125 lines
4 KiB
Python
125 lines
4 KiB
Python
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"""Compute gammainc and gammaincc for large arguments and parameters
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and save the values to data files for use in tests. We can't just
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compare to mpmath's gammainc in test_mpmath.TestSystematic because it
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would take too long.
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Note that mpmath's gammainc is computed using hypercomb, but since it
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doesn't allow the user to increase the maximum number of terms used in
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the series it doesn't converge for many arguments. To get around this
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we copy the mpmath implementation but use more terms.
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This takes about 17 minutes to run on a 2.3 GHz Macbook Pro with 4GB
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ram.
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Sources:
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[1] Fredrik Johansson and others. mpmath: a Python library for
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arbitrary-precision floating-point arithmetic (version 0.19),
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December 2013. http://mpmath.org/.
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"""
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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 numpy import pi
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from scipy.special._mptestutils import mpf2float
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try:
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import mpmath as mp # type: ignore[import]
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except ImportError:
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pass
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def gammainc(a, x, dps=50, maxterms=10**8):
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"""Compute gammainc exactly like mpmath does but allow for more
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summands in hypercomb. See
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mpmath/functions/expintegrals.py#L134
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in the mpmath github repository.
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"""
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with mp.workdps(dps):
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z, a, b = mp.mpf(a), mp.mpf(x), mp.mpf(x)
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G = [z]
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negb = mp.fneg(b, exact=True)
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def h(z):
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T1 = [mp.exp(negb), b, z], [1, z, -1], [], G, [1], [1+z], b
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return (T1,)
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res = mp.hypercomb(h, [z], maxterms=maxterms)
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return mpf2float(res)
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def gammaincc(a, x, dps=50, maxterms=10**8):
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"""Compute gammaincc exactly like mpmath does but allow for more
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terms in hypercomb. See
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mpmath/functions/expintegrals.py#L187
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in the mpmath github repository.
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"""
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with mp.workdps(dps):
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z, a = a, x
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if mp.isint(z):
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try:
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# mpmath has a fast integer path
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return mpf2float(mp.gammainc(z, a=a, regularized=True))
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except mp.libmp.NoConvergence:
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pass
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nega = mp.fneg(a, exact=True)
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G = [z]
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# Use 2F0 series when possible; fall back to lower gamma representation
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try:
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def h(z):
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r = z-1
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return [([mp.exp(nega), a], [1, r], [], G, [1, -r], [], 1/nega)]
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return mpf2float(mp.hypercomb(h, [z], force_series=True))
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except mp.libmp.NoConvergence:
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def h(z):
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T1 = [], [1, z-1], [z], G, [], [], 0
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T2 = [-mp.exp(nega), a, z], [1, z, -1], [], G, [1], [1+z], a
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return T1, T2
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return mpf2float(mp.hypercomb(h, [z], maxterms=maxterms))
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def main():
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t0 = time()
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# It would be nice to have data for larger values, but either this
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# requires prohibitively large precision (dps > 800) or mpmath has
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# a bug. For example, gammainc(1e20, 1e20, dps=800) returns a
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# value around 0.03, while the true value should be close to 0.5
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# (DLMF 8.12.15).
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print(__doc__)
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pwd = os.path.dirname(__file__)
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r = np.logspace(4, 14, 30)
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ltheta = np.logspace(np.log10(pi/4), np.log10(np.arctan(0.6)), 30)
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utheta = np.logspace(np.log10(pi/4), np.log10(np.arctan(1.4)), 30)
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regimes = [(gammainc, ltheta), (gammaincc, utheta)]
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for func, theta in regimes:
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rg, thetag = np.meshgrid(r, theta)
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a, x = rg*np.cos(thetag), rg*np.sin(thetag)
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a, x = a.flatten(), x.flatten()
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dataset = []
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for i, (a0, x0) in enumerate(zip(a, x)):
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if func == gammaincc:
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# Exploit the fast integer path in gammaincc whenever
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# possible so that the computation doesn't take too
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# long
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a0, x0 = np.floor(a0), np.floor(x0)
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dataset.append((a0, x0, func(a0, x0)))
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dataset = np.array(dataset)
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filename = os.path.join(pwd, '..', 'tests', 'data', 'local',
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'{}.txt'.format(func.__name__))
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np.savetxt(filename, dataset)
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print("{} minutes elapsed".format((time() - t0)/60))
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if __name__ == "__main__":
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main()
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