tutorial.ipynb

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    "# Use the geostatistical toolbox container\n",
    "\n",
    "This short tutorial shows, how you can interact with the container using the help of `toolbox-runner`. \n",
    "The runner is still under development, and interacting with the result files is still a bit messy.\n",
    "Right now, the results are placed into a temporary folder and the result files are extracted by hand. In  stable release,\n",
    "`toolbox-runner` will have helper functions for that purpose."
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    "from toolbox_runner import list_tools\n",
    "import io\n",
    "import tempfile\n",
    "import json\n",
    "import pandas as pd\n",
    "import xarray as xr\n",
    "import numpy as np\n",
    "from pprint import pprint"
   ]
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    "Use `list_tools` to get a list or dict of all tool images present on your system. Additionally, a CSV file with example data is loaded.\n",
    "The `list_tools` function accepts also a prefix, if you did not prefix your tool container with `'tbr_'`."
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      "{'cross-validation': cross-validation: Leave-one-out cross-validation  FROM tbr_skgstat:latest VERSION: 1.0,\n",
      " 'kriging': kriging: Kriging interpolation  FROM tbr_skgstat:latest VERSION: 1.0,\n",
      " 'profile': profile: Dataset Profile  FROM tbr_profile:latest VERSION: 0.2,\n",
      " 'sample': sample: Sample field data  FROM tbr_skgstat:latest VERSION: 1.0,\n",
      " 'simulation': simulation: Geostatistical simulation  FROM tbr_skgstat:latest VERSION: 1.0,\n",
      " 'variogram': variogram: Variogram fitting  FROM tbr_skgstat:latest VERSION: 1.1}\n"
     ]
    }
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   "source": [
    "tools = list_tools(as_dict=True)\n",
    "pprint(tools)"
   ]
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   "execution_count": 3,
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     "text": [
      "        x       y  lead\n",
      "0  181072  333611   299\n",
      "1  181025  333558   277\n",
      "2  181165  333537   199\n",
      "3  181298  333484   116\n",
      "4  181307  333330   117\n"
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (x: 50, y: 105)\n",
       "Dimensions without coordinates: x, y\n",
       "Data variables:\n",
       "    prec     (x, y) float32 0.4414 0.4412 0.4426 0.4426 ... 3.987 3.998 3.992</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-8e576602-fd2e-408a-b692-181a542ce018' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-8e576602-fd2e-408a-b692-181a542ce018' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span>x</span>: 50</li><li><span>y</span>: 105</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-e72d0890-9205-4b4a-aa35-09346aa3963e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-e72d0890-9205-4b4a-aa35-09346aa3963e' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-a4fa2592-5d8a-4a25-a559-7cc86d658f94' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a4fa2592-5d8a-4a25-a559-7cc86d658f94' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>prec</span></div><div class='xr-var-dims'>(x, y)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>...</div><input id='attrs-61b7b1db-b766-4b67-aecc-0211a5280c8d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-61b7b1db-b766-4b67-aecc-0211a5280c8d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-44625858-8416-40ff-a927-35ee1f4b21f9' class='xr-var-data-in' type='checkbox'><label for='data-44625858-8416-40ff-a927-35ee1f4b21f9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.441444, 0.441238, 0.442608, ..., 0.397872, 0.397873, 0.398873],\n",
       "       [0.514816, 0.513774, 0.513158, ..., 0.471693, 0.474968, 0.479044],\n",
       "       [0.528682, 0.529469, 0.530613, ..., 0.496112, 0.494906, 0.4937  ],\n",
       "       ...,\n",
       "       [3.370672, 3.402019, 3.426166, ..., 3.678835, 3.613726, 3.542363],\n",
       "       [3.366747, 3.328666, 3.341913, ..., 3.741339, 3.678434, 3.753727],\n",
       "       [3.320999, 3.254253, 3.221964, ..., 3.986949, 3.99786 , 3.992284]],\n",
       "      dtype=float32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5bb442f8-f4e2-4e07-a629-df19403a23f3' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-5bb442f8-f4e2-4e07-a629-df19403a23f3' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
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       "<xarray.Dataset>\n",
       "Dimensions:  (x: 50, y: 105)\n",
       "Dimensions without coordinates: x, y\n",
       "Data variables:\n",
       "    prec     (x, y) float32 ..."
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   "source": [
    "# load some data samples\n",
    "df = pd.read_csv('in/meuse.csv')\n",
    "coords = df[['x', 'y']].values\n",
    "vals = df.lead.values\n",
    "print(df.head())\n",
    "\n",
    "ds = xr.open_dataset('in/cmip_prec.nc')\n",
    "ds"
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    "## General info about tools\n",
    "\n",
    "Although using `toolbox-runner` is not mandatory and the tool container are self-contained, there are some helpful functions.\n",
    "You can get structured metadata about each tool:"
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      "Variogram fitting\n",
      "Estimate an empirical variogram and fit a model\n",
      "\n",
      "PARAMETERS\n",
      "---------\n",
      "\n",
      "## coordinates\n",
      "input type:    file\n",
      "description:   Pass either a (N, D) shaped numpy array, or a .mat file containing the matrix of observation location coordinates\n",
      "\n",
      "## values\n",
      "input type:    file\n",
      "description:   Pass either a (N, 1) shaped numpy array or a .mat file containing the matrix of observations\n",
      "\n",
      "## n_lags\n",
      "input type:    integer\n",
      "description:   no description provided\n",
      "\n",
      "## bin_func\n",
      "input type:    enum\n",
      "description:   no description provided\n",
      "\n",
      "## model\n",
      "input type:    enum\n",
      "description:   no description provided\n",
      "\n",
      "## estimator\n",
      "input type:    enum\n",
      "description:   no description provided\n",
      "\n",
      "## maxlag\n",
      "input type:    string\n",
      "description:   Can be 'median', 'mean', a number < 1 for a ratio of maximum separating distance or a number > 1 for an absolute distance\n",
      "\n",
      "## fit_method\n",
      "input type:    enum\n",
      "description:   no description provided\n",
      "\n",
      "## use_nugget\n",
      "input type:    bool\n",
      "description:   Enable the nugget parameter. Defaults to False, which will set the nugget parameter to 0.\n",
      "\n",
      "## fit_range\n",
      "input type:    float\n",
      "description:   Only valid if fit_method='manual'. The variogram effective range.\n",
      "\n",
      "## fit_sill\n",
      "input type:    float\n",
      "description:   Only valid if fit_method='manual'. The variogram sill.\n",
      "\n",
      "## fit_nugget\n",
      "input type:    float\n",
      "description:   Only valid if fit_method='manual'. The variogram nugget.\n",
      "\n",
      "## fit_sigma\n",
      "input type:    enum\n",
      "description:   Use a distance dependent weight on fits to favor closer bins. Do not set for\n",
      "\n"
     ]
    }
   ],
   "source": [
    "vario = tools.get('variogram')\n",
    "\n",
    "print(vario.title)\n",
    "print(vario.description)\n",
    "print('\\nPARAMETERS\\n---------\\n')\n",
    "for key, conf in vario.parameters.items():\n",
    "    print(f\"## {key}\")\n",
    "    print(f\"input type:    {conf['type']}\")\n",
    "    print(f\"description:   {conf.get('description', 'no description provided')}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variogram\n",
    "\n",
    "Run the variogram tool to estimate a base variogram, which will then be used for the other tools.\n",
    "The variogram parameterization is stored in a `'./out/variogram.json'` in the result tarball. Right now, we have to read \n",
    "this ourselfs and parse the json\n",
    "\n",
    "The container does also produce HTML and JSON plotly figures, a PDF figure and a copy of all settings of the `skg.Variogram` instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'bin_func': 'scott',\n",
      " 'dist_func': 'euclidean',\n",
      " 'estimator': 'matheron',\n",
      " 'fit_method': 'trf',\n",
      " 'fit_sigma': None,\n",
      " 'maxlag': 1372.6660191029719,\n",
      " 'model': 'exponential',\n",
      " 'n_lags': 10,\n",
      " 'normalize': False,\n",
      " 'use_nugget': False,\n",
      " 'verbose': False}\n"
     ]
    }
   ],
   "source": [
    "# get the tool\n",
    "vario = tools.get('variogram')\n",
    "\n",
    "# run\n",
    "step = vario.run(result_path='./test', coordinates=coords, values=vals, maxlag='median', model='exponential', bin_func='scott')\n",
    "\n",
    "# the parameters are stored in variogram.json\n",
    "vario_params = step.get('variogram.json')\n",
    "pprint(vario_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "\n",
    "Run a geostatistical simulation using the variogram from the last step. The simulation result is returned as `.mat` files. \n",
    "Right now, we need to put these into a file-like object and read them using numpy. That will be improved in the future.\n",
    "\n",
    "The current version of the tool can only return the mean and standard deviation of the simulated fields. A future version\n",
    "will have the optional export of a netCDF containing every simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating variogram...\n",
      "exponential Variogram\n",
      "---------------------\n",
      "Estimator:         matheron\n",
      "Effective Range:   1372.67\n",
      "Sill:              17740.72\n",
      "Nugget:            0.00\n",
      "        \n",
      "Starting 10 iterations seeded 42\n",
      "\n",
      "['STDERR.log', 'STDOUT.log', 'result.json', 'simulation_mean.dat', 'simulation_std.dat', 'variogram.html', 'variogram.json', 'variogram.pdf']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[171.82328018, 177.51347383, 164.87992787, ..., 121.29299786,\n",
       "        146.47249759, 181.21038282],\n",
       "       [173.66173153, 187.09362293, 169.08039522, ..., 129.47851113,\n",
       "        138.09837756, 168.64932544],\n",
       "       [192.41124558, 199.84261111, 184.90009063, ..., 178.66673437,\n",
       "        147.14080855, 184.20576035],\n",
       "       ...,\n",
       "       [154.72179719, 184.44261002, 185.62482896, ...,  98.83145353,\n",
       "        112.23031823, 130.52692855],\n",
       "       [192.51765686, 180.46835029, 158.42274169, ...,  92.45844056,\n",
       "        106.70579276, 125.39187714],\n",
       "       [165.30685215, 169.39535479, 187.13380149, ..., 112.48571592,\n",
       "        116.8817058 , 129.10454359]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simu = tools.get('simulation')\n",
    "\n",
    "# run a simulation\n",
    "step = simu.run(result_path='./test', coordinates=coords, values=vals, variogram=vario_params, n_simulations=10, grid='50x50')\n",
    "\n",
    "# print the log\n",
    "print(step.log)\n",
    "\n",
    "# print all outputs\n",
    "print(step.outputs)\n",
    "\n",
    "# .dat files can be loaded to numpy. Load the mean of all simulations\n",
    "mean = step.get('simulation_mean.dat')\n",
    "\n",
    "mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the simulation result\n",
    "\n",
    "The tool does not yet include an automatic plot as result (like variogram), but we can easily build this using plotly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "        <script type=\"text/javascript\">\n",
       "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
       "        if (window.MathJax && window.MathJax.Hub && window.MathJax.Hub.Config) {window.MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
       "        if (typeof require !== 'undefined') {\n",
       "        require.undef(\"plotly\");\n",
       "        requirejs.config({\n",
       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-2.12.1.min']\n",
       "            }\n",
       "        });\n",
       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
       "        });\n",
       "        }\n",
       "        </script>\n",
       "        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.offline as py\n",
    "import plotly.graph_objects as go\n",
    "py.init_notebook_mode(connected=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
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       "config": {
        "linkText": "Export to plot.ly",
        "plotlyServerURL": "https://plot.ly",
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   "source": [
    "fig = go.Figure()\n",
    "\n",
    "xx = np.mgrid[coords[:,0].min():coords[:,0].max():50j]\n",
    "yy = np.mgrid[coords[:,1].min():coords[:,1].max():50j]\n",
    "\n",
    "fig.add_trace(go.Heatmap(z=mean.T, x=xx, y=yy))\n",
    "fig.add_trace(go.Scatter(x=coords[:,0], y=coords[:,1], mode='markers', marker=dict(color=vals)))\n",
    "py.iplot(fig)"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kriging\n",
    "\n",
    "We can pass the same variogram to the kriging tool and compare interpolation and simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OUTPUTS: ['STDERR.log', 'STDOUT.log', 'kriging.dat', 'result.json', 'sigma.dat', 'variogram.html', 'variogram.json', 'variogram.pdf']\n"
     ]
    }
   ],
   "source": [
    "krig = tools.get('kriging')\n",
    "\n",
    "# run kringing with the same variogram\n",
    "step = krig.run(result_path='./test', coordinates=coords, values=vals, variogram=vario_params, algorithm='ordinary', grid='50x50')\n",
    "\n",
    "# print outputs\n",
    "print(f'OUTPUTS: {step.outputs}')\n",
    "\n",
    "# get the kriging field\n",
    "krig_field = step.get('kriging.dat')"
   ]
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  {
   "cell_type": "code",
   "execution_count": 10,
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   ],
   "source": [
    "fig = go.Figure()\n",
    "\n",
    "xx = np.mgrid[coords[:,0].min():coords[:,0].max():50j]\n",
    "yy = np.mgrid[coords[:,1].min():coords[:,1].max():50j]\n",
    "\n",
    "fig.add_trace(go.Heatmap(z=krig_field.T, x=xx, y=yy))\n",
    "fig.add_trace(go.Scatter(x=coords[:,0], y=coords[:,1], mode='markers', marker=dict(color=vals)))\n",
    "py.iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling\n",
    "\n",
    "We can use the geostatistics toolbox for sample, as well. We need any kind of field input and specifiy the number of samples. Right now, the toolbox supports random sampling and sampling on a regular grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[46. 37.]\n",
      " [30. 52.]\n",
      " [36. 46.]\n",
      " [20.  9.]\n",
      " [19.  9.]] [1.56643319 1.21410108 1.09151483 0.90275711 0.79714686]\n"
     ]
    }
   ],
   "source": [
    "sample = tools.get('sample')\n",
    "\n",
    "# run the step, pass the netCDF DataArray values in. Passing netCDF directly is currently not yet supported\n",
    "step = sample.run(result_path='./test', field=ds.prec.values, sample_size=200, method='random', seed=42)\n",
    "\n",
    "sam_coords = step.get('coordinates.dat')\n",
    "sam_values = step.get('values.dat')\n",
    "\n",
    "print(sam_coords[:5], sam_values[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These coordinates and values can now be used in the variogram tool again. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-validation\n",
    "\n",
    "The geostatistics toolbox can also be used for cross-validation of variogram. Here, we will use the new samples from the last part and derive two new variograms. Both are then assessed using cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'bin_func': 'even',\n",
      " 'dist_func': 'euclidean',\n",
      " 'estimator': 'matheron',\n",
      " 'fit_method': 'trf',\n",
      " 'fit_sigma': None,\n",
      " 'maxlag': 36.61966684720111,\n",
      " 'model': 'exponential',\n",
      " 'n_lags': 25,\n",
      " 'normalize': False,\n",
      " 'use_nugget': False,\n",
      " 'verbose': False}\n",
      "{'bin_func': 'even',\n",
      " 'dist_func': 'euclidean',\n",
      " 'estimator': 'matheron',\n",
      " 'fit_method': 'trf',\n",
      " 'fit_sigma': None,\n",
      " 'maxlag': 36.61966684720111,\n",
      " 'model': 'gaussian',\n",
      " 'n_lags': 25,\n",
      " 'normalize': False,\n",
      " 'use_nugget': False,\n",
      " 'verbose': False}\n"
     ]
    }
   ],
   "source": [
    "cv = tools.get('cross-validation')\n",
    "\n",
    "# calculate the two variograms\n",
    "v1 = vario.run(result_path='./test', coordinates=sam_coords, values=sam_values, maxlag='median', n_lags=25, model='exponential')\n",
    "v2 = vario.run(result_path='./test', coordinates=sam_coords, values=sam_values, maxlag='median', n_lags=25, model='gaussian')\n",
    "\n",
    "v1_params = v1.get('variogram.json')\n",
    "v2_params = v2.get('variogram.json')\n",
    "\n",
    "pprint(v1_params)\n",
    "pprint(v2_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimating variogram...\n",
      "exponential Variogram\n",
      "---------------------\n",
      "Estimator:         matheron\n",
      "Effective Range:   36.62\n",
      "Sill:              0.61\n",
      "Nugget:            0.00\n",
      "        \n",
      "Took 2.65 seconds.\n",
      "RMSE: 1.0448182745681351\n",
      "\n",
      "Estimating variogram...\n",
      "gaussian Variogram\n",
      "------------------\n",
      "Estimator:         matheron\n",
      "Effective Range:   36.62\n",
      "Sill:              0.71\n",
      "Nugget:            0.00\n",
      "        \n",
      "Took 3.04 seconds.\n",
      "RMSE: 17.731107405500516\n",
      "\n"
     ]
    }
   ],
   "source": [
    "cv1 = cv.run(result_path='./test', coordinates=sam_coords, values=sam_values, variogram=v1_params, measure='rmse')\n",
    "cv2 = cv.run(result_path='./test', coordinates=sam_coords, values=sam_values, variogram=v2_params, measure='rmse')\n",
    "\n",
    "print(cv1.log)\n",
    "print(cv2.log)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see, that the cross-validation of the variogram models clearly favors the exponential over the gaussian model for the random sample laken in the last step."
   ]
  }
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