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| author | mattip <matti.picus@gmail.com> | 2019-04-12 10:27:33 +0300 |
|---|---|---|
| committer | mattip <matti.picus@gmail.com> | 2019-05-20 18:45:27 +0300 |
| commit | 9578dcfbe744854312690ea79063e50d67fc88a2 (patch) | |
| tree | c81fd1e43aa3a2a5124aae8575dcb427746b8ef9 /doc/source/reference/random/parallel.rst | |
| parent | c53b2eb729bae1f248a2654dfcfa4a3dd3e2902b (diff) | |
| download | numpy-9578dcfbe744854312690ea79063e50d67fc88a2.tar.gz | |
BUG: __dealloc__ can be called without __init__ in some error modes
skip doctests that require scipy
move original mtrand module to _mtrand
adjust documentation for namespace change
Diffstat (limited to 'doc/source/reference/random/parallel.rst')
| -rw-r--r-- | doc/source/reference/random/parallel.rst | 143 |
1 files changed, 143 insertions, 0 deletions
diff --git a/doc/source/reference/random/parallel.rst b/doc/source/reference/random/parallel.rst new file mode 100644 index 000000000..41e47039d --- /dev/null +++ b/doc/source/reference/random/parallel.rst @@ -0,0 +1,143 @@ +Parallel Random Number Generation +================================= + +There are three strategies implemented that can be used to produce +repeatable pseudo-random numbers across multiple processes (local +or distributed). + +.. _independent-streams: + +.. currentmodule:: numpy.random + +Independent Streams +------------------- + +:class:`~pcg64.PCG64`, :class:`~threefry.ThreeFry` +and :class:`~philox.Philox` support independent streams. This +example shows how many streams can be created by passing in different index +values in the second input while using the same seed in the first. + +.. code-block:: python + + from numpy.random.entropy import random_entropy + from numpy.random import PCG64 + + entropy = random_entropy(4) + # 128-bit number as a seed + seed = sum([int(entropy[i]) * 2 ** (32 * i) for i in range(4)]) + streams = [PCG64(seed, stream) for stream in range(10)] + + +:class:`~philox.Philox` and :class:`~threefry.ThreeFry` are +counter-based RNGs which use a counter and key. Different keys can be used +to produce independent streams. + +.. code-block:: python + + import numpy as np + from numpy.random import ThreeFry + + key = random_entropy(8) + key = key.view(np.uint64) + key[0] = 0 + step = np.zeros(4, dtype=np.uint64) + step[0] = 1 + streams = [ThreeFry(key=key + stream * step) for stream in range(10)] + +.. _jump-and-advance: + +Jump/Advance the PRNG state +--------------------------- + +Jump +**** + +``jump`` advances the state of the PRNG *as-if* a large number of random +numbers have been drawn. The specific number of draws varies by PRNG, and +ranges from :math:`2^{64}` to :math:`2^{512}`. Additionally, the *as-if* +draws also depend on the size of the default random number produced by the +specific PRNG. The PRNGs that support ``jump``, along with the period of +the PRNG, the size of the jump and the bits in the default unsigned random +are listed below. + ++-----------------+-------------------------+-------------------------+-------------------------+ +| PRNG | Period | Jump Size | Bits | ++=================+=========================+=========================+=========================+ +| DSFMT | :math:`2^{19937}` | :math:`2^{128}` | 53 | ++-----------------+-------------------------+-------------------------+-------------------------+ +| MT19937 | :math:`2^{19937}` | :math:`2^{128}` | 32 | ++-----------------+-------------------------+-------------------------+-------------------------+ +| PCG64 | :math:`2^{128}` | :math:`2^{64}` | 64 | ++-----------------+-------------------------+-------------------------+-------------------------+ +| Philox | :math:`2^{256}` | :math:`2^{128}` | 64 | ++-----------------+-------------------------+-------------------------+-------------------------+ +| ThreeFry | :math:`2^{256}` | :math:`2^{128}` | 64 | ++-----------------+-------------------------+-------------------------+-------------------------+ +| Xoroshiro128 | :math:`2^{128}` | :math:`2^{64}` | 64 | ++-----------------+-------------------------+-------------------------+-------------------------+ +| Xorshift1024 | :math:`2^{1024}` | :math:`2^{512}` | 64 | ++-----------------+-------------------------+-------------------------+-------------------------+ + +``jump`` can be used to produce long blocks which should be long enough to not +overlap. + +.. code-block:: python + + from numpy.random.entropy import random_entropy + from numpy.random import Xorshift1024 + + entropy = random_entropy(2).astype(np.uint64) + # 64-bit number as a seed + seed = entropy[0] * 2**32 + entropy[1] + blocked_rng = [] + for i in range(10): + rng = Xorshift1024(seed) + rng.jump(i) + blocked_rng.append(rng) + + +Advance +******* +``advance`` can be used to jump the state an arbitrary number of steps, and so +is a more general approach than ``jump``. :class:`~pcg64.PCG64`, +:class:`~threefry.ThreeFry` and :class:`~philox.Philox` +support ``advance``, and since these also support independent +streams, it is not usually necessary to use ``advance``. + +Advancing a PRNG updates the underlying PRNG state as-if a given number of +calls to the underlying PRNG 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 PRNG. +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 + PRNG 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 + PRNG. For example, two 16-bit integer values can be simulated + from a single draw of a 32-bit PRNG. + +Advancing the PRNG state resets any pre-computed random numbers. This is +required to ensure exact reproducibility. + +This example uses ``advance`` to advance a :class:`~pcg64.PCG64` +generator 2 ** 127 steps to set a sequence of random number generators. + +.. code-block:: python + + from numpy.random import PCG64 + brng = PCG64() + brng_copy = PCG64() + brng_copy.state = brng.state + + advance = 2**127 + brngs = [brng] + for _ in range(9): + brng_copy.advance(advance) + brng = PCG64() + brng.state = brng_copy.state + brngs.append(brng) + +.. end block + |
