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Expected %zd from C header, got %zd from PyObject%s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %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 typemultiple bases have vtable conflict: '%.200s' and '%.200s'__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.__%.4s__ returned non-%.4s (type %.200s)intan integer is requiredvalue too large to convert to intvalue too large to convert to uint32_tcan't convert negative value to uint32_tUnable to initialize pickling for %.200sname '%U' is not definednumpy/random/_pcg64.cpython-312-aarch64-linux-gnu.so.p/numpy/random/_pcg64.pyx.c%s (%s:%d)Module '_pcg64' has already been imported. Re-initialisation is not supported.builtinscython_runtime__builtins__does not matchnumpy.random._pcg64compile time Python version %d.%d of module '%.100s' %s runtime version %d.%d0x100000000000000000x9e3779b97f4a7c15f39cc0605cedc835numpy.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 compiled against API version 0x%x but this version of numpy is 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.random.bit_generatorBitGeneratortypenumpydtypeflatiterbroadcastndarraygenericnumbersignedintegerunsignedintegerinexactfloatingcomplexfloatingflexiblecharacterufuncSeedSequenceSeedlessSequencedoublePOISSON_LAM_MAXLEGACY_POISSON_LAM_MAXuint64_tMAXSIZEwrap_int%.200s does not export expected C function %.200sPyObject *(PyObject *, PyObject *)C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)_pcg64.pyxinit numpy.random._pcg64numpy.random._commonnumpy.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). while calling a Python objectNULL result without error in PyObject_Callnumpy.random._pcg64.PCG64.jump_inplacenumpy.random._pcg64.PCG64DXSM.jump_inplacenumpy.random._pcg64.PCG64.state.__get__numpy.random._pcg64.PCG64DXSM.state.__get__instance exception may not have a separate valuecalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptionexactly__reduce_cython__%.200s() takes %.8s %zd positional argument%.1s (%zd given)numpy.random._pcg64.PCG64.__reduce_cython__numpy.random._pcg64.PCG64DXSM.__reduce_cython__numpy.random._pcg64.PCG64.state.__set____del__numpy.random._pcg64.PCG64DXSM.state.__set__%s() got multiple values for keyword argument '%U'%.200s() keywords must be strings%s() got an unexpected keyword argument '%U'at mostat least__init__numpy.random._pcg64.PCG64.__init__Missing type objectCannot convert %.200s to %.200sjumpednumpy.random._pcg64.PCG64.jumpedadvancenumpy.random._pcg64.PCG64.advancenumpy.random._pcg64.PCG64.__setstate_cython____setstate_cython__numpy.random._pcg64.PCG64DXSM.__init__numpy.random._pcg64.PCG64DXSM.jumpednumpy.random._pcg64.PCG64DXSM.advancenumpy.random._pcg64.PCG64DXSM.__setstate_cython__state Get or set the PRNG state Returns ------- state : dict Dictionary containing the information required to describe the state of the PRNG 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" `_ numpy.random._pcg64.PCG64 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" `_ _pcg64invalid vtable found for imported typeE̟d߅C]`#XB @ImportErrorPCG64PCG64DXSMTypeErrorValueError*?advance__all__bit_generator__class__cline_in_tracebackdeltadisabledtypeemptyenableformatgcgenerate_stateget__getstate__has_uint32__import__inc__init___initializingisenabledjumps__main____name__npnumpynumpy.core.multiarray failed to importnumpy.core.umath failed to import__pyx_state__pyx_vtable____reduce____reduce_cython____reduce_ex__seedself._bitgen,self.rng_state cannot be converted to a Python object for pickling__setstate____setstate_cython____spec__statestate must be a dictstate must be for a {0} RNG__test__uint64uinteger 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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