{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e9b43d48",
   "metadata": {},
   "source": [
    "October 3 2021"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d457eb0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from collections import Counter\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc924833",
   "metadata": {},
   "source": [
    "Build random adjacency matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "adff5db6",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 300\n",
    "p = 1/500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2d2ca984",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_A():\n",
    "    A = (np.random.random((N, N)) < p).astype('float')\n",
    "    for i in range(N):\n",
    "        A[i,i] = 0\n",
    "\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            A[i,j] = A[j,i]\n",
    "    return A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e851af65",
   "metadata": {},
   "source": [
    "Start with random state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bc753e2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_state():\n",
    "    return 2*((np.random.random(N) > 0.5).astype('float') - 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2791c6bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(E, A, x):\n",
    "    return E + x.T @ A @ x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2bf4888",
   "metadata": {},
   "source": [
    "Test values that we get from random states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8911b677",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[92.0, 100.0, 108.0, 112.0, 116.0]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ctr = Counter()\n",
    "A = get_A()\n",
    "E = np.sum(A)\n",
    "for _ in range(1000):\n",
    "    c = cost(E, A, random_state())\n",
    "    ctr[c] += 1\n",
    "sorted(ctr.keys())[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15e53821",
   "metadata": {},
   "source": [
    "Try minimizing with simple local search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c048ca68",
   "metadata": {},
   "outputs": [],
   "source": [
    "def local_search(A, f, x):\n",
    "    E = np.sum(A)\n",
    "    best = f(E, A, x)\n",
    "    loops = 0\n",
    "    print('-')\n",
    "    print('start cost:', best)\n",
    "    while True:\n",
    "        if loops % 20 == 0:\n",
    "            print('loop', loops, 'cost:', best)\n",
    "        bestpos = None\n",
    "        for i in range(N):\n",
    "            x[i] *= -1\n",
    "            newcost = f(E, A, x)\n",
    "            if newcost < best:\n",
    "                best = newcost\n",
    "                bestpos = i\n",
    "            x[i] *= -1\n",
    "        if bestpos == None:\n",
    "            break\n",
    "        x[bestpos] *= -1\n",
    "        loops += 1\n",
    "    print('final cost:', best)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "df09b153",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-\n",
      "start cost: 164.0\n",
      "loop 0 cost: 164.0\n",
      "loop 20 cost: 64.0\n",
      "final cost: 12.0\n"
     ]
    }
   ],
   "source": [
    "x = random_state()\n",
    "x = local_search(A, cost, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49ac40b4",
   "metadata": {},
   "source": [
    "New idea: try the functional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b0684e8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(b, f):\n",
    "    return lambda *args: f(*args) * (b - f(*args)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "877338a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "cost2 = g(N, cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c69de6b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-\n",
      "start cost: 1872.0\n",
      "loop 0 cost: 1872.0\n",
      "loop 20 cost: -4691232.0\n",
      "loop 40 cost: -15178592.0\n",
      "final cost: -24809488.0\n",
      "22.0 diff from cost2\n",
      "-\n",
      "start cost: 292.0\n",
      "loop 0 cost: 292.0\n",
      "loop 20 cost: 124.0\n",
      "loop 40 cost: 44.0\n",
      "final cost: 0.0\n",
      "-\n",
      "start cost: 0.0\n",
      "loop 0 cost: 0.0\n",
      "final cost: 0.0\n",
      "0.0 diff from cost2\n",
      "-\n",
      "start cost: 0.0\n",
      "loop 0 cost: 0.0\n",
      "final cost: 0.0\n"
     ]
    }
   ],
   "source": [
    "for _ in range(2):\n",
    "    x_old = np.copy(x)\n",
    "    x2 = local_search(A, cost2, x)\n",
    "    print(np.sum(x2 - x_old), 'diff from cost2')\n",
    "    x = local_search(A, cost, x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "907f509b",
   "metadata": {},
   "source": [
    "The above works, but only if you end up at 0.\n",
    "\n",
    "What about a simple 1-D function?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "465259ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x):\n",
    "    return -30*np.cos(x)*np.minimum(9/x/x, 3) + 90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d9d38227",
   "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": [
    "inps = np.linspace(-20, 20, 100000)\n",
    "plt.plot(inps, func(inps))\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "91c5dc01",
   "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"
    },
    {
     "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": [
    "inps = np.linspace(-20, 20, 100000)\n",
    "func2 = g(0.3, func)\n",
    "plt.plot(inps, func2(inps))\n",
    "plt.grid()\n",
    "\n",
    "plt.figure()\n",
    "inps = np.linspace(-0.1, +0.1)\n",
    "plt.plot(inps, func2(inps))\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fef6e33",
   "metadata": {},
   "source": [
    "Now try minimizing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "330374ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import fmin_bfgs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a250e1a9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 89.860280\n",
      "         Iterations: 5\n",
      "         Function evaluations: 12\n",
      "         Gradient evaluations: 6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([43.93680628])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = fmin_bfgs(func, np.random.random()*100)\n",
    "output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9aea9b45",
   "metadata": {},
   "outputs": [],
   "source": [
    "perturbation = 0.002"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "db06c3c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f2: 40.791713368857685\n",
      "f: 37.646039959742446\n",
      "f2: 34.499612763860256\n",
      "f: 43.93678638616231\n",
      "f2: 47.08143253552639\n",
      "f: 43.93681548161869\n",
      "f2: 47.0814365274836\n",
      "f: 43.93681438759613\n",
      "f2: 47.08143437008191\n",
      "f: 50.22568323596555\n",
      "f2: 47.08144050768827\n",
      "f: 47.081410821902644\n",
      "f2: 47.08143543894255\n",
      "f: 43.93686060069825\n",
      "f2: 40.79171667620592\n",
      "f: 37.64604460355624\n",
      "f2: 34.4996126890453\n",
      "f: 31.35221981497576\n",
      "f2: 31.35222029916411\n",
      "f: 31.352220943027163\n",
      "f2: 28.203539150973803\n",
      "f: 25.053079361077984\n",
      "f2: 21.900077619729817\n",
      "f: 12.406541444066196\n",
      "f2: 15.580294407337428\n",
      "f: 18.743252373453963\n",
      "f2: 21.900078467482757\n",
      "f: 25.0530795700924\n",
      "f2: 21.900076720580216\n",
      "f: 18.743252122005565\n",
      "f2: 15.580294356421883\n",
      "f: 18.743252979090745\n",
      "f2: 9.210964519819845\n",
      "f: 18.743252803422546\n",
      "f2: 21.900077179121773\n",
      "f: 18.743253556081196\n",
      "f2: 21.900076821941006\n",
      "f: 12.406543856320107\n",
      "f2: 15.580294276885754\n",
      "f: 12.406539741078568\n",
      "f2: 15.580294361919822\n",
      "f: 12.40653742120357\n",
      "f2: 9.210964368916205\n",
      "f: 12.406540720974439\n",
      "f2: 15.580294140482058\n",
      "f: 18.743253751425396\n",
      "f2: 21.900077475480106\n",
      "f: 25.053061861039964\n",
      "f2: 28.203539396247777\n",
      "f: 18.74325233054155\n",
      "f2: 15.580294315661964\n",
      "f: 12.406542966790052\n",
      "f2: 9.210964376543624\n",
      "f: 5.959392064131659\n",
      "f2: 2.4587141785207045\n",
      "f: -1.364988533164196e-08\n",
      "f2: -1.420277156408731e-08\n",
      "f: 2.6769595365763472e-08\n",
      "f2: -1.1065216845389931e-08\n",
      "f: 2.0699121355853213e-09\n",
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      "f: -1.3441297029136173e-08\n",
      "f2: -1.311143235865524e-08\n",
      "f: -1.5719277920523282e-08\n",
      "f2: 1.8119113799977288e-07\n",
      "f: -1.2092239962104246e-08\n",
      "f2: -9.278245678574003e-09\n",
      "f: -7.251859279925366e-09\n",
      "f2: -3.739445379567644e-08\n",
      "f: -1.4513937924802566e-08\n"
     ]
    }
   ],
   "source": [
    "i = 0\n",
    "while  i < 200:\n",
    "    output = fmin_bfgs(func2, output[0] + (np.random.random()-0.5)*perturbation, disp=False)\n",
    "    print('f2:', output[0])\n",
    "    output = fmin_bfgs(func, output[0] + (np.random.random()-0.5)*perturbation, disp=False)\n",
    "    print('f:', output[0])\n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "664dfe5a",
   "metadata": {},
   "source": [
    "So the alternating minimizations can find the minima with energy $0$, amidst many local minima!"
   ]
  }
 ],
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