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uH~v^H~(HHxpHPhHt(L9gt"JHHtgLGHHAAHtHBHtHH6 HHuIHHRH+Hu H8!HuH-:H H9Gu>HHH/u H!HYHHHu,H-I:HHHuaH+u H HFH;uH~HFHXHH;uH~vmH^0HHXpHHhHt7L9ct1LHuIܾMHCIHAHtHAHtHH9LHuIIHI/Hu IMHu MbHH9Cu3HLH+u HIHHHu%"HLHu¾H/u HSI.u IDL3HHuH-8HL$8HޙHALMtA+LHuH-T8IFIH4LMtAHHuH-8dI.u IHNLHMH/u HhZHHuH-7 H*LH>y HAMHy HLHH/u HL$0kHHuH-,7}HΘLHxFH/u HL$4-HHuH-67HpLHly}H/H-6u HEHtH+u H1MtI.u IMtImu IH\$@H |KH|$HLD3rfHt)H/u HLHHH/u HLt$pLl$xH$H$H$HtH+u HH$MtI/u IjIHL$hH3RHĈA_A\@SUVWAUAVAWH`HzH3HD$XL5L3HL$0HT$8HE3Lt$(IHT$(H LDEI.Hu IL$Hu ejH+u HMuH JIM(MehMe IExI$HIE0HIE8IM@IH HAH9_uH^HtHH-@H-HLEdHHJHHH HHtHB`H )HHHu%;HuH HHSLH LHHt-HCHHLMtAHHuUH-3nMtI.u IhHtH+u HTHH.H8H+u H$HmHT$@H E3LHD$HLt$@Ht$PVHMtI.u IH.u HHunrH;=Lt=H)H豛upLH;tHH莛uq)HSILBIE`IHHHu,rH-2LH AGD3bMuH(uI/u IL$HL$XH3H`A_A^A]_^][LSHHMKH]`#MCICIKHE̟d߅CCICHICHBIS)D$PICICIC)D$` HĀ[LSHHMKHXB ICICMCHIKCICHBIS)D$PICICIC)D$`HĀ[HMLLHLPLRHLPLRHLHLJAAA AH\$Hl$Ht$ WH9HE̟d߅CLZ3HH]`#IPIHHHOHLOLH?H HHHOHGHGILfH:LfH~L;K LHLMLLLI;LGHHHOGLHLfH:LfH~L;LLMLLLGH\$Hl$ Ht$(_HLIHBLIBHBLIBHBLIBDADI H\$UVWATAUAVAWH@L$3IH$M@DDMHfDLMu M'At{AAMfH:HfI:MHfH~HHD$fH~HHHHD$I(T$ILfH~fH:fH:LML$L;fH~LAEMOAMIfH:HIIHD$(fH~IILfI:HIH?IHD$ IIgMD$ AEHD$8fH~IGLIHD$0ID$0HLL ILALGH$fH:HHMfH~HM;HIHHHH]LEH$H@A_A^A]A\_^]%>%(H(MA8HI H(@SEHALALtA@McPLHcL#IcJHCHHCDtDH#LL3I[ffH; IuHfuHH(t9t(tt H(vGH(IH(MH(H\$Ht$H|$ AVH HL3m؈D$@@=tO H"H  u)Ut HH  L@2@u?HH8t$HtLƺIHL nAm3H\$0Ht$8H|$HH A^ùH\$WH0@- 3H\$@H0_ȉS؈D$ =u6g3@ j룹4HHX L@PHHVWAVH@ILu93Bw@HSHuX`؉\$0LƋI؉D$0LƋI ؉D$0u6u2L3IHHSHtL3Ituji`````a&aDaVahazaaaaaaa bb6bLb\btbbbbbbbbcc.c@cNc\ctcccccccdd.dFdZdndd`dddde(e>eVezeeeeeeff(f>> 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" `_ numpy.random._pcg64.PCG64DXSMPCG64DXSM(seed=None) -- BitGenerator for the PCG-64 DXSM 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 DXSM is a 128-bit implementation of O'Neill's permutation congruential generator ([1]_, [2]_). PCG-64 DXSM 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 CM DXSM 128/64. It differs from `PCG64` in that it uses the stronger DXSM output function, a 64-bit "cheap multiplier" in the LCG, and outputs from the state before advancing it rather than advance-then-output. `PCG64DXSM` 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 DXSM RNG is represented by 2 128-bit unsigned integers. **State and Seeding** The `PCG64DXSM` 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, 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" `_ _pcg64__module___cython_3_2_4._common_types_metatypefunc_doc__doc__func_name__name____qualname__func_dict__dict__func_globals__globals__func_closure__closure__func_code__code__func_defaults__defaults____kwdefaults____annotations___is_coroutine__dictoffset____vectorcalloffset____weaklistoffset____reduce___cython_3_2_4.cython_function_or_methodnumpy/random/_pcg64.pyx../numpy/__init__.cython-30.pxdcpython/type.pxdnumpy/random/bit_generator.pxd 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. jumped 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 a 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. advance__reduce_cython____setstate_cython__ 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 a 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. numpy._core._multiarray_umathnumpy.core._multiarray_umath_ARRAY_API_ARRAY_API is not PyCapsule object_ARRAY_API is NULL pointermodule compiled against ABI version 0x%x but this version of numpy is 0x%xmodule was compiled against NumPy C-API version 0x%x (NumPy 1.23) but the running NumPy has C-API version 0x%x. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem.FATAL: module compiled as unknown endianFATAL: module compiled as little endian, but detected different endianness at runtime__init__numpy.random._pcg64.PCG64.__init__numpy.random._pcg64.PCG64.jump_inplacenumpy.random._pcg64.PCG64.jumpednumpy.random._pcg64.PCG64.state.__get__numpy.random._pcg64.PCG64.state.__set__numpy.random._pcg64.PCG64.advancenumpy.random._pcg64.PCG64.__reduce_cython__numpy.random._pcg64.PCG64.__setstate_cython__numpy.random._pcg64.PCG64DXSM.__init__numpy.random._pcg64.PCG64DXSM.jump_inplacenumpy.random._pcg64.PCG64DXSM.jumpednumpy.random._pcg64.PCG64DXSM.state.__get__numpy.random._pcg64.PCG64DXSM.state.__set__numpy.random._pcg64.PCG64DXSM.advancenumpy.random._pcg64.PCG64DXSM.__reduce_cython__numpy.random._pcg64.PCG64DXSM.__setstate_cython____del__numpy.random.bit_generatorBitGeneratorbuiltinstypenumpydtypeflatiterbroadcastndarraygenericnumberintegersignedintegerunsignedintegerinexactfloatingcomplexfloatingflexiblecharacterufuncSeedSequenceSeedlessSeedSequenceSeedlessSequencenumpy.random._commonInterpreter change detected - this module can only be loaded into one interpreter per process.name__loader__loader__file__origin__package__parent__path__submodule_search_locationsModule '_pcg64' has already been imported. Re-initialisation is not supported.cython_runtime__builtins__numpy.random._pcg64init numpy.random._pcg64xڥRMO1M$TʡjqBR@@zJhؓ`صۛf/U9=rc~ 4N]g̛?2I#@ζ(9b"*aN"$:=#=FRaqH&yhkGIGcM D !=JkX$EWK̑l#5^S*/$࢕'qjn޹h-k\Ь׷Pb@4̷8 kAqrqllxNd#"J:v6v6Ga$щ\v 26\-cTH@۬'a`3IF&hƂŸ\gBF? 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Expected %zd from C header, got %zd from PyObject%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd-%zd from PyObjectbase class '%.200s' is not a heap typeextension type '%.200s' has no __dict__ slot, but base type '%.200s' has: either add 'cdef dict __dict__' to the extension type or add '__slots__ = [...]' to the base typeinvalid vtable found for imported typemultiple bases have vtable conflict: '%.200s' and '%.200s'Unable to initialize pickling for %.200s__pyx_capi__%.200s does not export expected C %.8s %.200sC %.8s %.200s.%.200s has wrong signature (expected %.500s, got %.500s)variablefunction_cython_3_2_4Shared Cython type %.200s is not a type objectShared Cython type %.200s has the wrong size, try recompiling__name__ must be set to a string object__qualname__ must be set to a string object__defaults__ must be set to a tuple objectchanges to cyfunction.__defaults__ will not currently affect the values used in function calls__kwdefaults__ must be set to a dict objectchanges to cyfunction.__kwdefaults__ will not currently affect the values used in function calls__annotations__ must be set to a dict object%.200s() %s (%zd given)%.200s() %sBad call flags for CyFunctiontakes no argumentstakes exactly one argumenttakes no keyword argumentsunbound method %.200S() needs an argumentneeds an argumentcan't convert negative value to uint32_tdoes not matchcompile time Python version %d.%d of module '%.100s' %s runtime version %d.%dzlibdecompressFailed to import '%.20s.decompress' - cannot initialise module strings. 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