How to choose l-curve ranges for gamma and delta

l_curve_choosing_points.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cfd4a4ab",
   "metadata": {},
   "source": [
    "# Choosing the sweep_range for $\\gamma$ $\\delta$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22db564c",
   "metadata": {},
   "source": [
    "**Background**\n",
    "\n",
    "From James Green function pdf:\n",
    "\n",
    "The variance is given by $C(0)$, we have (by evaluating at small $r$ using `SymPy 1.9`):\n",
    "\n",
    "$ C(0) = \\frac{1}{(4 \\pi\\gamma\\delta)} $ \n",
    "\n",
    "The autocovariance has a characteristic length scale of:\n",
    "\n",
    "$ L = \\sqrt{\\frac{\\gamma}{\\delta}}$\n",
    "\n",
    "Lets plot our current l-curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "58366228",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "#Plotting imports\n",
    "from matplotlib import pyplot as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "import sys\n",
    "sys.path.append('/home/brecinos/smith_glacier/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91bc307a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ficetools import graphics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "287c68de",
   "metadata": {},
   "outputs": [],
   "source": [
    "l_curves_exp_paths = ['~/smith_glacier/plots/temp/gamma_alpha_lcurve.csv',\n",
    "                     '~/smith_glacier/plots/temp/gamma_beta_lcurve.csv',\n",
    "                     '~/smith_glacier/plots/temp/delta_beta_gnd_lcurve.csv']\n",
    "\n",
    "gamma_alpha_exp = pd.read_csv(l_curves_exp_paths[0])\n",
    "gamma_beta_exp = pd.read_csv(l_curves_exp_paths[1])\n",
    "delta_beta_gnd_exp = pd.read_csv(l_curves_exp_paths[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2bba30d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 518.4x1209.6 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = 1.2\n",
    "tick_options_lc = {'axis':'both','which':'both','bottom':True,\n",
    "    'top':False,'left':True,'right':False,'labelleft':True, 'labelbottom':True}\n",
    "\n",
    "fig1 = plt.figure(figsize=(6*g, 14*g))#, constrained_layout=True)\n",
    "spec = gridspec.GridSpec(3, 1, hspace=0.3, wspace=0.3)#, hspace=0.05)\n",
    "\n",
    "ax0 = plt.subplot(spec[0])\n",
    "graphics.plot_lcurve_scatter(gamma_alpha_exp, 'gamma_alpha', ax=ax0, xlim_min=None, xlim_max=10e9, ylim_min=None,\n",
    "                              ylim_max=3e6, xytext=(40,5), rot=40)\n",
    "ax0.set_title(\"gamma-alpha $\\it{L-curve}$\", fontsize=14)\n",
    "\n",
    "ax1 = plt.subplot(spec[1])\n",
    "graphics.plot_lcurve_scatter(gamma_beta_exp, 'gamma_beta', ax=ax1, xlim_min=None, xlim_max=10e9, ylim_min=None,\n",
    "                              ylim_max=1e6, xytext=(40,5), rot=40)\n",
    "ax1.set_title(\"gamma-beta $\\it{L-curve}$\", fontsize=14)\n",
    "\n",
    "ax2 = plt.subplot(spec[2])\n",
    "graphics.plot_lcurve_scatter(delta_beta_gnd_exp, 'delta_beta_gnd', ax=ax2, xlim_min=None, xlim_max=10e12, ylim_min=None,\n",
    "                              ylim_max=7e5, xytext=(35,15), rot=35)\n",
    "ax2.set_title(\"delta_beta_gnd $\\it{L-curve}$\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2074a276",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "\n",
    "gamma_beta = [10.0, 1.0] #from the lcurve plot! \n",
    "gamma_alpha = [100.0, 10.0]\n",
    "\n",
    "delta_alpha = 1.0e-5\n",
    "delta_beta = 1.0e-5\n",
    "delta_beta_gnd = 3.0e-5\n",
    "\n",
    "c_0_alpha = []\n",
    "c_0_beta = []\n",
    "len_scale_alpha = []\n",
    "len_scale_beta = []\n",
    "\n",
    "for beta, alpha in zip(gamma_beta, gamma_alpha):\n",
    "    \n",
    "    var_a = 1/(4*math.pi*alpha*delta_alpha)\n",
    "    length_scale_a = np.sqrt(alpha/delta_alpha)\n",
    "    \n",
    "    c_0_alpha.append(var_a)\n",
    "    len_scale_alpha.append(length_scale_a)\n",
    "    \n",
    "    var_b = 1/(4*math.pi*beta*delta_beta) \n",
    "    length_scale_b = np.sqrt(beta/delta_beta)\n",
    "    \n",
    "    c_0_beta.append(var_b)\n",
    "    len_scale_beta.append(length_scale_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "11b63138",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance gamma_alpha [79.57747154594766, 795.7747154594766]\n"
     ]
    }
   ],
   "source": [
    "print('Covariance gamma_alpha', c_0_alpha) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "77e28867",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance length scale gamma_alpha [3162.2776601683795, 999.9999999999999]\n"
     ]
    }
   ],
   "source": [
    "print('Covariance length scale gamma_alpha', len_scale_alpha) # in m?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a2606800",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance gamma_beta [795.7747154594766, 7957.7471545947665]\n"
     ]
    }
   ],
   "source": [
    "print('Covariance gamma_beta', c_0_beta)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9639ff9a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance length scale gamma_beta [999.9999999999999, 316.2277660168379]\n"
     ]
    }
   ],
   "source": [
    "print('Covariance length scale gamma_beta', len_scale_beta) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de975d64",
   "metadata": {},
   "source": [
    "We can take the first *l-curve* values of for gamma and delta as a starting point. Well more like a **middle point** and construct *l-curves* which vary $\\gamma$ and $\\delta$ as a function of the **covariance and the length scale** instead:\n",
    "\n",
    "$ \\gamma_{\\alpha} , \\delta_{\\alpha} = F(C0_{\\alpha}, L_{\\alpha})$\n",
    "\n",
    "$ p_{\\alpha} =  \\sqrt{\\frac{1}{4\\pi C0_{\\alpha}}}$\n",
    "\n",
    "$ \\gamma_{\\alpha} = L_{\\alpha} * p_{\\alpha} $\n",
    "\n",
    "$ \\delta_{\\alpha} = \\frac{1}{L_{\\alpha}} * p_{\\alpha} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06c44218",
   "metadata": {},
   "source": [
    "Dan suggested finding the geometric mean of the values above, I think it will be easy if we round them to the neareast 10. Here is an example of how the range of covariances will vary for:\n",
    "\n",
    "**gamma_alpha**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7b8bca35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This will be our middle point for our covariance range 250.0\n",
      "This will be our middle point for our length scale 1780.0\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import gmean\n",
    "\n",
    "cov_m = np.round(gmean(c_0_alpha)/10)*10\n",
    "len_m =  np.round(gmean(len_scale_alpha)/10)*10\n",
    "\n",
    "print(\"This will be our middle point for our covariance range\", cov_m)\n",
    "print(\"This will be our middle point for our length scale\", len_m)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4136a03b",
   "metadata": {},
   "source": [
    "**gamma_alpha** with **length scale constant**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "770d1116",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance will vary from [100. 150. 200. 250. 300. 350. 400.]\n",
      "------------------------------------------------------------------\n",
      "And length_scale will be kept constant 1780.0\n"
     ]
    }
   ],
   "source": [
    "btm = [cov_m - (cov_m / 5) * i for i in range(4)]\n",
    "top = [cov_m + (cov_m / 5) * i for i in range(4)]\n",
    "cov_a = np.unique(np.concatenate((btm, top)))\n",
    "print('Covariance will vary from', cov_a)\n",
    "print('------------------------------------------------------------------')\n",
    "print('And length_scale will be kept constant', len_m)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f0220fc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma_alpha will be vary from [50.21287294 40.99863907 35.50586296 31.75740927 28.99041571 26.83990956\n",
      " 25.10643647]\n",
      "------------------------------------------------------------------\n",
      "delta_gamma will be vary from [1.58480220e-05 1.29398558e-05 1.12062438e-05 1.00231692e-05\n",
      " 9.14985977e-06 8.47112409e-06 7.92401100e-06]\n"
     ]
    }
   ],
   "source": [
    "p = np.sqrt(1 / (4 * math.pi * cov_a))\n",
    "gamma = len_m * p\n",
    "delta = (1/len_m)*p\n",
    "\n",
    "print('gamma_alpha will be vary from', gamma)\n",
    "print('------------------------------------------------------------------')\n",
    "print('delta_gamma will be vary from', delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "687292fe",
   "metadata": {},
   "source": [
    "**gamma_alpha** with **covariance constant**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5f418693",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lenght scale will vary from [ 712. 1068. 1424. 1780. 2136. 2492. 2848.]\n",
      "------------------------------------------------------------------\n",
      "And the convariance will be kept constant 250.0\n"
     ]
    }
   ],
   "source": [
    "btm = [len_m - (len_m / 5) * i for i in range(4)]\n",
    "top = [len_m + (len_m / 5) * i for i in range(4)]\n",
    "len_a = np.unique(np.concatenate((btm, top)))\n",
    "print('Lenght scale will vary from', len_a)\n",
    "print('------------------------------------------------------------------')\n",
    "print('And the convariance will be kept constant', cov_m)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5a83b356",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma_alpha will be vary from [12.70296371 19.05444556 25.40592741 31.75740927 38.10889112 44.46037297\n",
      " 50.81185483]\n",
      "------------------------------------------------------------------\n",
      "delta_gamma will be vary from [2.50579230e-05 1.67052820e-05 1.25289615e-05 1.00231692e-05\n",
      " 8.35264099e-06 7.15940657e-06 6.26448074e-06]\n"
     ]
    }
   ],
   "source": [
    "p = np.sqrt(1 / (4 * math.pi * cov_m))\n",
    "gamma = len_a* p\n",
    "delta = (1/len_a)*p\n",
    "\n",
    "print('gamma_alpha will be vary from', gamma)\n",
    "print('------------------------------------------------------------------')\n",
    "print('delta_gamma will be vary from', delta)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}