mirror of
https://github.com/vale981/bachelor_thesis
synced 2025-03-10 04:46:40 -04:00
hiro98
b47b9886c8
took me way longer to find my error in thinking about this then to fix the code ^^.
152 lines
5 KiB
Python
152 lines
5 KiB
Python
"""
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Simple monte carlo integration implementation.
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Author: Valentin Boettcher <hiro@protagon.space>
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"""
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import numpy as np
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from scipy.optimize import minimize_scalar, root
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def _process_interval(interval):
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assert len(interval) == 2, 'An interval has two endpoints'
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a, b = interval
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if b < a:
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a, b = b, a
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return [a, b]
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def integrate(f, interval, point_density=1000, seed=None, **kwargs):
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"""Monte-Carlo integrates the functin `f` in an interval.
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:param f: function of one variable, kwargs are passed to it
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:param tuple interval: a 2-tuple of numbers, specifiying the
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integration range
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:returns: the integration result
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:rtype: float
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"""
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interval = _process_interval(interval)
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if seed:
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np.random.seed(seed)
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interval_length = (interval[1] - interval[0])
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num_points = int(interval_length * point_density)
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points = np.random.uniform(interval[0], interval[1], num_points)
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sample = f(points, **kwargs)
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integral = np.sum(sample)/num_points*interval_length
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# the deviation gets multiplied by the square root of the interval
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# lenght, because it is the standard deviation of the integral.
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deviation = np.std(sample)*np.sqrt(1/(num_points - 1))*interval_length
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return integral, deviation
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def find_upper_bound(f, interval, **kwargs):
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"""Find the upper bound of a function.
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:param f: function of one scalar and some kwargs that are passed
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on to it
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:param interval: interval to look in
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:returns: the upper bound of the function
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:rtype: float
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"""
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upper_bound = minimize_scalar(lambda *args: -f(*args, **kwargs),
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bounds=interval, method='bounded')
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if upper_bound.success:
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return -upper_bound.fun
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else:
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raise RuntimeError('Could not find an upper bound.')
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def sample_unweighted(f, interval, upper_bound=None, seed=None,
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chunk_size=100, report_efficiency=False, **kwargs):
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"""Samples a distribution proportional to f by hit and miss.
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Implemented as a generator.
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:param f: function of one scalar to sample, should be positive,
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superflous kwargs are passed to it
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:param interval: the interval to sample from
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:param upper_bound: an upper bound to the function, optional
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:param seed: the seed for the rng, if not specified, the system
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time is used
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:param chunk_size: the size of the chunks of random numbers
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allocated per unit interval
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:yields: random nubers following the distribution of f
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:rtype: float
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"""
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interval = _process_interval(interval)
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interval_length = (interval[1] - interval[0])
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upper_bound_fn, upper_bound_integral, upper_bound_integral_inverse = None, None, None
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# i know....
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if not upper_bound:
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upper_bound_value = find_upper_bound(f, interval, **kwargs)
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def upper_bound_fn(x): return upper_bound_value
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def upper_bound_integral(x): return upper_bound_value*x
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def upper_bound_integral_inverse(y): return y/upper_bound_value
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elif len(upper_bound) == 2:
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upper_bound_fn, upper_bound_integral =\
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upper_bound
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def upper_inv(points): # not for performance right now...
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return np.array([root(lambda y: upper_bound_integral(y) - x, x0=0,
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jac=upper_bound_fn).x for x in points]).T
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upper_bound_integral_inverse = upper_inv
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elif len(upper_bound) == 3:
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upper_bound_fn, upper_bound_integral, upper_bound_integral_inverse =\
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upper_bound
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else:
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raise ValueError('The upper bound must be `None` or a three element sequence!')
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def allocate_random_chunk():
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return np.random.uniform([upper_bound_integral(interval[0]), 0],
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[upper_bound_integral(interval[1]), 1],
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[int(chunk_size*interval_length), 2])
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total_points = 0
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total_accepted = 0
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while True:
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points = allocate_random_chunk()
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points[:, 0] = upper_bound_integral_inverse(points[:, 0])
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sample_points = points[:, 0] \
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[np.where(f(points[:, 0]) > \
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points[:, 1]*upper_bound_fn(points[:, 0]))]
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if report_efficiency:
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total_points += points.size
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total_accepted += sample_points.size
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for point in sample_points:
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yield (point, total_accepted/total_points) \
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if report_efficiency else point
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def sample_unweighted_array(num, *args, report_efficiency=False, **kwargs):
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"""Sample `num` elements from a distribution. The rest of the
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arguments is analogous to `sample_unweighted`.
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"""
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sample_arr = np.empty(num)
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samples = sample_unweighted(*args, report_efficiency=report_efficiency,
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**kwargs)
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for i, sample in zip(range(num), samples):
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if report_efficiency:
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sample_arr[i], _ = sample
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else:
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sample_arr[i] = sample
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return (sample_arr, next(samples)[1]) if report_efficiency else sample_arr
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