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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)C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)%.200s does not export expected C variable %.200sInterpreter change detected - this module can only be loaded into one interpreter per process.Shared Cython type %.200s is not a type objectShared Cython type %.200s has the wrong size, try recompilingunbound method %.200S() needs an argumentvalue too large to convert to int%.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.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject%s() got an unexpected keyword argument '%U'%.200s() keywords must be strings%s() got multiple values for keyword argument '%U'invalid vtable found for imported typemultiple bases have vtable conflict: '%.200s' and '%.200s'__annotations__ must be set to a dict object__qualname__ must be set to a string object__name__ 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 callsvalue too large to convert to uint32_tcan't convert negative value to uint32_tfunction's dictionary may not be deletedsetting function's dictionary to a non-dictinstance 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_inplace%.200s() takes %.8s %zd positional argument%.1s (%zd given)numpy.random._pcg64.PCG64.__setstate_cython__numpy.random._pcg64.PCG64DXSM.__setstate_cython__numpy.random._pcg64.PCG64.jumpedCannot convert %.200s to %.200snumpy.random._pcg64.PCG64DXSM.jumpednumpy.random._pcg64.PCG64.__reduce_cython__numpy.random._pcg64.PCG64DXSM.__reduce_cython__numpy.random._pcg64.PCG64DXSM.advancenumpy.random._pcg64.PCG64.advancenumpy.random._pcg64.PCG64DXSM.__init__numpy.random._pcg64.PCG64.__init__numpy.random._pcg64.PCG64.state.__get__numpy.random._pcg64.PCG64DXSM.state.__get__ while calling a Python objectNULL result without error in PyObject_Callnumpy.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.%d0x9e3779b97f4a7c15f39cc0605cedc835_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 1.20) 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).PyObject *(PyObject *, PyObject *)C function %.200s.%.200s has wrong signature (expected %.500s, got %.500s)%.200s does not export expected C function %.200s_cython_3_1_0.cython_function_or_method 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" `_ 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" `_ 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. 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. self._bitgen,self.rng_state cannot be converted to a Python object for picklingnumpy._core.umath failed to importnumpy._core.multiarray failed to importPCG64DXSM.__setstate_cython__state must be for a {0} RNGPCG64DXSM.__reduce_cython__AH BfASb %vT %vSQat<~]!1 #1qAH BfASb %vT %vS$l. 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