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use a cummulative integral value

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hiro98 2020-04-03 19:44:39 +02:00
parent 09cf85e64a
commit c3259a82b6
1 changed files with 22 additions and 9 deletions
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31
prog/python/qqgg/monte_carlo.py
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@ -153,11 +153,12 @@ def sample_unweighted_array(num, *args, report_efficiency=False, **kwargs):
def integrate_vegas(f, interval, seed=None, num_increments=5,
point_density=1000, epsilon=1e-3, alpha=1.5, **kwargs):
point_density=1000, epsilon=1e-2, alpha=1.5, **kwargs):
"""Integrate the given function (in one dimension) with the vegas
algorithm to reduce variance. This implementation follows the
description given in JOURNAL OF COMPUTATIONAL 27, 192-203 (1978),
but does not calculate a cumulative estimate.
description given in JOURNAL OF COMPUTATIONAL 27, 192-203 (1978).
All iterations contribute to the final result.
:param f: function of one variable, kwargs are passed to it
:param tuple interval: a 2-tuple of numbers, specifiying the
@ -170,8 +171,8 @@ def integrate_vegas(f, interval, seed=None, num_increments=5,
interval
:param epsilon: the breaking condition, if the magnitude of the
difference between the increment positions in subsequent
iterations does not change more then epsilon*num_increments
the computation is considered to have converged
iterations does not change more then epsilon the computation
is considered to have converged
:param alpha: controls the the convergence speed, should be
between 1 and 2
@ -215,9 +216,16 @@ def integrate_vegas(f, interval, seed=None, num_increments=5,
K = num_increments*1000
increment_borders = interval_borders[1:-1] - interval_borders[0]
integrals = []
variances = []
while True:
interval_lengths = interval_borders[1:] - interval_borders[:-1]
integral, integral_steps, variance = evaluate_integrand(interval_borders, interval_lengths)
integral, integral_steps, variance = \
evaluate_integrand(interval_borders, interval_lengths)
integrals.append(integral)
variances.append(variance)
# alpha controls the convergence speed
μ = np.abs(integral_steps)/integral
@ -257,8 +265,13 @@ def integrate_vegas(f, interval, seed=None, num_increments=5,
rest = new_increments[i]
interval_borders[1:-1] = interval_borders[0] + increment_borders
if np.linalg.norm(increment_borders - new_increment_borders)\
*num_increments < epsilon:
return integral, np.sqrt(variance), interval_borders
if np.linalg.norm(increment_borders - new_increment_borders) < epsilon:
integrals = np.array(integrals)
variances = np.array(variances)
integral = np.sum(integrals**3/variances**2) \
/np.sum(integrals**2/variances**2)
mean_variance = 1/np.sqrt(np.sum(integrals**2/variances**2))*integral
return integral, np.sqrt(mean_variance), interval_borders
increment_borders = new_increment_borders