Spherical Hankel function of 2nd kind

hankel-benchmark.ipynb

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   "source": [
    "import numpy as np\n",
    "from scipy.special import spherical_jn, spherical_yn\n",
    "from scipy.special import sph_jnyn\n",
    "\n",
    "def spherical_hn2(n, z):\n",
    "    return spherical_jn(n, z) - 1j * spherical_yn(n, z)"
   ]
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   "cell_type": "code",
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   "outputs": [],
   "source": [
    "z = 20\n",
    "max_order = 150"
   ]
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     "text": [
      "3.21 ms ± 162 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "for n in range(max_order + 1):\n",
    "    spherical_hn2(n, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "501 µs ± 6.75 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "spherical_hn2(np.arange(max_order + 1), z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mg/.local/lib/python3.6/site-packages/ipykernel_launcher.py:1: DeprecationWarning: `sph_jnyn` is deprecated!\n",
      "scipy.special.sph_jnyn is deprecated in scipy 0.18.0. Use scipy.special.spherical_jn and scipy.special.spherical_yn instead. Note that the new function has a different signature.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "name": "stdout",
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     "text": [
      "51.3 µs ± 194 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "jn, jnp, yn, ynp = sph_jnyn(max_order, z)\n",
    "jn - 1j * yn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Do some more realistic work in the loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi0 = 0.2\n",
    "phi = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.4 ms ± 292 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "d = 0\n",
    "for m in range(-max_order, max_order + 1):\n",
    "    d += spherical_hn2(abs(m), z) / spherical_hn2(abs(m), z) * np.exp(1j * m * (phi0 - phi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.53 ms ± 17.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "hr = spherical_hn2(range(0, max_order + 1), z)\n",
    "hr0 = spherical_hn2(range(0, max_order + 1), z)\n",
    "d = 0\n",
    "for m in range(-max_order, max_order + 1):\n",
    "    d += hr[abs(m)] / hr0[abs(m)] * np.exp(1j * m * (phi0 - phi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mg/.local/lib/python3.6/site-packages/ipykernel_launcher.py:1: DeprecationWarning: `sph_jnyn` is deprecated!\n",
      "scipy.special.sph_jnyn is deprecated in scipy 0.18.0. Use scipy.special.spherical_jn and scipy.special.spherical_yn instead. Note that the new function has a different signature.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/home/mg/.local/lib/python3.6/site-packages/ipykernel_launcher.py:3: DeprecationWarning: `sph_jnyn` is deprecated!\n",
      "scipy.special.sph_jnyn is deprecated in scipy 0.18.0. Use scipy.special.spherical_jn and scipy.special.spherical_yn instead. Note that the new function has a different signature.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.46 ms ± 6.02 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "jn, jnp, yn, ynp = sph_jnyn(max_order, z)\n",
    "hr = jn - 1j * yn\n",
    "jn, jnp, yn, ynp = sph_jnyn(max_order, z)\n",
    "hr0 = jn - 1j * yn\n",
    "d = 0\n",
    "for m in range(-max_order, max_order + 1):\n",
    "    d += hr[abs(m)] / hr0[abs(m)] * np.exp(1j * m * (phi0 - phi))"
   ]
  }
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