3. analytic.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from ipywidgets import interact, IntSlider, FloatSlider\n",
    "\n",
    "import chugunov_indicator as chug"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We make the assumption that our intercept function is separable, i.e.\n",
    "$$\n",
    "    C(\\bar{A}, \\overline{Z^2}, Z_1, Z_2) = C_0 + C_1(\\overline{Z^2}) + C_2(\\bar{A}) + C_3(Z_1, Z_2),\n",
    "$$\n",
    "for some constant $C_0$ and functions $C_1, C_2, C_3$, and that screening is skippable if\n",
    "$$\n",
    "    C \\leq 3 \\log_{10} T - \\log_{10} \\rho =: y_0.\n",
    "$$\n",
    "\n",
    "Based on the results of the previous notebook, we assume that $C$ is independent of $\\bar{Z}, A_1, A_2$.\n",
    "\n",
    "To test this, we need to examine slices of $C$ on a 4D grid for $\\bar{A}, \\overline{Z^2}, Z_1, Z_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "T_ = np.logspace(7, 9.35, 100)\n",
    "D_ = np.logspace(-4, 8, 100)\n",
    "\n",
    "T, D = np.meshgrid(T_, D_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "minmaxes = {\n",
    "    \"abar\": FloatSlider(value=1, min=1, max=75),\n",
    "    \"z2bar\": FloatSlider(value=1, min=1, max=1000),\n",
    "    \"z1\": IntSlider(value=1, min=1, max=25),\n",
    "    \"z2\": IntSlider(value=1, min=1, max=25)\n",
    "}\n",
    "\n",
    "linspaces = {param: np.linspace(slider.min, slider.max, 100) for param, slider in minmaxes.items()}\n",
    "linspaces[\"z2bar\"] = np.logspace(0, 3, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def configuration_space(x: str) -> tuple[dict, dict]:\n",
    "    minmaxes_ = {**minmaxes}\n",
    "    del minmaxes_[x]\n",
    "\n",
    "    X = {x: linspaces[x][...]}\n",
    "    return X, minmaxes_\n",
    "\n",
    "def C(X, params) -> np.ndarray:\n",
    "    X = {x: v[..., None, None, None] for x, v in X.items()}\n",
    "    return chug.intercept_from_vars(T, D, **X, **params).squeeze()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we make a plot of $C_1(\\overline{Z^2})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "version_major": 2,
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      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='abar', max=75.0, min=1.0), IntSlider(value=1, descri…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "328d5843c0024cdb90d017f5ac986818",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "\n",
    "fig1, ax1 = plt.subplots(constrained_layout=True)\n",
    "\n",
    "X1, minmaxes1 = configuration_space(\"z2bar\")\n",
    "\n",
    "ax1.set_title(\"$C_1$ vs $\\\\overline{Z^2}$\")\n",
    "ax1.set_xscale(\"log\")\n",
    "\n",
    "mins1 = {k: v.min for k, v in minmaxes1.items()}\n",
    "z2bar = linspaces[\"z2bar\"]\n",
    "log_z2bar = np.log10(z2bar)\n",
    "\n",
    "C1 = C(X1, mins1)\n",
    "C1 -= (y0 := C1[0])\n",
    "\n",
    "line1, = ax1.plot(z2bar, C1, linestyle=\"dotted\")\n",
    "\n",
    "@interact(**minmaxes1)\n",
    "def update1(**kwargs) -> None:\n",
    "    C1 = C(X1, kwargs)\n",
    "    C1 -= C1[0]\n",
    "    line1.set_ydata(C1)\n",
    "\n",
    "    grad = np.gradient(C1, log_z2bar)\n",
    "    m, dm = grad.mean(), grad.std()\n",
    "    line1.set_label(f\"$m = {m:.2f} \\\\pm {dm:.3g}$\")\n",
    "\n",
    "    ax1.legend()\n",
    "\n",
    "#fig1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As revealed above, we have $C_1 \\propto \\log_{10} \\overline{Z^2}$, with the proportionality constant $m$ being between 1 and 1.10, depending on the values of $Z_1, Z_2$. We can then average this slope over a grid of this data to find a reasonable slope to use for all cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "_z2bar, _z1, _z2, _T, _D = np.meshgrid(\n",
    "    z2bar[::10], linspaces[\"z1\"][::10], linspaces[\"z2\"][::10],\n",
    "    T_, D_, sparse=True\n",
    ")\n",
    "\n",
    "_C = chug.analytic.intercept_from_vars(_T, _D, abar=1, z2bar=_z2bar, z1=_z1, z2=_z2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0298324707166073, 0.028324944137614712)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad = np.gradient(_C, log_z2bar[::10], axis=1)\n",
    "M = grad.mean(axis=0)\n",
    "(m1 := M.mean()), M.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As such, we can safely set $C_1(\\overline{Z^2}) = 1.03 \\log_{10} \\overline{Z^2}$.\n",
    "\n",
    "From there, we make the graph for $\\bar{A}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a47c623e60614719aab54960cfcbdfde",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='z2bar', max=1000.0, min=1.0), IntSlider(value=1, des…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c4f2b90a6d5242018e7edf1886a80cd9",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2, ax2 = plt.subplots(constrained_layout=True)\n",
    "\n",
    "X2, minmaxes2 = configuration_space(\"abar\")\n",
    "\n",
    "ax2.set_title(\"$C_2$ vs $\\\\bar{A}$\")\n",
    "\n",
    "mins2 = {k: v.min for k, v in minmaxes2.items()}\n",
    "abar = linspaces[\"abar\"]\n",
    "\n",
    "C2 = C(X2, mins2)\n",
    "C2 -= (y0 := C2[0])\n",
    "\n",
    "curve2, = ax2.plot(abar, C2, linestyle=\"dotted\", color=\"red\")\n",
    "predict2, = ax2.plot(\n",
    "    abar, _C2 := 10.4*(abar**(-0.0207) - abar**0.0207),\n",
    "    linestyle=\"--\", color=\"green\"\n",
    ")\n",
    "\n",
    "predict2.set_label(\"$C_2 = \\\\mathrm{const} + 10.4(\\\\bar{A}^{-0.0207} - \\\\bar{A}^{0.0207})$\")\n",
    "ax2.legend()\n",
    "\n",
    "@interact(**minmaxes2)\n",
    "def update2(**kwargs) -> None:\n",
    "    C2 = C(X2, kwargs)\n",
    "    C2 -= y0\n",
    "    curve2.set_ydata(C2)\n",
    "    predict2.set_ydata(_C2 + C2[0])\n",
    "\n",
    "#fig2.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the shape of this graph, we anticipate a function of the form\n",
    "$$\n",
    "    C_2(\\bar{A}) = a_2 (\\bar{A}^{-k_2} - \\bar{A}^{k_2}),\n",
    "$$\n",
    "for positive $a_2, k_2$ and $k_2$ small. We could allow for different coefficients and exponents on each of the terms, but the fit should be effective enough without that.\n",
    "\n",
    "Since variations in $\\overline{Z^2}, Z_1, Z_2$ only change the height of the graph, we don't have to fit on a grid this time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def C2_func(abar: np.ndarray, a2: float, k2: float) -> np.ndarray:\n",
    "    return a2 * (abar**(-k2) - abar**(k2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([10.41502026,  0.02076143]),\n",
       " array([[ 6.43761066e-01, -1.28067482e-03],\n",
       "        [-1.28067482e-03,  2.54772856e-06]]))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt, pcov = curve_fit(C2_func, abar, C2, p0=[8, 0.33])\n",
    "popt, pcov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "a2, k2 = popt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A plot of $C_2$ with these parameters is included in the graph above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, while $C_3(Z_1, Z_2)$ is symmetric in $Z_1, Z_2$, we don't anticipate further separability, as `chugunov_2009` has a significant dependence on the product $Z_1 Z_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d70804f4f7124e7290516ee89eeb48cd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='abar', max=75.0, min=1.0), FloatSlider(value=1.0, de…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1b607f5eea5d4c809db1d8d7ed47b06c",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig3, ax3 = plt.subplots(constrained_layout=True)\n",
    "\n",
    "X3, minmaxes3 = configuration_space(\"z1\")\n",
    "\n",
    "ax3.set_title(\"$C_3$ vs $\\\\bar{A}$\")\n",
    "\n",
    "mins3 = {k: v.min for k, v in minmaxes3.items()}\n",
    "z1 = linspaces[\"z1\"]\n",
    "z2 = mins3[\"z2\"]\n",
    "\n",
    "C3 = C(X3, mins3)\n",
    "y0 = C3[0]\n",
    "\n",
    "a3, k3 = 7.73078747, 0.02600378\n",
    "\n",
    "curve3, = ax3.plot(z1, C3, linestyle=\"dotted\", color=\"red\")\n",
    "predict3, = ax3.plot(z1, y0 + a3*((z1**k3 + z2**k3)**2 - (1 + z2**k3)**2), linestyle=\"--\", color=\"green\")\n",
    "\n",
    "predict3.set_label(\"$C_3 = \\\\mathrm{const} + 7.73[(Z_1^{0.026} + Z_2^{0.026})^2 - 4]$\")\n",
    "ax3.legend()\n",
    "\n",
    "@interact(**minmaxes3)\n",
    "def update3(**kwargs) -> None:\n",
    "    C3 = C(X3, kwargs)\n",
    "    curve3.set_ydata(C3)\n",
    "\n",
    "    z2 = kwargs[\"z2\"]\n",
    "    _C3 = a3*((z1**k3 + z2**k3)**2 - (1 + z2**k3)**2)\n",
    "    predict3.set_ydata(_C3 + C3[0])\n",
    "\n",
    "#fig3.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, we make the ansatz\n",
    "$$\n",
    "    C_3(Z_1, Z_2) = a_3 [(Z_1^{k_3} + Z_2^{k_3})^2 - 4]\n",
    "$$\n",
    "for positive $a_3, k_3$ and $k_3$ small. The exponent has to be $k_3$ for both by symmetry, and the term in parentheses is squared so that $C_3$ has a term proportional to $(Z_1 Z_2)^{k_3}$ in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def C3_func(Z: tuple[np.ndarray, np.ndarray], a3: float, k3: float) -> np.ndarray:\n",
    "    return a3 * ((Z[0]**k3 + Z[1]**k3)**2 - 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "_z1, _z2, _T, _D = np.meshgrid(\n",
    "    __z1 := linspaces[\"z1\"][::5], __z2 := linspaces[\"z2\"][::5],\n",
    "    T_, D_, sparse=True\n",
    ")\n",
    "\n",
    "_C = chug.analytic.intercept_from_vars(_T, _D, abar=1, z2bar=1, z1=_z1, z2=_z2)\n",
    "_C -= chug.analytic.intercept_from_vars(_T, _D, abar=1, z2bar=1, z1=1, z2=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "_z1_, _z2_ = np.meshgrid(__z1, __z2)\n",
    "_z1_, _z2_ = _z1_.ravel(), _z2_.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([7.73078747, 0.02600378]),\n",
       " array([[ 4.26855648e-01, -1.34298478e-03],\n",
       "        [-1.34298478e-03,  4.22569821e-06]]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt, pcov = curve_fit(C3_func, (_z1_, _z2_), _C.ravel(), p0=[7.65, 0.0262])\n",
    "popt, pcov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "a3, k3 = popt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, since $C_1(1) = C_2(1) = C_3(1, 1) = 0$, we get $C_0 = C(1, 1, 1, 1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.791064415919347"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0 = chug.analytic.intercept_from_vars(_T, _D, abar=1, z2bar=1, z1=1, z2=1)[0, 0]\n",
    "C0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With that, we can put together the final function for predicting whether screening can be fixed:\n",
    "$$\n",
    "    C(\\bar{A}, \\overline{Z^2}, Z_1, Z_2) \\approx 20.79 + 1.03 \\log_{10} \\overline{Z^2} + 10.42(\\bar{A}^{-0.02} - \\bar{A}^{0.02}) + 7.73[(Z_1^{0.026} + Z_2^{0.026})^2 - 4].\n",
    "$$\n",
    "Absorbing all constant terms into $C_0$ simplifies this to\n",
    "$$\n",
    "    C(\\bar{A}, \\overline{Z^2}, Z_1, Z_2) \\approx -10.132 + 1.03 \\log_{10} \\overline{Z^2} + 10.42(\\bar{A}^{-0.02} - \\bar{A}^{0.02}) + 7.73(Z_1^{0.026} + Z_2^{0.026})^2.\n",
    "$$"
   ]
  }
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