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    "# Exercise sheet\n",
    "\n",
    "Some general remarks about the exercises:\n",
    "* For your convenience functions from the lecture are included below. Feel free to reuse them without copying to the exercise solution box.\n",
    "* For each part of the exercise a solution box has been added, but you may insert additional boxes. Do not hesitate to add Markdown boxes for textual or LaTeX answers (via `Cell > Cell Type > Markdown`). But make sure to replace any part that says `YOUR CODE HERE` or `YOUR ANSWER HERE` and remove the `raise NotImplementedError()`.\n",
    "* Please make your code readable by humans (and not just by the Python interpreter): choose informative function and variable names and use consistent formatting. Feel free to check the [PEP 8 Style Guide for Python](https://www.python.org/dev/peps/pep-0008/) for the widely adopted coding conventions or [this guide for explanation](https://realpython.com/python-pep8/).\n",
    "* Make sure that the full notebook runs without errors before submitting your work. This you can do by selecting `Kernel > Restart & Run All` in the jupyter menu.\n",
    "* For some exercises test cases have been provided in a separate cell in the form of `assert` statements. When run, a successful test will give no output, whereas a failed test will display an error message.\n",
    "* Each sheet has 100 points worth of exercises. Note that only the grades of sheets number 2, 4, 6, 8 count towards the course examination. Submitting sheets 1, 3, 5, 7 & 9 is voluntary and their grades are just for feedback.\n",
    "\n",
    "Please fill in your name here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "be2b5237",
   "metadata": {},
   "outputs": [],
   "source": [
    "NAME = \"Kees van Kempen\"\n",
    "NAMES_OF_COLLABORATORS = \"\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6037899a",
   "metadata": {},
   "source": [
    "---"
   ]
  },
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   },
   "source": [
    "**Exercise sheet 9**"
   ]
  },
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   "source": [
    "## Running code on the compute cluster: lattice scalar field\n",
    "\n",
    "**Goal**: Learn how to scale up simulations by transitioning from running them in the notebook to stand-alone scripts on the compute cluster.\n",
    "\n",
    "In lecture 7 we implemented the Metropolis-Hastings simulation of a lattice scalar field using the following code:\n",
    "\n",
    "```Python\n",
    "import numpy as np\n",
    "rng = np.random.default_rng()  \n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def potential_v(x,lamb):\n",
    "    '''Compute the potential function V(x).'''\n",
    "    return lamb*(x*x-1)*(x*x-1)+x*x\n",
    "\n",
    "def neighbor_sum(phi,s):\n",
    "    '''Compute the sum of the state phi on all 8 neighbors of the site s.'''\n",
    "    w = len(phi)\n",
    "    return (phi[(s[0]+1)%w,s[1],s[2],s[3]] + phi[(s[0]-1)%w,s[1],s[2],s[3]] +\n",
    "            phi[s[0],(s[1]+1)%w,s[2],s[3]] + phi[s[0],(s[1]-1)%w,s[2],s[3]] +\n",
    "            phi[s[0],s[1],(s[2]+1)%w,s[3]] + phi[s[0],s[1],(s[2]-1)%w,s[3]] +\n",
    "            phi[s[0],s[1],s[2],(s[3]+1)%w] + phi[s[0],s[1],s[2],(s[3]-1)%w] )\n",
    "\n",
    "def scalar_action_diff(phi,site,newphi,lamb,kappa):\n",
    "    '''Compute the change in the action when phi[site] is changed to newphi.'''\n",
    "    return (2 * kappa * neighbor_sum(phi,site) * (phi[site] - newphi) +\n",
    "            potential_v(newphi,lamb) - potential_v(phi[site],lamb) )\n",
    "\n",
    "def scalar_MH_step(phi,lamb,kappa,delta):\n",
    "    '''Perform Metropolis-Hastings update on state phi with range delta.'''\n",
    "    site = tuple(rng.integers(0,len(phi),4))\n",
    "    newphi = phi[site] + rng.uniform(-delta,delta)\n",
    "    deltaS = scalar_action_diff(phi,site,newphi,lamb,kappa)\n",
    "    if deltaS < 0 or rng.uniform() < np.exp(-deltaS):\n",
    "        phi[site] = newphi\n",
    "        return True\n",
    "    return False\n",
    "\n",
    "def run_scalar_MH(phi,lamb,kappa,delta,n):\n",
    "    '''Perform n Metropolis-Hastings updates on state phi and return number of accepted transtions.'''\n",
    "    total_accept = 0\n",
    "    for _ in range(n):\n",
    "        total_accept += scalar_MH_step(phi,lamb,kappa,delta)\n",
    "    return total_accept\n",
    "\n",
    "def batch_estimate(data,observable,k):\n",
    "    '''Devide data into k batches and apply the function observable to each.\n",
    "    Returns the mean and standard error.'''\n",
    "    batches = np.reshape(data,(k,-1))\n",
    "    values = np.apply_along_axis(observable, 1, batches)\n",
    "    return np.mean(values), np.std(values)/np.sqrt(k-1)\n",
    "\n",
    "lamb = 1.5\n",
    "kappas = np.linspace(0.08,0.18,11)\n",
    "width = 3\n",
    "num_sites = width**4\n",
    "delta = 1.5  # chosen to have ~ 50% acceptance\n",
    "equil_sweeps = 1000\n",
    "measure_sweeps = 2\n",
    "measurements = 2000\n",
    "\n",
    "mean_magn = []\n",
    "for kappa in kappas:\n",
    "    phi_state = np.zeros((width,width,width,width))\n",
    "    run_scalar_MH(phi_state,lamb,kappa,delta,equil_sweeps * num_sites)\n",
    "    magnetizations = np.empty(measurements)\n",
    "    for i in range(measurements):\n",
    "        run_scalar_MH(phi_state,lamb,kappa,delta,measure_sweeps * num_sites)\n",
    "        magnetizations[i] = np.mean(phi_state)\n",
    "    mean, err = batch_estimate(np.abs(magnetizations),lambda x:np.mean(x),10)\n",
    "    mean_magn.append([mean,err])\n",
    "    \n",
    "plt.errorbar(kappas,[m[0] for m in mean_magn],yerr=[m[1] for m in mean_magn],fmt='-o')\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.ylabel(r\"$|m|$\")\n",
    "plt.title(r\"Absolute field average on $3^4$ lattice, $\\lambda = 1.5$\")\n",
    "plt.show()\n",
    "```\n",
    "The goal will be to reproduce and extend its output.\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
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   "source": [
    "**(a)** Turn the simulation into a standalone script `latticescalar.py` (similar to `ising.py`) that takes the relevant parameters e.g.\n",
    "```bash\n",
    "$ python3 latticescalar.py -l 1.5 -k 0.12 -w 3 -n 1000\n",
    "```\n",
    "for $\\lambda=1.5$, $\\kappa=0.12$, $w=3$, and $1000$ measurements, together with optional parameters $\\delta$ and numbers of sweeps, as command line arguments and stores the relevant simulation outcomes in an hdf5-file. **(40 pts)**"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1c6c1b73",
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import h5py\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Load data\n",
    "output_filename = \"preliminary_simulation.h5\"\n",
    "with h5py.File(output_filename,'r') as f:\n",
    "    handler = f[\"mean-magn\"]\n",
    "    mean_magn = np.array(handler)\n",
    "    kappas = handler.attrs[\"kappas\"]\n",
    "\n",
    "# Plotterdeplotterdeplot\n",
    "plt.figure()\n",
    "plt.errorbar(kappas,[m[0] for m in mean_magn],yerr=[m[1] for m in mean_magn],fmt='-o')\n",
    "plt.xlabel(r\"$\\kappa$\")\n",
    "plt.ylabel(r\"$|m|$\")\n",
    "plt.title(r\"Absolute field average on $3^4$ lattice, $\\lambda = 1.5$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e506d9a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "filename: ./data_l1.5_k0.08_w3_d1.5_20221124103953.hdf5\n",
      "current_time :\t\t\t 1669285905.690512\n",
      "delta :\t\t\t 1.5\n",
      "equil_sweeps :\t\t\t 100\n",
      "kappa :\t\t\t 0.08\n",
      "lamb :\t\t\t 1.5\n",
      "measure_sweeps :\t\t\t 2\n",
      "measurements :\t\t\t 0\n",
      "num_sites :\t\t\t 81\n",
      "start time :\t\t\t 1669285819.6413248\n",
      "width :\t\t\t 3\n",
      "[ 0.06375525  0.11291112  0.17949721 ...  0.04632559  0.00727746\n",
      " -0.00997054]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([  29.,  212.,  821., 2077., 2958., 3007., 2033.,  890.,  235.,\n",
       "          28.]),\n",
       " array([-0.48756734, -0.389454  , -0.29134068, -0.19322737, -0.09511404,\n",
       "         0.00299929,  0.10111262,  0.19922595,  0.29733926,  0.3954526 ,\n",
       "         0.49356592], dtype=float32),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 3,
     "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": [
    "import h5py\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Load data\n",
    "import glob\n",
    "import os\n",
    "\n",
    "list_of_files = glob.glob('./data*.hdf5') # * means all if need specific format then *.csv\n",
    "latest_file = max(list_of_files, key=os.path.getctime)\n",
    "print('filename:', latest_file)\n",
    "\n",
    "#output_filename = \"data_l1.5_k0.08_w3_d1.5_20221124103953.hdf5\"\n",
    "#output_filename = latest_file\n",
    "output_filename = \"testding.hdf5\"\n",
    "with h5py.File(output_filename,'r') as f:\n",
    "    #print(np.array(f[\"magnetizations\"]))\n",
    "    handler = f[\"magnetizations\"]\n",
    "    for key in handler.attrs.keys():\n",
    "        print(key, ':\\t\\t\\t', handler.attrs[key])\n",
    "    magnetizations = np.array(handler)\n",
    "    print(magnetizations)\n",
    "    kappa = handler.attrs[\"kappa\"]\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "plt.hist(magnetizations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "89d85e77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.06375525,  0.11291112,  0.17949721, ...,  0.04632559,\n",
       "        0.00727746, -0.00997054], dtype=float32)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "magnetizations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4640925",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "261f895518cc39ffdc0eadcef4c3dd65",
     "grade": false,
     "grade_id": "cell-51479ca8a1c07968",
     "locked": true,
     "points": 30,
     "schema_version": 3,
     "solution": false,
     "task": true
    }
   },
   "source": [
    "**(b)** Write a bash script `job_latticescalar.sh` that submits an array job to the cluster for $w=3$ and $2000$ measurements and $\\lambda = 1.0, 1.5, 2.0$ and $\\kappa = 0.08, 0.09, ..., 0.18$ (so 33 simulations in total). Submit the job to the `hefstud` slurm partition (do not run all 33 in parallel). **(30 pts)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9b27fee7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# The results are gathered by running `sbatch ../job_latticescalar.sh` from ~/NWI-NM042B_2022/Exercise sheet 9/results.\n",
    "# This is done to gather the log files in the results folder."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "711111db",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "0181a075dd61572ba8c2f5027bbb8b74",
     "grade": false,
     "grade_id": "cell-88a18366f80a2168",
     "locked": true,
     "points": 30,
     "schema_version": 3,
     "solution": false,
     "task": true
    }
   },
   "source": [
    "**(c)** Load the stored data into this notebook and reproduce the plot above (with $\\lambda = 1$ and $\\lambda=2$ added). **(30 pts)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e4aaf772",
   "metadata": {},
   "outputs": [
    {
     "ename": "UFuncTypeError",
     "evalue": "ufunc 'subtract' did not contain a loop with signature matching types (dtype('float64'), dtype('<U3')) -> None",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mUFuncTypeError\u001b[0m                            Traceback (most recent call last)",
      "Input \u001b[0;32mIn [28]\u001b[0m, in \u001b[0;36m<cell line: 26>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     28\u001b[0m kap \u001b[38;5;241m=\u001b[39m parameters[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mk\u001b[39m\u001b[38;5;124m\"\u001b[39m]\n\u001b[1;32m     29\u001b[0m \u001b[38;5;66;03m#print(filename, lam, kap)\u001b[39;00m\n\u001b[1;32m     30\u001b[0m \u001b[38;5;66;03m#print(lambdas, lam)\u001b[39;00m\n\u001b[0;32m---> 31\u001b[0m idx_lam \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mwhere(np\u001b[38;5;241m.\u001b[39mabs(\u001b[43mlambdas\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mlam\u001b[49m) \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m.01\u001b[39m)\n\u001b[1;32m     32\u001b[0m \u001b[38;5;66;03m#idx_kap = np.argwhere(np.isclose(kappas, kap))\u001b[39;00m\n\u001b[1;32m     33\u001b[0m idx_kap \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mwhere(kappas \u001b[38;5;241m==\u001b[39m kap)\n",
      "\u001b[0;31mUFuncTypeError\u001b[0m: ufunc 'subtract' did not contain a loop with signature matching types (dtype('float64'), dtype('<U3')) -> None"
     ]
    }
   ],
   "source": [
    "result_files = glob.glob('results/batch_data_*.hdf5')\n",
    "prefix = \"results/batch_data_\"\n",
    "\n",
    "# Know how the file names are formed, but I really want to\n",
    "# do something funky.\n",
    "# Yes, we trust the metadata in the filename.\n",
    "files = {}\n",
    "for result_file in result_files:\n",
    "    params = {}\n",
    "    raw_params = result_file[len(prefix):].split('_')\n",
    "    for i in raw_params:\n",
    "        key = i[0]\n",
    "        value = i[1:]\n",
    "        # The key will be 2 for the date part. Ignore this.\n",
    "        if key == '2':\n",
    "            continue\n",
    "        params[key] = value\n",
    "    files[result_file] = params\n",
    "\n",
    "# For each measurement, we are interested in the mean and standard deviation,\n",
    "# so two values per set of kappa and lambda.\n",
    "lambdas = np.arange(3)*.5 + 1.0\n",
    "kappas  = np.arange(11)*.01 + .08\n",
    "results = np.zeros((len(lambdas), len(kappas), 2))\n",
    "\n",
    "for filename, parameters in files.items():\n",
    "    lam = parameters[\"l\"]\n",
    "    kap = parameters[\"k\"]\n",
    "    #print(filename, lam, kap)\n",
    "    #print(lambdas, lam)\n",
    "    idx_lam = np.where(lambdas - lam)\n",
    "    #idx_kap = np.argwhere(np.isclose(kappas, kap))\n",
    "    idx_kap = np.where(kappas == kap)\n",
    "    print(idx_lam, idx_kap)\n",
    "    with h5py.File(filename,'r') as f:\n",
    "        handler = f[\"magnetizations\"]\n",
    "        magnetizations = np.array(handler)\n",
    "    results[idx_lam][idx_kap] = np.mean(magnetizations), np.std(magnetizations)\n",
    "\n",
    "print(results)\n",
    "# for idx_lam, lam in enumerate(lambdas):\n",
    "#     for idx_kap, kap in enumerate(kappas):\n",
    "#         with h5py.File(file,'r') as f:\n",
    "#             handler = f[\"magnetizations\"]\n",
    "#             magnetizations = np.array(handler)\n",
    "        \n",
    "#         results[idx_lam][idx_kap] = np.mean(magnetizations), np.std(magnetizations)"
   ]
  }
 ],
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