(phQISSKrSSKJrJr SSKJrJrJr SSK J r \r \r Sr SrSrSSjrSS jrSS jrSS jrSS jrS rg)N)fftifft) gammaincinvndtrndtri)primes_from_2_toc [5n[[[R"U55S-5H4nX-(d UR U5 X-nX-(dM US:XdM4 O US:waUR U5 [ U5$)zLReturn a sorted list of the unique prime factors of a positive integer. )setrintnpsqrtaddsorted)nfactorsps E/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/_qmvnt.py_factorize_intr.sueG c"''!*o1 25 KKN GA55 6  3  Av A '?cUS- n[U5n[U5nSnSnXS:aIXU-n[[U5[U5[U55nUS:XaUS- nSnOUS- nXS:aMIU$)zCompute a primitive root of the prime number `p`. Used in the CBC lattice construction. References ---------- .. [1] https://en.wikipedia.org/wiki/Primitive_root_modulo_n r r)rlenpowr )rpmrrrkdrds r_primitive_rootr >s QBR G G A A A % !*  QQQ ( 7 FAA FA % Hrc[US-5nUSn[R"U5n[R"SS[R"US- 5-/5nSnSn[R"SUS-5nUS- S-n[ U5n [R"U[ S9n [US- 5Hn XU -U-XS-'M [R"X- U 5n X- n X-U - S-n [U 5n[SU5H|n[R"U S US-S S S2XS-US S S2/5nXSUS- XOS- U---n[U[U5-5RR5nXX'M~ Xq- nXQ4$) a;Compute a QMC lattice generator using a Fast CBC construction. Parameters ---------- n_dim : int > 0 The number of dimensions for the lattice. n_qmc_samples : int > 0 The desired number of QMC samples. This will be rounded down to the nearest prime to enable the CBC construction. Returns ------- q : float array : shape=(n_dim,) The lattice generator vector. All values are in the open interval ``(0, 1)``. actual_n_qmc_samples : int The prime number of QMC samples that must be used with this lattice, no more, no less. References ---------- .. [1] Nuyens, D. and Cools, R. "Fast Component-by-Component Construction, a Reprise for Different Kernels", In H. Niederreiter and D. Talay, editors, Monte-Carlo and Quasi-Monte Carlo Methods 2004, Springer-Verlag, 2006, 371-385. r ?g?rrdtypegUUUUUU?N) rr oneshstackaranger r rangeminimumrrrealargmin)n_dim n_qmc_samplesprimesbtgmqwzmgpermjpncfcs reordereds r _cbc_latticer>Ys8ma/ 0F2JM B C %!) 445 6B A A !UQYA  q A &A 771C D 1q5\7{m3U  ::m*D 1D B " wA QB 1e_II dqsGDbDM c!HTrTN   AaC2c7Y.. / c!f  " " ) ) +w A rc [U5nSn US:Xa[U5[U5- n Sn O[XhS-5n Sn Sn Sn X:avX:aq[[R "S5U -5n U"XX#4SU0UD6upnX- n SSX- S--- nU UX- -- n [R "U5U -n X:aX:aMqXU 4$) aPAutomatically rerun the integration to get the required error bound. Parameters ---------- func : callable Either :func:`_qmvn` or :func:`_qmvt`. covar, low, high : array As specified in :func:`_qmvn` and :func:`_qmvt`. rng : Generator, optional default_rng(), yada, yada error : float > 0 The desired error bound. limit : int > 0: The rough limit of the number of integration points to consider. The integration will stop looping once this limit has been *exceeded*. **kwds : Other keyword arguments to pass to `func`. When using :func:`_qmvt`, be sure to include ``nu=`` as one of these. Returns ------- prob : float The estimated probability mass within the bounds. est_error : float 3 times the standard error of the batch estimates. n_samples : int The number of integration points actually used. rr gV瞯 n_batches The number of points to sample. This number will be divided into `n_batches` batches that apply random offsets of the sampling lattice for each batch in order to estimate the error. covar : (n, n) float array Possibly singular, positive semidefinite symmetric covariance matrix. low, high : (n,) float array The low and high integration bounds. rng : Generator, optional default_rng(), yada, yada lattice : 'cbc' or callable The type of lattice rule to use to construct the integration points. n_batches : int > 0, optional The number of QMC batches to apply. Returns ------- prob : float The estimated probability mass within the bounds. est_error : float 3 times the standard error of the batch estimates. rrrr@r rN)_permuted_choleskyshaperBr>maxr zerosr(r)fullcopyrandomastyper absphinvmeanr)r5rFrGrHrAlattice n_batchescholohirctr:rcidcirM error_varr2r.y i_samplesr8dcpvir4xr<rNrLs r_qmvnrrs-6%U6KCR ! A TB BqEBJA BqEBJA B &C DI#AE3q~q+ABA} !a%'(A -(1,I 9  GGM2 & WW]C ( WWYq!A!a%9$szz|3A # AAEAIAAF +Aa!eQhKArrE Qrr1uX%AQTBRUQY"$%ARUQY"$%ABbBWWY !a% (  Ui'1q51AE9 +.BGGI&&I )I I %%rc^^^ ^ ^ ^ ^ ^[XU5umm m TRSm T S- mTSn[T SU- 5n[T SU- 5nUm UT - m UU U U U U UU4SjnUT4$)aTransform the multivariate normal integration into a QMC integrand over a unit hypercube. The dimensionality of the resulting hypercube integration domain is one less than the dimensionality of the original integrand. Note that this transformation subsumes the integration bounds in order to account for infinite bounds. The QMC integration one does with the returned integrand should be on the unit hypercube. Parameters ---------- covar : (n, n) float array Possibly singular, positive semidefinite symmetric covariance matrix. low, high : (n,) float array The low and high integration bounds. use_tent : bool, optional If True, then use tent periodization. Only helpful for lattice rules. Returns ------- integrand : Callable[[NDArray], NDArray] The QMC-integrable integrand. It takes an ``(n_qmc_samples, ndim_integrand)`` array of QMC samples in the unit hypercube and returns the ``(n_qmc_samples,)`` evaluations of at these QMC points. ndim_integrand : int The dimensionality of the integrand. Equal to ``n-1``. rr rVcT>[U5n[[R"US55nUT:Xde[R"X45n[R"UT 5n[R"UT5nUR 5n[ ST5HnT(a[SXS- -S- 5nOXS- n[XHU--5X7S- SS24'T USU24USU2SS24-n T Xw4n [TUU - U - 5n[TUU - U - 5n X- nXe-nM U$)Nrr r) rr atleast_1dr[r\r]r)r`rarB)zsndim_qmcr.rlr:rnrorprqr<rhrrerirjrgrfrndim_integranduse_tents r integrand%_mvn_qmc_integrand..integrand8s-r7BMM"Q%01 >))) HHh. / GGM2 & WW]C ( WWYq!ABsG a(sGF +A!eQhKArrE Qrr1uX%AQTBRUQY"$%ARUQY"$%ABB r)rXrYrB)rFrGrHryrhr:rrzrerirjrgrfrrxs ` @@@@@@@r_mvn_qmc_integrandr|s}:%U6KCR ! AUN TB BqEBJA BqEBJA B b&C. n $$rc ~[S[R"U55n[R"U[RS9n[R"U[RS9n[ X#U- XH- 5upn U R Sn Sn Sn[U [X-S55unn[R"U5S-n[U5GH'n[R"U5n[R"U U45n[U 5GHnUUU-UR5-nUUR[5-n[SU-S- 5nUS:XaDUS:a'[R"S[!US- U5-5nOz[R""U5nOc[%WUW--5n[R&"SS9 UUS 2S S 24==U US 2US- 4S S 2[R(4U-- ss'S S S 5 UUS S 24n[R"U5n[R"U5n[R&"SS9 U UW-U- nU UU-U- nS S S 5 SUWS :'SUWS :'[U5S :n [U5S :n![+UU 5UU '[+UU!5UU!'UU- nUU-nGM UR-5U - US-- nU U- n US- U-US-- UU--nGM* S [R"U5-n"UU-n#U U"U#4$!,(df  GN.=f!,(df  N=f) aMultivariate t integration over box bounds. Parameters ---------- m : int > n_batches The number of points to sample. This number will be divided into `n_batches` batches that apply random offsets of the sampling lattice for each batch in order to estimate the error. nu : float >= 0 The shape parameter of the multivariate t distribution. covar : (n, n) float array Possibly singular, positive semidefinite symmetric covariance matrix. low, high : (n,) float array The low and high integration bounds. rng : Generator, optional default_rng(), yada, yada lattice : 'cbc' or callable The type of lattice rule to use to construct the integration points. n_batches : int > 0, optional The number of QMC batches to apply. Returns ------- prob : float The estimated probability mass within the bounds. est_error : float 3 times the standard error of the batch estimates. n_samples : int The number of samples actually used. r#r$rr@r rignore)invalidNi rW)rZr rasarrayfloat64rXrYr>r(r)r&r[r^r_r r`r ones_likeraerrstatenewaxisrBrb)$r5nurFrGrHrArcrdsnrerfrgrrMrkr2r.rmr8ror<rpr4rqrr:rnrlsirloishiislo_maskhi_maskrNrLs$ r_qmvtrRs> S"''"+ B **S +C ::d"** -D$U"Hdi@KCR ! A DI#As1>1'=>A} -(1,I 9  WW] # HHa' (qA!y 3::</A # AAEAIAAv6KQ$: :;A QA!a"f*%[[2ab!eHABAIq"**} = AAH31a4B &A &AX.!uqy2~!uqy2~/AdRiLAdRiL$i!mG$i!mGT']+AgJT']+AgJQB "HBGLWWY !a% (  Ui'1q51AE9 WZBGGI&&I )I I %%532 /.s?6LL. L+ . L< c *[R"U[RS9n[R"U[RS9n[R"U[RS9nURSnURXw4:wa [ S5eURU4:wdURU4:wa [ S5e[R "[R "[R"U5S55nSXS:H'XX-nXh-nXH-nXHSS2[R4-n[R"U5n [R "S[R-5n [U5GHn U S -U-n U n SnSnSnSnSn[X5HnUUU4U:dM[R "UUU45nUS:aUUSU 24U SU -nUUU- U- nUUU- U- n[U5[U5- nUU::dMuUnUnUnUnUn M X:aXKU 4XMU 4'[U[RU SU 24[RU SU 245 [U[RU S -S2U 4[RU S -S2U 45 [U[RU S -U 2U 4[RXS -U 245 [X[U 5 [XkU 5 X:aXX4'SXKU S -S24'[U S -U5H=nUUU 4==U-ss'UUU S -US -24==UUU 4XKS -US -2U 4--ss'M? [U5U:aC[R "U*U-S- 5[R "U*U-S- 5- X-- X'OUU-S- X'US :aUX'O US :aUX'XKSU S -24==U-ss'X[==U-ss'Xk==U-ss'GMSXKS2U 4'X[Xk-S- X'GM XEU4$) a+Compute a scaled, permuted Cholesky factor, with integration bounds. The scaling and permuting of the dimensions accomplishes part of the transformation of the original integration problem into a more numerically tractable form. The lower-triangular Cholesky factor will then be used in the subsequent integration. The integration bounds will be scaled and permuted as well. Parameters ---------- covar : (n, n) float array Possibly singular, positive semidefinite symmetric covariance matrix. low, high : (n,) float array The low and high integration bounds. tol : float, optional The singularity tolerance. Returns ------- cho : (n, n) float array Lower Cholesky factor, scaled and permuted. new_low, new_high : (n,) float array The scaled and permuted low and high integration bounds. r$rz!expected a square symmetric arrayzLexpected integration boundaries the same dimensions as the covariance matrixr@r#Nrr i )r arrayrrY ValueErrorrmaximumdiagrr[rQr)rB _swap_slicess_r`exp)rFrGrHtolrenew_lonew_hirrnrlsqtprepkimckdemr<lo_mhi_mrprilo_ihi_ides rrXrXs4 ((5 +C XXc ,F XXd"** -F ! A yyQF<== ||tv||t3 '  BGGCL#. /BBSyM LF LFICam C  A 771ruu9 D 1X1um   qA1a4y3WWSAY'q5ArrE QrU*Aq A +q A +YT*9BCDDB 6d)CBK beeBFmRUU1bqb5\ : beeBFGRK0"%%Q 2C D beeAE"HaK0"%%E"H 2E F B ' B ' 8I C1q56 N1q5!_AqD R Aq1uQU{N#s1a4y31uQU{A~3F'FF#%3x#~ q 01BFFD54rTrrr|rrXrrrrsYF22-     68|/&j@&L=%@W&tcLr