chore: import upstream snapshot with attribution

books/PRML/PRML-master-Python/prml/sampling/__init__.py

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+from prml.sampling.metropolis import metropolis
+from prml.sampling.metropolis_hastings import metropolis_hastings
+from prml.sampling.rejection_sampling import rejection_sampling
+from prml.sampling.sir import sir
+
+
+__all__ = [
+    "metropolis",
+    "metropolis_hastings",
+    "rejection_sampling",
+    "sir"
+]

books/PRML/PRML-master-Python/prml/sampling/metropolis.py

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+import random
+import numpy as np
+
+
+def metropolis(func, rv, n, downsample=1):
+    """
+    Metropolis algorithm
+
+    Parameters
+    ----------
+    func : callable
+        (un)normalized distribution to be sampled from
+    rv : RandomVariable
+        proposal distribution which is symmetric at the origin
+    n : int
+        number of samples to draw
+    downsample : int
+        downsampling factor
+
+    Returns
+    -------
+    sample : (n, ndim) ndarray
+        generated sample
+    """
+    x = np.zeros((1, rv.ndim))
+    sample = []
+    for i in range(n * downsample):
+        x_new = x + rv.draw()
+        accept_proba = func(x_new) / func(x)
+        if random.random() < accept_proba:
+            x = x_new
+        if i % downsample == 0:
+            sample.append(x[0])
+    sample = np.asarray(sample)
+    assert sample.shape == (n, rv.ndim), sample.shape
+    return sample

books/PRML/PRML-master-Python/prml/sampling/metropolis_hastings.py

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+import random
+import numpy as np
+
+
+def metropolis_hastings(func, rv, n, downsample=1):
+    """
+    Metropolis Hastings algorith
+
+    Parameters
+    ----------
+    func : callable
+        (un)normalized distribution to be sampled from
+    rv : RandomVariable
+        proposal distribution
+    n : int
+        number of samples to draw
+    downsample : int
+        downsampling factor
+
+    Returns
+    -------
+    sample : (n, ndim) ndarray
+        generated sample
+    """
+    x = np.zeros((1, rv.ndim))
+    sample = []
+    for i in range(n * downsample):
+        x_new = x + rv.draw()
+        accept_proba = func(x_new) * rv.pdf(x - x_new) / (func(x) * rv.pdf(x_new - x))
+        if random.random() < accept_proba:
+            x = x_new
+        if i % downsample == 0:
+            sample.append(x[0])
+    sample = np.asarray(sample)
+    assert sample.shape == (n, rv.ndim), sample.shape
+    return sample

books/PRML/PRML-master-Python/prml/sampling/rejection_sampling.py

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+import random
+import numpy as np
+
+
+def rejection_sampling(func, rv, k, n):
+    """
+    perform rejection sampling n times
+
+    Parameters
+    ----------
+    func : callable
+        (un)normalized distribution to be sampled from
+    rv : RandomVariable
+        distribution to generate sample
+    k : float
+        constant to be multiplied with the distribution
+    n : int
+        number of samples to draw
+
+    Returns
+    -------
+    sample : (n, ndim) ndarray
+        generated sample
+    """
+    assert hasattr(rv, "draw"), "the distribution has no method to draw random samples"
+    sample = []
+    while len(sample) < n:
+        sample_candidate = rv.draw()
+        accept_proba = func(sample_candidate) / (k * rv.pdf(sample_candidate))
+        if random.random() < accept_proba:
+            sample.append(sample_candidate[0])
+    sample = np.asarray(sample)
+    assert sample.shape == (n, rv.ndim), sample.shape
+    return sample

books/PRML/PRML-master-Python/prml/sampling/sir.py

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+import numpy as np
+
+
+def sir(func, rv, n):
+    """
+    sampling-importance-resampling
+
+    Parameters
+    ----------
+    func : callable
+        (un)normalized distribution to be sampled from
+    rv : RandomVariable
+        distribution to generate sample
+    n : int
+        number of samples to draw
+
+    Returns
+    -------
+    sample : (n, ndim) ndarray
+        generated sample
+    """
+    assert hasattr(rv, "draw"), "the distribution has no method to draw random samples"
+    sample_candidate = rv.draw(n * 10)
+    weight = np.squeeze(func(sample_candidate) / rv.pdf(sample_candidate))
+    assert weight.shape == (n * 10,), weight.shape
+    weight /= np.sum(weight)
+    index = np.random.choice(n * 10, n, p=weight)
+    sample = sample_candidate[index]
+    return sample