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IxHIuLIxHIuLIxHIuLiMAEtAEIExHIEuL9H5BHH9CH5IMH5HϙLI9Gz 5IIM x HI H5NLIIMx HI IEH;Ù LHpMIyLL$19IHe LL$LHLAQIHILD$'D$fDxHIEIx HIrHQH=5zKAHtHExHHE)HXD[]A\A]A^A_Ix HIdMtIxHI+MtIx HIE1HZQH=4JMZIOHIBL5LLAąXE1LLLLLL$LL$ fLxH@hH H@(HL1LЅL Ix HI H59HHH9C 2IM H5 HƖLI9G 2IIM x HIt H5ELeIIM x HI IEH; LppMtSI~tL:HHf HD$LLAVHt$AHxBHHu9H//DH@hHH@(HLLAE Ix HIQ H5HHH9C& 1IM% H5HwLI9G U1IIM x HI] H5LIIM x HI^ IEH;k LppMI~HH' HD$LLAVHt$AHx HH E Ix HI_ H5ȩHHH9C _0IM H5ԨHULI9G 30IIM x HIS H5ԩLIIM x HIT LL4'IG x HIF H5/HHH9C /IM IGCIGHƃHAWH)HHcAH9AIx HI" H5H*HH9C, /IM IGIG H HH A_AGHH HH   Ix HI^ H<$IuDHhIEHIELHLϻsfDL`LPELL $DLHIZfDI}AtAIEHxLxH`HHS!I@L fDfDLHH)HHHLHcAH9HH,H5H8}XHAA@LXvfDkI&L(KI2LLfDfDLfDLIfDLx A_zDLXLKL>H51L8x@L#HH HKHH5H8HI-LLkHHLLHD$}LhHH5AAH8GCH0LLL$LT$LT$LL$0+IWH IiAGAWHH HcAH9?#fDAGAWHH HHcAH9 ILH HgHHEHHA`Ht@L`L9t(HCHLH $%H $t1Hy`HQ`HHLH5c@E1H81IH; LPXIMIExHIEt3'fHx?H=#8yLHH߅H58H80GQLILD$LHLD$HL$L$IHԅHIG`HtHL`L9t(HCHLL$'$L$t1I`L$IG`LL$L$MWL$HwHsLH5>E1H81\TLD$21'H@`H5HH%LHHHńH9Gu3H|$+H|$HHHHHuH;H5LnIH@`HtlHHt`LHHtSH-H9Gu4H|$H|$AHHH>HHuHvHdH5<H8[HH;H5y<H8HwH HS1L;dfHH9E1L9`JtI9CLH $HT$!H $&HT$IHK1L;dyHH91H9|HtI9WLL$HT$HL$`!L$5HT$HL$H@AWHAVH AUATUHSH|$@Ht$Ht$8xHD$IIҹHD$1fL1҃H ILLl$MHMMIHIIHLLLt$IILMIIHLHD$HIIHT$HMLIIHL<LMHMHLIIMLILIL M?Ht$HHHHHHHHD$HHT$[]A\A]A^A_MMHIIIMLIHL<LMHMHLIIMLIIMHT$H[]A\A]A^A_ff.fAWAVAUATUSH/LVLfoELELLML )D$'HD$1HE̟d߅CHD$H]`#L1҃H IHLl$IHLLIHHIHHLLt$IILIHILLHD$LLIIHT$IMLIIL<LIILIHIHMMHLIL L?LL$Ht$LHHHLHHHD$HHT$HD$HT$foL$)M[]A\A]A^A_fIILIIIMLIIL<LIILIHIHMMIHLff.AWAVAUATUSH/LVLfoELELLML )D$'HD$11HD$HXB fL1҃H IHLl$IHLLIHHIHHLLt$IILIHILLHD$LLIIHT$IMLIIL<LIILIHIHMMHLIL L?LL$Ht$LHHHLHHHD$HHT$HD$HT$foL$)M[]A\A]A^A_fIILIIIMLIIL<LIILIHIHMMIHLff.HHLIE̟d߅CHFHqH9HHHHIpHIxHH]`#HIHIHHHIHIPff.HH?HH>H8H?H~H8HH~H8HH~p2@ LFLHLLHLVL^HLPLXWO HHShared Cython type %.200s is not a type objectShared Cython type %.200s has the wrong size, try recompiling%.200s() keywords must be strings%s() got multiple values for keyword argument '%U'base 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 type__annotate__ cannot be deleted__annotate__ must be callable or None__int__ returned non-int (type %.200s). The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.__int__ returned non-int (type %.200s)%.200s does not export expected C %.8s %.200sC %.8s %.200s.%.200s has wrong signature (expected %.500s, got %.500s)Interpreter change detected - this module can only be loaded into one interpreter per process.cython __annotate__ called without 'self' argumentvalue too large to convert to intFailed to import '%.20s.decompress' - cannot initialise module strings. String compression was configured with the C macro 'CYTHON_COMPRESS_STRINGS=%d'.%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject%s() got an unexpected keyword argument '%U'invalid vtable found for imported typemultiple bases have vtable conflict: '%.200s' and '%.200s'unbound method %.200S() needs an argumentjoin() result is too long for a Python string while calling a Python objectNULL result without error in PyObject_Callvalue too large to convert to uint32_tcan't convert negative value to uint32_t__qualname__ must be set to a string object__name__ must be set to a string object__kwdefaults__ must be set to a dict objectchanges to cyfunction.__kwdefaults__ will not currently affect the values used in function calls__defaults__ must be set to a tuple objectchanges to cyfunction.__defaults__ will not currently affect the values used in function calls__annotations__ must be set to a dict objectinstance exception may not have a separate valuecalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptionnumpy.random._pcg64.PCG64.jump_inplacenumpy.random._pcg64.PCG64DXSM.jump_inplacenumpy.random._pcg64.PCG64.jumpedCannot convert %.200s to %.200s%.200s() takes %.8s %zd positional argument%.1s (%zd given)numpy.random._pcg64.PCG64DXSM.jumpednumpy.random._pcg64.PCG64DXSM.__setstate_cython__numpy.random._pcg64.PCG64.__setstate_cython____annotate__ must return a dictnumpy.random._pcg64.PCG64DXSM.__reduce_cython__numpy.random._pcg64.PCG64.__reduce_cython__numpy.random._pcg64.PCG64.advancenumpy.random._pcg64.PCG64DXSM.advancenumpy.random._pcg64.PCG64DXSM.__init__numpy.random._pcg64.PCG64.__init__numpy.random._pcg64.PCG64.state.__get__numpy.random._pcg64.PCG64DXSM.state.__get__numpy.random._pcg64.PCG64DXSM.state.__set__numpy.random._pcg64.PCG64.state.__set__Unable to initialize pickling for %.200sModule '_pcg64' has already been imported. Re-initialisation is not supported.compile time Python version %d.%d of module '%.100s' %s runtime version %d.%d_ARRAY_API is not PyCapsule objectmodule compiled against ABI version 0x%x but this version of numpy is 0x%xmodule was compiled against NumPy C-API version 0x%x (NumPy 1.25) 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 runtimenumpy.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)._cython_3_2_8.cython_function_or_methodPlaceholder __annotate__ function to allow 'functools.wraps' to work on Cython functions._cython_3_2_8._common_types_metatypePCG64DXSM(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" `_ 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" `_ needs an argument%.200s() %stakes no keyword argumentstakes exactly one argument%.200s() %s (%zd given)takes no argumentsBad call flags for CyFunction_cython_3_2_8__pyx_capi____loader__loader__file__origin__package__parent__path__submodule_search_locationsan integer is requireddecompresszlib__reduce_cython__keywords must be stringsnumpy/random/_pcg64.pyxat mostat leastjumpedMissing type object__setstate_cython__exactlyadvancename '%U' is not defined__init____del__builtinscython_runtime__builtins__does not matchnumpy._core._multiarray_umathnumpy.core._multiarray_umath_ARRAY_API_ARRAY_API is NULL pointerBitGeneratornumpy.random.bit_generatornumpydtypeflatiterbroadcastndarraygenericnumberunsignedintegerinexactcomplexfloatingflexiblecharacterufuncSeedlessSeedSequencevariablenumpy.random._commonfunctioninit numpy.random._pcg64__reduce____module____vectorcalloffset____weaklistoffset__func_doc__doc__func_name__name____qualname__func_dict__dict__func_globals__globals__func_closure__closure__func_code__code__func_defaults__defaults____kwdefaults____annotations____annotate___is_coroutinenumpy.random._pcg64.PCG64DXSMstatenumpy.random._pcg64.PCG64xڥRMo1M a+@ڪTB[~  {ݵ7d/c9q=1?wCB{b%Ϟ7;oZ&QC.q%>PpI60\uCbnWD0CD;5?Jz-n:(І(Be]T#^#1RxuxmӣN:#\s[F9w+k|[kn 47 AqphGo!وȚ]+:ž /αщ\926\r1RЀhk.(BEcL!Iڱ'>uиsa޽Η PݦMkP8@ )|l*f/f'eukȺXmGmeYa_iШŠŚۭ2Ku#.f &U"0"JLicufs{ 6꛰Y+}ulIpY+M?N9<,u[6-\T/?KA%-Ei1mgyruZ>LKZ\i KُoyelYf~dc48 uo~îg0000000000004u6tsrivqafgav7760c1eeri1l '"O           +?'[[  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 an 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. 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 an 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. 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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