kinetic_ising_simulation_inference.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "becoming-berkeley",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "formal-collectible",
   "metadata": {},
   "source": [
    "## Kinetic Ising Model simulation\n",
    "Ising model with $N$ spins $\\{-1,1\\}$, cuplings matrix $J_{ij}$ and external field $h_i$. \n",
    "\n",
    "At each time step $\\delta t$ each spin $s_i$ flips with a probability \n",
    "$$p_{flip} = \\gamma \\delta t \\frac 1 2 [1-s_i(t)\\tanh H_i(t)] \\quad with \\quad\n",
    "H_i = h_i + \\sum_{j \\ne i} J_{ij}s_j(t)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "optical-latin",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "colored-classics",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulation(J,h,gamma,steps,dt):\n",
    "    S = [-np.ones(N)]\n",
    "    for i in tqdm(range(1,steps)):\n",
    "        s = np.copy(S[-1])\n",
    "        H = h + np.dot(J,s)\n",
    "        p_flip = gamma*dt*0.5*(1-s*np.tanh(H))\n",
    "        p = np.random.rand(N)\n",
    "        s[p<p_flip]*=-1\n",
    "        S.append(s)\n",
    "    S = np.array(S).T\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "attempted-prospect",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 99999/99999 [00:02<00:00, 35967.69it/s]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(201098)\n",
    "\n",
    "N = 100\n",
    "#########################################\n",
    "J = np.random.normal(0,1,(N,N))\n",
    "np.fill_diagonal(J,0)\n",
    "h = np.random.normal(0,1,N)\n",
    "\n",
    "p_real = np.concatenate((J.flatten(),h))\n",
    "##########################################\n",
    "gamma = 1\n",
    "steps = 100_000#1_000_000\n",
    "dt = 0.1\n",
    "##########################################\n",
    "##SIMULATION\n",
    "S = simulation(J,h,gamma,steps,dt)\n",
    "\n",
    "filename = 'DATA/spins_N'+str(N)+'_steps'+str(steps)+'_dt'+str(dt)+'_gamma'+str(gamma)+'.npy'\n",
    "np.save(filename,S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "hazardous-ground",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Spin evlolution in time. [$s_i=1$ yellow, $s_i=-1$ blue]')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,5))\n",
    "plt.imshow(S[:10,:],aspect = 'auto', cmap = 'binary', interpolation = 'None')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel(r'$s_i$')\n",
    "plt.title(r'Spin evlolution in time. [$s_i=1$ yellow, $s_i=-1$ blue]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "indonesian-emission",
   "metadata": {},
   "source": [
    "### NB\n",
    "$S$ is $S_{it}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cognitive-silver",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "### Equations\n",
    "\n",
    "$$\n",
    "\\dot C_{ij} = \\delta t ^{-1} \\cdot [\\langle s_i(t+\\delta t)\\cdot s_j(t) \\rangle_{t} - C_{i,j}] \\\\\n",
    "C_{ij} = \\langle s_i(t)\\cdot s_j(t) \\rangle_{t} \\\\\n",
    "L = \\frac 1 {N_t} \\sum_t\\sum_i \\Big[ h_i\\cdot s_i(t) + \\big[\\sum_{j\\ne i} J_{ij}\\cdot (\\gamma^{-1}\\dot{C_{ij}} + C_{ij})\\big] - \\log \\cosh H_i(t)\\Big]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "noticed-glory",
   "metadata": {},
   "source": [
    "### $C$ and $\\dot C$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "practical-replacement",
   "metadata": {},
   "outputs": [],
   "source": [
    "def C_and_Cdot(S,dt):\n",
    "    N = S.shape[0]\n",
    "    C = np.dot(S, S.T)/S.shape[1]\n",
    "    C_dot = np.dot(S[:,1:], S[:,:-1].T)/(S.shape[1]-1)\n",
    "    C_dot -= C\n",
    "    C_dot /= dt\n",
    "        \n",
    "    return C,C_dot        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "medical-consciousness",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "C,C_dot = C_and_Cdot(S,dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "compatible-insert",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100001)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "occupational-giant",
   "metadata": {},
   "source": [
    "## L\n",
    "In order to speed up the L function we use matrices.\n",
    "\n",
    "$equations$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "placed-still",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logcosh(x):\n",
    "    #the funcion is even, the trick is to avoid e^x\n",
    "    x = np.abs(x)\n",
    "    return np.log(1/2) + x + np.log(1 + np.exp(-2*x))\n",
    "\n",
    "#versione ottimizzata della funzione (e' super piu veloce); sfrutta numpy e le matrici\n",
    "def L(p,S,C,C_dot,gamma):\n",
    "    N_t = S.shape[1]\n",
    "    N = S.shape[0]\n",
    "    \n",
    "    # p are the params, S is the spins history\n",
    "    J = p[:N*N].reshape((N,N))     # NxN matrix\n",
    "    np.fill_diagonal(J,0)          #removing the diagonal terms for easier sums\n",
    "    h = p[N*N:]                    # N vector\n",
    "    \n",
    "    #### A #####\n",
    "    A = np.dot(S.T,h)\n",
    "    A = np.mean(A)\n",
    "    \n",
    "    #### B #####\n",
    "    B = J*(C_dot/gamma + C)\n",
    "    B = np.sum(B)\n",
    "    \n",
    "    #### C #####\n",
    "    C = np.tile(h,(N_t,1)).T\n",
    "    C += np.dot(J,S)\n",
    "    C = - logcosh(C)\n",
    "    C = np.mean(np.sum(C,axis=0))\n",
    "    \n",
    "    L = A+B+C\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "growing-purchase",
   "metadata": {},
   "outputs": [],
   "source": [
    "#generating random parameters\n",
    "np.random.seed(234)\n",
    "p = np.random.normal(0,1,N*N+N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "configured-place",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 429 ms, sys: 84.6 ms, total: 513 ms\n",
      "Wall time: 436 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-755.7987002991665"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time L(p,S,C,C_dot,gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "distributed-mining",
   "metadata": {},
   "source": [
    "## Gradinent\n",
    "$$\n",
    "\\frac {\\partial L}{\\partial h_i} = \\langle s_i(t) - \\tanh{H_i(t)} \\rangle_t \\\\\n",
    "\\frac {\\partial L}{\\partial J_{ij}} = \\gamma ^ {-1} \\dot{C_{ij}} + C_{ij} - \\langle \\tanh{(H_i(t))}s_j(t)  \\rangle_t\n",
    "$$\n",
    "\n",
    "Also in this case we use matrices to speed up the computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "mineral-motion",
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad_L(p,S,C,C_dot,gamma):\n",
    "    N_t = S.shape[1]\n",
    "    N = S.shape[0]\n",
    "    \n",
    "    # p are the params, S is the spins history\n",
    "    J = p[:N*N].reshape((N,N))     # NxN matrix\n",
    "    np.fill_diagonal(J,0)          #removing the diagonal terms for easier sums\n",
    "    h = p[N*N:]                    # N vector\n",
    "    \n",
    "    #grad wrt h\n",
    "    H = (h + np.dot(J,S).T).T\n",
    "    G_1 = np.mean(S-np.tanh(H),axis=1)\n",
    "    \n",
    "    #grad wrt J\n",
    "    G_0 = C_dot/gamma + C\n",
    "    G_0 -= (np.dot(np.tanh(H),S.T))/N_t\n",
    "    \n",
    "    #new\n",
    "    np.fill_diagonal(G_0,0)\n",
    "    return np.concatenate((G_0.flatten(),G_1))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "purple-october",
   "metadata": {},
   "source": [
    "## Test the gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "final-attendance",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.0729427905720943\n",
      "-0.07294347597053275\n"
     ]
    }
   ],
   "source": [
    "param = 1\n",
    "\n",
    "x = np.ones(N*N + N) + 10\n",
    "dx = 0.00001\n",
    "print(grad_L(x,S,C,C_dot,gamma)[param])\n",
    "y_i = L(x,S,C,C_dot,gamma)\n",
    "x[param]+=dx\n",
    "y_f = L(x,S,C,C_dot,gamma)\n",
    "print((y_f-y_i)/dx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "immediate-defense",
   "metadata": {},
   "source": [
    "### Maximization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "criminal-jumping",
   "metadata": {},
   "source": [
    "### SGA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "circular-underwear",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 150/150 [02:43<00:00,  1.09s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  6519.353068478515\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1284f0c0a0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1234)\n",
    "l_r = 0.2\n",
    "STEPS = 150\n",
    "p_0 = np.random.normal(0,2,N*N+N)\n",
    "\n",
    "ris = [L(p_0,S,C,C_dot,gamma)]\n",
    "for i in tqdm(range(STEPS)):\n",
    "    p_0 += l_r*grad_L(p_0,S,C,C_dot,gamma)\n",
    "    ris.append(L(p_0,S,C,C_dot,gamma))\n",
    "    if ris[-1]<ris[-2]: break\n",
    "\n",
    "print('MSE: ',np.sum((p_0-p_real)**2))  \n",
    "plt.plot(ris)\n",
    "plt.figure()\n",
    "plt.plot(p_0,p_real,'o')\n",
    "plt.plot([min(p_real),max(p_real)],[min(p_real),max(p_real)],'--',color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dried-nitrogen",
   "metadata": {},
   "source": [
    "### NAG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "lined-pickup",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 150/150 [02:44<00:00,  1.09s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  2260.8106236716067\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1284ee7610>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1234)\n",
    "p_nag = np.random.normal(0,2,N*N+N)\n",
    "v = np.zeros(N*N+N)\n",
    "### PARAMS\n",
    "steps = 150\n",
    "l_r = 0.1\n",
    "fric = 0.9\n",
    "\n",
    "\n",
    "ris = [L(p_nag,S,C,C_dot,gamma)]\n",
    "for i in tqdm(range(steps)):\n",
    "    v = fric*v + l_r * (grad_L(p_nag+fric*v,S,C,C_dot,gamma))\n",
    "    p_nag += v\n",
    "    ris.append(L(p_nag,S,C,C_dot,gamma))\n",
    "\n",
    "print('MSE: ',np.sum((p_nag-p_real)**2))      \n",
    "plt.plot(ris)\n",
    "plt.figure()\n",
    "plt.plot(p_nag,p_real,'o')\n",
    "plt.plot([min(p_real),max(p_real)],[min(p_real),max(p_real)],'--',color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "palestinian-residence",
   "metadata": {},
   "source": [
    "### RMS prop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "universal-species",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 300/300 [03:17<00:00,  1.52it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  9950.582046870695\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1284e676d0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_rms = np.random.normal(0,2,N*N+N)\n",
    "s = np.zeros(N*N+N)\n",
    "### PARAMS\n",
    "steps = 300\n",
    "l_r = 0.05\n",
    "beta = 0.9\n",
    "eps = 10**(-8)\n",
    "\n",
    "#ris = [L(p_rms,S,C,C_dot,gamma)]\n",
    "for i in tqdm(range(steps)):\n",
    "    g = grad_L(p_rms,S,C,C_dot,gamma) \n",
    "    s = beta * s + (1-beta)*g*g\n",
    "    p_rms += l_r*g/np.sqrt(s+eps)                                      \n",
    "    \n",
    "    #ris.append(L(p_rms,S,C,C_dot,gamma))\n",
    "\n",
    "print('MSE: ',np.sum((p_rms-p_real)**2))      \n",
    "#plt.plot(ris)\n",
    "plt.figure()\n",
    "plt.plot(p_rms,p_real,'o')\n",
    "plt.plot([min(p_real),max(p_real)],[min(p_real),max(p_real)],'--',color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "resident-prerequisite",
   "metadata": {},
   "source": [
    "## ADAM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "incredible-guitar",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 149/149 [01:30<00:00,  1.65it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  56410.95465516484\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1284ffd220>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_adam = np.random.normal(0,2,N*N+N)\n",
    "s = np.zeros(N*N+N)\n",
    "m = np.zeros(N*N+N)\n",
    "\n",
    "s_h = np.zeros(N*N+N)\n",
    "m_h = np.zeros(N*N+N)\n",
    "\n",
    "### PARAMS\n",
    "steps = 150\n",
    "l_r = 0.1\n",
    "beta1 = 0.9\n",
    "beta2 = 0.9\n",
    "eps = 10**(-8)\n",
    "\n",
    "ris = [L(p_adam,S,C,C_dot,gamma)]\n",
    "for i in tqdm(range(1,steps)):\n",
    "    g = grad_L(p_adam,S,C,C_dot,gamma)\n",
    "    m = beta1 * m + (1-beta1)*g\n",
    "    s = beta2 * s + (1-beta2)*g*g\n",
    "    m_h = 1/(1-beta1**i)*m\n",
    "    s_h = 1/(1-beta2**i)*s\n",
    "    \n",
    "    p_adam += l_r*m_h/np.sqrt(s_h+eps)                                      \n",
    "    #ris.append(L(p_adam,S,C,C_dot,gamma))\n",
    "\n",
    "print('MSE: ',np.sum((p_adam-p_real)**2))  \n",
    "#plt.plot(ris)\n",
    "plt.figure()\n",
    "plt.plot(p_adam,p_real,'o')\n",
    "plt.plot([min(p_real),max(p_real)],[min(p_real),max(p_real)],'--',color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "floating-separate",
   "metadata": {},
   "source": [
    "### IDEAS\n",
    "by now the best optimizer is RMS, the ideas to speed up the compuing are :\n",
    "- parallelize the optimization, how? IDK (split verticaly S) FUNIZONAAAAA\n",
    "- use mini batch to optimize\n",
    "- numba : doesn't support mean function so we have to rewrite everything from scratch (see below)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "optimum-radiation",
   "metadata": {},
   "source": [
    "### Mini batch + RMS\n",
    "In this case we take only $B$ spins removing everything else. (Don't work)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "native-dream",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_ind(N,x):\n",
    "    diff = (x - x[0])*N\n",
    "    out = list(x)\n",
    "    for d in diff[1:]:\n",
    "        out += list(x+d)\n",
    "    out += list(x+N*N)\n",
    "    return out\n",
    "\n",
    "def mini_grad(B,p,S,C,C_dot,gamma):\n",
    "    N_t = S.shape[1]\n",
    "    N = S.shape[0]\n",
    "    \n",
    "    ins = np.random.choice(np.arange(0,N),B,replace = False)\n",
    "    ins = np.sort(ins)\n",
    "    ins_p = gen_ind(N,ins)\n",
    "    \n",
    "    p = np.copy(p[ins_p])\n",
    "    C = np.copy(C[ins,:][:,ins])\n",
    "    C_dot = np.copy(C_dot[ins,:][:,ins])\n",
    "    S = np.copy(S[ins,])\n",
    "    grad = grad_L(p,S,C,C_dot,gamma)\n",
    "    out = np.zeros(N*N+N)\n",
    "    out[ins_p]+=grad\n",
    "    \n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "ceramic-secretariat",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:58<00:00,  3.44it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  82.46710470062673\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ff0115484f0>]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_rms = np.random.normal(0,2,N*N+N)\n",
    "s = np.zeros(N*N+N)\n",
    "### PARAMS\n",
    "steps = 200\n",
    "l_r = 0.05\n",
    "beta = 0.9\n",
    "eps = 10**(-8)\n",
    "\n",
    "#ris = [L(p_rms,S,C,C_dot,gamma)]\n",
    "for i in tqdm(range(steps)):\n",
    "    g = mini_grad(5,p_rms,S,C,C_dot,gamma)\n",
    "    s = beta * s + (1-beta)*g*g\n",
    "    p_rms += l_r*g/np.sqrt(s+eps)                                      \n",
    "    \n",
    "    #ris.append(L(p_rms,S,C,C_dot,gamma))\n",
    "\n",
    "print('MSE: ',np.sum((p_rms-p_real)**2))      \n",
    "#plt.plot(ris)\n",
    "plt.figure()\n",
    "plt.plot(p_rms,p_real,'o')\n",
    "plt.plot([min(p_real),max(p_real)],[min(p_real),max(p_real)],'--',color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "involved-walker",
   "metadata": {},
   "source": [
    "### Mini batch 2\n",
    "In this case we keep all the spins but we compute only the gradient of $B$ spins. Maybe this is parallelizable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "headed-music",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [02:04<00:00,  1.61it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  19.472428810728257\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ff0114ee280>]"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_rms = np.random.normal(0,2,N*N+N)\n",
    "s = np.zeros(N*N+N)\n",
    "### PARAMS\n",
    "steps = 200\n",
    "l_r = 0.05\n",
    "beta = 0.9\n",
    "eps = 10**(-8)\n",
    "B = 110 - 30\n",
    "#ris = [L(p_rms,S,C,C_dot,gamma)]\n",
    "for i in tqdm(range(steps)):\n",
    "    g = grad_L(p_rms,S,C,C_dot,gamma)\n",
    "    #-----------------------------------------------------------------\n",
    "    ins = np.random.choice(np.arange(0,N*N+N),B,replace = False)\n",
    "    ins = np.sort(ins)\n",
    "    g[ins] = 0\n",
    "    #-----------------------------------------------------------------\n",
    "\n",
    "    s = beta * s + (1-beta)*g*g\n",
    "    p_rms += l_r*g/np.sqrt(s+eps)                                      \n",
    "    \n",
    "    #ris.append(L(p_rms,S,C,C_dot,gamma))\n",
    "\n",
    "print('MSE: ',np.sum((p_rms-p_real)**2))      \n",
    "#plt.plot(ris)\n",
    "plt.figure()\n",
    "plt.plot(p_rms,p_real,'o')\n",
    "plt.plot([min(p_real),max(p_real)],[min(p_real),max(p_real)],'--',color ='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "specialized-wound",
   "metadata": {},
   "source": [
    "### Numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "pleased-necklace",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import njit\n",
    "import numpy as np\n",
    "@njit\n",
    "def n_mean(a):\n",
    "    N = len(a)\n",
    "    m = 0\n",
    "    for i in (a):\n",
    "        m=m+i\n",
    "    return m/N\n",
    "\n",
    "@njit\n",
    "def n_sum(a,b):\n",
    "    return a+b\n",
    "\n",
    "@njit(parallel = True)\n",
    "def n_sum2(a,b):\n",
    "    N =len(a)\n",
    "    c = np.zeros(N)\n",
    "    for i in range(N):   \n",
    "        c[i] = a[i] + b[i]\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "literary-panel",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.8 µs ± 91.2 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "20.9 µs ± 339 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit n_mean(np.ones(10000))\n",
    "%timeit np.mean(np.ones(10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "deadly-notion",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "185 ms ± 553 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "358 ms ± 3.82 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "305 ms ± 23.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "a = np.ones(100_000_000)\n",
    "%timeit a+a\n",
    "%timeit n_sum(a,a)\n",
    "%timeit n_sum2(a,a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "iraqi-climb",
   "metadata": {},
   "source": [
    "### Parallelization (main idea)\n",
    "We can split verticaly the dataset and parallelize the times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "handmade-sponsorship",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 732 ms, sys: 47.3 ms, total: 780 ms\n",
      "Wall time: 678 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.05340978,  0.20598168, ...,  0.37731449,\n",
       "       -0.20931929,  0.11740606])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time grad_L(p,S,C,C_dot,gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "phantom-decision",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.05340968, 0.20598167, 0.31839137])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(grad_L(p,S[:,:50_000],C,C_dot,gamma)[:4] + grad_L(p,S[:,50_000:],C,C_dot,gamma)[:4])/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "informational-crawford",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 532 ms, sys: 51.2 ms, total: 583 ms\n",
      "Wall time: 275 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.04287258,  0.20460154, ...,  0.40837589,\n",
       "       -0.14058914,  0.09859042])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "from dask import delayed\n",
    "a = delayed(grad_L)(p,S[:,:25_000],C,C_dot,gamma)\n",
    "b = delayed(grad_L)(p,S[:,25_000:50_000],C,C_dot,gamma)\n",
    "c = delayed(grad_L)(p,S[:,50_000:75_000],C,C_dot,gamma)\n",
    "d =delayed(grad_L)(p,S[:,75_000:],C,C_dot,gamma)\n",
    "x = delayed(sum)([a,b])\n",
    "x.compute()/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "stainless-costa",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}