timing-test_combine-common-operations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_as_is(nu, nv, nw):\n",
    "    \"\"\"Implementation as in Pull Request.\"\"\"\n",
    "    \n",
    "    # Create dummy data\n",
    "    u1 = np.arange(nu)+1\n",
    "    u2 = 2*u1\n",
    "\n",
    "    v1 = np.arange(nv)+1\n",
    "    v2 = 2*v1\n",
    "\n",
    "    w1 = np.arange(nw)+1\n",
    "    w2 = 2*w1\n",
    "\n",
    "    tol = 0.01\n",
    "\n",
    "    Gxx = (\n",
    "        np.arctan((v1*w1)/(u1*np.sqrt(u1**2+v1**2+w1**2)+tol)) -\n",
    "        np.arctan((v1*w1)/(u2*np.sqrt(u2**2+v1**2+w1**2)+tol)) +\n",
    "        np.arctan((v2*w1)/(u2*np.sqrt(u2**2+v2**2+w1**2)+tol)) -\n",
    "        np.arctan((v2*w1)/(u1*np.sqrt(u1**2+v2**2+w1**2)+tol)) +\n",
    "        np.arctan((v2*w2)/(u1*np.sqrt(u1**2+v2**2+w2**2)+tol)) -\n",
    "        np.arctan((v1*w2)/(u1*np.sqrt(u1**2+v1**2+w2**2)+tol)) +\n",
    "        np.arctan((v1*w2)/(u2*np.sqrt(u2**2+v1**2+w2**2)+tol)) -\n",
    "        np.arctan((v2*w2)/(u2*np.sqrt(u2**2+v2**2+w2**2)+tol))\n",
    "    )\n",
    "    Gyx = (\n",
    "        np.log(np.sqrt(u1**2+v1**2+w1**2)-w1) -\n",
    "        np.log(np.sqrt(u2**2+v1**2+w1**2)-w1) +\n",
    "        np.log(np.sqrt(u2**2+v2**2+w1**2)-w1) -\n",
    "        np.log(np.sqrt(u1**2+v2**2+w1**2)-w1) +\n",
    "        np.log(np.sqrt(u1**2+v2**2+w2**2)-w2) -\n",
    "        np.log(np.sqrt(u1**2+v1**2+w2**2)-w2) +\n",
    "        np.log(np.sqrt(u2**2+v1**2+w2**2)-w2) -\n",
    "        np.log(np.sqrt(u2**2+v2**2+w2**2)-w2)\n",
    "    )\n",
    "    Gzx = (\n",
    "        np.log(np.sqrt(u1**2+v1**2+w1**2)-v1) -\n",
    "        np.log(np.sqrt(u2**2+v1**2+w1**2)-v1) +\n",
    "        np.log(np.sqrt(u2**2+v2**2+w1**2)-v2) -\n",
    "        np.log(np.sqrt(u1**2+v2**2+w1**2)-v2) +\n",
    "        np.log(np.sqrt(u1**2+v2**2+w2**2)-v2) -\n",
    "        np.log(np.sqrt(u1**2+v1**2+w2**2)-v1) +\n",
    "        np.log(np.sqrt(u2**2+v1**2+w2**2)-v1) -\n",
    "        np.log(np.sqrt(u2**2+v2**2+w2**2)-v2)\n",
    "    )\n",
    "\n",
    "    return Gxx, Gyx, Gzx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_suggested(nu, nv, nw):\n",
    "    \"\"\"Just combining some frequent operations.\"\"\"\n",
    "\n",
    "    # Create dummy data\n",
    "    u1 = np.arange(nu)+1\n",
    "    u2 = 2*u1\n",
    "    v1 = np.arange(nv)+1\n",
    "    v2 = 2*v1\n",
    "    w1 = np.arange(nw)+1\n",
    "    w2 = 2*w1\n",
    "    tol = 0.01\n",
    "\n",
    "    # Squared functions\n",
    "    su1 = u1*u1\n",
    "    su2 = u2*u2\n",
    "    sv1 = v1*v1\n",
    "    sv2 = v2*v2\n",
    "    sw1 = w1*w1\n",
    "    sw2 = w2*w2\n",
    "\n",
    "    # Multiplications\n",
    "    v1w1 = v1*w1\n",
    "    v1w2 = v1*w2\n",
    "    v2w1 = v1*w2\n",
    "    v2w2 = v2*w2\n",
    "\n",
    "    # Square root of sums\n",
    "    su1v1w1 = np.sqrt(su1+sv1+sw1)\n",
    "    su2v1w1 = np.sqrt(su2+sv1+sw1)\n",
    "    su1v2w1 = np.sqrt(su1+sv2+sw1)\n",
    "    su2v2w1 = np.sqrt(su2+sv2+sw1)\n",
    "    su1v1w2 = np.sqrt(su1+sv1+sw2)\n",
    "    su2v1w2 = np.sqrt(su2+sv1+sw2)\n",
    "    su1v2w2 = np.sqrt(su1+sv2+sw2)\n",
    "    su2v2w2 = np.sqrt(su2+sv2+sw2)\n",
    "\n",
    "    Gxx = (\n",
    "        np.arctan(v1w1/(u1*su1v1w1+tol)) -\n",
    "        np.arctan(v1w1/(u2*su2v1w1+tol)) +\n",
    "        np.arctan(v2w1/(u2*su2v2w1+tol)) -\n",
    "        np.arctan(v2w1/(u1*su1v2w1+tol)) +\n",
    "        np.arctan(v2w2/(u1*su1v2w2+tol)) -\n",
    "        np.arctan(v1w2/(u1*su1v1w2+tol)) +\n",
    "        np.arctan(v1w2/(u2*su2v1w2+tol)) -\n",
    "        np.arctan(v2w2/(u2*su2v2w2+tol))\n",
    "    )\n",
    "    Gyx = (\n",
    "        np.log(su1v1w1-w1) -\n",
    "        np.log(su2v1w1-w1) +\n",
    "        np.log(su2v2w1-w1) -\n",
    "        np.log(su1v2w1-w1) +\n",
    "        np.log(su1v2w2-w2) -\n",
    "        np.log(su1v1w2-w2) +\n",
    "        np.log(su2v1w2-w2) -\n",
    "        np.log(su2v2w2-w2)\n",
    "    )\n",
    "    Gzx = (\n",
    "        np.log(su1v1w1-v1) -\n",
    "        np.log(su2v1w1-v1) +\n",
    "        np.log(su2v2w1-v2) -\n",
    "        np.log(su1v2w1-v2) +\n",
    "        np.log(su1v2w2-v2) -\n",
    "        np.log(su1v1w2-v1) +\n",
    "        np.log(su2v1w2-v1) -\n",
    "        np.log(su2v2w2-v2)\n",
    "    )\n",
    "\n",
    "    return Gxx, Gyx, Gzx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  => For len(u/v/w) = 1\n",
      "\n",
      "As is in PR :: 249 µs ± 34.9 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
      "Suggestion  :: 117 µs ± 8.48 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n",
      "\n",
      "====================\n",
      "  => For len(u/v/w) = 1000000\n",
      "\n",
      "As is in PR :: 418 ms ± 9.36 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "Suggestion  :: 249 ms ± 6.75 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "====================\n"
     ]
    }
   ],
   "source": [
    "for nn in [1, 1e6]:\n",
    "\n",
    "    print('  => For len(u/v/w) = %i\\n' %nn)\n",
    "    print('As is in PR :: ', end='')\n",
    "    %timeit test_as_is(nn, nn, nn)\n",
    "    print('Suggestion  :: ', end='')\n",
    "    %timeit test_suggested(nn, nn, nn)\n",
    "    print('\\n'+20*'=')"
   ]
  }
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