GL_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "import numpy as np\n",
    "import cvxpy as cp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from src.IterativeFitting import IterativeFitting as IF\n",
    "from src.CorrFuncs import covariance_matrix, trend_est"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example in GL Paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([2,6,11])\n",
    "Nx = np.array([337,167,186,212])\n",
    "M1x = 451\n",
    "Lx = np.array([np.log(0.80),np.log(1.16),np.log(1.57)])\n",
    "vx = np.array([0.0542,0.0563,0.0563])\n",
    "A0 = M1x*Nx[1:]/(Nx.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "it_fit_ex = IF(Lx,A0,Nx,M1x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A, B, a0, b0 = it_fit_ex.convexProgram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 70.33038633,  95.48567119, 124.67758726])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "160.50635522335585"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "C1 = covariance_matrix(A,B,a0,b0,vx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.0542    , 0.01882672, 0.01943165],\n",
       "       [0.01882672, 0.0563    , 0.02068641],\n",
       "       [0.01943165, 0.02068641, 0.0563    ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.01882672, 0.0563    ],\n",
       "       [0.01943165, 0.02068641]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sub_C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1.],\n",
       "       [1., 1.]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sub_mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use seaborn's heatmap function which has an option to mask parts of the matrix\n",
    "# sub_C1 = C1[1:, :-1]\n",
    "# sub_mask = np.triu(np.ones_like(sub_C1, dtype=bool))\n",
    "# sub_mask = np.zeros_like(sub_C1)\n",
    "mask = np.triu(np.ones_like(C1, dtype=bool))  # Mask for the upper triangle\n",
    "plt.figure(figsize=(8, 6))\n",
    "sns.set(font_scale=1.6)\n",
    "sns.heatmap(C1, annot=True, mask=mask, cmap='Blues', cbar=True, square=True,  fmt=\".4f\",\n",
    "            xticklabels=[f'Lvl{i+1}' for i in range(3)], \n",
    "            yticklabels=[f'Lvl{i+1}' for i in range(3)], vmin=.01,vmax=0.03)\n",
    "# plt.title('Upper Triangle of Covariance Matrix--Convex GL')\n",
    "plt.savefig(\"images/Convex_GL_covar.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True],\n",
       "       [False,  True,  True],\n",
       "       [False, False,  True]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_GL = it_fit_ex.GL()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 70.20458464,  95.46963796, 124.85560373]),\n",
       " 160.47017367350816,\n",
       " array([96.79541536, 90.53036204, 87.14439627]),\n",
       " 176.52982632649184,\n",
       " 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_GL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "451.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(A_GL[0]) + A_GL[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_GLN = it_fit_ex.GL_linesearch()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 70.33753879,  95.44494158, 124.66704769]),\n",
       " 160.55047193677308,\n",
       " array([96.66246121, 90.55505842, 87.33295231]),\n",
       " 176.44952806322692,\n",
       " 2)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_GLN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.045430215893878516, 0.0004268215544488761)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trend_est(A,B,a0,b0,vx,x,Lx,unadj=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example from alochol data in $\\verb+dosresmeta+$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([9.06,27.,45.,64.8])\n",
    "Nx = np.array([414,261,228,44,34])\n",
    "A0 = np.array([61,69,22,19])\n",
    "M1x = np.sum(A0) + 126\n",
    "Lx = np.array([-0.2231435,-0.0001,0.5306283,0.8754687])\n",
    "vx = np.array([0.2233380,0.2337519,0.3765137,0.4440046])\n",
    "vx *= vx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "alcohol_data = IF(Lx,A0,Nx,M1x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "result_alc = alcohol_data.convexProgram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([67.12135054, 68.86105977, 18.64972113, 17.32195872]),\n",
       " array([193.87864946, 159.13894023,  25.35027887,  16.67804128]),\n",
       " 125.04590983884529,\n",
       " 288.9540901611547)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_alc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### RR example where everything works"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1.8286, 9.1992, 22.8571, 35.6667, 58.4257])\n",
    "A = np.array([38., 43., 32., 16., 27.])\n",
    "a0 = 28\n",
    "M1 = np.sum(A) + a0\n",
    "B = np.array([22185.73, 43030.54, 53088.96, 45348.09, 19790.79, 19919.85])\n",
    "L = np.array([-0.41673, -0.39555, -0.48842, -0.27903, 0.20232])\n",
    "v = np.array([0.2510976, 0.2456013, 0.2633819, 0.3208115, 0.2861643])\n",
    "v *= v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "RR_ex = IF(L,A,B,M1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_GLRR, a0_GLRR, B_GLRR, b0_GLRR, iter_GLRR = RR_ex.GL(OR=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([33.88106778, 42.96697564, 33.41520852, 17.88177706, 29.21975009])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_GLRR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "b_GLRR, se_GLRR = trend_est(A_GLRR,B_GLRR,a0_GLRR,b0_GLRR,v,x,L,unadj=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.007131624060147025 1.5176081960353128e-05\n"
     ]
    }
   ],
   "source": [
    "print(b_GLRR, se_GLRR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_cvxRR, B_cvxRR, a0_cvxRR, b0_cvxRR = RR_ex.convexProgram(OR=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.59728749176199"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0_cvxRR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([34.00610242, 42.85317043, 33.35834454, 17.94921829, 29.23587682])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_cvxRR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "b_cvxRR, se_cvxRR = trend_est(A_cvxRR,B_cvxRR,a0_cvxRR,b0_cvxRR,v,x,L,unadj=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007137599341147913"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_cvxRR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.007137599341147913,\n",
       " 1.5165650431946001e-05,\n",
       " -0.002945971690368591,\n",
       " 1.5864902051567542e-05)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trend_est(A_cvxRR,B_cvxRR,a0_cvxRR,b0_cvxRR,v,x,L,unadj=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "C2 = covariance_matrix(A_cvxRR,B_cvxRR,a0_cvxRR,b0_cvxRR,v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask = np.triu(np.ones_like(C2, dtype=bool))  # Mask for the upper triangle\n",
    "plt.figure(figsize=(8, 6))\n",
    "sns.set(font_scale=1.6)\n",
    "sns.heatmap(C2, annot=True, mask=mask, cmap='Blues', cbar=True, square=True,  fmt=\".4f\",\n",
    "            xticklabels=[f'Lvl{i+1}' for i in range(5)], \n",
    "            yticklabels=[f'Lvl{i+1}' for i in range(5)], vmin=.03,vmax=0.045)\n",
    "# plt.title('Upper Triangle of Covariance Matrix--Convex GL')\n",
    "plt.savefig(\"images/Convex_GL_covarRR.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our convex formulation matches EXACTLY with what is in $\\verb+dosresmeta+$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### OR Example that doesn't work on $\\verb+dosresmeta+$ but works for our method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([2,6,11])\n",
    "Nx = np.array([337,167,186,212])\n",
    "M1x = 451\n",
    "Lx = np.array([np.log(0.80),np.log(1.16),np.log(1.57)])\n",
    "vx = np.array([0.0542,0.0563,0.0563])\n",
    "A0 = Nx[1:] - 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Johnson/Documents/Sasha_Research/CvxFitting/src/IterativeFitting.py:172: RuntimeWarning: invalid value encountered in log\n",
      "  e = L + np.log(a0) + np.log(B) - np.log(A) - np.log(b0)\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "array must not contain infs or NaNs",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-8f943be46992>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0malcohol_data_2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mIF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mLx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mA0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mNx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mM1x\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0malcohol_data_2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mGL\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/Documents/Sasha_Research/CvxFitting/src/IterativeFitting.py\u001b[0m in \u001b[0;36mGL\u001b[0;34m(self, OR)\u001b[0m\n\u001b[1;32m    173\u001b[0m             \u001b[0mH\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mc0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    174\u001b[0m             \u001b[0mH\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 175\u001b[0;31m             \u001b[0mA\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mH\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0massume_a\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"pos\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    176\u001b[0m             \u001b[0mi\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    177\u001b[0m             \u001b[0mdiff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Library/Python/3.8/lib/python/site-packages/scipy/linalg/_basic.py\u001b[0m in \u001b[0;36msolve\u001b[0;34m(a, b, sym_pos, lower, overwrite_a, overwrite_b, check_finite, assume_a, transposed)\u001b[0m\n\u001b[1;32m    139\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    140\u001b[0m     \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0matleast_2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_asarray_validated\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck_finite\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcheck_finite\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 141\u001b[0;31m     \u001b[0mb1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0matleast_1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_asarray_validated\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck_finite\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcheck_finite\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    142\u001b[0m     \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ma1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    143\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Library/Python/3.8/lib/python/site-packages/scipy/_lib/_util.py\u001b[0m in \u001b[0;36m_asarray_validated\u001b[0;34m(a, check_finite, sparse_ok, objects_ok, mask_ok, as_inexact)\u001b[0m\n\u001b[1;32m    285\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'masked arrays are not supported'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    286\u001b[0m     \u001b[0mtoarray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray_chkfinite\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcheck_finite\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 287\u001b[0;31m     \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtoarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    288\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mobjects_ok\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    289\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'O'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Library/Python/3.8/lib/python/site-packages/numpy/lib/function_base.py\u001b[0m in \u001b[0;36masarray_chkfinite\u001b[0;34m(a, dtype, order)\u001b[0m\n\u001b[1;32m    601\u001b[0m     \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    602\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchar\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtypecodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'AllFloat'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 603\u001b[0;31m         raise ValueError(\n\u001b[0m\u001b[1;32m    604\u001b[0m             \"array must not contain infs or NaNs\")\n\u001b[1;32m    605\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: array must not contain infs or NaNs"
     ]
    }
   ],
   "source": [
    "alcohol_data_2 = IF(Lx,A0,Nx,M1x)\n",
    "alcohol_data_2.GL()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([101.12206468, 128.33876093]),\n",
       " array([65.87793532, 57.66123907]),\n",
       " 221.5391743924633,\n",
       " 115.46082560753669)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alcohol_data_2.convexProgram()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see here, our method is working when their method doesn't work. Notice we don't have to give any initial guess. As such, we do not need to know any crude observed totals for the cases initially."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grid values where it works vs when it doesn't work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([2,6])\n",
    "Nx = np.array([337,167,186,212])\n",
    "M1x = 451\n",
    "Lx = np.array([np.log(0.80),np.log(1.16),np.log(1.57)])\n",
    "A0 = np.array([74,90,122])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Johnson/Documents/Sasha_Research/CvxFitting/src/IterativeFitting.py:163: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  c0 = 1/a0 + 1/b0\n",
      "/Users/Johnson/Documents/Sasha_Research/CvxFitting/src/IterativeFitting.py:172: RuntimeWarning: divide by zero encountered in log\n",
      "  e = L + np.log(a0) + np.log(B) - np.log(A) - np.log(b0)\n",
      "/Users/Johnson/Documents/Sasha_Research/CvxFitting/src/IterativeFitting.py:172: RuntimeWarning: invalid value encountered in log\n",
      "  e = L + np.log(a0) + np.log(B) - np.log(A) - np.log(b0)\n"
     ]
    }
   ],
   "source": [
    "x,y = np.meshgrid(np.arange(1,Nx[1],1),np.arange(1,Nx[2],1))\n",
    "A0_vals = np.vstack([x.flatten(),y.flatten()]).T*1.\n",
    "z = np.array([122 for _ in range(A0_vals.shape[0])])\n",
    "z = np.array([z]).T\n",
    "A0_vals = np.hstack((A0_vals,z))\n",
    "failed_A0=[]\n",
    "succeeded_A0 = []\n",
    "for i in range(len(A0_vals)):\n",
    "    alcohol_data_2 = IF(Lx,A0_vals[i],Nx,M1x)\n",
    "    try:\n",
    "        alcohol_data_2.GL()\n",
    "        succeeded_A0+=[A0_vals[i]]\n",
    "    except:\n",
    "        failed_A0+=[A0_vals[i]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fee811a5b80>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "failed_A0 = np.array(failed_A0)\n",
    "succeeded_A0=np.array(succeeded_A0)\n",
    "plt.scatter(failed_A0[:,0],failed_A0[:,1],label=\"Failed\")\n",
    "plt.scatter(succeeded_A0[:,0],succeeded_A0[:,1],c='red',label=\"Succeeded\")\n",
    "plt.scatter(A0[0],A0[1],c='black',label=\"Initial\")\n",
    "plt.scatter(alcohol_data_2.convexProgram()[0][0],alcohol_data_2.convexProgram()[0][1],c='olive',label=\"Ours\")\n",
    "plt.xlabel(\"x-dimension of A\")\n",
    "plt.ylabel(\"y-dimension of A\")\n",
    "plt.legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grid Search on N vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([9.06,27.,45.,64.8])\n",
    "# Nx = np.array([414,261,228,44,34])\n",
    "A = np.array([126,61,69,22,19])\n",
    "Nx = A + 2.\n",
    "# A = Nx - 5.\n",
    "# A0 = A[1:]\n",
    "# A0 = np.array([61,69,22,19]) + 0.\n",
    "M1x = np.sum(A)\n",
    "A0 = M1x*Nx[1:]/(Nx.sum())\n",
    "# A0 = A[1:] + 0.\n",
    "# Lx = np.array([-0.2231435,-0.0001,0.5306283,0.8754687])\n",
    "Lx = np.array([-200,-250,-300,-700])\n",
    "vx = np.array([0.2233380,0.2337519,0.3765137,0.4440046])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([60.94788274, 68.68729642, 23.21824104, 20.31596091])"
      ]
     },
     "execution_count": 342,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   1.77769239, -109.86512984,  -74.9522335 , -330.28627809]),\n",
       " 810.3259490428073,\n",
       " array([ 61.22230761, 180.86512984,  98.9522335 , 351.28627809]),\n",
       " -682.3259490428073,\n",
       " 2)"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IF(Lx,A0,Nx,M1x).GL()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([62.9999995 , 70.99999944, 23.99999981, 10.99999988]),\n",
       " array([5.00201146e-07, 5.64836782e-07, 1.86621818e-07, 1.00000001e+01]),\n",
       " 128.00000136865125,\n",
       " -1.368651254551878e-06)"
      ]
     },
     "execution_count": 344,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "IF(Lx,A0,Nx,M1x).convexProgram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Covariance matrix for broken case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([9.06,27.,45.,64.8])\n",
    "Nx = np.array([414,261,228,44,34])\n",
    "# Nx[0] = 127\n",
    "A0 = np.array([61,69,22,19])\n",
    "# Nx[1:] = A0 + 1\n",
    "M1x = np.sum(A0) + 126\n",
    "Lx = np.array([-0.2231435,-0.0001,0.5306283,0.8754687])\n",
    "vx = np.array([0.2233380,0.2337519,0.3765137,0.4440046])\n",
    "vx *= vx\n",
    "# vx = np.array([0.001,0.01,0.2,0.9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "alcohol_data = IF(Lx,A0,Nx,M1x)\n",
    "A_alc, B_alc, a0_alc, b0_alc = alcohol_data.convexProgram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C4 = covariance_matrix(A_alc,B_alc,a0_alc,b0_alc,vx)\n",
    "mask = np.triu(np.ones_like(C4, dtype=bool))  # Mask for the upper triangle\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "sns.set(font_scale=1.6)\n",
    "sns.heatmap(C4, annot=True, fmt=\".4f\", mask=mask, cmap='Blues', cbar=True, square=True, \n",
    "            xticklabels=[f'Lvl{i+1}' for i in range(4)], \n",
    "            yticklabels=[f'Lvl{i+1}' for i in range(4)], vmin=.01,vmax=0.02)\n",
    "# plt.title('Upper Triangle of Covariance Matrix--Solved Hamling')\n",
    "plt.savefig(\"images/GL_break_work.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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