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AI|$LID$H8IL0H/iV_fLVSH=AH5BHGHHIMH|$H5\HGHHIMIGH5/LHHIMI/tHnI9F]MnMPInIEHEI.LLH؋ImII,$'HEHMHEHIH=*L蒍HHI/ZH贅Hmg HT$t$Ut$T$fLLLXIHH=AHH56yIMy eLUXIsE1{ AoDH=ёTxILTA~ I|$ID$HxILpH/tTL`TH=IHH5>xIMtLfD1۽ @HTWI fDH=ِ\wI1 UIHLHLRI/LD$SD$LS H H=(A-z 1E1SIL(S- AA I/;H -DH=H(yLLL蠊IH1L VHHpH  AH='UySIHLHL\QI/}LD$FRD$hDL0RM1MD AE1DLQw cf{RIOLQI|$ID$HxILpH/XQNLpQD AQIL8QOA VRIHLHLOI/LD$PD$DLPLPLL$PL$ AE1DHP&QI LWPBIfDH={D$Lh>,H H=A e1E1>IL>-.AA1I/;H DH=PdLLLuIH1L@HHpH AH=5d>IHLHL<cf[=IOL<I|$ID$HxILpH/Xd>> 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 and 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" `_ 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 and 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" `_ AAPA`ApAuintegeruint64__test__state must be for a {0} RNGstate must be a dictstate__setstate_cython____setstate__self._bitgen,self.rng_state cannot be converted to a Python object for picklingseed__reduce_ex____reduce_cython____reduce____pyx_vtable__numpy.core.umath failed to importnumpy.core.multiarray failed to importnumpynp__name____main__jumps__init__inc__import__has_uint32__getstate__getgenerate_stateformatemptydtypecline_in_traceback__class__bit_generator__all__advanceValueErrorTypeErrorPCG64DXSMPCG64ImportError<;LHH hhT5!40x!, -(../x/0$x080L0`1tx11H2h223H33$3<4PX4px44x55,x6d(77 h==?A A\ B C D E F| H K M 8P R8 Y X` a\ a j 8k HtDtXX$phzRx $FJ w?:*3$"D@ \8 t+SL+{+h,U`,,g8-D-P-R(-S<-RP4.pd.x.c.*Ha/4JBBB A(G@ (D BBBE ^ (D EBBE U (D EBBF d?FBB B(A0D8DP 8A0A(B BBBH N 8A0A(B BBBH d4 BFBB B(A0D8DP 8A0A(B BBBH N 8A0A(B BBBH L HD{BBB B(D0D8H 8A0A(B BBBB X xFFBB E(A0A8DPtXH`YXFP 8D0A(B BBBH XH LFBB E(A0A8DPtXH`YXFP 8D0A(B BBBH  T LSIIEE B(A0D8  0A(B BBBH A0G(B BBB$ DT@O^C MAAH8 \T FBB B(A0D8JP 8D0A(B BBBG $ ]9OWC MAAH 8] FBB B(A0D8JP 8D0A(B BBBG  enX XfL FBB B(A0D8DpxIYxFpu 8A0A(B BBBH Xh LsL FBB B(A0D8DpxIYxFpu 8A0A(B BBBH  @0H \kFBB B(A0A8Dp 8D0A(B BBBD H$ kFBB B(A0A8Dp 8D0A(B BBBD p ,H FBB B(A0A8D` 8D0A(B BBBE H FBB B(A0A8D` 8D0A(B BBBE cPc @ H]P]o`  `@)@h ooooX]0@@@P@`@p@@@@@@@@@AA A0A@APA`ApAAAAAAAAABB B0B@BPB`BpBBBBBBBBBCC C0C@CPC`CpCCCCCCCCCDD D0D@DPD`DpDDDDDDDDDEE E0E@EPE`EpEEEEb 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. 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