153 lines
5.5 KiB
Python
153 lines
5.5 KiB
Python
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"""Compute a grid of values for Wright's generalized Bessel function
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and save the values to data files for use in tests. Using mpmath directly in
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tests would take too long.
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This takes about 10 minutes to run on a 2.7 GHz i7 Macbook Pro.
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"""
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from functools import lru_cache
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import os
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from time import time
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import numpy as np
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from scipy.special._mptestutils import mpf2float
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try:
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import mpmath as mp
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except ImportError:
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pass
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# exp_inf: smallest value x for which exp(x) == inf
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exp_inf = 709.78271289338403
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# 64 Byte per value
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@lru_cache(maxsize=100_000)
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def rgamma_cached(x, dps):
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with mp.workdps(dps):
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return mp.rgamma(x)
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def mp_wright_bessel(a, b, x, dps=50, maxterms=2000):
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"""Compute Wright's generalized Bessel function as Series with mpmath.
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"""
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with mp.workdps(dps):
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a, b, x = mp.mpf(a), mp.mpf(b), mp.mpf(x)
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res = mp.nsum(lambda k: x**k / mp.fac(k)
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* rgamma_cached(a * k + b, dps=dps),
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[0, mp.inf],
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tol=dps, method='s', steps=[maxterms]
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)
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return mpf2float(res)
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def main():
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t0 = time()
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print(__doc__)
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pwd = os.path.dirname(__file__)
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eps = np.finfo(float).eps * 100
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a_range = np.array([eps,
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1e-4 * (1 - eps), 1e-4, 1e-4 * (1 + eps),
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1e-3 * (1 - eps), 1e-3, 1e-3 * (1 + eps),
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0.1, 0.5,
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1 * (1 - eps), 1, 1 * (1 + eps),
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1.5, 2, 4.999, 5, 10])
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b_range = np.array([0, eps, 1e-10, 1e-5, 0.1, 1, 2, 10, 20, 100])
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x_range = np.array([0, eps, 1 - eps, 1, 1 + eps,
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1.5,
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2 - eps, 2, 2 + eps,
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9 - eps, 9, 9 + eps,
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10 * (1 - eps), 10, 10 * (1 + eps),
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100 * (1 - eps), 100, 100 * (1 + eps),
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500, exp_inf, 1e3, 1e5, 1e10, 1e20])
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a_range, b_range, x_range = np.meshgrid(a_range, b_range, x_range,
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indexing='ij')
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a_range = a_range.flatten()
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b_range = b_range.flatten()
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x_range = x_range.flatten()
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# filter out some values, especially too large x
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bool_filter = ~((a_range < 5e-3) & (x_range >= exp_inf))
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bool_filter = bool_filter & ~((a_range < 0.2) & (x_range > exp_inf))
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bool_filter = bool_filter & ~((a_range < 0.5) & (x_range > 1e3))
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bool_filter = bool_filter & ~((a_range < 0.56) & (x_range > 5e3))
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bool_filter = bool_filter & ~((a_range < 1) & (x_range > 1e4))
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bool_filter = bool_filter & ~((a_range < 1.4) & (x_range > 1e5))
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bool_filter = bool_filter & ~((a_range < 1.8) & (x_range > 1e6))
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bool_filter = bool_filter & ~((a_range < 2.2) & (x_range > 1e7))
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bool_filter = bool_filter & ~((a_range < 2.5) & (x_range > 1e8))
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bool_filter = bool_filter & ~((a_range < 2.9) & (x_range > 1e9))
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bool_filter = bool_filter & ~((a_range < 3.3) & (x_range > 1e10))
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bool_filter = bool_filter & ~((a_range < 3.7) & (x_range > 1e11))
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bool_filter = bool_filter & ~((a_range < 4) & (x_range > 1e12))
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bool_filter = bool_filter & ~((a_range < 4.4) & (x_range > 1e13))
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bool_filter = bool_filter & ~((a_range < 4.7) & (x_range > 1e14))
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bool_filter = bool_filter & ~((a_range < 5.1) & (x_range > 1e15))
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bool_filter = bool_filter & ~((a_range < 5.4) & (x_range > 1e16))
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bool_filter = bool_filter & ~((a_range < 5.8) & (x_range > 1e17))
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bool_filter = bool_filter & ~((a_range < 6.2) & (x_range > 1e18))
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bool_filter = bool_filter & ~((a_range < 6.2) & (x_range > 1e18))
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bool_filter = bool_filter & ~((a_range < 6.5) & (x_range > 1e19))
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bool_filter = bool_filter & ~((a_range < 6.9) & (x_range > 1e20))
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# filter out known values that do not meet the required numerical accuracy
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# see test test_wright_data_grid_failures
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failing = np.array([
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[0.1, 100, 709.7827128933841],
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[0.5, 10, 709.7827128933841],
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[0.5, 10, 1000],
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[0.5, 100, 1000],
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[1, 20, 100000],
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[1, 100, 100000],
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[1.0000000000000222, 20, 100000],
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[1.0000000000000222, 100, 100000],
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[1.5, 0, 500],
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[1.5, 2.220446049250313e-14, 500],
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[1.5, 1.e-10, 500],
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[1.5, 1.e-05, 500],
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[1.5, 0.1, 500],
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[1.5, 20, 100000],
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[1.5, 100, 100000],
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]).tolist()
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does_fail = np.full_like(a_range, False, dtype=bool)
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for i in range(x_range.size):
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if [a_range[i], b_range[i], x_range[i]] in failing:
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does_fail[i] = True
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# filter and flatten
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a_range = a_range[bool_filter]
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b_range = b_range[bool_filter]
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x_range = x_range[bool_filter]
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does_fail = does_fail[bool_filter]
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dataset = []
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print(f"Computing {x_range.size} single points.")
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print("Tests will fail for the following data points:")
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for i in range(x_range.size):
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a = a_range[i]
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b = b_range[i]
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x = x_range[i]
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# take care of difficult corner cases
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maxterms = 1000
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if a < 1e-6 and x >= exp_inf/10:
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maxterms = 2000
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f = mp_wright_bessel(a, b, x, maxterms=maxterms)
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if does_fail[i]:
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print("failing data point a, b, x, value = "
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f"[{a}, {b}, {x}, {f}]")
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else:
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dataset.append((a, b, x, f))
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dataset = np.array(dataset)
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filename = os.path.join(pwd, '..', 'tests', 'data', 'local',
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'wright_bessel.txt')
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np.savetxt(filename, dataset)
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print("{:.1f} minutes elapsed".format((time() - t0)/60))
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if __name__ == "__main__":
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main()
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