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E11LX AYADLA E15H{H9Hb[LLM|IbH1L[HH|H XN AH=r?E&vXIHLHLHH9]jIMIFIFHHHGHcHDLHEL8EPLGAŅM1AE1I/AHt H+Mt I(H bEDH=,sMk I,$AJH<$tH $HHD$HH:H(D[]A\A]A^A_LhDLXDHHDL8DLL(D1LDE1I. H5ϔHH9]P]hIM0IFIFH HX H/ LF‰H9] I. H|$It$DHh;GI,$LXCHHCL8CWLLD$#CLD$fHLD$CLD$fLB]1LLSFH$HlLBH-L%2HEHHH=%A1HLHDHp HggHmH BAH=^* q@+FIbH$E1E1AI.LLAE1f.EIH IM I/$I~H;=lInHMnHEIEI.gLHLPlHmII,$M HmImH-H}H9HAHL kHH I/H/cHm=THt$T$=T$t$7DLLLZAIHZfH=HH5iITfDL=OfE1QAfDcAI-H=L=HGLHHHIMHkLH5 <H81@O5L>> from numpy.random import Generator, PCG64DXSM, SeedSequence >>> sg = SeedSequence(1234) >>> rg = [Generator(PCG64DXSM(s)) for s in sg.spawn(10)] **Compatibility Guarantee** ``PCG64DXSM`` makes a guarantee that a fixed seed will always produce the same random integer stream. References ---------- .. [1] `"PCG, A Family of Better Random Number Generators" `_ .. [2] O'Neill, Melissa E. `"PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation" `_ Get or set the PRNG state Returns ------- state : dict Dictionary containing the information required to describe the state of the PRNG PCG64(seed=None) BitGenerator for the PCG-64 pseudo-random number generator. Parameters ---------- seed : {None, int, array_like[ints], SeedSequence}, optional A seed to initialize the `BitGenerator`. If None, then fresh, unpredictable entropy will be pulled from the OS. If an ``int`` or ``array_like[ints]`` is passed, then it will be passed to `SeedSequence` to derive the initial `BitGenerator` state. One may also pass in a `SeedSequence` instance. Notes ----- PCG-64 is a 128-bit implementation of O'Neill's permutation congruential generator ([1]_, [2]_). PCG-64 has a period of :math:`2^{128}` and supports advancing an arbitrary number of steps as well as :math:`2^{127}` streams. The specific member of the PCG family that we use is PCG XSL RR 128/64 as described in the paper ([2]_). ``PCG64`` provides a capsule containing function pointers that produce doubles, and unsigned 32 and 64- bit integers. These are not directly consumable in Python and must be consumed by a ``Generator`` or similar object that supports low-level access. Supports the method :meth:`advance` to advance the RNG an arbitrary number of steps. The state of the PCG-64 RNG is represented by 2 128-bit unsigned integers. **State and Seeding** The ``PCG64`` state vector consists of 2 unsigned 128-bit values, which are represented externally as Python ints. One is the state of the PRNG, which is advanced by a linear congruential generator (LCG). The second is a fixed odd increment used in the LCG. The input seed is processed by `SeedSequence` to generate both values. The increment is not independently settable. **Parallel Features** The preferred way to use a BitGenerator in parallel applications is to use the `SeedSequence.spawn` method to obtain entropy values, and to use these to generate new BitGenerators: >>> from numpy.random import Generator, PCG64, SeedSequence >>> sg = SeedSequence(1234) >>> rg = [Generator(PCG64(s)) for s in sg.spawn(10)] **Compatibility Guarantee** ``PCG64`` makes a guarantee that a fixed seed will always produce the same random integer stream. References ---------- .. [1] `"PCG, A Family of Better Random Number Generators" `_ .. [2] O'Neill, Melissa E. `"PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation" `_ __pyx_capi__name__loader__loader__file__origin__package__parent__path__submodule_search_locationsan integer is requiredname '%U' is not definednumpy/random/_pcg64.c%s (%s:%d)%d.%dbuiltinscython_runtime__builtins__18446744073709551616numpy.random.bit_generatorBitGeneratornumpydtypeflatiterbroadcastndarraygenericnumberunsignedintegerinexactcomplexfloatingflexiblecharacterufuncSeedSequenceSeedlessSequencenumpy.random._commondoubleLEGACY_POISSON_LAM_MAXuint64_tMAXSIZEwrap_int_pcg64.pyxinit numpy.random._pcg64stringsourceat leastat mostjumpedMissing type object__init____del__numpy.random._pcg64.PCG64DXSMstateadvance__reduce_cython____setstate_cython__numpy.random._pcg64.PCG64!"!!!qԠڠۭҭ/'1\bcZ="self._bitgen,self.rng_state cannot be converted to a Python object for picklingnumpy.core.umath failed to importnumpy.core.multiarray failed to importstate must be for a {0} RNGstate must be a dictcline_in_traceback__setstate_cython__generate_state__reduce_cython__bit_generatorImportError__pyx_vtable__has_uint32ValueError__reduce_ex__TypeErrorPCG64DXSMuinteger__setstate____getstate__advanceuint64__reduce____import__formatstatenumpyjumpsemptydtype__class__PCG64__test__seed__name____main____init__incget__all__np<@;='0 lm|pX @8L`t`@p8LPtP !$p##$0%%0'P'()403$ 7p 8 8 9 :0 A H pS8 ^ g q( @t `  p @ ,0@zRx $FJ w?;*3$"DOX<{ldQP{c$0&DaHx&Da(D` D D0$X<At K ` H Q A@ G h H $0WBDA LAB$_kBIC YABDBEL E(A0A8E@8D0A(B BBB8<W~BEH A(A0b(D BBB8x`BBE A(A0J(D BBBMbjHBBE B(A0A8DP8D0A(B BBB<AD A AI G AH V AI G AC (\(BAG U DBK P BHE A(D0JHfA\0D(A BBBPHBBA s EBI A BBC D BBH H IBM d0`BBB B(D0D8Hh 8A0A(B BBBF  8F0A(B BBBA x$HAt K ` H QD` D 0DtBEG e EBF lEB4$|BAD B DBA @ AEJ 8\BEA G(G0s (D ABBF DL BIA [ ABF L ABA \ AEF \ (BEI A(G0u (D ABBJ [ (D ABBD \ (D DBBH d@!BBE E(D0A8F 8A0A(B BBBH d 8A0A(B BBBJ 8BBB A(J(A BBBH'BBBB B(A0D8DP 8D0A(B BBBA H0*BBBB B(A0D8DP 8D0A(B BBBA ,|-BHH h CBA ,X.BHH h CBA ,/BHH h CBA , /BHH h CBA T<h0 BBB E(A0A8DPeXI`YXFP_ 8D0A(B BBBF T 7 BBB E(A0A8DPeXI`YXFP_ 8D0A(B BBBF T= BBB E(A0A8D`hIpYhF`b 8D0A(B BBBH TD 0H BBB E(A0A8D`hIpYhF`b 8D0A(B BBBH H Ry BBB B(A0D8JP 8D0A(B BBBE H [y BBB B(A0D8JP 8D0A(B BBBE H4 dBBB B(A0A8Dp& 8D0A(B BBBG H tBBB B(A0A8Dp& 8D0A(B BBBG H BBB B(A0A8D`l 8D0A(B BBBI H BBB B(A0A8D`l 8D0A(B BBBI d  T| H1EEE B(A0D8 0A(B BBBB A0G(B BBB$ 0<K^C MAA$ H5KWC MAA$ `g8 5L +`^ ^@mx @ 0m8mo`   p(8 ooooHm6@F@V@f@v@@@@@@@@@AA&A6AFAVAfAvAAAAAAAAABB&B6BFBVBfBvBBBBBBBBBCC&C6CFCVCfCvCCCCCCCCCDD&D6DFDVDfDvDDDDDDDDDEE&E6EFEVEfEvEEEEEEEEE advance(delta) Advance the underlying RNG as-if delta draws have occurred. Parameters ---------- delta : integer, positive Number of draws to advance the RNG. Must be less than the size state variable in the underlying RNG. Returns ------- self : PCG64 RNG advanced delta steps Notes ----- Advancing a RNG updates the underlying RNG state as-if a given number of calls to the underlying RNG have been made. In general there is not a one-to-one relationship between the number output random values from a particular distribution and the number of draws from the core RNG. This occurs for two reasons: * The random values are simulated using a rejection-based method and so, on average, more than one value from the underlying RNG is required to generate an single draw. * The number of bits required to generate a simulated value differs from the number of bits generated by the underlying RNG. For example, two 16-bit integer values can be simulated from a single draw of a 32-bit RNG. Advancing the RNG state resets any pre-computed random numbers. This is required to ensure exact reproducibility. jumped(jumps=1) Returns a new bit generator with the state jumped. Jumps the state as-if jumps * 210306068529402873165736369884012333109 random numbers have been generated. Parameters ---------- jumps : integer, positive Number of times to jump the state of the bit generator returned Returns ------- bit_generator : PCG64DXSM New instance of generator jumped iter times Notes ----- The step size is phi-1 when multiplied by 2**128 where phi is the golden ratio. advance(delta) Advance the underlying RNG as-if delta draws have occurred. Parameters ---------- delta : integer, positive Number of draws to advance the RNG. Must be less than the size state variable in the underlying RNG. Returns ------- self : PCG64 RNG advanced delta steps Notes ----- Advancing a RNG updates the underlying RNG state as-if a given number of calls to the underlying RNG have been made. In general there is not a one-to-one relationship between the number output random values from a particular distribution and the number of draws from the core RNG. This occurs for two reasons: * The random values are simulated using a rejection-based method and so, on average, more than one value from the underlying RNG is required to generate an single draw. * The number of bits required to generate a simulated value differs from the number of bits generated by the underlying RNG. For example, two 16-bit integer values can be simulated from a single draw of a 32-bit RNG. Advancing the RNG state resets any pre-computed random numbers. This is required to ensure exact reproducibility. jumped(jumps=1) Returns a new bit generator with the state jumped. Jumps the state as-if jumps * 210306068529402873165736369884012333109 random numbers have been generated. Parameters ---------- jumps : integer, positive Number of times to jump the state of the bit generator returned Returns ------- bit_generator : PCG64 New instance of generator jumped iter times Notes ----- The step size is phi-1 when multiplied by 2**128 where phi is the golden ratio. ``hD `EXEP(E HE @D 8F0hE(F DE PDEEEDFXE ؒD ВE ȒFE EE E FEC'C"DxxE pDhE`EX@CPPHE HpD@E8E00D(D E pE8E A`=HM;B jD)paj@aYBp@4BЀx_BP sgB0~yBP}BbD5i b@aYBP4B`_BЭ{gByBGCC: (GNU) 10.2.1 20210130 (Red Hat 10.2.1-11) p^O- ^{Y @_d _Q `{ `c aO a @a&Г% paxX a&ؓ b b b! cI FWet WFk F G~ =H`s IM! I4Gh[xlpPH d e L  Pf @g`> ixm j j `kt k| `m' nB n([ pnph M  '3?MlHx@phؑ*0JБY8g ȑX 0 \   zB  `  H  vB  P   8 p     X (   0  P}^  0~      Ѐ E U @e y      (P>HYj~` ؐ Py 7Mhx Эy -xG Py8Ȓؒ  pU k А Ȑ(>Y(~ @@80 ('@h7 D K EY (E k E } D  F hE F D E  PD E E E! 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