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v<t&H <Hn~MIM@H m:kHCIHHLMtA=HHu vIGLHNILMtA=yH/H-@[u?H;4H/u H:IG`HIL@AHHu'H-ZLH ]uD3Hu!H(u:IMH.u H:H\$XIHl$`Ht$hH0A_A^_LATAUHHH3HD$`HLI[E3IkHHAIsHI{HL$@HMsM{HuH50ZH+HLu9H MHAH9uHHtHH="@H=HLG$9HH:HHH HHtHB(8H HYHHu%8HuH G:HhyLH 8HuH5XY HCHHLMtAy;HLHH+u H8H |HAH9)uH(HtHH5@H5HLF8HH4HHH HHtHB"7H HSHHu%6HuH A9HbxLH 7Ht$@HuH5MXHCHH=LMtAn:HHuH+H5XHH+u H7H:9H9GuLLwIIH)u H7IHHD$P3HD$XL|$H6HHunH5WMtI/u I=7MtI.u I)7HtHmu H7ILH 'rD35HHHT$HHGHALL+IHHHHl$XH?L Q7HMtI/u I6Hmu H6H/u H{6I.u Il6HuH5VBH;7t HFHvu IHIH6HHuH5;VD$(E3LDl$ 3H̻yaH+u H5H+I:6HHuH5UD$(E3LDl$ Hiy$H+H5UVH^5HH+u HJ5HUHNhuHF`HHHHuH5RUH(u 5HLHmu H4L|$pLt$xH$H$H$H$MtI,$u I4IHL$`H3 HĘA]A\LVAUHHLH3H$HBE3I[AIkHI{ McEMsM{EHL$`Ll$PLl$XH=ISLl$@E3IHHHICĬH/Hu H3HuH-Td E3E33HlH+u H3H-S4 HHHHt6HHuH-S H$E3HLHu p H/u H83HL$`IHٿH\$XLt$@HALMtA5LHuH-%S{ IFIHELMtAF5HHuH-R I.u I2AHH,5LHu  H/u Hk2I{؅yH-R I.u I=2M2L%HL$`I$HAHǾLMtA4LHuH-!R& IGIHALMtAB4HHuH-Q I/u I1HFH;g2uEHLH.u Hx1HHD$pHսH$AG L|$x@tcA}H 2H;u HAXH'H 2H;u HAXHHHj1LHwH-'Q, uAADDMGHL$pIHHH.u H!HhHg!HHu,H-AH]!HHuH/u H E3D$ E3I}HHu nH!H9Gu3HLH/u He IH HHu%.H LHu»H.u H I.u I HH\$HHHHuH-!@!HL$@HHALMtA@"LHuH-?IFIHLMtA"HHuH-?kI.u IZHLHMH.u H-oHHuH-H?HLHSy HLH2y HլLHH.u HL$XHHuH->HLHxJH.u HYL$\GHHuH-p>;HrLH~H.H->>u HHtH/u HMtI.u IMtImu IHD$HH zXHt$PLH|$`D3HD$HjH\$HHt)H.u HLHIH/u HkL$L$L$H$H$HtH.u H/H$HtH+u HIH$H3HĨA\[@SUVWAUAVAWH`HH3HD$XL5#L3HL$0HT$8HE3Lt$(IHT$(H LD5I.Hu IsL$Hu ejH+u HMMuH IM(MehMe IExI$H߹IE0H4IE8IM@IH HAH9uHHtHH-R@H-IHLETHHjHHH HHtHBXH IH艕HHu%3HuH wH[LH DHHt-HCHHLMtAHHuUH-Q;nMtI.u IHtH+u HHH.HH+u HHHT$@H E3LHD$HLt$@Ht$PFHMtI.u IH.u HpHunrH;-Lt=HQH聢upLH;tH.H^uq)HSILB3IE`IHHHu,rH-:LH !TD3gMuH(uI/u IL$HL$XH3qH`A_A^A]_^][@SUWATAUAVAWHPHI]`#L E3HJHE̟d߅CHD$@EL$EH$)D$MMMMu HH\$Ht$tdHHMHD$(MELLJIHD$ H(L$ IfofI~fsfH~MLE$$LMLL,ML;LLGHIIHD$8IHHLLLIHD$0H(D$0HfD$HD$HHHNZIH?MLD$@H(L$@H foIfsMfH~L$fI~H\$HCHH+N(M;ILSLLLLCH$HPA_A^A]A\_][@SUWATAUAVAWHPHE3LHXB HJAHD$@EL $EH$)D$EEEMu HL\$Ht$tdHHMHD$(MEHLHIHD$ H(L$ IfofH~fsfH~MLE$$LMLN,MM;LLGIIIHD$8IHILLLIHD$0H(D$0HfD$HD$HHHNJIH?MLD$@H(L$@H foIfsMfH~L$fI~L\$ICHI+N(M;II[HHIMCH$HPA_A^A]A\_][HMLLHLPLRHLPLRHLHLJAAA AH\$Hl$Ht$ WH9HE̟d߅CLZ3HH]`#IPIHHHOHLOLH?H HHOHHGHHOILLHL;K LOLMLLLI;LGHHHOLHLHOLL;LOLMLLLGH\$Hl$ Ht$(_HLIHBLIBHBLIBHBLIBDADI H(MA8HI H(@SEHALALtA@McPLHcL#IcJHCHHCDtDH#LL3I[ffH; uHfuHH(t9t(tt H(vGH(IH(MH(H\$Ht$H|$ AVH HL3m؈D$@@=tO HH s u)Ut HRH C @2@u?HH8t$HtLƺIHL A3H\$0Ht$8H|$HH A^ùH\$WH0@e 3H\$@H0_ȉLS؈D$ =ڧu6g3@ j룹4HHX L@PHHVWAVH@ILu9ȡ3Bw@H^HuX؉\$0LƋI؉D$0LƋI ؉D$0u6u2L3IHH]HtL3IItu>> 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.PCG64DXSM PCG64DXSM(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" `_ _pcg64O# `% `#`$ `'`(`P&`8&`&`&`%`% `l# $ `0% ``# $`x#`h&`%`$ `&`\#`$`$ $`$$`D$ # `d# &`#`$ `@% `#`# `%`%`% L$`,$`# `X$ `# `h#`4$`0(( X(# &`' #`% `P%`$ `h$ `%` %`#`#`(P $ `$ ` &`# `<$`& & % # `t$`$ `__module___cython_3_1_2._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_1_2.cython_function_or_method""##0#numpy/random/_pcg64.pyx../numpy/__init__.cython-30.pxdcpython/type.pxdnumpy/random/bit_generator.pxd +Qd?gcnp RNG__all__getincpop__func____init____main____name__seedself__spec____test__PCG64__class__deltadtypeemptyjumpsnumpystateenablejumped__module____reduce__uint64advancedisable__getstate____qualname____set_name____setstate__uintegerPCG64DXSMTypeErrorisenabled__pyx_state__reduce_ex__ValueErrorhas_uint32__pyx_vtable__ImportError14 JaYd!]!1qPCG64.jumped_initializing_is_coroutinePCG64.advancebit_generator__reduce_cython__generate_state__setstate_cython__PCG64DXSM.jumpedPCG64DXSM.advanceasyncio.coroutinescline_in_tracebacknumpy.random._pcg64state must be for a state must be a dictPCG64.__reduce_cython__PCG64.__setstate_cython__numpy/random/_pcg64.pyxAH BfASb %vT %vS$l. Qa #1qAH BfASb %vT %vSQat<~]!1 #1qPCG64DXSM.__reduce_cython__PCG64DXSM.__setstate_cython__numpy._core.multiarray failed to importnumpy._core.umath failed to importself._bitgen,self.rng_state cannot be converted to a Python object for pickling 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 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. 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 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. 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_generatorBitGeneratorbuiltinstypenumpydtypeflatiterbroadcastndarraygenericnumberintegersignedintegerunsignedintegerinexactfloatingcomplexfloatingflexiblecharacterufuncSeedSequenceSeedlessSequencenumpy.random._commondoublePOISSON_LAM_MAXLEGACY_POISSON_LAM_MAXuint64_tMAXSIZEPyObject *(PyObject *, PyObject *)wrap_intInterpreter 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._pcg640x100000000000000000x9e3779b97f4a7c15f39cc0605cedc835numpy.core.multiarray failed to import (auto-generated because you didn't call 'numpy.import_array()' after cimporting numpy; use 'numpy._import_array' to disable if you are certain you don't need it).name '%U' is not defined while calling a Python objectNULL result without error in PyObject_Callraise: arg 3 must be a traceback or Noneinstance exception may not have a separate valuecalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptionexception causes must derive from BaseException%s() got multiple values for keyword argument '%U'%.200s() keywords must be strings%s() got an unexpected keyword argument '%U'at leastat mostexactlys%.200s() takes %.8s %zd positional argument%.1s (%zd given)Missing type objectCannot convert %.200s to %.200skeywords must be stringsjoin() result is too long for a Python string%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. 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.No module named '%U'_cython_3_1_2Shared 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 objectfunction's dictionary may not be deletedsetting function's dictionary to a non-dict__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.%d__pyx_capi__%.200s does not export expected C variable %.200sC variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)%.200s does not export expected C function %.200sC function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)__int__ returned non-int (type %.200s). 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