Power Method.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.linalg import norm, null_space\n",
    "from scipy.optimize import minimize\n",
    "from xmps.spin import paulis, U4\n",
    "def merge(A, B):\n",
    "    # -A- -B-  ->  -A-B-\n",
    "    #  |   |        ||\n",
    "    return np.tensordot(A, B, [2, 1]).transpose([0, 2, 1, 3]).reshape(2*A.shape[0], 2, 2)\n",
    "N = 4\n",
    "U = np.linalg.qr(np.random.randn(N, N)+1j*np.random.randn(N, N))[0]\n",
    "No = U@np.diag(np.random.randn(N)+1j*np.random.randn(N))@U.conj().T\n",
    "\n",
    "z = np.array([1, 0])\n",
    "z = np.kron(z, z)\n",
    "def sv_min(mat): return minimize(lambda v: -(z@U4(-v)@mat.conj().T@mat@U4(v)@z).real, np.random.randn(15))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "def put_env_on_left_site(q, ret_n=False):\n",
    "    # Take a matrix q (2x2) and create U such that \n",
    "    # (right 0-|---|--0\n",
    "    #          | u |        =  q_{ij}\n",
    "    # (left) i-|---|--j \n",
    "    q = q.T\n",
    "    a, b, c, d = q.reshape(-1)\n",
    "    n = np.sqrt(np.abs(a)**2+ np.abs(c)**2+ np.abs(b)**2+ np.abs(d)**2)\n",
    "    guess = np.array([[a, c.conj(), b, d.conj()], [c, -a.conj(), d, -b.conj()]])/n\n",
    "    orth = null_space(guess).conj().T\n",
    "    A = np.concatenate([guess, orth], axis=0)\n",
    "    A = cirq.unitary(cirq.SWAP)@A\n",
    "    if ret_n:\n",
    "        return A, n\n",
    "    else:\n",
    "        return A\n",
    "def get_env_off_left_site(A):\n",
    "    z = np.array([1, 0])\n",
    "    return np.tensordot(np.tensordot(A.reshape(2, 2, 2, 2), z, [3, 0]), z, [1, 0]).T\n",
    "\n",
    "def put_env_on_right_site(q, ret_n=False):\n",
    "    q = q\n",
    "    a, b, c, d = q.reshape(-1)\n",
    "    n = np.sqrt(np.abs(a)**2+ np.abs(c)**2+ np.abs(b)**2+ np.abs(d)**2)\n",
    "    guess = np.array([[a, b, d.conj(), -c.conj()], [c, d, -b.conj(), a.conj()]])/n\n",
    "    orth = null_space(guess).conj().T\n",
    "    A = np.concatenate([guess, orth], axis=0)\n",
    "    #A = cirq.unitary(cirq.SWAP)@A\n",
    "    if ret_n:\n",
    "        return A, n\n",
    "    else:\n",
    "        return A\n",
    "\n",
    "def get_env_off_right_site(A):\n",
    "    z = np.array([1, 0])\n",
    "    return np.tensordot(np.tensordot(A.reshape(2, 2, 2, 2), z, [2, 0]), z, [0, 0])\n",
    "\n",
    "\n",
    "N = 50\n",
    "for _ in range(50):\n",
    "    q = np.random.randn(2, 2)+1j*np.random.randn(2, 2)\n",
    "    assert np.allclose(get_env_off_left_site(np.prod(put_env_on_left_site(q, ret_n=True))), q)\n",
    "    assert np.allclose(get_env_off_right_site(np.prod(put_env_on_right_site(q, ret_n=True))), q)\n",
    "    U = put_env_on_left_site(q)\n",
    "    V = put_env_on_right_site(q)\n",
    "    assert np.allclose(V.conj().T@V, np.eye(U.shape[0]))\n",
    "    assert np.allclose(U.conj().T@U, np.eye(U.shape[0]))\n",
    "    \n",
    "for _ in range(N):\n",
    "    A = iMPS().random(2, 2).left_canonicalise()[0]\n",
    "    B = iMPS().random(2, 2).left_canonicalise()[0]#np.tensordot(expm(-1j*Z*dt), A, [1, 0])\n",
    "\n",
    "    U = Environment(tensor_to_unitary(A), 'U')\n",
    "    U_ = Environment(tensor_to_unitary(B), 'U\\'')\n",
    "\n",
    "    x, r = Map(merge(A, A), merge(B, B)).right_fixed_point()\n",
    "    x_, l = Map(merge(A, A), merge(B, B)).left_fixed_point()\n",
    "    L = put_env_on_right_site(l)\n",
    "    R = put_env_on_left_site(r)\n",
    "    assert np.allclose(get_env_off_left_site(put_env_on_left_site(r)), r)\n",
    "    assert np.allclose(get_env_off_right_site(put_env_on_right_site(l)), l)\n",
    "    U = put_env_on_left_site(r)\n",
    "    V = put_env_on_right_site(l)\n",
    "    assert np.allclose(V.conj().T@V, np.eye(U.shape[0]))\n",
    "    assert np.allclose(U.conj().T@U, np.eye(U.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "UsageError: Line magic function `%autoreload` not found.\n"
     ]
    }
   ],
   "source": [
    "% autoreload 2\n",
    "from xmps.iMPS import iMPS, Map, TransferMatrix\n",
    "A = iMPS().random(2, 2).left_canonicalise()\n",
    "B = iMPS().random(2, 2).left_canonicalise()\n",
    "E = Map(A[0], B[0]).asmatrix()\n",
    "xs, L = np.linalg.eig(E.conj().T)\n",
    "xs_, R = np.linalg.eig(E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.96022439, 0.72454277, 1.12865704, 1.15355882])"
      ]
     },
     "execution_count": 420,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(np.linalg.eig(No)[0])**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9870528934194964"
      ]
     },
     "execution_count": 421,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sv_min(E).fun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import reduce\n",
    "def krylov(A, v, k):\n",
    "    As = [v]\n",
    "    for _ in range(k):\n",
    "        As.append(A@As[-1]/norm(A@As[-1]))\n",
    "    return np.array(As)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7690150868558495"
      ]
     },
     "execution_count": 451,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 100\n",
    "np.abs(E@krylov(E, np.random.randn(4), N)[-1]/krylov(E, np.random.randn(4), N)[-1])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 19/5000 [00:00<01:56, 42.60it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-1.6663834375491906-1.7521241785596813e-17j)\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "63b78e2bdd6d4cd1907be4b89a970c9d",
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       "version_minor": 0
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      "text/plain": [
       "HBox(children=(IntProgress(value=0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.704913\n",
      "         Iterations: 27\n",
      "         Function evaluations: 1986\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
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      "         Current function value: -0.706239\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.706868\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.706829\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.706878\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.706941\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707000\n",
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      "         Function evaluations: 2216\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707047\n",
      "         Iterations: 46\n",
      "         Function evaluations: 2062\n",
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      "Optimization terminated successfully.\n",
      "         Current function value: -0.707078\n",
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      "         Function evaluations: 1175\n",
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      "Optimization terminated successfully.\n",
      "         Current function value: -0.707096\n",
      "         Iterations: 6\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 5\n",
      "         Function evaluations: 361\n",
      "         Gradient evaluations: 14\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707107\n",
      "         Iterations: 3\n",
      "         Function evaluations: 100\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707107\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707107\n",
      "         Iterations: 30\n",
      "         Function evaluations: 2463\n",
      "         Gradient evaluations: 98\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 3\n",
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      "Optimization terminated successfully.\n",
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      "         Function evaluations: 550\n",
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      "Optimization terminated successfully.\n",
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      "         Function evaluations: 125\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707090\n",
      "         Iterations: 4\n",
      "         Function evaluations: 125\n",
      "         Gradient evaluations: 5\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707091\n",
      "         Iterations: 3\n",
      "         Function evaluations: 100\n",
      "         Gradient evaluations: 4\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707095\n",
      "         Iterations: 7\n",
      "         Function evaluations: 200\n",
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      "Optimization terminated successfully.\n",
      "         Current function value: -0.707095\n",
      "         Iterations: 3\n",
      "         Function evaluations: 100\n",
      "         Gradient evaluations: 4\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707096\n",
      "         Iterations: 16\n",
      "         Function evaluations: 1510\n",
      "         Gradient evaluations: 60\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707097\n",
      "         Iterations: 14\n",
      "         Function evaluations: 575\n",
      "         Gradient evaluations: 23\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707104\n",
      "         Iterations: 3\n",
      "         Function evaluations: 100\n",
      "         Gradient evaluations: 4\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 7\n",
      "         Function evaluations: 300\n",
      "         Gradient evaluations: 12\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 2\n",
      "         Function evaluations: 75\n",
      "         Gradient evaluations: 3\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 2\n",
      "         Function evaluations: 75\n",
      "         Gradient evaluations: 3\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 42\n",
      "         Function evaluations: 2546\n",
      "         Gradient evaluations: 101\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 20\n",
      "         Function evaluations: 1464\n",
      "         Gradient evaluations: 58\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 8\n",
      "         Function evaluations: 628\n",
      "         Gradient evaluations: 25\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 7\n",
      "         Function evaluations: 450\n",
      "         Gradient evaluations: 18\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 3\n",
      "         Function evaluations: 100\n",
      "         Gradient evaluations: 4\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 5\n",
      "         Function evaluations: 587\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 32\n",
      "         Function evaluations: 2111\n",
      "         Gradient evaluations: 84\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 3\n",
      "         Function evaluations: 100\n",
      "         Gradient evaluations: 4\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 4\n",
      "         Function evaluations: 1019\n",
      "         Gradient evaluations: 40\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 19\n",
      "         Function evaluations: 1384\n",
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      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 10\n",
      "         Function evaluations: 937\n",
      "         Gradient evaluations: 37\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 4\n",
      "         Function evaluations: 537\n",
      "         Gradient evaluations: 21\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 612\n",
      "         Gradient evaluations: 24\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707106\n",
      "         Iterations: 63\n",
      "         Function evaluations: 4027\n",
      "         Gradient evaluations: 160\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 27\n",
      "         Function evaluations: 1962\n",
      "         Gradient evaluations: 78\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 6\n",
      "         Function evaluations: 787\n",
      "         Gradient evaluations: 31\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 15\n",
      "         Function evaluations: 1322\n",
      "         Gradient evaluations: 52\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 44\n",
      "         Function evaluations: 2612\n",
      "         Gradient evaluations: 104\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 43\n",
      "         Function evaluations: 2165\n",
      "         Gradient evaluations: 86\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 9\n",
      "         Function evaluations: 711\n",
      "         Gradient evaluations: 28\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 12\n",
      "         Function evaluations: 1489\n",
      "         Gradient evaluations: 59\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 0\n",
      "         Function evaluations: 487\n",
      "         Gradient evaluations: 19\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 7\n",
      "         Function evaluations: 914\n",
      "         Gradient evaluations: 36\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 3\n",
      "         Function evaluations: 437\n",
      "         Gradient evaluations: 17\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 6\n",
      "         Function evaluations: 739\n",
      "         Gradient evaluations: 29\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 5\n",
      "         Function evaluations: 789\n",
      "         Gradient evaluations: 31\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 662\n",
      "         Gradient evaluations: 26\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 5\n",
      "         Function evaluations: 200\n",
      "         Gradient evaluations: 8\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 75\n",
      "         Gradient evaluations: 3\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 75\n",
      "         Gradient evaluations: 3\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 13\n",
      "         Function evaluations: 1312\n",
      "         Gradient evaluations: 52\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 582\n",
      "         Gradient evaluations: 23\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 7\n",
      "         Function evaluations: 250\n",
      "         Gradient evaluations: 10\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 75\n",
      "         Gradient evaluations: 3\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 5\n",
      "         Function evaluations: 969\n",
      "         Gradient evaluations: 38\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 12\n",
      "         Function evaluations: 784\n",
      "         Gradient evaluations: 31\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 11\n",
      "         Function evaluations: 1059\n",
      "         Gradient evaluations: 42\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 1\n",
      "         Function evaluations: 286\n",
      "         Gradient evaluations: 11\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 10\n",
      "         Function evaluations: 1098\n",
      "         Gradient evaluations: 43\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 26\n",
      "         Function evaluations: 1795\n",
      "         Gradient evaluations: 71\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 10\n",
      "         Function evaluations: 762\n",
      "         Gradient evaluations: 30\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 27\n",
      "         Function evaluations: 1150\n",
      "         Gradient evaluations: 46\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 11\n",
      "         Function evaluations: 787\n",
      "         Gradient evaluations: 31\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 23\n",
      "         Function evaluations: 1318\n",
      "         Gradient evaluations: 52\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 12\n",
      "         Function evaluations: 650\n",
      "         Gradient evaluations: 26\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 9\n",
      "         Function evaluations: 586\n",
      "         Gradient evaluations: 23\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 34\n",
      "         Function evaluations: 1870\n",
      "         Gradient evaluations: 74\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 15\n",
      "         Function evaluations: 1187\n",
      "         Gradient evaluations: 47\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 23\n",
      "         Function evaluations: 975\n",
      "         Gradient evaluations: 39\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 2\n",
      "         Function evaluations: 484\n",
      "         Gradient evaluations: 19\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 10\n",
      "         Function evaluations: 1012\n",
      "         Gradient evaluations: 40\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fergusbarratt/miniconda3/envs/myenv/lib/python3.7/site-packages/scipy/optimize/optimize.py:1020: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  rhok = 1.0 / (numpy.dot(yk, sk))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Divide-by-zero encountered: rhok assumed large\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 16\n",
      "         Function evaluations: 1783\n",
      "         Gradient evaluations: 70\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 16\n",
      "         Function evaluations: 775\n",
      "         Gradient evaluations: 31\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 11\n",
      "         Function evaluations: 837\n",
      "         Gradient evaluations: 33\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 15\n",
      "         Function evaluations: 1237\n",
      "         Gradient evaluations: 49\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 32\n",
      "         Function evaluations: 1915\n",
      "         Gradient evaluations: 76\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 23\n",
      "         Function evaluations: 925\n",
      "         Gradient evaluations: 37\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 10\n",
      "         Function evaluations: 450\n",
      "         Gradient evaluations: 18\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 36\n",
      "         Function evaluations: 2328\n",
      "         Gradient evaluations: 93\n",
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 11\n",
      "         Function evaluations: 1143\n",
      "         Gradient evaluations: 45\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 14\n",
      "         Function evaluations: 928\n",
      "         Gradient evaluations: 37\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -0.707105\n",
      "         Iterations: 4\n",
      "         Function evaluations: 175\n",
      "         Gradient evaluations: 7\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "from scipy.linalg import norm\n",
    "import cirq\n",
    "from qmps.represent import ShallowFullStateTensor, Environment\n",
    "from qmps.tools import unitary_to_tensor, tensor_to_unitary\n",
    "from xmps.tensor import rotate_to_hermitian\n",
    "from qmps.ground_state import Hamiltonian\n",
    "from scipy.linalg import expm\n",
    "from xmps.spin import paulis\n",
    "from tqdm import tqdm_notebook\n",
    "\n",
    "def gate(v, symbol='U'):\n",
    "    #return ShallowCNOTStateTensor(2, v[:-1])\n",
    "    return ShallowFullStateTensor(2, v, symbol)\n",
    "    #return FullStateTensor(U4(v))\n",
    "\n",
    "\n",
    "\n",
    "def obj(p_, A, WW):\n",
    "    p, rs = p_[:15], p_[15:]\n",
    "    \n",
    "    B = iMPS([unitary_to_tensor(cirq.unitary(gate(p)))]).left_canonicalise()[0]\n",
    "    U = Environment(tensor_to_unitary(A), 'U')\n",
    "    U_ = Environment(tensor_to_unitary(B), 'U\\'')\n",
    "\n",
    "    r = rotate_to_hermitian((rs[:4]+1j*rs[4:]).reshape(2, 2))\n",
    "    r /= np.sqrt(np.trace(r.conj().T@r))\n",
    "    l = r\n",
    "    \n",
    "    R = Environment(put_env_on_left_site(r), 'R')\n",
    "    L = Environment(put_env_on_right_site(l.conj().T), 'L')\n",
    "    \n",
    "    W = Environment(WW, 'W')\n",
    "\n",
    "    qbs = cirq.LineQubit.range(6)\n",
    "    C = cirq.Circuit.from_ops([cirq.H(qbs[3]), cirq.CNOT(*qbs[3:5]),\n",
    "                               U(*qbs[2:4]),\n",
    "                               U(*qbs[1:3]),\n",
    "                               W(*qbs[2:4]),\n",
    "                               L(*qbs[0:2]),\n",
    "                               R(*qbs[4:]),\n",
    "                               cirq.inverse(U_)(*qbs[1:3]),\n",
    "                               cirq.inverse(U_)(*qbs[2:4]),\n",
    "                               cirq.CNOT(*qbs[3:5]), cirq.H(qbs[3])])\n",
    "\n",
    "    s = cirq.Simulator(dtype=np.complex128)\n",
    "    return -np.abs(s.simulate(C).final_state[0])*2\n",
    "\n",
    "from xmps.iOptimize import find_ground_state\n",
    "g0, g1 = 1.5, 0.2\n",
    "A, es = find_ground_state(Hamiltonian({'ZZ':-1, 'X':g0}).to_matrix(), 2, tol=1e-2, noisy=True)\n",
    "print(es[-1])\n",
    "N = 23\n",
    "\n",
    "T = np.linspace(0, 10, 100)\n",
    "dt = T[1]-T[0]\n",
    "res = minimize(obj, np.random.randn(N), \n",
    "               (A[0], np.eye(4)), \n",
    "               method='Nelder-Mead',\n",
    "               options={'disp':True})\n",
    "params = res.x\n",
    "\n",
    "WW = expm(-1j*Hamiltonian({'ZZ':-1, 'X':g1}).to_matrix()*2*dt)\n",
    "ps = [params]\n",
    "ops = paulis(0.5)\n",
    "evs = []\n",
    "les = []\n",
    "errs = [res.fun]\n",
    "for _ in tqdm_notebook(T):\n",
    "    A_ = iMPS([unitary_to_tensor(cirq.unitary(gate(params)))]).left_canonicalise()\n",
    "    evs.append(A_.Es(ops))\n",
    "    les.append(A_.overlap(A))\n",
    "    res = minimize(obj, params, (A_[0], WW), options={'disp':True})\n",
    "    params = res.x\n",
    "    errs.append(res.fun)\n",
    "    ps.append(params)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import norm\n",
    "from qmps.represent import StateGate\n",
    "import cirq\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Power method (non-quantum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
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       "            fig.send_message(\"refresh\", {});\n",
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       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
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       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1a2965c048>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def ev_min(M, max_iters=50, tol = 1e-3):\n",
    "    q = M.shape[0]\n",
    "    v = np.random.randn(2*q)\n",
    "    vs = [v/norm(v)]\n",
    "    conv = [0]\n",
    "\n",
    "    for _ in range(max_iters):\n",
    "        def x(θ):\n",
    "            #θ[-1] = θ[-2] = θ[-3] = θ[-4] = θ[-5]= 0\n",
    "            return cirq.unitary(StateGate(θ))@np.array([0, 0, 0, 1])\n",
    "        \n",
    "        def overlap(x, y, M=None):\n",
    "            q = x.shape[0]\n",
    "            M = np.eye(int(q/2)) if M is None else M\n",
    "            xx = (x[:int(q/2)]+1j*x[int(q/2):])\n",
    "            yy = (y[:int(q/2)]+1j*y[int(q/2):])\n",
    "            xx/=norm(xx)\n",
    "            yy/=norm(yy)\n",
    "            return -np.abs(xx.conj().T@M@yy)\n",
    "        \n",
    "        def c_overlap(x, y, M=None):\n",
    "            q = x.shape[0]\n",
    "            M = np.eye(int(q/2)) if M is None else M\n",
    "            xx = x\n",
    "            yy = y\n",
    "            xx/=norm(xx)\n",
    "            yy/=norm(yy)\n",
    "            return -np.abs(xx.conj().T@M@yy)  \n",
    "        \n",
    "        res = minimize(lambda θ: c_overlap(x(θ), x(vs[-1]), M), np.random.randn(6))\n",
    "        vs.append(res.x)\n",
    "        conv.append(c_overlap(x(vs[-2]), x(vs[-1]), M))\n",
    "        if np.abs(conv[-1]-conv[-2])<tol:\n",
    "            break\n",
    "        \n",
    "    return conv, vs[-1]\n",
    "\n",
    "N = 4\n",
    "M = np.random.randn(N, N)+1j*np.random.randn(N, N)\n",
    "M = M+M.conj().T+1e-1*(M-M.conj().T)\n",
    "M/=norm(M)\n",
    "#print(norm((M@M.conj().T-M.conj().T@M)))\n",
    "plt.figure()\n",
    "plt.plot(ev_min(M)[0])\n",
    "plt.axhline(-max(np.abs(np.linalg.eig(M)[0])), 0, 1, c='black', linestyle='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "def left_gate(rs):\n",
    "    r = (rs[:4]+1j*rs[4:]).reshape(2, 2)\n",
    "    r /= np.sqrt(np.trace(r.conj().T@r))\n",
    "    return Environment(put_env_on_left_site(r), 'R')\n",
    "def right_gate(rs):\n",
    "    r = (rs[:4]+1j*rs[4:]).reshape(2, 2)\n",
    "    r /= np.sqrt(np.trace(r.conj().T@r))\n",
    "    return Environment(put_env_on_right_site(r.conj().T), 'R')\n",
    "\n",
    "def largest_eig_variational(p, p_, max_iters=20, tol=1e-3):\n",
    "    \"\"\"\n",
    "    \"\"\"\n",
    "    A = iMPS([unitary_to_tensor(cirq.unitary(gate(p)))]).left_canonicalise()[0]\n",
    "    B = iMPS([unitary_to_tensor(cirq.unitary(gate(p_)))]).left_canonicalise()[0]\n",
    "    x, r = Map(A, B).left_fixed_point()    \n",
    "    \n",
    "    U = Environment(tensor_to_unitary(A), 'U')\n",
    "    U_ = Environment(tensor_to_unitary(B), 'U\\'')\n",
    "    rs = [np.random.randn(8)]\n",
    "    conv = []\n",
    "    \n",
    "    for k in range(max_iters):\n",
    "        def obj(rs, rs_):\n",
    "            R = left_gate(rs_)\n",
    "            L = right_gate(rs)\n",
    "\n",
    "            qbs = cirq.LineQubit.range(5)\n",
    "            C = cirq.Circuit.from_ops([cirq.H(qbs[2]), cirq.CNOT(*qbs[2:4]),\n",
    "                                       U(*qbs[1:3]),\n",
    "                                       L(*qbs[0:2]),\n",
    "                                       R(*qbs[3:5]),\n",
    "                                       cirq.inverse(U_)(*qbs[1:3]),\n",
    "                                       cirq.CNOT(*qbs[2:4]), cirq.H(qbs[2])])\n",
    "            \n",
    "\n",
    "            s = cirq.Simulator(dtype=np.complex128)\n",
    "            return -np.abs(s.simulate(C).final_state[0])*2\n",
    "        res = minimize(lambda x: obj(x, rs[-1]), np.random.randn(8), tol=1e-4)\n",
    "        rs.append(res.x)\n",
    "        conv.append(res.fun)\n",
    "        \n",
    "        if k>1 and np.abs(conv[-1]-conv[-2])<tol and np.abs(conv[-2]-conv[-3])<tol:\n",
    "            break    \n",
    "    return x, -np.array(conv)[1:], rs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cirq\n",
    "from numpy.random import randn\n",
    "from xmps.iMPS import iMPS, Map\n",
    "from qmps.represent import unitary_to_tensor, Environment\n",
    "from qmps.represent import ShallowCNOTStateTensor, ShallowQAOAStateTensor, ShallowFullStateTensor\n",
    "from qmps.tools import tensor_to_unitary\n",
    "def gate(v, symbol='U'):\n",
    "    #return ShallowCNOTStateTensor(2, v)\n",
    "    #return ShallowQAOAStateTensor(2, v)\n",
    "    return ShallowFullStateTensor(2, v, symbol)\n",
    "    #return FullStateTensor(U4(v))\n",
    "    \n",
    "class LeftFullGate(cirq.Gate):\n",
    "    \"\"\"\n",
    "    Parametrisation of tr 1 non unitary on right hand site (gate goes on left of diagram). \n",
    "    Singular values are np.array([cos(a), sin(a)])\"\"\"\n",
    "    def __init__(self, params, D=2):\n",
    "        self.params = params\n",
    "    def _decompose_(self, qubits):\n",
    "        a, b, c, d, e, f = self.params\n",
    "        return [cirq.Rx(a*2)(qubits[0]), cirq.inverse(cirq.S(qubits[0])),\n",
    "                cirq.Rz(b)(qubits[1]), cirq.Rx(c)(qubits[1]), cirq.Rz(d)(qubits[1]),\n",
    "                cirq.CNOT(qubits[1], qubits[0]),\n",
    "                cirq.Rx(f)(qubits[1]), cirq.Rz(e)(qubits[1])] \n",
    "    def singular_values(self):\n",
    "        return np.abs(np.array([np.cos(self.params[0]), np.sin(self.params[0])]))\n",
    "    def num_qubits(self):\n",
    "        return 2\n",
    "    \n",
    "class RightFullGate(cirq.Gate):\n",
    "    \"\"\"\n",
    "    Parametrisation of tr 1 non unitary on left hand site (gate goes on right of diagram). \n",
    "    Singular values are np.array([np.sqrt((1-np.sin(a)*np.sin(b))/2), np.sqrt((1+np.sin(a)*np.sin(b))/2)])\"\"\"\n",
    "    def __init__(self, params, D=2):\n",
    "        self.params = params\n",
    "    def _decompose_(self, qubits):\n",
    "        return [cirq.SWAP(*qubits),\n",
    "                cirq.inverse(LeftFullGate(self.params)(*qubits)),\n",
    "                cirq.SWAP(*qubits)] \n",
    "    def singular_values(self):\n",
    "        return np.abs(np.array([np.cos(self.params[0]), np.sin(self.params[0])]))\n",
    "    \n",
    "    def num_qubits(self):\n",
    "        return 2\n",
    "    \n",
    "N = 30\n",
    "for _ in range(N):\n",
    "    a, b, c, d, e, f = x = randn(6)\n",
    "    L = LeftFullGate(x)(*cirq.LineQubit.range(2))\n",
    "    U = cirq.unitary(L)\n",
    "    z = np.array([1, 0])\n",
    "    v1 = np.linalg.svd(np.tensordot(np.tensordot(U.reshape(2, 2, 2, 2), z, [-2, 0]), z, [0, 0]))[1]\n",
    "    v2 = np.array([np.abs(np.cos(a)), np.abs(np.sin(a))])\n",
    "    v2.sort(), v1.sort()\n",
    "    assert np.allclose(v1, v2)\n",
    "    \n",
    "for _ in range(N):\n",
    "    a, b, c, d, e, f = x = randn(6)\n",
    "    L = RightFullGate(x)(*cirq.LineQubit.range(2))\n",
    "    U = cirq.unitary(L)\n",
    "    z = np.array([1, 0])\n",
    "    v1 = np.linalg.svd(np.tensordot(np.tensordot(U.reshape(2, 2, 2, 2), z, [-1, 0]), z, [1, 0]))[1]\n",
    "    v2 = np.array([np.abs(np.cos(a)), np.abs(np.sin(a))])\n",
    "    v2.sort(), v1.sort()\n",
    "    assert np.allclose(v1, v2)\n",
    "dt = 1e-4\n",
    "H = np.random.randn(4, 4)+1j*np.random.randn(4, 4)\n",
    "H = (H+H.conj().T)/2*np.trace(H@H.conj().T)\n",
    "def largest_eig_variational(p, p_, max_iters=20, tol=1e-3, dt=1e-3):\n",
    "    \"\"\"\n",
    "    \"\"\"\n",
    "    A = iMPS([unitary_to_tensor(cirq.unitary(gate(p)))]).left_canonicalise()\n",
    "    #B = iMPS([unitary_to_tensor(cirq.unitary(gate(p_)))]).left_canonicalise()[0]\n",
    "    B = (A+dt*A.dA_dt([H])).left_canonicalise()\n",
    "    A, B = A[0], B[0]\n",
    "    x, r = Map(A, B).left_fixed_point()    \n",
    "    \n",
    "    U = Environment(tensor_to_unitary(A), 'U')\n",
    "    U_ = Environment(tensor_to_unitary(B), 'U\\'')\n",
    "    rs = [np.zeros(6)]\n",
    "    conv = []\n",
    "    \n",
    "    for k in range(max_iters):\n",
    "        def obj(rs, rs_):\n",
    "            R = RightFullGate(rs_)\n",
    "            L = LeftFullGate(rs)\n",
    "\n",
    "            qbs = cirq.LineQubit.range(5)\n",
    "            C = cirq.Circuit.from_ops([cirq.H(qbs[2]), cirq.CNOT(*qbs[2:4]),\n",
    "                                       U(*qbs[1:3]),\n",
    "                                       L(*qbs[0:2]),\n",
    "                                       R(*qbs[3:5]),\n",
    "                                       cirq.inverse(U_)(*qbs[1:3]),\n",
    "                                       cirq.CNOT(*qbs[2:4]), cirq.H(qbs[2])])\n",
    "            \n",
    "            s = cirq.Simulator(dtype=np.complex128)\n",
    "            return -np.abs(s.simulate(C).final_state[0])*2\n",
    "        s = np.zeros(2)\n",
    "        guess = np.array([0.2, *s, 0, *(-s)]) #\n",
    "        res = minimize(lambda x: obj(x, rs[-1]), guess)\n",
    "        rs.append(res.x)\n",
    "        conv.append(res.fun)\n",
    "        \n",
    "        if k>1 and np.abs(conv[-1]-conv[-2])<tol and np.abs(conv[-2]-conv[-3])<tol:\n",
    "            break    \n",
    "    return x, -np.array(conv)[1:], rs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6min 9s, sys: 3.66 s, total: 6min 13s\n",
      "Wall time: 7min 28s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "X, Y  = np.random.randn(15), np.random.randn(15)\n",
    "eps = 3\n",
    "x, ress, rs = largest_eig_variational(X, Y, dt = 0.01, max_iters=200, tol=1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       "\n",
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       "    fig.ondownload(fig, format);\n",
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       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
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       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
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       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"pdf\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a2af2ada0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib as mpl\n",
    "mpl.style.use('pub_fast')\n",
    "plt.figure()\n",
    "ts = np.array(list(range(len(ress))))\n",
    "plt.axhline(np.abs(x), c='black', linestyle = '--', label='eigenvalue')\n",
    "plt.plot(ts, ress, label='estimate')\n",
    "\n",
    "plt.scatter(ts, ress, marker='.')\n",
    "#plt.plot(ts, np.cumsum(ress)/np.arange(1, len(ress)+1), label='average')\n",
    "#plt.scatter(ts, np.cumsum(ress)/np.arange(1, len(ress)+1), marker='.')\n",
    "\n",
    "#plt.ylim([0.0, 1])\n",
    "plt.xlabel('iterations')\n",
    "plt.legend()\n",
    "#plt.savefig('/Users/fergusbarratt/Desktop/eig_convergence.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}