pc_hypothesis_2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "parameters:\n",
    "- n_p - number of members of party in power\n",
    "- n_o - number of members of party in opposition\n",
    "- n is the total\n",
    "- m number of bills"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_p=110;\n",
    "n_o=100;\n",
    "n=n_p+n_o;\n",
    "m=400;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "bills are of 4 types:\n",
    "- nonpartisan assigned with prob pr_nonpart\n",
    "- partisan, policy - only party in power wants them (pr_pol is the frewuency of those, among the partisan ones)\n",
    "- partisan, operational, pr_opp: both parties \n",
    "- partisan, trolling, pr_troll: only opposition wants it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr_nonpart=0;\n",
    "pr_pol=.7;\n",
    "pr_opp=.12;\n",
    "pr_troll=0.02;\n",
    "a=np.zeros([n,m]);\n",
    "avg=np.zeros([n,m]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr_nonpart=0;\n",
    "pr_pol=.25;\n",
    "pr_opp=.25;\n",
    "pr_troll=0.25;\n",
    "a=np.zeros([n,m]);\n",
    "avg=np.zeros([n,m]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "produce a voting record for one bill:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bill(pr_p,pr_po,pr_op,pr_tr,b_p,b_o,p_sl):\n",
    "    b=np.zeros([b_p+b_o]);\n",
    "    if 0:\n",
    "        print('a')\n",
    "    else:\n",
    "        dec = np.random.rand(1)\n",
    "        if dec<pr_po:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*int(np.random.binomial(1,0.98))-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*int(np.random.binomial(1,0.88))-1;\n",
    "        elif dec<pr_po+pr_op:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*int(np.random.binomial(1,.98))-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*int(np.random.binomial(1,0.12))-1;\n",
    "        elif dec<pr_po+pr_op+pr_tr:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*int(np.random.binomial(1,0.75))-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*int(np.random.binomial(1,0.02))-1;\n",
    "        else:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*int(np.random.binomial(1,.02))-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*int(np.random.binomial(1,0.75))-1;\n",
    "    return(b);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "first check if it's nonpartisan: then vote for it with probability 50%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bill_avg(pr_p,pr_po,pr_op,pr_tr,b_p,b_o,p_sl):\n",
    "    b=np.zeros([b_p+b_o]);\n",
    "    if np.random.rand(1)<pr_nonpart:\n",
    "        for k in range(b_p+b_o):\n",
    "            b[k]=0.3;\n",
    "    else:\n",
    "        if np.random.rand(1)<pr_po:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*p_sl-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*(1-p_sl)-1;\n",
    "        elif np.random.rand(1)<pr_op:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*0.9-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*0.9-1;\n",
    "        else:\n",
    "            for k in np.arange(b_p):\n",
    "                b[k]=2*(1-p_sl)-1;\n",
    "            for k in np.arange(b_p+1,b_p+b_o):\n",
    "                b[k]=2*p_sl-1;\n",
    "    return(b);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for policy bills, power party voteds with probability p_sl, opposition party woth prob 1-p_sl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for household bills, both parties vote for them with prob .7 (should be a parameter!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "else, if it's trolling bill, opposition votes for it w prob p_sl, power party 1-p_sl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "produce m bills, and do svd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "209\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l in range(m):\n",
    "    a[:,l]=bill(pr_nonpart,pr_pol,pr_opp,pr_troll,n_p,n_o,.85);\n",
    "    avg[:,l]=bill_avg(pr_nonpart,pr_pol,pr_opp,pr_troll,n_p,n_o,.85);\n",
    "\n",
    "print(np.linalg.matrix_rank(avg))\n",
    "print(np.linalg.matrix_rank(a))\n",
    "[u,s,v]=np.linalg.svd(a);\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "passed_indices = []\n",
    "failed_indices = []\n",
    "for i in range(m):\n",
    "    if sum(a[:,i]) > 0:\n",
    "        passed_indices.append(i)\n",
    "    else:\n",
    "        failed_indices.append(i)\n",
    "plt.scatter(v[0,passed_indices], v[1,passed_indices], c='g')\n",
    "plt.scatter(v[0,failed_indices], v[1,failed_indices], c='r')\n",
    "plt.title('Eigenbills')\n",
    "plt.show()\n",
    "#plt.scatter(u[0,:n_p], u[1,:n_p], c='r')\n",
    "#plt.scatter(u[0,n_p:], u[1,n_p:], c='b')\n",
    "#plt.title('Eigenmembers')\n",
    "#plt.show()\n",
    "plt.scatter(u[:n_p,0], u[:n_p,1], c='r')\n",
    "plt.scatter(u[n_p+1:,0], u[n_p+1:,1], c='b')\n",
    "plt.title('Eigenmembers')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEICAYAAAC3Y/QeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAbd0lEQVR4nO3df3Bd5X3n8fdHsp1BQA3YCuGXJZo4mTVx6i5adrvbtMmahh8pcWA3LFTOOs3uKlhhFna3swPVTEnS0TbLhg3bNnYrpkzZQQmhBRIIThNwQ9JMhwY5pdgGXAyxAMcBYRfTRYyx5e/+cc6FK+neq3ulc+6VdD6vmTO65znnnvPcM1ff89znPD8UEZiZWbG0tToDZmbWfA7+ZmYF5OBvZlZADv5mZgXk4G9mVkAO/mZmBeTgb4UhqVfSd5twnk9J+mGN7d+WtKnSvpJC0nvyzqPZklZnwCxrkvYBpwMTZcl/GhHXAsMtyVSZiLik1Xkwc/C3xeqyiHi41Zkwm69c7WOFUaGK5SOS9kg6LGmLpO9L+o9l2z8t6SlJ/yDpO5K6yraFpGskPSPpVUlfkaTJp9Mfpsd+WtL6sg2PlJ+nRn4vlfSkpH+UtF/Sb2VwGcwAB38rKEkrgT8HbgRWAHuAf1m2fQPw28AVQCfwV8DXphzm14F/BnwAuBK4qGzbPweeBVYCNwH3SjqtwWz+CfCZiDgZeD/wlw2+36wqB39brL6RlshLy3+asv1SYHdE3BsRx4DfB35Wtv0a4Pci4ql0+/8A1pWX/oEvRsSrEfE88D1gXdm2l4FbI+JoRHyd5Oby0QY/w1FgjaSfi4h/iIgfN/h+s6oc/G2x+nhEnFK23DZl+5nAC6WVSEY4fLFsexfwf0o3D+AQIOCssn3KbxbjwEll6/tj8qiJo+k5G/FvSG5So2mV1C81+H6zqhz8ragOAGeXVtL6+rPLtr9AUuVSfgM5ISL+us7jnzXlGcAq4KeNZDAiHouIDcA7gW8AdzfyfrNaHPytqB4E1kr6uKQlwGeBd5Vt/yPgRknnAUhaLukTDRz/ncB/lrQ0fd8/AbbV+2ZJy9J+Ccsj4ijwGnC8gfOb1eTgb4vVA5L+X9lyX/nGiHgF+ARwM3AQWAOMAEfS7fcB/xO4S9JrwC6gkfb5fwOsBl4BBoF/GxEHG/wMnwT2pee/Buht8P1mVcmTuZiBpDaSOv/eiPheq/NjljeX/K2wJF0k6RRJ7yBp1ing0RZny6wpHPytyH6JpC3+K8BlJC2E3mhtlsyaw9U+ZmYF5JK/mVkBLYiB3VauXBnd3d2tzoaZ2YKyY8eOVyKis9K2BRH8u7u7GRkZaXU2zMwWFEmj1ba52sfMrIAc/M3MCsjB38ysgBz8zcwKyMHfzKyAFkRrHzOzxWZ45zAD2wcYPTxKu9qZiAlWnLACgENvHGLV8lUMrh+kd20+4/k5+JuZNdnwzmH6Huhj/Og4ABMxAcDBN94e+HX08Ch9D/QB5HIDcLWPmVmTDWwfeCvw1zJ+dJyN926k+9ZuhncOZ5oHB38zsyZ7/vDzDe1f+hWQ5Q3Awd/MrEmGdw7TfWs3QeMDao4fHWdg+0BmeXGdv5lZE0yt55+N0cNVR2tomEv+ZmZNUG89fy3tas8oNw7+ZmZN0Wg9fyWlVkFZcPA3M2uC0044bc7HOGnZSRnkJOHgb2aWo9JD3vI2/LP1+puvZ5CjhB/4mpnlJIuHvOVm00qoGpf8zczmoFSyb/t827TOWFk85M2LS/5mZrM0tWQ/dUiGLB7y5iXXkr+k90l6vGx5TdL1kj4naX9Z+qV55sPMLA+VSvbjR8e57tvXzbozV7PkWvKPiD3AOgBJ7cB+4D7gN4EvR8SX8jy/mVmeqpXsD75xMJMHvHlqZp3/euDZiMiui5qZWQutWr6q1VmYtWYG/6uAr5WtXyvpCUm3Szp16s6S+iSNSBoZGxtrXi7NzOo0uH6QjqUdrc7GrDQl+EtaBnwM+LM0aSvwbpIqoQPALVPfExFDEdETET2dnZ3NyKaZWUN61/YydNkQXcu7EKJreddbE7JMlcXQDF3Lu+Z8jJJmlfwvAX4cES8BRMRLETEREceB24ALmpQPM7NM9a7tZd/1+zh+03H2Xb+PK8+7suJ+cx2aoWNpB4PrB+d0jHLNCv5XU1blI+mMsm2XA7ualA8zs1xte2Zb5sdsVzubfmFTpjN65R78JZ0I/Bpwb1nyzZJ2SnoC+DDwX/LOh5lZM+TRtn8iJrjj7+5YWJO5RMTrEbEiIg6XpX0yItZGxAci4mMRcSDvfLxleBi6u6GtLfk7nO3UaGZWXMM7h2lTPmHVk7nMxfAw9PXBeNopY3Q0WQfozX6CZDMrjlJv3yyHXZ7Kk7nM1sDA24G/ZHwcNm6EJUugv3/yNv9KMLM6NWMcnywncylWyf/5GnVxExOwdWvyessW/0ows4bUW9ffsbRj1jcJT+ZSr/7+pEQvJaX3egwNJYF/06bKvxIGsqtzM7PFo1pv3xUnrJjUD2DosqFZn2MhtvNvvv7+pCQ/kd4pI5JlJhMTSQl/osodttavBzMrrEtXVx6f8srzrpzUD2C2zTUXajv/5hua/d11Wom/3KqFO5aHmeWnWvv+Sun11N2vOGEFK05YMekXQ5bt/BdvnX+1kvtcdHTAYHZ3XjNbPKrV+VdKn6nufnPPZrZ8dEsm+apm8Zb8s9benvya8MNeM6ugWp1/pfSZ6u7z6CU8lYN/PZYtgzvucOA3s6oqjfBZrZ5+ptFARw+PsuQLS+h/sL/qPnO1eIP/isoj681KPQ+KzazQKo3wWa2evrRvrd7AEzHB1pGtud0AFAsgsPX09MTIyEhjb1q5Eg5mOJNOVxfs25fd8cys8FbevLKuGb+6lncxuH6w4Qe+knZERE+lbYu35J9l4Iekk5eZWYYOvXGorv1KE8MvqIHdFo327LpVm5lBY9NAZj2wm4N/vfJoOmpmhdboNJAe2K0VurLrVm1mBtMfEp+49MSaD4E9sFuzuXOXmeWkd23vtAe5+rwq7uuB3eqRVUm9vT0Z5M1t/M2sSap1AltQA7tJ2pdO2fi4pJE07TRJD0l6Jv17auYnfs97sjnOxETSwctj+ZtZkzTSYWy2mlXy/3BErCtrb3oDsD0iVgPb0/VsPfJIdscaH09K/74BmFkTNNJhbLZy7+QlaR/QExGvlKXtAT4UEQcknQE8EhHvq3aMWXXyUuU6sznp6PD4Pma2YLS6k1cA35W0Q1I6FRanl03a/jPg9KlvktQnaUTSyNjYWBOyWQdP5mJmi0QzWvv8ckTsl/RO4CFJT5dvjIiQNO3nR0QMAUOQlPybkM/6eDIXM1sEci/5R8T+9O/LwH3ABcBLaXUP6d+XMz9xXj1yPZmLmWVoeOcw3bd20/b5Nrpv7c50CIdacg3+kk6UdHLpNfARYBdwP7Ap3W0T8M3MT+7JXMxsnhveOUzfA32MHh4liFzG8Kkm75L/6cAPJf0d8CPgwYj4C+CLwK9Jega4MF3PVhYl/7a2pL+AlPz1w14zy9DA9gHGj06eNjbrMXyqybXOPyKeA36hQvpBYH2e586k5H/8uIdxNrPcNDL1Y9bcw3cm3d1u329muWhk6sesLd7gPziY1NHP1ego9PX5BmBmmWtGT95qFm/w7+1N6uhLdfbLls3+WG7fb2Y5aEZP3moW7zSOU/X3wx//cVKPPxvS7N9rZtYCtXr4FmNI5/5+2Lp1bsdw+34zW0QWb7VPuaGh+vdds2b6swK37zezRaYYwb+RZp+/+quTnxW4fb+ZLULFqPNfsqT+G0B7Oxw7NvtzmZnNE60e1bP1+vpm3qfEE7WbWQEUI/hv2QKbN9e3b14DwpmZzSPFCP6Q3ADq0civBDOzBaoYTT3r0d6eBP56bxJmZgtYsYL/mjXw5JOV03fvbn5+zMxapDjVPgCvv95YupnZIlWs4F9tCkZPzWhmBVOs4F9tiAYP3WBmBVOs4H/ppY2lm5ktUrkFf0nnSPqepCcl7ZZ0XZr+OUn7JT2eLs2LvNu2NZZuZrZI5dna5xjw3yLix+kk7jskPZRu+3JEfCnHc1fmOn8zMyDHkn9EHIiIH6ev/xF4Cjgrr/PVxXX+ZmZAk+r8JXUDvwj8TZp0raQnJN0u6dQq7+mTNCJpZGxsLJuMVJra0cM1m1kB5R78JZ0E3ANcHxGvAVuBdwPrgAPALZXeFxFDEdETET2dnZ3ZZGbq1I4ertnMCirXHr6SlpIE/uGIuBcgIl4q234b8K088zBNb6+DvZkVXp6tfQT8CfBURPzvsvQzyna7HNiVVx7MzKyyPEv+/wr4JLBT0uNp2m8DV0taBwSwD/hMjnkwM7MKcgv+EfFDQBU2uVG9mVmLFauHr5mZAQ7+ZmaF5OBvZlZADv5mZgXk4G9mVkAO/mZmBeTgb2ZWQA7+ZmYF5OBvZlZADv5mZgXk4G9mVkAO/mZmBeTgb2ZWQA7+ZmYF5OBvZlZADv5mZgXk4G9mVkAtC/6SLpa0R9JeSTe0Kh9mZkXUkuAvqR34CnAJsIZkXt81rciLmVkRtarkfwGwNyKei4g3gbuADS3Ki5lZ4bQq+J8FvFC2/mKa9hZJfZJGJI2MjY01NXNmZovdvH3gGxFDEdETET2dnZ2tzo6Z2aLSquC/HzinbP3sNM3MzJqgVcH/MWC1pHMlLQOuAu5vUV7MzApnSStOGhHHJF0LfAdoB26PiN2tyIuZWRG1JPgDRMQ2YFurzm9mVmTz9oGvmZnlx8HfzKyAHPzNzArIwd/MrIAc/M3MCsjB38ysgBz8zcwKyMHfzKyAHPzNzArIwd/MrIAc/M3MCsjB38ysgBz8zcwKyMHfzKyAHPzNzArIwd/MrIAc/M3MCiiX4C/pf0l6WtITku6TdEqa3i3pDUmPp8sf5XF+MzOrLa+S/0PA+yPiA8DfAzeWbXs2ItalyzU5nd/MzGrIJfhHxHcj4li6+ihwdh7nMTOz2WlGnf+ngW+XrZ8r6W8lfV/SB5twfjMzm2LJbN8o6WHgXRU2DUTEN9N9BoBjwHC67QCwKiIOSjof+Iak8yLitQrH7wP6AFatWjXbbJqZWQWzDv4RcWGt7ZI+Bfw6sD4iIn3PEeBI+nqHpGeB9wIjFY4/BAwB9PT0xGzzaWZm0+XV2udi4L8DH4uI8bL0Tknt6eufB1YDz+WRBzMzq27WJf8Z/CHwDuAhSQCPpi17fgX4gqSjwHHgmog4lFMezMysilyCf0S8p0r6PcA9eZzTzMzq5x6+ZmYF5OBvZlZADv5mZgXk4G9mVkAO/mZmBeTgb2ZWQA7+ZmYF5OBvZlZADv5mZgXk4G9mVkAO/mZmBeTgb2ZWQA7+ZmYF5OBvZlZADv5mZgXk4G9mVkAO/mZmBeTgb2ZWQLkFf0mfk7Rf0uPpcmnZthsl7ZW0R9JFeeXBzMwqy2sC95IvR8SXyhMkrQGuAs4DzgQelvTeiJjIOS9mZpZqRbXPBuCuiDgSET8B9gIXtCAfZmaFlXfwv1bSE5Jul3RqmnYW8ELZPi+maZNI6pM0ImlkbGws52yamRXLnIK/pIcl7aqwbAC2Au8G1gEHgFsaOXZEDEVET0T0dHZ2ziWbZmY2xZzq/CPiwnr2k3Qb8K10dT9wTtnms9M0MzNrkjxb+5xRtno5sCt9fT9wlaR3SDoXWA38KK98mJnZdHm29rlZ0joggH3AZwAiYreku4EngWPAZ93Sx8ysuXIL/hHxyRrbBoHBvM5tZma1uYevmVkBOfibmRWQg7+ZWQsN7xym+9Zu2j7fRvet3QzvHG7KefMe3sHMzKoY3jlM3wN9jB8dB2D08Ch9D/QB0Lu2N9dzu+RvZtYiA9sH3gr8JeNHxxnYPpD7uR38zcxaZPTwaEPpWXLwNzNrgf4H+2tuz7v+38HfzKzJ+h/sZ+vI1pr7lOr/87oBOPibmTXZ0I6huvbLs/7fwd/MrMkmGhjRZvTwaC5VQA7+ZmZN1q72hvbPowrIwd/MrEn6H+xnyReWNFTyL8m6CsidvMzMmqCeh7wzybIJqIO/mVmOhncOM7B9IJPA3Wh1US0O/mZmOZk6fMNczaa6qBoHfzOzjPU/2M/QjqFMg3XWHPzNzDKURd1+M+QS/CV9HXhfunoK8GpErJPUDTwF7Em3PRoR1+SRBzOzZhveOZxr4J/3df4R8e9KryXdAhwu2/xsRKzL47xmZq1Sqt/P08nLTs7sWLlW+0gScCXwr/M8j5lZq1Uanjlrrx55NbNj5d3J64PASxHxTFnauZL+VtL3JX2w2hsl9UkakTQyNjaWczbNzObm+cPPtzoLDZl18Jf0sKRdFZYNZbtdDXytbP0AsCoifhH4r8BXJf1cpeNHxFBE9ERET2dn52yzaWbWFKuWr6q6bXPP5ibmpD6zDv4RcWFEvL/C8k0ASUuAK4Cvl73nSEQcTF/vAJ4F3ju3j2Bm1nqD6wfpWNoxKa1jaQd3XnEnWz66JZNznHnSmZkcB/Kt9rkQeDoiXiwlSOqUksfVkn4eWA08l2MezMyaondtL0OXDdG1vAshupZ3MXTZ0Ftz8WbRUmdp+9I5H6Mkzwe+VzG5ygfgV4AvSDoKHAeuiYhDOebBzKxpetf2Vp14PYsOXwtibJ+I+FSFtHuAe/I6p5mZ1cdDOpuZFZCDv5m1xvAwdHdDW1vydzi/ycoXi3nfw9fMrKbhYejrg/G0U9ToaLIO0Fu5ztzgQ90fyuxYLvmbWf6mlvKvu+7twF8yPg4D+UxW3kql2buysPfQ3kyOAy75m1neKpXyq3l+YfWSnUnWI3xm2YvYJX8zy9fAwPRSfjWrqveSXYiGdgxlerxavYgb5eBvZtNl+TC23tL80qUwONjYsef5Q+Nabfun9gaeScfSDgbXN3h9anDwN7PJStU0o6MQ8fbD2NkG1npL81Jjx806nzmo1jqnXe0MXTbEihNW1HWcqb2Fs+Dgb1YU9ZaSK1XTzOVh7OAgdNRRyn3zzcnnmCm/WeczB33nVx7fv+/8PnrX9nLSspNmPEa72tl3/b5MAz/4ga9ZMTTStLJaNc1sH8aWjr9x48z7lh4G15PfrPOZg9KAbqX5fNvVTt/5fW+l1/MAN695gF3yNyuCRkrJ1appImDJEujvn5ze35+kS9OXs856e7/2Ojootbcnx9u4sXJ+N26ElSuTJaLyMTo63s5Ppfw22ZaPbuHY7xwjbgqO/c6xSSN81vsAt/vWboZ3Zlud5eBvVgSNlJJrVdNMTMDWrW8H1P7+ZH2iSun0pz+FU09NSu3V9ql0/FoOHkyWStra4PXX3z7X1PzOM5WGga5k9PAofQ/0ZXoDcPA3K4JqpflVq6bXrQNs2lS7pD40NPlvLa++Wn9Tz7no6qq+rZ58tkD5MNAzGT86zsD27J5nKKr9dJpHenp6YmRkpNXZMFu4ptahQ1K637QJ7rhjcvrSpUmVyZtv1j5mROMtdPI0U37meawrTQBfax5gIY7fdLzuY0raERE9lba55G9WBL29Sem3qysJkF1dyfq2bdNL5UePzhz4AU6auaWK1a+eXwFZdvJyyd+syNra5n2JuG4LvORfrtKvgI6lHQ239XfJ32yxmmsP18UynELp+US15xT1tDSaR2aaEjITETHrBfgEsJtkSsaeKdtuBPYCe4CLytIvTtP2AjfUc57zzz8/zGyKO++M6OiISMq0ydLRkaTP5RgLcVm/Pvk8tfYpIGAkqsTVuZb8dwFXAD8oT5S0hmQO3/PSYL9FUns6eftXgEuANcDV6b5m1qgseriWngXUsmJFssxne9Ohjqu1+KnVEqig5hT8I+KpiNhTYdMG4K6IOBIRPyEp5V+QLnsj4rmIeBO4K93XzBqVVQ/X3l7YvLnyts2b4ZVXkuXOO+sbpqEVSp+5Uh+Fjo7GB4wrgLzq/M8CXihbfzFNq5Y+jaQ+SSOSRsbGxnLKptkCVqvtfqO2bEkCfXnd+ebNSXpJeYuhvC1pcOSZ0meu1qrJs4NNM2Pwl/SwpF0VllxL7BExFBE9EdHT2dmZ56nMFqasS7lbtsCxY0kN+bFjkwN/SW8v7NtX/ZfCbGzePL2G/ujRt1/P9Itj6mcu5fH48eSvA39FM95eI+LCWRx3P3BO2frZaRo10s2sEaWgNjCQVHusWpUEwWYEu9KNYWho8rANJ54Ib7yRBN62NjjhhOQ5xLJlcOTI5GO0tycdzyrdZMpN/ZynnZasHzrU3M+8yGTSzl/SI8BvRcRIun4e8FWSOv4zge3AakDA3wPrSYL+Y8BvRMTuWsd3O38zs8bVauc/pyGdJV0O/AHQCTwo6fGIuCgidku6G3gSOAZ8NiIZl1TStcB3gHbg9pkCv5mZZc89fM3MFin38DUzs0kc/M3MCsjB38ysgBz8zcwKyMHfzKyAHPzNzApoQTT1lDQGjLbg1CuBV1pw3vnM12Q6X5PpfE2ma8U16YqIiuPjLIjg3yqSRqq1kS0qX5PpfE2m8zWZbr5dE1f7mJkVkIO/mVkBOfjXNsMUR4XkazKdr8l0vibTzatr4jp/M7MCcsnfzKyAHPzNzArIwR+Q9AlJuyUdl9QzZduNkvZK2iPporL0i9O0vZJuaH6um0fS5yTtl/R4ulxatq3i9SmCIn0HZiJpn6Sd6fejNKnTaZIekvRM+vfUVuczT5Jul/SypF1laRWvgRK/n353npD0T5udXwf/xC7gCuAH5YmS1gBXAecBFwNbJLVLage+AlwCrAGuTvddzL4cEevSZRtUvz6tzGSzFPQ7MJMPp9+PUgHqBmB7RKwmmc1vsd8g/5Tk/6BctWtwCcnshquBPmBrk/L4Fgd/ICKeiog9FTZtAO6KiCMR8RNgL8nUlBcAeyPiuYh4E7gr3bdoql2fIvB3YGYbgDvS13cAH29hXnIXET8ADk1JrnYNNgD/NxKPAqdIOqM5OU04+Nd2FvBC2fqLaVq19MXs2vTn6e1lP9+LeB1KivzZKwngu5J2SOpL006PiAPp658Bp7cmay1V7Rq0/Pszpzl8FxJJDwPvqrBpICK+2ez8zDe1rg/JT9LfJfkH/13gFuDTzcudLQC/HBH7Jb0TeEjS0+UbIyIkFbpd+Xy7BoUJ/hFx4Szeth84p2z97DSNGukLUr3XR9JtwLfS1VrXZ7Er8mefJiL2p39flnQfSbXYS5LOiIgDaZXGyy3NZGtUuwYt//642qe2+4GrJL1D0rkkD2d+BDwGrJZ0rqRlJA89729hPnM1pS7ycpIH5FD9+hRBob4DtUg6UdLJpdfAR0i+I/cDm9LdNgFF/IVd7RrcD/z7tNXPvwAOl1UPNUVhSv61SLoc+AOgE3hQ0uMRcVFE7JZ0N/AkcAz4bERMpO+5FvgO0A7cHhG7W5T9ZrhZ0jqSap99wGcAal2fxS4ijhXsO1DL6cB9kiCJKV+NiL+Q9Bhwt6T/QDIk+5UtzGPuJH0N+BCwUtKLwE3AF6l8DbYBl5I0khgHfrPp+fXwDmZmxeNqHzOzAnLwNzMrIAd/M7MCcvA3MysgB38zswJy8DczKyAHfzOzAvr/Tz3U0WPTLmUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#[u,s,v]=np.linalg.svd(a);\n",
    "v_t = np.zeros((2,m))\n",
    "for i in range(m):\n",
    "    v_t[0,i] = sum(a[:n_p,i])\n",
    "    v_t[1,i] = sum(a[n_p+1:,i])\n",
    "\n",
    "passed_indices = []\n",
    "failed_indices = []\n",
    "for i in range(m):\n",
    "    if sum(a[:,i]) > 0:\n",
    "        passed_indices.append(i)\n",
    "    else:\n",
    "        failed_indices.append(i)\n",
    "plt.scatter(v_t[0,passed_indices], v_t[1,passed_indices], c='g')\n",
    "plt.scatter(v_t[0,failed_indices], v_t[1,failed_indices], c='r')\n",
    "plt.title('Eigenbills')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def std_vot_mat(a):\n",
    "    a_sorted = np.copy(a)\n",
    "    [u,s,v]=np.linalg.svd(a);\n",
    "    a1 = 1;\n",
    "    a2 = 0;\n",
    "    b1 = 1;\n",
    "    b2 = 0;\n",
    "    mem_inds = sorted(range(u.shape[0]), key=lambda k: b1*u[k,0]+b2*u[k,1])\n",
    "    bill_inds = sorted(range(v.shape[0]), key=lambda k: a1*v[0,k]+a2*v[1,k])\n",
    "    for i in range(a.shape[0]):\n",
    "        for j in range(a.shape[1]):\n",
    "            a_sorted[i,j] = a[mem_inds[i], bill_inds[j]]\n",
    "    return a_sorted\n",
    "\n",
    "a_sorted = std_vot_mat(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "'''\n",
    "mem_inds = sorted(range(len(mem)), key=lambda k: mem[k])\n",
    "bill_inds = sorted(range(len(bill_params)), key=lambda k: 10*np.exp(bill_params[k][0])+0.1*bill_params[k][1])\n",
    "a_sorted = np.copy(a)\n",
    "for i in range(a.shape[0]):\n",
    "    for j in range(a.shape[1]):\n",
    "        a_sorted[i,j] = a[mem_inds[i], bill_inds[j]]\n",
    "plt.imshow(a_sorted)\n",
    "plt.show()\n",
    "'''\n",
    "plt.imshow(a)\n",
    "plt.show()\n",
    "plt.imshow(a_sorted)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = -1*np.ones((2,5))\n",
    "a[0,0]=1\n",
    "a[1,0]=0\n",
    "plt.imshow(a)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}