simple N^2 gravitational potential calculator in numba

potential.ipynb

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     "text": [
      "13.8 ms ± 142 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
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   "source": [
    "import numba\n",
    "import numpy as np\n",
    "\n",
    "@numba.njit(parallel=True,fastmath=True)\n",
    "def potential(X, eps, dtype=np.float32, nthread=1):\n",
    "    # things to check:\n",
    "    # - parallel and serial give same answer\n",
    "    # - big halos give same answer for dtype=np.float64 and float32\n",
    "    \n",
    "    numba.set_num_threads(nthread)\n",
    "    \n",
    "    N = len(X)\n",
    "    pot = np.zeros(N, dtype=dtype)\n",
    "    eps2 = dtype(eps**2)\n",
    "    \n",
    "    for i in numba.prange(N):\n",
    "        x1,y1,z1 = X[i][0],X[i][1],X[i][2]\n",
    "        for j in range(N):\n",
    "            x2,y2,z2 = X[j][0],X[j][1],X[j][2]\n",
    "            invr = dtype(1.)/np.sqrt( (x1 - x2)**2 + (y1 - y2)**2 + (z1 - z2)**2 + eps2)\n",
    "            pot[i] += invr\n",
    "            \n",
    "    pot -= 1/eps  # remove self-potential\n",
    "    return pot\n",
    "\n",
    "rng = np.random.default_rng()\n",
    "pos = rng.random((10**4,3), dtype=np.float32)\n",
    "\n",
    "%timeit potential(pos, 1e-3, nthread=16)"
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