d ||dz z } t | t |j |j fS # t $ r1 t | t | t | z fcY S w xY wr )r\ r rf r rn ro r_ )rF rO r r r: r s r2 _mean_stdevr s PYYNAr41uu GHHH A,C4T{{ / s O OOO 4 4 4T{{E$KK%)) 333334s (A 8BBc @ t | }t | |k rt d |dk rt d t | |z t | |z t fdt | | D }||dz z S )NzDcovariance requires that both inputs have same number of data pointsr} z,covariance requires at least two data pointsc 3 4 K | ]\ }}|z |z z V d S r6 r0 r8 xiyir ybars r2 r; z covariance.<locals>.<genexpr> 4 AAVRT b4i(AAAAAAr1 r4 )r r r% r )rS yr: sxyr r s @@r2 r r s AA 1vv{{ deee1uu LMMM 77Q;D 77Q;D AAAAAs1ayyAAA A AC !a%=r1 c t | }t | |k rt d |dk rt d t | |z t | |z t fdt | | D }t fd| D }t fd|D } |t ||z z S # t $ r t d w xY w)NzEcorrelation requires that both inputs have same number of data pointsr} z-correlation requires at least two data pointsc 3 4 K | ]\ }}|z |z z V d S r6 r0 r s r2 r; z correlation.<locals>.<genexpr> r r1 c 3 , K | ]}|z xz V d S r6 r0 r8 r r9 r s r2 r; z correlation.<locals>.<genexpr> 0 00R$Y!#000000r1 c 3 , K | ]}|z xz V d S r6 r0 )r8 r r9 r s r2 r; z correlation.<locals>.<genexpr> r r1 z&at least one of the inputs is constant)r r r% r r r ) rS r r: r r[ syyr9 r r s @@@r2 r r s+ AA 1vv{{ efff1uu MNNN 77Q;D 77Q;D AAAAAs1ayyAAA A AC 00000a000 0 0C 00000a000 0 0CHT#)__$$ H H H FGGGHs C' 'DLinearRegressionslope interceptF) proportionalc r t | }t | |k rt d |dk rt d |rAt d t | | D }t d | D }njt | |z t | |z t fdt | | D }t fd| D } ||z }n # t $ r t d w xY w|rd n | z z }t || S ) NzKlinear regression requires that both inputs have same number of data pointsr} z3linear regression requires at least two data pointsc 3 & K | ] \ }}||z V d S r6 r0 )r8 r r s r2 r; z$linear_regression.<locals>.<genexpr>/ s* 33vr227333333r1 c 3 K | ] }||z V d S r6 r0 )r8 r s r2 r; z$linear_regression.<locals>.<genexpr>0 s& ''r27''''''r1 c 3 4 K | ]\ }}|z |z z V d S r6 r0 r s r2 r; z$linear_regression.<locals>.<genexpr>4 s4 EERBI"t),EEEEEEr1 c 3 , K | ]}|z xz V d S r6 r0 r s r2 r; z$linear_regression.<locals>.<genexpr>5 s0 44BdNAa'444444r1 z x is constant r )r r r% r r r ) rS r r r: r r[ r r r9 r r s @@@r2 r r sk $J AA 1vv{{ klll1uu STTT 533Q33333''Q'''''Aww{Aww{EEEEE3q!99EEEEE44444!44444/c / / / o.../#< )<I %9 = = ==s 9C? ?Dc | dz }t | dk rpd||z z }d|z dz |z dz |z dz |z dz |z d z |z d z |z d z |z }d |z d z |z dz |z dz |z dz |z dz |z dz |z dz }||z }|||z z S |dk r| nd| z }t t | }|dk r^|dz }d|z dz |z dz |z dz |z dz |z d z |z d z |z d z }d |z d z |z d!z |z d"z |z d#z |z d$z |z d%z |z dz }n]|dz }d&|z d'z |z d(z |z d)z |z d*z |z d+z |z d,z |z d-z }d.|z d/z |z d0z |z d1z |z d2z |z d3z |z d4z |z dz }||z }|dk r| }|||z z S )5N ?g333333?g Q ?g^}o)@gE.kR@g U l@g*u>l@g N@g"]Ξ@gnC`@gu @giK~j@gv|E@gd|1@gfRr@gu.2@g~y@gn8(E@r r g @g?g鬷ZaI?ggElD?g7\?guSS?g=. @gj%b@gHw@gjRe?g9dh? >g('߿A?g~z ?g@3?gɅ3?g3fRx?gIFl @gt>g*Yn>gESB\T?gN;A+?gUR1?gE F?gPn@g&>@gi<g@F>gtcI,\>gŝI?g*F2v?gC4?gO1?)r r r$ )pr sigmar rr r rS s r2 _normal_dist_inv_cdfr A s CA Aww% q1u 0140145601456 11 566 1 1 56 6 1 1 56 6 1 1 56 6 11 566 1140145601456 11 566 1 1 56 6 1 1 56 6 1 1 56 6 #IQY #XX37A c!ffW ACxx G1A51256712567 22 677 2 2 67 7 2 2 67 7 2 2 67 7 22 2A51256712567 22 677 2 2 67 7 2 2 67 7 2 2 67 7 G1A51256712567 22 677 2 2 67 7 2 2 67 7 2 2 67 7 22 3Q61256712567 22 677 2 2 67 7 2 2 67 7 2 2 67 7 c A3ww B U r1 )r c ( e Zd Z dddZd#dZed Zdd d Zd Zd Z d Z d$dZ d Z d Z ed Zed Zed Zed Zed Zd Zd Zd Zd Zd Zd ZeZd ZeZ d Z d Z d Z d! Z d" Z!dS )%r z(Arithmetic mean of a normal distributionz+Standard deviation of a normal distribution_mu_sigmar r c |dk rt d t | | _ t | | _ d S )Nr zsigma must be non-negative)r rf r r )selfr r s r2 __init__zNormalDist.__init__ s; N 3;;!">?? ?99Ell r1 c ( | t | S r6 )r )clsrF s r2 from_sampleszNormalDist.from_samples s ?sK%%&&r1 N)seedc | t j nt j | j | j | j cfdt | D S )Nc ( g | ]} S r0 r0 )r8 r gaussr r s r2 r z&NormalDist.samples.<locals>.<listcomp> s% 333Qb% 333r1 )randomr Randomr r r )r r: r r r r s @@@r2 sampleszNormalDist.samples sY G $ &-2E2E2KHdk E333333%((3333r1 c | j | j z }|st d || j z }t ||z d|z z t t |z z S )Nz$pdf() not defined when sigma is zerog )r r r r! r r# )r rS r diffs r2 pdfzNormalDist.pdf sb >;, J!"HII I48|4$;$/233d3>6J6JJJr1 c | j st d ddt || j z | j t z z z z S )Nz$cdf() not defined when sigma is zeror r )r r r" r _SQRT2r rS s r2 cdfzNormalDist.cdf sI 6{ J!"HII IcCTX $+2F G H HHIIr1 c |dk s|dk rt d | j dk rt d t || j | j S )Nr r z$p must be in the range 0.0 < p < 1.0z-cdf() not defined when sigma at or below zero)r r r r )r r s r2 inv_cdfzNormalDist.inv_cdf s[ 88qCxx!"HII I ;# !"QRR R#Atx===r1 r c B fdt d D S )Nc @ g | ]} |z S r0 )r )r8 r r: r s r2 r z(NormalDist.quantiles.<locals>.<listcomp> s) 999 QU##999r1 r4 )r )r r: s ``r2 r zNormalDist.quantiles s0 :9999U1a[[9999r1 c t |t st d | |}}|j |j f|j |j fk r||}}|j |j }}|r|st d ||z }t |j |j z }|s%dt |d|j z t z z z S |j |z |j |z z }|j |j z t ||z |t ||z z z z } || z |z } || z |z } dt | | | | z t | | | | z z z S )Nz$Expected another NormalDist instancez(overlap() not defined when sigma is zeror r+ ) r r rg r r r r r r" r r r$ r ) r otherXYX_varY_vardvr r{ bx1x2s r2 overlapzNormalDist.overlap s %,, D BCC CU1 Hae !% 0 0 0aqAz1:u NE N!"LMM M U] !%!%- =R3>F#: ;<<< < EEMAEEM ) Hqx $rBwc%%-6H6H1H'H"I"I I!er\!er\d15599quuRyy011DrQUU2YY9N4O4OOPPr1 c T | j st d || j z | j z S )Nz'zscore() not defined when sigma is zero)r r r r s r2 zscorezNormalDist.zscore s6 { M!"KLL LDH ++r1 c | j S r6 r r s r2 r zNormalDist.mean s 5xr1 c | j S r6 r* r+ s r2 r zNormalDist.median s 6xr1 c | j S r6 r* r+ s r2 r zNormalDist.mode s xr1 c | j S r6 r r+ s r2 r zNormalDist.stdev s 8{r1 c " | j | j z S r6 r/ r+ s r2 r zNormalDist.variance s +{T[((r1 c t |t r5t | j |j z t | j |j S t | j |z | j S r6 r r r r r r$ r% s r2 __add__zNormalDist.__add__! Z b* % % L bfrvouRY /J/JKK K"&2+ry111r1 c t |t r5t | j |j z t | j |j S t | j |z | j S r6 r2 r3 s r2 __sub__zNormalDist.__sub__/ r5 r1 c ^ t | j |z | j t | z S r6 r r r r r3 s r2 __mul__zNormalDist.__mul__= , "&2+ry488';<<<r1 c ^ t | j |z | j t | z S r6 r9 r3 s r2 __truediv__zNormalDist.__truediv__E r; r1 c 8 t | j | j S r6 r r r r$ s r2 __pos__zNormalDist.__pos__M s ("&"),,,r1 c : t | j | j S r6 r? r@ s r2 __neg__zNormalDist.__neg__Q s 226'29---r1 c | |z S r6 r0 r3 s r2 __rsub__zNormalDist.__rsub__W s Fbzr1 c | t |t st S | j |j k o| j |j k S r6 )r r NotImplementedr r r3 s r2 __eq__zNormalDist.__eq__] s: P"j)) "! !v :BI$::r1 c : t | j | j f S r6 )hashr r r+ s r2 __hash__zNormalDist.__hash__c s MTXt{+,,,r1 c P t | j d| j d| j dS )Nz(mu=z, sigma=))r? r- r r r+ s r2 __repr__zNormalDist.__repr__g s. t**%OO48OOt{OOOOr1 c | j | j fS r6 r r+ s r2 __getstate__zNormalDist.__getstate__j s x$$r1 c $ |\ | _ | _ d S r6 r )r states r2 __setstate__zNormalDist.__setstate__m s % $+++r1 )r r )r )"r- r. r/ __slots__r classmethodr r r r r r r& r( propertyr r r r r r4 r7 r: r= rA rC __radd__rE __rmul__rH rK rN rP rS r0 r1 r2 r r s- . :? I # # # # ' ' [' "& 4 4 4 4 4 K K KJ J J > > > : : : : Q Q QD , , , X X X X ) ) X) 2 2 2 2 2 2 = = == = =- - -. . . H H; ; ; - - -P P P% % %& & & & &r1 r r6 )rs )r )J__all__r` r r sys fractionsr decimalr itertoolsr r bisectr r r r r r! r" r# r$ r% functoolsr& operatorr' collectionsr( r) r* r rm r rP r\ rb rD rA rr rv rE r| float_infomant_digr __annotations__rf r r r r r r r r r r r r r r r r r r r r r r r _statistics ImportErrorr r0 r1 r2 <module>rg sv hT . % % % % % % % % , , , , , , , , < < < < < < < < < < < < < < < < < < < < 8 8 8 8 8 8 8 8 8 8 c j 3 3 3 l& & & & R 4 4 4>+ + + \ $ 3>22Q6 6 6 6 #3 #3 #5 # # # #S S W <" " ",# # # #LG G G&5, 5, 5, 5,p+ + +0 , &E+ E+ E+ E+PB B B<K K Kr ; (4 (4 (4 (4 (4b)% )% )% )%X& & & & R? ? ? ?$? ? ? ?$ 4 4 4( 8 H H HB : 02HII 05 8> 8> 8> 8> 8>|G G G V 0000000 D \& \& \& \& \& \& \& \& \& \&s D D'&D'