Find an adequate resolution smearing oversample

find_adequate_resolution.ipynb

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  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "f5160716",
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import refnx\n",
    "from refnx import reflect as refnx_reflect\n",
    "import timeit\n",
    "\n",
    "import numpy as np\n",
    "# a typical Q range set of points measured by TOF-NR\n",
    "q = np.geomspace(0.01, 0.2, 101)\n",
    "dq = q * 0.05\n",
    "\n",
    "w = np.array([[0, 2.07, 0, 0],\n",
    "              [100, 3.47, 0, 3],\n",
    "              [300, -0.5, 0.00001, 3],\n",
    "              [100, 3.47, 0, 3],\n",
    "              [300, -0.5, 0.00001, 3],\n",
    "              [0, 6.36, 0, 3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "6b490c2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = refnx_reflect.Structure()\n",
    "for i, slab in enumerate(w):\n",
    "    m = refnx_reflect.SLD(complex(slab[1], slab[2]))\n",
    "    s |= m(slab[0], slab[-1])\n",
    "    \n",
    "model = refnx_reflect.ReflectModel(s, bkg=0)\n",
    "model.dq.value = 5.0\n",
    "model.quad_order = 17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "f5180d62",
   "metadata": {},
   "outputs": [],
   "source": [
    "def diff(a, b):\n",
    "    return np.abs((a - b) / b)\n",
    "\n",
    "def find_adequate_resolution(model, x, x_err=None, threads=-1, rtol=0.05):\n",
    "    _dq_type = model.dq_type\n",
    "    _quad_order = model.quad_order\n",
    "    _threads = model.threads\n",
    "    _dq = model.dq.value\n",
    "    \n",
    "    diffs = {}\n",
    "\n",
    "    try:\n",
    "        model.dq_type='pointwise'\n",
    "        model.quad_order = 201\n",
    "        model.threads = threads\n",
    "        best_r = model.model(x, x_err=x_err)\n",
    "\n",
    "        model.dq_type='constant'\n",
    "        if x_err is not None:\n",
    "            dq = 100 * np.mean(x_err/x)\n",
    "\n",
    "        print(f\"Quad order:      % difference,              time (s)\")        \n",
    "        # try no smear\n",
    "        model.dq.value = 0\n",
    "        none_r = model.model(x)\n",
    "        _t = timeit.Timer(\"model.model(x)\", globals=locals()).repeat(number=20, repeat=5)\n",
    "        print(f\"No smear  :      {100 * np.max(diff(none_r, best_r)): <25}, {np.mean(_t): ^8}\")\n",
    "        \n",
    "        model.dq.value = dq\n",
    "        continuous_r = model.model(x)\n",
    "        _t = timeit.Timer(\"model.model(x)\", globals=locals()).repeat(number=20, repeat=5)\n",
    "        print(f\"Continuous:      {100 * np.max(diff(continuous_r, best_r)): <25}, {np.mean(_t): ^8}\")\n",
    "        \n",
    "        if x_err is None:\n",
    "            x_err = _dq * x\n",
    "\n",
    "        for qo in range(1, 101, 2):\n",
    "            model.dq_type = 'pointwise'\n",
    "            model.quad_order = qo\n",
    "            r = model.model(x, x_err=x_err)\n",
    "            \n",
    "            diffs[qo] = np.max(diff(r, best_r))\n",
    "            _t = timeit.Timer(\"model.model(x, x_err=x_err)\", globals=locals()).repeat(number=20, repeat=5)\n",
    "            print(f\"Pointwise: {qo:<4}, {100 * np.max(diff(r, best_r)): <25}, {np.mean(_t): ^8}\")\n",
    "    finally:\n",
    "        model.threads = _threads\n",
    "        model.quad_order = _quad_order\n",
    "        model.dq_type = _dq_type\n",
    "        model.dq.value = _dq\n",
    "    \n",
    "    # find the lowest quad_order for which you satisfy the tolerance\n",
    "    for k, v in diffs.items():\n",
    "        if v < rtol:\n",
    "            return k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "12a1ee98",
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   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Quad order:      % difference,              time (s)\n",
      "No smear  :      87.62278377619023        , 0.004772618412971497\n",
      "Continuous:      5.934856302567495        , 0.037357107549905774\n",
      "Pointwise: 1   , 368.0047544673799        , 0.005014491081237793\n",
      "Pointwise: 3   , 108.3561706334832        , 0.013524832949042321\n",
      "Pointwise: 5   , 56.24173757561278        , 0.014011584967374802\n",
      "Pointwise: 7   , 20.13888797908223        , 0.022984862327575684\n",
      "Pointwise: 9   , 3.305520733643539        , 0.024128807708621025\n",
      "Pointwise: 11  , 2.692858632142202        , 0.030209342390298842\n",
      "Pointwise: 13  , 2.1542188568601848       , 0.03211847990751267\n",
      "Pointwise: 15  , 1.7013668796641648       , 0.04141804426908493\n",
      "Pointwise: 17  , 1.3215564087095482       , 0.057372669130563735\n",
      "Pointwise: 19  , 1.0007546661118902       , 0.06933653503656387\n",
      "Pointwise: 21  , 0.7272279537180877       , 0.06541916765272618\n",
      "Pointwise: 23  , 0.49175157088758087      , 0.05971390157938004\n",
      "Pointwise: 25  , 0.5740754302168882       , 0.06798989921808243\n",
      "Pointwise: 27  , 0.5043096855993633       , 0.07712197974324227\n",
      "Pointwise: 29  , 0.16488300114770837      , 0.07353278212249278\n",
      "Pointwise: 31  , 0.26843666000897853      , 0.09225127771496773\n",
      "Pointwise: 33  , 0.31672110420689853      , 0.10340539067983627\n",
      "Pointwise: 35  , 0.42988837051212886      , 0.09722417257726193\n",
      "Pointwise: 37  , 0.5322144873609873       , 0.09131810069084167\n",
      "Pointwise: 39  , 0.6251732739350431       , 0.09332728050649167\n",
      "Pointwise: 41  , 0.7099853980190032       , 0.0993193406611681\n",
      "Pointwise: 43  , 0.7876697565759285       , 0.10350952334702015\n",
      "Pointwise: 45  , 0.3486123458505503       , 0.11353656686842442\n",
      "Pointwise: 47  , 0.13969724128497601      , 0.11122776791453362\n",
      "Pointwise: 49  , 0.11491612538413187      , 0.12902318574488164\n",
      "Pointwise: 51  , 0.20117499303727035      , 0.12322373352944851\n",
      "Pointwise: 53  , 0.22168121937118654      , 0.1260330155491829\n",
      "Pointwise: 55  , 0.2326132256207918       , 0.12990813031792642\n",
      "Pointwise: 57  , 0.2279332575871147       , 0.13689285926520825\n",
      "Pointwise: 59  , 0.21253185430997523      , 0.13912916146218776\n",
      "Pointwise: 61  , 0.18962808782448626      , 0.14705765545368193\n",
      "Pointwise: 63  , 0.16143584768752675      , 0.1510664764791727\n",
      "Pointwise: 65  , 0.12952571864046541      , 0.1517138347029686\n",
      "Pointwise: 67  , 0.0950374185819811       , 0.171964718028903\n",
      "Pointwise: 69  , 0.08605490972095102      , 0.17203781493008136\n",
      "Pointwise: 71  , 0.08334787898237196      , 0.17165488861501216\n",
      "Pointwise: 73  , 0.09046672947289981      , 0.1763641882687807\n",
      "Pointwise: 75  , 0.054737720564031145     , 0.17652337066829205\n",
      "Pointwise: 77  , 0.10826068765608746      , 0.18465997762978076\n",
      "Pointwise: 79  , 0.1310309994924026       , 0.18573067225515844\n",
      "Pointwise: 81  , 0.1687129194358679       , 0.19075977467000485\n",
      "Pointwise: 83  , 0.20591336251847048      , 0.19403040036559105\n",
      "Pointwise: 85  , 0.24254331672158322      , 0.19687076173722745\n",
      "Pointwise: 87  , 0.2785372475494332       , 0.20455852672457694\n",
      "Pointwise: 89  , 0.28357202004080595      , 0.2146530222147703\n",
      "Pointwise: 91  , 0.06811190446391893      , 0.21141146421432494\n",
      "Pointwise: 93  , 0.052295489300434525     , 0.21456486769020558\n",
      "Pointwise: 95  , 0.049454094965603504     , 0.2298251323401928\n",
      "Pointwise: 97  , 0.07032272194403144      , 0.22960584349930285\n",
      "Pointwise: 99  , 0.08055479802646841      , 0.23020706400275232\n"
     ]
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       "9"
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     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "find_adequate_resolution(model, q, x_err=dq, threads=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f229edb1",
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